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-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LICHEN M047Q02- 0 1 2 8 9"}, {"from": "gpt", "value": "Using the formula, calculate the diameter of the lichen, 16 years after the ice disappeared. Show your calculation. LICHEN SCORING 1 Full credit Code 2: 14mm (units not required).  Code 2 should be given as long as the correct answer is 14 whether working out is shown or not. Partial credit Code 1: Partial responses including: \u2022 C o r r e c t  s u b s t i t u t i o n  o f  v a l u e  i n  t h e  f o r m u l a  b u t  i n c o r r e c t  a n s w e r  O r  m i s s i n g answer. \u2022 I n c o m p l e t e  a n s w e r s  ( e g ,   7 \u221a4). No credit Code 0: Other responses. Code 9: Missing. Example responses Code 2: 1412160.7 =\u2212\u00d7= dd 14mm 14  ReleasedPISAItems_Maths.doc  Page 8 years ddd 144 0.712 16 0.7 =\u00d7=\u2212\u00d7= (Note that here the calculations are all correct, but the unit is wrong. We will assume for now that it is the slip of the pen) Code 1: 1612160.7 =\u2212\u00d7= dd (wrong answer but correct substitution) 47121607 =\u2212\u00d7= dd . (incomplete answer)  Code 0: 16\n\nThis question is designed to test: To elicit student's  ability to apply a given formula."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about COINS M143Q01-0 1 8 9"}, {"from": "gpt", "value": "Ann measured the diameter of some lichen and found it was 35 millimetres. How many years ago did the ice disappear at this spot? Show your calculation. LICHEN SCORING 2 Full credit Code 2: 37 years (unit not required) whether working out is shown or not. Partial credit Code 1: Correct substitution of values in the formula but incorrect answer or missing answer. OR 36 years or 38 years. (Students may arrive at these answers using the trial and error method) No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 9 Example responses Code 2: 3712 2512 512 7 35 =\u2212=\u2212=\u2212\u00d7= tttt  years373771225 725 7575735\u2234\u00d7=+\u00d7=\u00d7=\u00d7=\u00f7   37 122525 557/35 2 =+== (Strictly incorrect algebraic repres entation, but we know what the student is trying to do)  t = 15  d = 12.1 t = 25  d = 25.2 t = 40  d = 37.0 t = 35  d = 33.6 t = 37  d = 35 So 37 years after the ice disappeared (Note that here the answer 37 is embedded in an equation that is correct)  756 = 35 = 7X \u221a(37-12) = 7X \u221a25 = 7X5 = 35 Code 1: 251237 4912 7 3512 0.7 35 2 2 ==\u2212\u00d7=\u2212\u00d7= tttt  1312 2512 512 0.7 35 2 2 =\u2212=\u2212=\u2212\u00d7= tttt  !12 512 512 0.7 35 hardToottt \u2212=\u2212=\u2212\u00d7=  Code 0: 79612 78412 2812 0.7 35 =\u2212=\u2212=\u2212\u00d7= tttt  40 years   ReleasedPISAItems_Maths.doc  Page 17 M143: Coins You are asked to design a new set of coins. All coins will be circular and coloured silver, but of different diameters.  Researchers have found out that an ideal coin system meets the following requirements: \u2022 d i a m e t e r s  o f  c o i n s  s h o u l d  n o t  b e  s m a l l e r  t h a n  1 5  m m  a n d  n o t  b e  l a r g e r  t h a n  4 5 mm. \u2022 g i v e n  a  c o i n ,  t h e  d i a m e t e r  o f  t h e  n e x t  c o i n  m u s t  b e  a t  l e a s t  3 0 %  l a r g e r . \u2022 t h e  m i n t i n g  m a c h i n e r y  c a n  o n l y  p r o d u c e  c o i n s  w i t h  d i a m e t e r s  o f  a  w h o l e  n u m b e r of millimetres (e.g. 17 mm is allowed, 17.3 mm is not).\n\nThis question is designed to test: To elicit student's  ability to apply a given formula."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PIZZAS M154Q01- 0 1 2 8 9"}, {"from": "gpt", "value": "You are asked to design a set of coins that satisfy the above requirements. You should start with a 15 mm coin and your set should contain as many coins as possible. What would be the diameters of the coins in your set? COINS SCORING 1 calculations. Code 1: 15 \u2013 20 \u2013 26 \u2013 34 \u2013 45. It is possible that the response could  be presented as actual drawings of the coins of the correct diameters.  This should be coded as 1 as well. Code 8: Gives a set of coins that satisfy the three criteria, but not the set that contains as many coins as possible, eg., 15 \u2013 21 \u2013 29 \u2013 39, or 15 \u2013 30 \u2013 45 OR The first three diameters correct, the last two incorrect (15 \u2013 20 \u2013 26 - ) OR The first four diameters correct, the last one incorrect (15 \u2013 20 \u2013 26 \u2013 34 - ) Code 0: Other responses. Code 9 : Missing. ReleasedPISAItems_Maths.doc  Page 27 M154: Pizzas A pizzeria serves two round pizzas of the same thickness in different sizes. The smaller one has a diameter of 30 cm and costs 30 zeds. The larger one has a diameter of 40 cm and costs 40 zeds.\n\nThis question is designed to test: Understanding and use of complicated information to do"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHAPES M158Q01- 0 1 8 9"}, {"from": "gpt", "value": "Which pizza is better value for money? Show your reasoning. PIZZAS SCORING 1 comparison Code 2: Gives general reasoning that the surface area of pizza increases more rapidly than the price of pizza to conclude that the larger pizza is better value. \u2022 The diameter of the pizzas is the same  number as their price, but the amount of pizza you get is found using diameter2 , so you will get more pizza per zeds from the larger one Code 1: Calculates the area and amount per zed for each pizza to conclude that the larger pizza is better value. \u2022 A r e a  o f  s m a l l e r  p i z z a  i s  0 . 2 5  x  \u03c0 x 30 x 30 = 225 \u03c0; amount per zed is 23.6 cm2 area of larger pizza is 0.25 x \u03c0 x 40 x 40 = 400 \u03c0; amount per zed is 31.4 cm2 so larger pizza is better value Code 8: They are the same value for money.  (This incorrect answer is coded separately, because we would like to keep track of how many students have this misconception). Code 0: Other incorrect responses OR a correct answer without correct reasoning. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 28 M158: Shapes   A  B  C\n\nThis question is designed to test: Applies understanding of area to solving a value for money"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHAPES M158Q03- 0 1 8 9"}, {"from": "gpt", "value": "Which of the figures has the largest area? Explain your reasoning. SHAPES SCORING 1 Code 1: Shape B, supported with plausible reasoning. \u2022 I t \u2019 s  t h e  l a r g e s t  a r e a  b e c a u s e  the others will fit inside it. Code 8: Shape B, without plausible support. Code 0: Other responses. Code 9: Missing. Example responses Code 1: \u2022 B .  I t  d o e s n \u2019 t  h a v e  i n d e n t s  i n  i t  w h i c h decreases the area.  A and C have gaps. \u2022 B ,  b e c a u s e  i t \u2019 s  a  f u l l  c i r c l e ,  a n d  t h e  o t h e rs are like circles with bits taken out. \u2022 B, because it has no open areas:  Code 8: \u2022 B. because it has the largest surface area \u2022 T h e  c i r c l e .   I t \u2019 s  p r e t t y  o b v i o u s . \u2022 B ,  b e c a u s e  i t  i s  b i g g e r . Code 0: \u2022 They are all the same. ReleasedPISAItems_Maths.doc  Page 29 Question 2: SHAPES M158Q02- 0 1 8 9 Describe a method for estimating the area of figure C. SHAPES SCORING 2 irregular shapes. Code 1: Reasonable method: \u2022 D r a w  a  g r i d  o f  s q u a r e s  o v e r  t h e  s h ape and count the squares that are more than half filled by the shape. \u2022 C u t  t h e  a r m s  o f f  t h e  s h a p e  a n d  r e a r r a n g e  t he pieces so that they fill a square then measure the side of the square. \u2022 Build a 3D model based on the shape and fill it with water. Measure the amount of water used and the depth of the water in the model.  Derive the area from the information. Code 8: Partial answers: \u2022 The student suggests to find the area of the circle and subtract the area of the cut out pieces.  However, the student does not mention about how to find out the area of the cut out pieces. \u2022 A d d  u p  t h e  a r e a  o f  e a c h  i n dividual arm of the shape Code 0:  Other responses. Code 9: Missing. NOTE: The key point for this question is whether the student offers a METHOD for determining the area.  The coding schemes (1, 8, 0) is a hierarchy of the extent to which the student describes a METHOD. Example responses Code 1: \u2022 You could fill the shape with lots of ci rcles, squares and ot her basic shapes so there is not a gap.  Work out the area of all of the shapes and add together. \u2022 Redraw the shape onto graph paper and count all of the squares it takes up. \u2022 D r a w i n g  a n d  c o u n t i n g  e q u a l  s i z e  b o x e s .   S m a l l e r  b o x e s  =  b e t t e r  a c c u r a c y (Here the student\u2019s description is brief, but we will be lenient about student\u2019s writing skills and regard the method offered by the student as correct) \u2022 M a k e  i t  i n t o  a  3 D  m o d e l  a n d  f i l l i n g  i t  w i t h  e x a c t l y  1 c m  o f  w a t e r  a n d  t h e n measure the volume of water required to fill it up. Code 8: \u2022 F i n d  t h e  a r e a  o f  B  t h e n  f i n d  t h e  a r e a s  o f  the cut out pieces and subtract them from the main area. \u2022 M i n u s  t h e  s h a p e  f r o m  t h e  c i r c l e \u2022 A d d  u p  t h e  a r e a  o f  e a c h  i n d i v i d u a l  p i e c e  e . g . , \u2022 Use a shape like that and pour a liquid into it. \u2022 U s e  g r a p h \u2022 H a l f  o f  t h e  a r e a  o f  s h a p e  B \u2022 F i g u r e  o u t  h o w  m a n y  m m2 are in one little leg things and times it by 8. ReleasedPISAItems_Maths.doc  Page 30 Code 0: \u2022 U s e  a  s t r i n g  a n d  m e a s u r e  t h e  p e r i m e t e r  o f  the shape.  Stretch the string out to a circle and measure the area of the circle using \u03c0 r2. (Here the method described by the student is wrong)\n\nThis question is designed to test: To assess students\u2019 strategies for measuring areas of"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q01"}, {"from": "gpt", "value": "Describe a method for estimating the perimeter of figure C. SHAPES SCORING 3 irregular shapes Code 1: Reasonable method: \u2022 Lay a piece of string over the outline of the shape then measure the length of string used. \u2022 C u t  t h e  s h a p e  u p  i n t o  s h o r t ,  n e a r l y  s t r a i ght pieces and join them together in a line, then measure the length of the line. \u2022 M e a s u r e  t h e  l e n g t h  o f  s o m e  o f  t h e  arms to find an average arm length then multiply by 8 (number of arms) X 2. Code 0: Other responses. Code 9: Missing. Example responses Code 1: \u2022 W o o l  o r  s t r i n g ! ! ! (Here although the answer is brief, the student did offer a METHOD for measuring the perimeter) \u2022 C u t  t h e  s i d e  o f  t h e  s h a p e  i n t o  s e c t i o n s .   M e a s u r e  e a c h  t h e n  a d d  t h e m together. (Here the student did not explicitly  say that each section needs to be approximately straight, but we will give t he benefit of the doubt,  that is, by offering the METHOD of cutting the shape into pieces, each piece is assumed to be easily measurable) Code 0: \u2022 M e a s u r e  a r o u n d  t h e  o u t s i d e . (Here the student did not suggest any METHOD of measuring. Simply saying \u201cmeasure it\u201d is not offering any method of how to go about measuring it) \u2022 S t r e t c h  o u t  t h e  s h a p e  t o  m a k e  i t  a  c i r c l e . (Here although a method is offered by the student, the method is wrong) ReleasedPISAItems_Maths.doc  Page 38 M215: Braking The approximate distance to stop a moving vehicle is the sum of: \u2022 t h e  d i s t a n c e  c o v e r e d  d u r i n g  t h e  t i m e  t h e  d r i v e r  t a k e s  t o  b e g i n  t o  a p p l y  t h e brakes (reaction-time distance) \u2022 t h e  d i s t a n c e  t r a v e l l e d  w h i l e  t h e  b r a k e s  a r e  a p p l i e d  ( b r a k i n g  d i s t a n c e ) The \u2018snail\u2019 diagram below gives the theoretical stopping distance for a vehicle in good braking conditions (a particularly alert driver, brakes and tyres in perfect condition, a dry road with a good surface) and how much the stopping distance depends on speed. 20.8 m245.5 m Distance to stop a vehicle. Time to stop the vehicle. Distance travelled during the braking time. Distance travelled during the driver\u2019s reaction time. 219 m 197.6 m 175.4 m 152.2 m 135.6 m 118 m 101 m 85.4 m 70.7 m 57.7 m 46 m 35.7 m 26.5 m 18.6 m 37.5 m 35.4 m 33.3 m 31.3 m 29.2 m 27.1 m 25 m 22.9 m 18.7 m 16.7 m 14.6 m 12.5 m 10.3 m 8.3 m 9.08 s 8.62 s 8.15 s 7.69 s 7.23 s 6.76 s 6.30 s 5.84 s 5.38 s 4.92 s 4.46 s 3.99 s 3.53 s 3.06 s 2.60 s 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 KPH ReleasedPISAItems_Maths.doc  Page 39 QUESTION 1: BRAKING M215Q01 If a vehicle is travelling at 110 kph, what distance does the vehicle travel during the driver\u2019s reaction time? BRAKING 1 SCORING GUIDE Code 1: 22.9 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q03"}, {"from": "gpt", "value": "If a vehicle is travelling at 110 kph, what is the total distance travelled before the vehicle stops? BRAKING SCORING 2 Code 1: 101 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q05"}, {"from": "gpt", "value": "If a vehicle is travelling at 110 kph, how long does it take to stop the vehicle completely? BRAKING 3 SCORING GUIDE Code 1: 5.84 seconds  (units not required) Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 40 Question 4: BRAKING M215Q04 If a vehicle is travelling at 110 kph, what is the distance travelled while the brakes are being applied? BRAKING 4 SCORING GUIDE Code 1: 78.1 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to derive a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PATIO M267Q01- 0 1 2 8 9"}, {"from": "gpt", "value": "A second driver, travelling in good conditions, stops her vehicle in a total distance of 70.7 metres.  At what speed was the vehicle travelling before the brakes were applied? BRAKING 5 SCORING GUIDE Code 1: 90 kph (units not necessary) Code 0: Other responses. Code 9 : Missing. ReleasedPISAItems_Maths.doc  Page 43 M267: Patio\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about DRUG CONCENTRATIONS M307Q01 - 0 1 2 9"}, {"from": "gpt", "value": "Nick wants to pave the rectangular patio of his new house. The patio has length 5.25 metres and width 3.00 metres. He needs 81 bricks per square metre. Calculate how many bricks Nick needs for the whole patio.  PATIO SCORING 1 Full credit Code 2: 1275, 1276  or 1275.75 (unit not required). Partial credit Code 1: 15.75 (units not required) OR 1215 bricks for 5m X 3m (This score is used for students who are able to calculate the number of bricks for an integer number of square metres, but not for fractions of square metres.  See example response.) OR Error in calculating the area, but multiplied by 81 correctly OR Rounded off the area and then multiplied by 81 correctly No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 44 Example responses Code 2: \u2022 5.25 X 3 = 15.75 X 81 = 1276 Code 1: \u2022 5.25 X 3 = 15.75 \u2022 15.75 X 81 = 9000 \u2022 81 X 15 = 1215; 1215 + 21 = 1236 \u2022 5.25 X 3.0 = 15.75 m2;   so 15.75 X 1275.75 = 1376 bricks. (Here the student got the first part right, but the second part wrong.  Give credit for the first part and ignore the second part.  So score as 1)  8 1  8 1  8 1  8 1  8 1 8 1  8 1  8 1  8 1  8 1 8 1  8 1  8 1  8 1  8 1  5m 3m ReleasedPISAItems_Maths.doc  Page 45 M307: Drug Concentrations\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BUILDING BLOCKS M309Q02"}, {"from": "gpt", "value": "A woman in hospital receives an injection of penicillin.  Her body gradually breaks the penicillin down so that one hour after the injection only 60% of the penicillin will remain active. This pattern continues: at the end of each hour only 60% of the penicillin that was present at the end of the previous hour remains active. Suppose the woman is given a dose of 300 millig rams of penicillin at 8 o\u2019clock in the morning. Complete this table showing the amount of penicillin that will remain active in the woman\u2019s blood at intervals of one hour from 0800 until 1100 hours. Time 0800 0900 1000 1100 Penicillin (mg) 300  DRUG CONCENTRATIONS SCORING 1 Full credit Code 2: All three table entries correct.  Time 0800 0900 1000 1100 Penicillin (mg) 300 180 108 64.8 or 65 Partial credit Code 1: One or two table entries correct. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 46 Amount of active drug (mg) 0 1 2 3 4 5 Time (days) after taking the drug 20 40 60 80 0 Question 2: DRUG CONCENTRATIONS M307Q02 Peter has to take 80 mg of a drug to control his blood pressure. The following graph shows the initial amount of the drug, and the amount that remains active in Peter\u2019s blood after one, two, three and four days. How much of the drug remains active at the end of the first day? A   6 mg. B 12 mg. C 26 mg. D 32 mg. DRUG CONCENTRATIONS SCORING 2 Full credit Code 1: D.  32mg. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 47 Question 3: DRUG CONCENTRATIONS M307Q03 From the graph for the previous question it can be seen that each day, about the same proportion of the previous day\u2019s drug remains active in Peter\u2019s blood. At the end of each day which of the following is the approximate percentage of the previous day\u2019s drug that remains active? A 20%. B 30%. C 40%. D 80%. DRUG CONCENTRATIONS SCORING 3 Full credit Code 1: C.  40%. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 48 M309: Building Blocks  Susan likes to build blocks from small cubes like the one shown in the following diagram: Susan has lots of small cubes like this one.  She uses glue to join cubes together to make other blocks. First, Susan glues eight of the cubes together to make the block shown in Diagram A: Then Susan makes the solid blocks shown in Diagram B and Diagram C below: Diagram B Diagram C Small cube Diagram A ReleasedPISAItems_Maths.doc  Page 49 Question 1: BUILDING BLOCKS M309Q01 How many small cubes will Susan need to make the block shown in Diagram B? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 1 Full credit Code 1: 12 cubes. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BUILDING BLOCKS M309Q04"}, {"from": "gpt", "value": "How many small cubes will Susan need to make the solid block shown in Diagram C? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 2 Full credit Code 1: 27 cubes. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 50 Question 3: BUILDING BLOCKS M309Q03 Susan realises that she used more small cubes than she really needed to make a block like the one shown in Diagram C.  She realises that she could have glued small cubes together to look like Diagram C, but the block could have been hollow on the inside. What is the minimum number of cubes she needs to make a block that looks like the one shown in Diagram C, but is hollow? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 3 Full credit Code 1: 26 cubes. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about EXPORTS M438Q01 - 0 1 9"}, {"from": "gpt", "value": "Now Susan wants to make a block that looks like a solid block that is 6 small cubes long, 5 small cubes wide and 4 small cubes high.  She wants to use the smallest number of cubes possible, by leaving t he largest possible hollow space inside the block. What is the minimum number of cubes Susan will need to make this block? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 4 Full credit Code 1: 96 cubes. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 55 M432: Reaction Time In a Sprinting event, the \u2018reaction time\u2019 is the time interval between the starter\u2019s gun firing and the athlete leaving the starting block.  The \u2018final time\u2019 includes both this reaction time, and the running time. The following table gives the reaction time and the final time of 8 runners in a 100 metre sprint race. Lane Reaction time (sec) Final time (sec) 1 0.147 10.09 2 0.136 9.99 3 0.197 9.87 4 0.180 Did not finish the race 5 0.210 10.17 6 0.216 10.04 7 0.174 10.08 8 0.193 10.13  ReleasedPISAItems_Maths.doc  Page 56 Question 1: REACTION TIME  M432Q01 - 0 1 9 Identify the Gold, Silver and Bronze medallists from this race.  Fill in the table below with the medallists' lane number, reaction time and final time. Medal Lane Reaction time (secs) Final time (secs) GOLD SILVER BRONZE REACTION TIME SCORING 1 Full credit Code 1: Medal Lane Reaction time (secs) Final time (secs) GOLD 3 0.197 9.87 SILVER 2 0.136 9.99 BRONZE 6 0.216 10.04 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 57 Question 2: REACTION TIME  M432Q02 - 0 1 9 To date, no humans have been able to react to a starter\u2019s gun in less than 0.110 second. If the recorded reaction time for a runner is less than 0.110 second, then a false start is considered to have occurred because the runner must have left before hearing the gun. If the Bronze medallist had a faster reaction time, would he have had a chance to win the Silver medal?  Give an explanation to support your answer. REACTION TIME SCORING 2 Full credit Code 1: Yes, with adequate explanation. \u2022 Yes. If he had a reaction time of 0.05 sec faster, he would have equalled second place. \u2022 Y e s ,  h e  w o u l d  h a v e  a  c h a n c e  t o  w i n  t h e  S i l v e r  m e d a l  i f  h i s  r e a c t i o n  t i m e  w a s less than or equal to 0.166 sec. \u2022 Y e s ,  w i t h  t h e  f a s t e s t  p o s s i b l e  r e a c t i o n  t i m e  h e  w o u l d  h a v e  d o n e  a  9 . 9 3  w h i c h is good enough for silver medal. No credit Code 0: Other responses, including yes without adequate explanation. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 58 M438: Exports The graphics below show information about exports from Zedland, a country that uses zeds as its currency.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about WATER TANK M 4 6 5 Q 0 1"}, {"from": "gpt", "value": "What was the total value (in millions of zeds) of exports from Zedland in 1998? Answer: .................................................. EXPORTS SCORING 1 Full credit Code 1:  27.1 million zeds or 27 100 000 zeds or 27.1 (unit not required). No credit Code 0: Other responses. Code 9: Missing. Distribution of exports from Zedland in 2000 Total annual exports from Zedland in millions of zeds, 1996-2000 Year Tobacco 7% Wool 5% Cotton fabric 26% Fruit juice 9% Rice 13% Tea 5% Meat 14% Other 21% 20.4 25.4 27.1 37.9 42.6 051015202530354045 1996 1997 1998 1999 2000 ReleasedPISAItems_Maths.doc  Page 59 Question 2: EXPORTS M438Q02 What was the value of fruit juice exported from Zedland in 2000? A 1.8 million zeds. B 2.3 million zeds. C 2.4 million zeds. D 3.4 million zeds. E 3.8 million zeds. EXPORTS SCORING 2 Full credit Code 1:  E.  3.8 million zeds. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 60 M465: Water Tank\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about COLOURED CANDIES M467Q01"}, {"from": "gpt", "value": "Which of the following graphs shows how the height of the water surface changes over time? 1.5 m 1.0 m 1.5 m Water tank A water tank has shape and dimensions as shown in the diagram. At the beginning the tank is empty.  Then it is filled with water at the rate of one litre per second. Height Time Height Time D Height E Height Time Time Height Time A B C ReleasedPISAItems_Maths.doc  Page 61 WATER TANK SCORING 1 Full credit Code 1: B. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 62 M467: Coloured Candies\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SCIENCE TESTS M468Q01"}, {"from": "gpt", "value": "Robert\u2019s mother lets him pick one candy from a bag.  He can\u2019t see the candies. The number of candies of each colour in the bag is shown in the following graph. What is the probability that Robert will pick a red candy? A 10% B 20% C 25% D 50% COLOURED CANDIES SCORING 1 Full credit Code 1: B.  20%. No credit Code 0: Other responses. Code 9: Missing. 0246 8Red Orange Yellow Green Blue Pink Purple Brown ReleasedPISAItems_Maths.doc  Page 63 M468: Science Tests\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SPRING FAIR M471Q01"}, {"from": "gpt", "value": "In Mei Lin\u2019s school, her science teacher gives tests that are marked out of 100.  Mei Lin has an average of 60 marks on her first four Science tests. On the fifth test she got 80 marks. What is the average of Mei Lin\u2019s marks in Science after all five tests? Average: ................................................. SCIENCE TESTS SCORING 1 Full credit Code 1: 64. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 64 M471: Spring Fair\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SWING M472Q01"}, {"from": "gpt", "value": "A game in a booth at a spring fair involves using a spinner first.  Then, if the spinner stops on an even number, the player is allowed to pick a marble from a bag.  The spinner and the marbles in the bag are represented in the diagram below. Prizes are given when a black marble is picked.  Sue plays the game once. How likely is it that Sue will win a prize? A Impossible. B Not very likely. C About 50% likely. D Very likely. E Certain. SPRING FAIR SCORING 1 Full credit Code 1: B.  Not very likely. No credit Code 0: Other responses. Code 9: Missing. 1 4 10 8 6 2 ReleasedPISAItems_Maths.doc  Page 65 D Height of feet Time C Height of feet Time BTime Height of feet Height of feet ATime M472: Swing\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STUDENT HEIGHTS M479Q01"}, {"from": "gpt", "value": "Mohammed is sitting on a swing.  He starts to swing.  He is trying to go as high as possible. Which diagram best represents the height of his feet above the ground as he swings? ReleasedPISAItems_Maths.doc  Page 66 SWING SCORING 1 Full credit Code 1: A. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 67 M479: Student Heights\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PAYMENTS BY AREA M480Q01"}, {"from": "gpt", "value": "In a mathematics class one day, the heights of all students were measured.  The average height of boys was 160 cm, and the average height of girls was 150 cm. Alena was the tallest \u2013 her height was 180 cm.  Zdenek was the shortest \u2013 his height was 130 cm. Two students were absent from class that day , but they were in class the next day. Their heights were measured, and the averages were recalculated.  Amazingly, the average height of the girls and the average height of the boys did not change. Which of the following conclusions can be drawn from this information? Circle \u2018Yes\u2019 or \u2018No\u2019 for each conclusion. Conclusion Can this conclusion be drawn? Both students are girls. Yes / No One of the students is a boy and the other is a girl. Yes / No Both students have the same height. Yes / No The average height of all students did not change. Yes / No Zdenek is still the shortest. Yes / No  STUDENT HEIGHTS SCORING 1 Full credit Code 1: \u2018No\u2019 for all conclusions. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 68 M480: Payments by Area People living in an apartment building decide to buy the building. They will put their money together in such a way that each will pay an amount that is proportional to the size of their apartment. For example, a man living in an apartment that occupies one fifth of the floor area of all apartments will pay one fifth of the total price of the building.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BOOKSHELVES M484Q01"}, {"from": "gpt", "value": "Circle Correct or Incorrect for each of the following statements. Statement Correct / Incorrect A person living in the largest apartment will pay more money for each square metre of his apartment than the person living in the smallest apartment. Correct / Incorrect If we know the areas of two apartments and the price of one of them we can calculate the price of the second. Correct / Incorrect If we know the price of the building and how much each owner will pay, then the total area of all apartments can be calculated.  Correct / Incorrect If the total price of the building were reduced by 10%, each of the owners would pay 10% less. Correct / Incorrect  PAYMENTS BY AREA SCORING 1 Full credit Code 1: Incorrect, Correct, Incorrect, Correct, in that order. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 69 Question 2: PAYMENTS BY AREA M480Q02 - 0 1 2 9 There are three apartments in the building.  The largest, apartment 1, has a total area of 95m2.  Apartments 2 and 3 have areas of 85m2 and 70m2 respectively.  The selling price for the building is 300 000 zeds. How much should the owner of apartment 2 pay?  Show your work. PAYMENTS BY AREA SCORING 2 Full credit Code 2: 102,000 zeds, with or without the calculation shown, and unit not required. \u2022 Apartment 2: 102 000 zeds \u2022 zeds Apt 102000 30000025085:2 = \u00d7 \u2212 \u2022 1200250300000=zeds for each square metre, so Apartment 2 is 102 000. Partial credit Code 1: Correct method, but minor computational error/s. \u2022 zeds Apt 10200 30000025085:2 = \u00d7 \u2212 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 70 M484: Bookshelves\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LITTER M505Q01 - 0 1 9"}, {"from": "gpt", "value": "To complete one set of bookshelves a carpenter needs the following components: 4 long wooden panels, 6 short wooden panels, 12 small clips, 2 large clips and 14 screws. The carpenter has in stock 26 long wooden panels, 33 short wooden panels, 200 small clips, 20 large clips and 510 screws. How many sets of bookshelves can the carpenter make? Answer: .................................................. BOOKSHELVES SCORING 1 Full credit Code 1: 5. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 71 M505: Litter\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about EARTHQUAKE M509Q01"}, {"from": "gpt", "value": "For a homework assignment on the envir onment, students collected information on the decomposition time of several types of litter that people throw away: Type of Litter Decomposition time Banana peel 1\u20133 years Orange peel 1\u20133 years Cardboard boxes 0.5 year Chewing gum 20\u201325 years Newspapers A few days Polystyrene cups Over 100 years A student thinks of displaying the results in a bar graph. Give one reason why a bar graph is unsuitable for displaying these data. LITTER SCORING 1 Full credit Code 1: Reason focuses on big variance in data. \u2022 T h e  d i f f e r e n c e  i n  t h e  l e n g t h s  o f  t h e  b a rs of the bar graph would be too big. \u2022 I f  y o u  m a k e  a  b a r  w i t h  l e n g t h  1 0  c e n t i m e t r e s  f o r  p o l y s t y r e n e ,  t h e  o n e  f o r cardboard boxes would be 0.05 centimetres. O R Reason focuses on the variability of the data for some categories. \u2022 The length of the bar for \u201cpol ystyrene cups\u201d is undetermined. \u2022 Y o u  c a n n o t  m a k e  o n e  b a r  f o r  1 \u2013 3  y e a r s  o r  o n e  b a r  f o r  2 0 \u2013 2 5  y e a r s . No credit Code 0: Other responses. \u2022 B e c a u s e  i t  w i l l  n o t  w o r k . \u2022 A  p i c t o g r a m  i s  b e t t e r . \u2022 Y o u  c a n n o t  v e r i f y  t h e  i n f o . \u2022 B e c a u s e  t h e  n u m b e r s  i n  t h e  t a b l e  a r e  o n l y  a p p r o x i m a t i o n s . Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 72 M509: Earthquake\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about CHOICES M510Q01"}, {"from": "gpt", "value": "A documentary was broadcast about earthquakes and how often earthquakes occur. It included a discussion about the predictability of earthquakes. A geologist stated: \u201cIn the next twenty years, the chance that an earthquake will occur in Zed City is two out of three\u201d. Which of the following best reflects the meaning of the geologist\u2019s statement ? A 13.3 2032=\u00d7 , so between 13 and 14 years from now there will be an earthquake in Zed City. B 32 is more than 21, so you can be sure there will be an earthquake in Zed City at some time during the next 20 years. C The likelihood that there will be an earthquake in Zed City at some time during the next 20 years is higher than the likelihood of no earthquake. D You cannot tell what will happen, because nobody can be sure when an earthquake will occur. EARTHQUAKE SCORING 1 Full credit Code 1: C.  The likelihood that there will be an earthquake in Zed City at some time during the next 20 years is higher than the likelihood of no earthquake. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 73 M510: Choices\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TEST SCORES M513Q01 - 0 1 9"}, {"from": "gpt", "value": "In a pizza restaurant, you can get a basic pizza with two toppings: cheese and tomato. You can also make up your own pizza with extra  toppings. You can choose from four different extra toppings: olives, ham, mushrooms and salami. Ross wants to order a pizza with two different extra  toppings. How many different combinations can Ross choose from? Answer: ..................................................combinations. CHOICES SCORING 1 Full credit Code 1: 6. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 74 M513: Test Scores\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHOES FOR KIDS M515Q01"}, {"from": "gpt", "value": "The diagram below shows the results on a Science test for two groups, labelled as Group A and Group B. The mean score for Group A is 62.0 and the mean for Group B is 64.5.  Students pass this test when their score is 50 or above. Looking at the diagram, the teacher claims that Group B did better than Group A in this test. The students in Group A don\u2019t agree with their teacher. They try to convince the teacher that Group B may not necessarily have done better. Give one mathematical argument, using the graph, that the students in Group A could use. TEST SCORES SCORING 1 Full credit Code 1: One valid argument is given. Valid  arguments could relate to the number of students passing, the disproportionate influence of the outlier, or the number of students with scores in the highest level. \u2022 M o r e  s t u d e n t s  i n  G r o u p  A  t h a n  i n  G r o u p  B  p a s s e d  t h e  t e s t . \u2022 I f  y o u  i g n o r e  t h e  w e a k e s t  G r o u p  A  s t u d e n t ,  t h e  s t u d e n t s  i n  G r o u p  A  d o  b e t t e r than those in Group B. \u2022 M o r e  G r o u p  A  s t u d e n t s  t h a n  G r o u p  B  s t u d e n t s  s c o r e d  8 0  o r  o v e r .  Scores on a Science test 0 1 2 3 4 5 6 0 - 9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100 Score Number of students Group A Group B ReleasedPISAItems_Maths.doc  Page 75 No credit Code 0: Other responses, including responses with no mathematical reasons, or wrong mathematical reasons, or responses that simply describe differences but are not valid arguments that Group B may not have done better. \u2022 G r o u p  A  s t u d e n t s  a r e  n o r m a l l y  b e t t e r  than Group B students in science. This test result is just a coincidence. \u2022 B e c a u s e  t h e  d i f f e r e n c e  b e t w e e n  t h e  h i g h e s t  a n d  l o w e s t  s c o r e s  i s  s m a l l e r  f o r Group B than for Group A. \u2022 G r o u p  A  h a s  b e t t e r  s c o r e  r e s u l t s  i n  t h e  8 0 - 8 9  r a n g e  a n d  t h e  5 0 - 5 9  r a n g e . \u2022 G r o u p  A  h a s  a  l a r g e r  i n t e r - q u a r t i l e  r a n g e  t h a n  G r o u p  B . Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 76 M515: Shoes for Kids The following table shows the recommended Zedland shoe sizes corresponding to various foot lengths.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SKATEBOARD M520Q02"}, {"from": "gpt", "value": "Marina\u2019s feet are 163 mm long.  Use the table to determine which Zedland shoe size Marina should try on . Answer: .................................................. SHOES FOR KIDS SCORING 1 Full credit Code 1: 26. No credit Code 0: Other responses. Code 9: Missing. Conversion table for kids shoe sizes in Zedland From (in mm) To (in mm) Shoe size 107 115 18 116 122 19 123 128 20 129 134 21 135 139 22 140 146 23 147 152 24 153 159 25 160 166 26 167 172 27 173 179 28 180 186 29 187 192 30 193 199 31 200 206 32 207 212 33 213 219 34 220 226 35 ReleasedPISAItems_Maths.doc  Page 77 M520: Skateboard Eric is a great skateboard fan. He visits a shop named SKATERS to check some prices. At this shop you can buy a complete board. Or you can buy a deck, a set of 4 wheels, a set of 2 trucks and a set of hardware, and assemble your own board. The prices for the shop\u2019s products are: Product Price in zeds Complete skateboard 82 or 84  Deck 40, 60 or 65  One set of 4 Wheels  14 or 36  One set of 2 Trucks 16  One set of hardware (bearings, rubber pads, bolts and nuts) 10 or 20  ReleasedPISAItems_Maths.doc  Page 78 Question 1: SKATEBOARD M520Q01a M520Q01b Eric wants to assemble his own skateboard. What is the minimum price and the maximum price in this shop for self-assembled skateboards? (a) Minimum price: .................................zeds. (b) Maximum price: ................................zeds. SKATEBOARD SCORING 1 Full credit Code 21: Both the minimum (80) and the maximum (137) correct. Partial credit Code 11: Only the minimum (80) correct. Code 12: Only the maximum (137) correct. No credit Code 00: Other responses. Code 99: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SKATEBOARD M520Q03"}, {"from": "gpt", "value": "The shop offers three different decks, two different sets of wheels and two different sets of hardware. There is only one choice for a set of trucks. How many different skateboards can Eric construct? A 6 B 8 C 10 D 12 SKATEBOARD SCORING 2 Full credit Code 1: D.  12. ReleasedPISAItems_Maths.doc  Page 79 No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TABLE TENNIS TOURNAMENT M521Q01 - 0 1 9"}, {"from": "gpt", "value": "Eric has 120 zeds to spend and wants to buy the most expensive skateboard he can afford. How much money can Eric afford to spend on each of the 4 parts?  Put your answer in the table below. Part Amount (zeds) Deck Wheels Trucks Hardware  SKATEBOARD SCORING 3 Full credit Code 1: 65 zeds on a deck, 14 on wheels, 16 on trucks and 20 on hardware. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 80 M521: Table Tennis Tournament\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LIGHTHOUSE M523Q01"}, {"from": "gpt", "value": "Teun, Riek, Bep and Dirk have formed a practice group in a table tennis club.  Each player wishes to play against each other  player once.  They have reserved two practice tables for these matches. Complete the following match schedule; by writing the names of the players playing in each match. P r a c t i c e  T a b l e  1  P r a c t i c e  T a b l e  2 Round 1  Teun - Riek Bep - Dirk Round 2 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 Round 3 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026   ReleasedPISAItems_Maths.doc  Page 81 TABLE TENNIS TOURNAMENT SCORING 1 Full credit Code 1:  Four remaining matches correctly described and distributed over rounds 2 and 3. \u2022  E . g . Practice Table 1 Practice Table 2 Round 1 Teun - Riek Bep - Dirk Round 2 Teun - Bep Riek \u2013 Dirk Round 3 Teun - Dirk Riek - Bep No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 82 M523: Lighthouse Lighthouses are towers with a light beacon on top.  Lighthouses assist sea ships in finding their way at night when they are sailing close to the shore. A lighthouse beacon sends out light flashes with a regular fixed pattern.  Every lighthouse has its own pattern. In the diagram below you see the pattern of a certain lighthouse. The light flashes alternate with dark periods. It is a regular pattern.  After some time the pattern repeats itself.  The time taken by one complete cycle of a pattern, before it starts to repeat, is called the period.  When you find the period of a pattern, it is easy to extend the diagram for the next seconds or minutes or even hours.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LIGHTHOUSE M523Q03 - 0 1 2 9"}, {"from": "gpt", "value": "Which of the following could be the period of the pattern of this lighthouse? A 2 seconds. B 3 seconds. C 5 seconds. D 12 seconds. LIGHTHOUSE SCORING 1 Full credit Code 1: C.  5 seconds. No credit Code 0: Other responses. Code 9: Missing. light dark 0 1 2 3 4 5 6 7 8 9 10 11 12 time (sec) 13 ReleasedPISAItems_Maths.doc  Page 83 Question 2: LIGHTHOUSE M523Q02 For how many seconds does the lighthouse send out light flashes in 1 minute? A 4 B 12 C 20 D 24 LIGHTHOUSE SCORING 2 Full credit Code 1: D.  24. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about DECREASING CO 2 LEVELS M 5 2 5 Q 0 2  -  0 1 9"}, {"from": "gpt", "value": "In the diagram below, make a graph of a possible pattern of light flashes of a lighthouse that sends out light flashes for 30 seconds per minute.  The period of this pattern must be equal to 6 seconds. LIGHTHOUSE SCORING 3 Full credit Code 2: The graph shows a pattern of light and dark with flashes for 3 seconds in every 6 seconds, and with a period of 6 seconds.  This can be done in the light dark 0 1 2 3 4 5 6 7 8 9 10 11 12 time (sec) ReleasedPISAItems_Maths.doc  Page 84 following ways: - 1  o n e - s e c o n d  f l a s h  a n d  a  t w o - s e c o n d  f l a s h  ( a n d  t h i s  c a n  b e  s h o w n  i n several ways), or - 1  t h r e e - s e c o n d  f l a s h  ( w h i c h  c a n  b e  s h o w n  i n  f o u r  d i f f e r e n t  w a y s ) . If two periods are shown, the pattern must be identical for each period. Partial credit Code 1: The graph shows a pattern of light and dark with flashes for 3 seconds in every 6 seconds, but the period is not 6 seconds.  If two periods are shown, the pattern must be identical for each period. \u2022 Three one-second flashes, alternating with 3 one-second dark periods. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 85 M525: Decreasing CO 2  Levels Many scientists fear that the increasing level of CO 2 gas in our atmosphere is causing climate change. The diagram below shows the CO 2 emission levels in 1990 (the light bars) for several countries (or regions), the emission levels in 1998 (the dark bars), and the percentage change in emission levels between 1990 and 1998 (the arrows with percentages). Percentage change in emission levels from 1990 to 1998. +11% -35% +10% +13% +15% -4% -16% +8% 612423218 692485236 1 209 4 208 1 213 3 040 6 0491 020 4 041 1 331 1 962 6 727 Emissions in 1990 (million tons CO 2) Emissions in 1998 (million tons CO 2) USA Russia Japan Canada Australia EU total Germany Netherlands ReleasedPISAItems_Maths.doc  Page 86 Question 1: DECREASING CO 2 LEVELS M 5 2 5 Q 0 1  -  0 1 2 9 In the diagram you can read that in the USA, the increase in CO 2 emission level from 1990 to 1998 was 11%. Show the calculation to demonstrate how the 11% is obtained. DECREASING CO 2 LEVELS SCORING 1 Full credit Code 2: Correct subtraction, and correct calculation of percentage. \u2022 6 7 2 7  \u2013  6 0 4 9  =  6 7 8 ,   11% 100%6049678\u2248\u00d7 . Partial credit Code 1: Subtraction error and percentage calculation correct, or subtraction correct but dividing by 6727. \u2022 89.9% 10067276049=\u00d7 , and 100-89.9=10.1%. No credit Code 0: Other responses, including just \u2018Yes\u2019 or \u2018No\u2019. \u2022 Y e s ,  i t  i s  1 1 % . Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q01 - 0 1 2 9"}, {"from": "gpt", "value": "Mandy analysed the diagram and claimed she discovered a mistake in the percentage change in emission levels: \u201cThe percentage decrease in Germany (16%) is bigger than the percentage decrease in the whole European Union (EU total, 4%). This is not possible, since Germany is part of the EU.\u201d Do you agree with Mandy when she says this is not possible? Give an explanation to support your answer. DECREASING CO 2 LEVELS SCORING 2 Full credit Code 1: No, with correct argumentation. \u2022 N o ,  o t h e r  c o u n t r i e s  f r o m  t h e  E U  c a n  h a ve increases e.g. the Netherlands so the total decrease in the EU can be smaller than the decrease in Germany. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 87 Question 3: DECREASING CO 2 LEVELS M 5 2 5 Q 0 3  -  0 1 2 9 Mandy and Niels discussed which country (or region) had the largest increase  of CO 2 emissions. Each came up with a different conclusion based on the diagram. Give two possible \u2018correct\u2019 answers to this question, and explain how you can obtain each of these answers. DECREASING CO 2 LEVELS SCORING 3 Full credit Code 2: Response identifies both mathematical approaches (the largest absolute increase and the largest relative increase), and names the USA and Australia. \u2022 U S A  h a s  t h e  l a r g e s t  i n c r e a s e  i n  m i l l i o n s  o f  t o n s ,  a n d  A u s t r a l i a  h a s  t h e  l a r g e s t increase in percentage. Partial credit Code 1: Response identifies or refers to both the largest absolute increase and the largest relative increase, but the countries are not identified, or the wrong countries are named. \u2022 R u s s i a  h a d  t h e  b i g g e s t  i n c r e a s e  i n  t h e  a m o u n t  o f  C O 2 (1078 tons), but Australia had the biggest pe rcentage increase (15%). No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 88 M535: Twisted Building In modern architecture, buildings often have unusual shapes. The picture below shows a computer model of a \u2018twisted building\u2019 and a plan of the ground floor.  The compass points show the orientation of the building. The ground floor of the building contains the main entrance and has room for shops. Above the ground floor there are 20 storeys containing apartments. The plan of each storey is similar to the plan of the ground floor, but each has a slightly different orientation from the stor ey below.  The cylinder contains the elevator shaft and a landing on each floor.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q02"}, {"from": "gpt", "value": "Estimate the total height of the building, in metres.  Explain how you found your answer. TWISTED BUILDING SCORING 1 Full credit Code 2:  Accept answers from 50 to 90 me tres if a correct explanation is given. \u2022 O n e  f l o o r  o f  t h e  b u i l d i n g  h a s  a  h e i g h t  o f  a b o u t  2 . 5  m e t e r s .   T h e r e  i s  s o m e extra room between floors.  Therefor e an estimate is 21 x 3 = 63 metres. \u2022 A l l o w  4  m  f o r  e a c h  s t o r y ,  s o  2 0  o f  t h e s e  g i v e s  8 0  m ,  p l u s  1 0  m  f o r  t h e  g r o u n d floor, so a total of 90 m. N S E W N S E W ReleasedPISAItems_Maths.doc  Page 89 Partial credit Code 1: Correct calculation method and explanation, but using 20 stories instead of 21. \u2022 E a c h  a p a r t m e n t  c o u l d  b e  3 . 5  m e t r e s  h i g h ,  2 0  s t o r i e s  o f  3 . 5  m e t r e s  g i v e s  a total height of 70 m. No credit Code 0: Other responses, including answer without any explanation, answers with other incorrect number of floors, and answers with unreasonable estimates of the height of each floor (4 m would be the upper limit). \u2022 Each floor is around 5 m high, so 5 \u00d7 21 equals 105 metres. \u2022 6 0  m . Code 9: Missing.  The following pictures are sideviews of the twisted building.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q03"}, {"from": "gpt", "value": "From which direction has Sideview 1 been drawn? A From the North. B From the West. C From the East. D From the South. TWISTED BUILDING SCORING 2 Full credit Code 1: C.  From the East. Sideview 1 S i d e v i e w  2 ReleasedPISAItems_Maths.doc  Page 90 No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about HEARTBEAT M537Q01 - 0 1 9"}, {"from": "gpt", "value": "From which direction has Sideview 2 been drawn? A From the North West. B From the North East. C From the South West. D From the South East. TWISTED BUILDING SCORING 3 Full credit Code 1: D.  From the South East. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 91 Question 4: TWISTED BUILDING M535Q04 - 0 1 2 9 Each storey containing apartments has a certain \u2018twist\u2019 compared to the ground floor. The top floor (the 20th floor above the ground floor) is at right angles to the ground floor. The drawing below represents the ground floor.  Draw in this diagram the plan of the 10th floor above the ground floor, showing how this floor is situated compared to the ground floor. TWISTED BUILDING SCORING 4 Full credit Code 2: A correct drawing, meaning correct rotation point and anti-clockwise rotation.  Accept angles from 40\u00b0 to 50\u00b0.  Partial credit Code 1: One of the rotation angle, the rotation point, or the rotation direction incorrect. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 92 M537: Heartbeat For health reasons people should limit their efforts, for instance during sports, in order not to exceed a certain heartbeat frequency. For years the relationship between a person\u2019s recommended maximum heart rate and the person\u2019s age was described by the following formula: Recommended maximum heart rate =  220 - age Recent research showed that this formula should be modified slightly.  The new formula is as follows: Recommended maximum heart rate =  208 \u2013 (0.7 \u00d7 age)\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SPACE FLIGHT M 5 4 3 Q 0 1"}, {"from": "gpt", "value": "A newspaper article stated: \u201cA result of using the new formula instead of the old one is that the recommended maximum number of heartbeats per minute for young people decreases slightly and for old people it increases slightly.\u201d From which age onwards does the recommended maximum heart rate increase as a result of the introduction of the new formula?  Show your work. HEARTBEAT SCORING 1 Full credit Code 1: Accept 41, or 40. \u2022 2 2 0  \u2013  age = 208 \u2013 0.7 \u00d7 age results in age = 40, so people above 40 will have a higher recommended maximum heart rate under the new formula. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 93 Question 2: HEARTBEAT M537Q02 - 0 1 9 The formula recommended maximum heart rate =  208 \u2013 (0.7 \u00d7 age) is also used to determine when physical training is most effective. Research has shown that physical training is most effective when the heartbeat is at 80% of the recommended maximum heart rate. Write down a formula for calculating the heart rate for most effective physical training, expressed in terms of age. HEARTBEAT SCORING 2 Full credit Code 1: Any formula that is the equivalent of multiplying the formula for recommended maximum heart rate by 80%. \u2022 h e a r t  r a t e  =  1 6 6  \u2013  0 . 5 6  \u00d7 age. \u2022 h e a r t  r a t e  =  1 6 6  \u2013  0 . 6  \u00d7 age. \u2022 h  =  1 6 6  \u2013  0 . 5 6  \u00d7 a. \u2022 h  =  1 6 6  \u2013  0 . 6  \u00d7 a. \u2022 h e a r t  r a t e  =  ( 2 0 8  \u2013  0 . 7 a g e )  \u00d7 0.8. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 94 M543: Space Flight Space station Mir remained in orbit for 15 years and circled Earth some 86 500 times during its time in space. The longest stay of one cosmonaut in the Mir was around 680 days.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STAIRCASE M547Q01"}, {"from": "gpt", "value": "Approximately how many times did this cosmonaut fly around Earth? A 110 B 1 100 C 11 000 D 110 000 SPACE FLIGHT SCORING 1 Full credit Code 1: C.  11 000. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 95 M547: Staircase\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about ROCK CONCERT M552Q01"}, {"from": "gpt", "value": "The diagram below illustrates a staircase with 14 steps and a total height of 252 cm: What is the height of each of the 14 steps? Height: ....................................................cm. STAIRCASE SCORING 1 Full credit Code 1:  18. No credit Code 0:  Other responses. Code 9:  Missing. Total height 252 cm Total depth 400 cm ReleasedPISAItems_Maths.doc  Page 96 M552: Rock Concert\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about NUMBER CUBES M555Q02"}, {"from": "gpt", "value": "For a rock concert a rectangular field of size 100 m by 50 m was reserved for the audience.  The concert was completely sold out and the field was full with all the fans standing. Which one of the following is likely to be the best estimate of the total number of people attending the concert? A 2 000 B 5 000 C 20 000 D 50 000 E 100 000 ROCK CONCERT SCORING 1 Full credit Code 1: C.  20 000. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 97 M555: Number Cubes\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SUPPORT FOR THE PRESIDENT M702Q01 - 0 1 2 9"}, {"from": "gpt", "value": "On the right, there is a picture of two dice. Dice are special number cubes for which the following rule applies: The total number of dots on two opposite faces is always seven. You can make a simple number cube by cutting, folding and gluing cardboard.  This can be done in many ways.  In the figure below you can see four cuttings that can be used to make cubes, with dots on the sides. Which of the following shapes can be folded together to form a cube that obeys the rule that the sum of opposite faces is 7? For each shape, circle either \u201cYes\u201d or \u201cNo\u201d in the table below. Shape Obeys the rule that the sum of opposite faces is 7? I Yes / No II Yes / No III Yes / No IV Yes / No  NUMBER CUBES SCORING 2 Full credit Code 1: No, Yes, Yes, No, in that order. No credit Code 0: Other responses. Code 9: Missing. I II IIIIV ReleasedPISAItems_Maths.doc  Page 98 M702: Support for the President\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about MOVING WALKWAYS M703Q01 - 0 1 9"}, {"from": "gpt", "value": "In Zedland, opinion polls were conducted to find out the level of support for the President in the forthcoming election.  Four newspaper publishers did separate nationwide polls.  The results for the four newspaper polls are shown below: Newspaper 1: 36.5% (poll conducted on January 6, with a sample of 500 randomly selected citizens with voting rights) Newspaper 2: 41.0% (poll conducted on January 20, with a sample of 500 randomly selected citizens with voting rights) Newspaper 3: 39.0% (poll conducted on January 20, with a sample of 1000 randomly selected citizens with voting rights) Newspaper 4: 44.5% (poll conducted on January 20, with 1000 readers phoning in to vote). Which newspaper\u2019s result is likely to be the best for predicting the level of support for the President if the election is held on January 25?  Give two reasons to support your answer. SUPPORT FOR THE PRESIDENT SCORING 1 Full credit Code 2: Newspaper 3.  The poll is more recent, with larger sample size, a random selection of the sample, and only voters were asked.  (Give at least two reasons).  Additional information (including irrelevant or incorrect information) should be ignored. \u2022 N e w s p a p e r  3 ,  b e c a u s e  t h e y  h a v e  s e l e c t e d  m o r e  c i t i z e n s  r a n d o m l y  w i t h  v o t i n g rights. \u2022 N e w s p a p e r  3  b e c a u s e  i t  h a s  a s k e d  1 0 0 0  p e o p l e ,  r a n d o m l y  s e l e c t e d ,  a n d  t h e date is closer to the election date so t he voters have less time to change their mind. \u2022 N e w s p a p e r  3  b e c a u s e  t h e y  w e r e  r a n d o m l y  s e l e c t e d  a n d  t h e y  h a d  v o t i n g rights. \u2022 N e w s p a p e r  3  b e c a u s e  i t  s u r v e y e d  m o r e  p e o p l e  c l o s e r  t o  t h e  d a t e . \u2022 N e w s p a p e r  3  b e c a u s e  t h e  1 0 0 0  p e o p l e  w e r e  r a n d o m l y  s e l e c t e d . Partial credit Code 1: Newspaper 3, with only one reason, or without explanation. \u2022 N e w s p a p e r  3 ,  b e c a u s e  t h e  p o l l  i s  c l o s e r  t o  e l e c t i o n  d a t e . \u2022 N e w s p a p e r  3 ,  b e c a u s e  m o r e  p e o p l e  w e r e  s u r v e y e d  t h a n  n e w s p a p e r s  1  a n d  2 . \u2022 N e w s p a p e r  3 . ReleasedPISAItems_Maths.doc  Page 99 No credit Code 0: Other responses. \u2022 N e w s p a p e r  4 .   M o r e  p e o p l e  m e a n s  m o r e  a c c u r a t e  r e s u l t s ,  a n d  p e o p l e  p h o n i n g in will have considered their vote better. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 100 time Distance from the start of the moving walkway A person walking on the ground A person walking on the moving walkway time Distance from the start of the moving walkway A person walking on the ground A person walking on the moving walkway A person standing still on the moving walkway M703: Moving Walkways\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about THE BEST CAR M704Q01"}, {"from": "gpt", "value": "On the right is a photograph of moving walkways. The following Distance-Time graph shows a comparison between \u201cwalking on the moving walkway\u201d and \u201cwalking on the ground next to the moving walkway.\u201d Assuming that, in the above graph, the walking pace is about the same for both persons, add a line to the graph that would represent the distance versus time for a person who is standing still on the moving walkway. MOVING WALKWAYS SCORING 1 Full credit Code 1: Accept a line below the two lines, but it must be closer to the line of \u201cA person walking on the ground\u201d than to the baseline.  ReleasedPISAItems_Maths.doc  Page 101 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 102 M704: The Best Car A car magazine uses a rating system to evaluate new cars, and gives the award of \u201cThe Car of the Year\u201d to the car with the highest total score.  Five new cars are being evaluated, and their ratings are shown in the table. Car Safety Features (S) Fuel Efficiency (F)External Appearance(E)Internal Fittings (T) Ca 3 1 2 3 M2 2 2 2 2 Sp 3 1 3 2 N1 1 3 3 3 KK 3 2 3 2 The ratings are interpreted as follows: 3  p o i n t s  =  E x c e l l e n t 2  p o i n t s  =  G o o d 1  p o i n t  =  F a i r\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STEP PATTERN M806Q01"}, {"from": "gpt", "value": "To calculate the total score for a car, the car magazine uses the following rule, which is a weighted sum of the individual score points: T o t a l  S c o r e  =  ( 3  x  S )  +  F  +  E  +  T Calculate the total score for Car \u201cCa\u201d.  Write your answer in the space below. Total score for \u201cCa\u201d: ............................... THE BEST CAR SCORING 1 Full credit Code 1: 15 points. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 103 Question 2: THE BEST CAR M704Q02 The manufacturer of car \u201cCa\u201d thought the rule for the total score was unfair. Write down a rule for calculating the total score so that Car \u201cCa\u201d will be the winner. Your rule should include all four of the variables, and you should write down your rule by filling in positive numbers in the four spaces in the equation below. Total score = \u2026\u2026\u2026 \u00d7 S + \u2026\u2026\u2026\u00d7 F + \u2026\u2026\u2026\u00d7 E + \u2026\u2026\u2026\u00d7 T. THE BEST CAR SCORING 2 Full credit Code 1: Correct rule that will make \u201cCa\u201d the winner. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 104 M806: Step Pattern\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q01"}, {"from": "gpt", "value": "Robert builds a step pattern using squares. Here are the stages he follows. As you can see, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3. How many squares should he use for the fourth stage? Answer: ..................................................squares. STEP PATTERN SCORING 1 Full credit Code 1: 10. No credit Code 0: Other responses. Code 9: Missing. Stage 1 Stage 2 Stage 3 ReleasedPISAItems_Maths.doc  Page 105 M836: Postal Charges The postal charges in Zedland are based on the weight of the items (to the nearest gram), as shown in the table below: Weight (to nearest gram) Charge Up to 20 g 0.46 zeds 21 g \u2013 50 g 0.69 zeds 51 g \u2013 100 g 1.02 zeds 101 g \u2013 200 g 1.75 zeds 201 g \u2013 350 g 2.13 zeds 351 g \u2013 500 g 2.44 zeds 501 g \u2013 1000 g 3.20 zeds 1001 g \u2013 2000 g 4.27 zeds 2001 g \u2013 3000 g 5.03 zeds\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q02 - 0 1 9"}, {"from": "gpt", "value": "Which one of the following graphs is the best representation of the postal charges in Zedland?  (The horizontal axis shows the weight in grams, and the vertical axis shows the charge in zeds.) 0123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 00123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 0123456 20 50 100 200 350 500 1000 2000 30000123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0A C D B ReleasedPISAItems_Maths.doc  Page 106 POSTAL CHARGES SCORING 1 Full credit Code 1: C. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q02 - 0 1 9"}, {"from": "gpt", "value": "Jan wants to send two items, weighing 40 grams and 80 grams respectively, to a friend. According to the postal charges in Zedland, decide whether it is cheaper to send the two items as one parcel, or send the items as two separate parcels.  Show your calculations of the cost in each case. POSTAL CHARGES SCORING 2 Full credit Code 1: It will be cheaper to send the items as two separate parcels.  The cost will be 1.71 zeds for two separate parcels, and 1.75 zeds for one single parcel containing both items. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 107 Source Publications for Released Items  OECD Sources  (available www.pisa.oecd.org) Test Questions (1) Interactive Web examples: http://pisa-sq.acer.edu.au (2) PISA 2003 sample question files: http://www.pisa.oecd.org Follow the links: What PISA Produces > PISA 2003 > Test questions Publications (3) OECD (Organisation for Economic Co-operation and Development ) (2002), Sample Tasks from the PISA 2000 Assessment: Reading,  Mathematical and Scientific Literacy , OECD, Paris. (4) OECD  (2000), Measuring Student Knowledge and Skills - The PISA 2000 Assessment of Reading, Mathematical and Scientific Literacy , OECD, Paris. (5) OECD  (2003), The PISA 2003 Assessment Framework - Mathematics, Reading, Science and Problem Solving Knowledge and Skills, OECD, Paris.  Unit S o u r c e Code Title (1) Interactive Web Examples (2) PISA 2003 Web Samples (3) PISA 2000 Sample Tasks (4) PISA 2000 Measuring Student K&S (5) PISA 2003 Assessment Framework M037 Farms \u0085 \u0085 ; M047 Lichen ; \u0085 \u0085 ; M124 Walking \u0085 ; M136 Apples \u0085 \u0085 ; M143 Coins ; \u0085 \u0085 ; M143 Cubes \u0085 ; M148 Continent Area \u0085 \u0085 ; M150 Growing Up \u0085 ; M154 Pizzas ; \u0085 \u0085 ; M158 Shapes ; \u0085 \u0085 ; M159 Speed of Racing Car \u0085 \u0085 ; M161 Triangles \u0085 \u0085 ; M179 Robberies \u0085 ; M215 Braking ; \u0085 \u0085 ; M266 Carpenter \u0085 ; M267 Patio ; \u0085 \u0085 ; M307 Drug Concentrations \u0085 \u0085 \u0085 \u0085 ; M309 Building Blocks \u0085 \u0085 \u0085 \u0085 ; M402 Internet Relay Chat \u0085 ; M413 Exchange Rate \u0085 ; ReleasedPISAItems_Maths.doc  Page 108 Unit S o u r c e Code Title (1) Interactive Web Examples (2) PISA 2003 Web Samples (3) PISA 2000 Sample Tasks (4) PISA 2000 Measuring Student K&S (5) PISA 2003 Assessment Framework M432 Reaction Time \u0085 \u0085 \u0085 \u0085 ; M438 Exports \u0085 ; M465 Water Tank \u0085 \u0085 \u0085 \u0085 ; M467 Coloured Candies \u0085 ; M468 Science Tests \u0085 ; M471 Spring Fair \u0085 ; M472 Swing \u0085 \u0085 \u0085 \u0085 ; M479 Student Heights \u0085 \u0085 \u0085 \u0085 ; M480 Payments by Area \u0085 \u0085 \u0085 \u0085 ; M484 Bookshelves \u0085 ; M505 Litter \u0085 ; M509 Earthquake \u0085 ; M510 Choices \u0085 ; M513 Test Scores \u0085 ; M515 Shoes for Kids \u0085 ; M520 Skateboard \u0085 ; M521 Table Tennis Tournament \u0085 ; M523 Lighthouse \u0085 \u0085 \u0085 \u0085 ; M525 Decreasing CO 2 Levels \u0085 ; M535 Twisted Building \u0085 \u0085 \u0085 \u0085 ; M537 Heartbeat \u0085 \u0085 \u0085 \u0085 ; M543 Space Flight \u0085 ; M547 Staircase \u0085 ; M552 Rock Concert \u0085 \u0085 \u0085 \u0085 ; M555 Number Cubes \u0085 ; M702 Support for the President \u0085 ; M703 Moving Walkways \u0085 \u0085 \u0085 \u0085 ; M704 The Best Car \u0085 ; M806 Step Pattern \u0085 ; M836 Postal Charges \u0085 \u0085 \u0085 \u0085 ;\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LICHEN M047Q02- 0 1 2 8 9"}, {"from": "gpt", "value": "Using the formula, calculate the diameter of the lichen, 16 years after the ice disappeared. Show your calculation. LICHEN SCORING 1 Full credit Code 2: 14mm (units not required).  Code 2 should be given as long as the correct answer is 14 whether working out is shown or not. Partial credit Code 1: Partial responses including: \u2022 C o r r e c t  s u b s t i t u t i o n  o f  v a l u e  i n  t h e  f o r m u l a  b u t  i n c o r r e c t  a n s w e r  O r  m i s s i n g answer. \u2022 I n c o m p l e t e  a n s w e r s  ( e g ,   7 \u221a4). No credit Code 0: Other responses. Code 9: Missing. Example responses Code 2: 1412160.7 =\u2212\u00d7= dd 14mm 14  ReleasedPISAItems_Maths.doc  Page 8 years ddd 144 0.712 16 0.7 =\u00d7=\u2212\u00d7= (Note that here the calculations are all correct, but the unit is wrong. We will assume for now that it is the slip of the pen) Code 1: 1612160.7 =\u2212\u00d7= dd (wrong answer but correct substitution) 47121607 =\u2212\u00d7= dd . (incomplete answer)  Code 0: 16\n\nThis question is designed to test: To elicit student's  ability to apply a given formula."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about COINS M143Q01-0 1 8 9"}, {"from": "gpt", "value": "Ann measured the diameter of some lichen and found it was 35 millimetres. How many years ago did the ice disappear at this spot? Show your calculation. LICHEN SCORING 2 Full credit Code 2: 37 years (unit not required) whether working out is shown or not. Partial credit Code 1: Correct substitution of values in the formula but incorrect answer or missing answer. OR 36 years or 38 years. (Students may arrive at these answers using the trial and error method) No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 9 Example responses Code 2: 3712 2512 512 7 35 =\u2212=\u2212=\u2212\u00d7= tttt  years373771225 725 7575735\u2234\u00d7=+\u00d7=\u00d7=\u00d7=\u00f7   37 122525 557/35 2 =+== (Strictly incorrect algebraic repres entation, but we know what the student is trying to do)  t = 15  d = 12.1 t = 25  d = 25.2 t = 40  d = 37.0 t = 35  d = 33.6 t = 37  d = 35 So 37 years after the ice disappeared (Note that here the answer 37 is embedded in an equation that is correct)  756 = 35 = 7X \u221a(37-12) = 7X \u221a25 = 7X5 = 35 Code 1: 251237 4912 7 3512 0.7 35 2 2 ==\u2212\u00d7=\u2212\u00d7= tttt  1312 2512 512 0.7 35 2 2 =\u2212=\u2212=\u2212\u00d7= tttt  !12 512 512 0.7 35 hardToottt \u2212=\u2212=\u2212\u00d7=  Code 0: 79612 78412 2812 0.7 35 =\u2212=\u2212=\u2212\u00d7= tttt  40 years   ReleasedPISAItems_Maths.doc  Page 17 M143: Coins You are asked to design a new set of coins. All coins will be circular and coloured silver, but of different diameters.  Researchers have found out that an ideal coin system meets the following requirements: \u2022 d i a m e t e r s  o f  c o i n s  s h o u l d  n o t  b e  s m a l l e r  t h a n  1 5  m m  a n d  n o t  b e  l a r g e r  t h a n  4 5 mm. \u2022 g i v e n  a  c o i n ,  t h e  d i a m e t e r  o f  t h e  n e x t  c o i n  m u s t  b e  a t  l e a s t  3 0 %  l a r g e r . \u2022 t h e  m i n t i n g  m a c h i n e r y  c a n  o n l y  p r o d u c e  c o i n s  w i t h  d i a m e t e r s  o f  a  w h o l e  n u m b e r of millimetres (e.g. 17 mm is allowed, 17.3 mm is not).\n\nThis question is designed to test: To elicit student's  ability to apply a given formula."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PIZZAS M154Q01- 0 1 2 8 9"}, {"from": "gpt", "value": "You are asked to design a set of coins that satisfy the above requirements. You should start with a 15 mm coin and your set should contain as many coins as possible. What would be the diameters of the coins in your set? COINS SCORING 1 calculations. Code 1: 15 \u2013 20 \u2013 26 \u2013 34 \u2013 45. It is possible that the response could  be presented as actual drawings of the coins of the correct diameters.  This should be coded as 1 as well. Code 8: Gives a set of coins that satisfy the three criteria, but not the set that contains as many coins as possible, eg., 15 \u2013 21 \u2013 29 \u2013 39, or 15 \u2013 30 \u2013 45 OR The first three diameters correct, the last two incorrect (15 \u2013 20 \u2013 26 - ) OR The first four diameters correct, the last one incorrect (15 \u2013 20 \u2013 26 \u2013 34 - ) Code 0: Other responses. Code 9 : Missing. ReleasedPISAItems_Maths.doc  Page 27 M154: Pizzas A pizzeria serves two round pizzas of the same thickness in different sizes. The smaller one has a diameter of 30 cm and costs 30 zeds. The larger one has a diameter of 40 cm and costs 40 zeds.\n\nThis question is designed to test: Understanding and use of complicated information to do"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHAPES M158Q01- 0 1 8 9"}, {"from": "gpt", "value": "Which pizza is better value for money? Show your reasoning. PIZZAS SCORING 1 comparison Code 2: Gives general reasoning that the surface area of pizza increases more rapidly than the price of pizza to conclude that the larger pizza is better value. \u2022 The diameter of the pizzas is the same  number as their price, but the amount of pizza you get is found using diameter2 , so you will get more pizza per zeds from the larger one Code 1: Calculates the area and amount per zed for each pizza to conclude that the larger pizza is better value. \u2022 A r e a  o f  s m a l l e r  p i z z a  i s  0 . 2 5  x  \u03c0 x 30 x 30 = 225 \u03c0; amount per zed is 23.6 cm2 area of larger pizza is 0.25 x \u03c0 x 40 x 40 = 400 \u03c0; amount per zed is 31.4 cm2 so larger pizza is better value Code 8: They are the same value for money.  (This incorrect answer is coded separately, because we would like to keep track of how many students have this misconception). Code 0: Other incorrect responses OR a correct answer without correct reasoning. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 28 M158: Shapes   A  B  C\n\nThis question is designed to test: Applies understanding of area to solving a value for money"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHAPES M158Q03- 0 1 8 9"}, {"from": "gpt", "value": "Which of the figures has the largest area? Explain your reasoning. SHAPES SCORING 1 Code 1: Shape B, supported with plausible reasoning. \u2022 I t \u2019 s  t h e  l a r g e s t  a r e a  b e c a u s e  the others will fit inside it. Code 8: Shape B, without plausible support. Code 0: Other responses. Code 9: Missing. Example responses Code 1: \u2022 B .  I t  d o e s n \u2019 t  h a v e  i n d e n t s  i n  i t  w h i c h decreases the area.  A and C have gaps. \u2022 B ,  b e c a u s e  i t \u2019 s  a  f u l l  c i r c l e ,  a n d  t h e  o t h e rs are like circles with bits taken out. \u2022 B, because it has no open areas:  Code 8: \u2022 B. because it has the largest surface area \u2022 T h e  c i r c l e .   I t \u2019 s  p r e t t y  o b v i o u s . \u2022 B ,  b e c a u s e  i t  i s  b i g g e r . Code 0: \u2022 They are all the same. ReleasedPISAItems_Maths.doc  Page 29 Question 2: SHAPES M158Q02- 0 1 8 9 Describe a method for estimating the area of figure C. SHAPES SCORING 2 irregular shapes. Code 1: Reasonable method: \u2022 D r a w  a  g r i d  o f  s q u a r e s  o v e r  t h e  s h ape and count the squares that are more than half filled by the shape. \u2022 C u t  t h e  a r m s  o f f  t h e  s h a p e  a n d  r e a r r a n g e  t he pieces so that they fill a square then measure the side of the square. \u2022 Build a 3D model based on the shape and fill it with water. Measure the amount of water used and the depth of the water in the model.  Derive the area from the information. Code 8: Partial answers: \u2022 The student suggests to find the area of the circle and subtract the area of the cut out pieces.  However, the student does not mention about how to find out the area of the cut out pieces. \u2022 A d d  u p  t h e  a r e a  o f  e a c h  i n dividual arm of the shape Code 0:  Other responses. Code 9: Missing. NOTE: The key point for this question is whether the student offers a METHOD for determining the area.  The coding schemes (1, 8, 0) is a hierarchy of the extent to which the student describes a METHOD. Example responses Code 1: \u2022 You could fill the shape with lots of ci rcles, squares and ot her basic shapes so there is not a gap.  Work out the area of all of the shapes and add together. \u2022 Redraw the shape onto graph paper and count all of the squares it takes up. \u2022 D r a w i n g  a n d  c o u n t i n g  e q u a l  s i z e  b o x e s .   S m a l l e r  b o x e s  =  b e t t e r  a c c u r a c y (Here the student\u2019s description is brief, but we will be lenient about student\u2019s writing skills and regard the method offered by the student as correct) \u2022 M a k e  i t  i n t o  a  3 D  m o d e l  a n d  f i l l i n g  i t  w i t h  e x a c t l y  1 c m  o f  w a t e r  a n d  t h e n measure the volume of water required to fill it up. Code 8: \u2022 F i n d  t h e  a r e a  o f  B  t h e n  f i n d  t h e  a r e a s  o f  the cut out pieces and subtract them from the main area. \u2022 M i n u s  t h e  s h a p e  f r o m  t h e  c i r c l e \u2022 A d d  u p  t h e  a r e a  o f  e a c h  i n d i v i d u a l  p i e c e  e . g . , \u2022 Use a shape like that and pour a liquid into it. \u2022 U s e  g r a p h \u2022 H a l f  o f  t h e  a r e a  o f  s h a p e  B \u2022 F i g u r e  o u t  h o w  m a n y  m m2 are in one little leg things and times it by 8. ReleasedPISAItems_Maths.doc  Page 30 Code 0: \u2022 U s e  a  s t r i n g  a n d  m e a s u r e  t h e  p e r i m e t e r  o f  the shape.  Stretch the string out to a circle and measure the area of the circle using \u03c0 r2. (Here the method described by the student is wrong)\n\nThis question is designed to test: To assess students\u2019 strategies for measuring areas of"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q01"}, {"from": "gpt", "value": "Describe a method for estimating the perimeter of figure C. SHAPES SCORING 3 irregular shapes Code 1: Reasonable method: \u2022 Lay a piece of string over the outline of the shape then measure the length of string used. \u2022 C u t  t h e  s h a p e  u p  i n t o  s h o r t ,  n e a r l y  s t r a i ght pieces and join them together in a line, then measure the length of the line. \u2022 M e a s u r e  t h e  l e n g t h  o f  s o m e  o f  t h e  arms to find an average arm length then multiply by 8 (number of arms) X 2. Code 0: Other responses. Code 9: Missing. Example responses Code 1: \u2022 W o o l  o r  s t r i n g ! ! ! (Here although the answer is brief, the student did offer a METHOD for measuring the perimeter) \u2022 C u t  t h e  s i d e  o f  t h e  s h a p e  i n t o  s e c t i o n s .   M e a s u r e  e a c h  t h e n  a d d  t h e m together. (Here the student did not explicitly  say that each section needs to be approximately straight, but we will give t he benefit of the doubt,  that is, by offering the METHOD of cutting the shape into pieces, each piece is assumed to be easily measurable) Code 0: \u2022 M e a s u r e  a r o u n d  t h e  o u t s i d e . (Here the student did not suggest any METHOD of measuring. Simply saying \u201cmeasure it\u201d is not offering any method of how to go about measuring it) \u2022 S t r e t c h  o u t  t h e  s h a p e  t o  m a k e  i t  a  c i r c l e . (Here although a method is offered by the student, the method is wrong) ReleasedPISAItems_Maths.doc  Page 38 M215: Braking The approximate distance to stop a moving vehicle is the sum of: \u2022 t h e  d i s t a n c e  c o v e r e d  d u r i n g  t h e  t i m e  t h e  d r i v e r  t a k e s  t o  b e g i n  t o  a p p l y  t h e brakes (reaction-time distance) \u2022 t h e  d i s t a n c e  t r a v e l l e d  w h i l e  t h e  b r a k e s  a r e  a p p l i e d  ( b r a k i n g  d i s t a n c e ) The \u2018snail\u2019 diagram below gives the theoretical stopping distance for a vehicle in good braking conditions (a particularly alert driver, brakes and tyres in perfect condition, a dry road with a good surface) and how much the stopping distance depends on speed. 20.8 m245.5 m Distance to stop a vehicle. Time to stop the vehicle. Distance travelled during the braking time. Distance travelled during the driver\u2019s reaction time. 219 m 197.6 m 175.4 m 152.2 m 135.6 m 118 m 101 m 85.4 m 70.7 m 57.7 m 46 m 35.7 m 26.5 m 18.6 m 37.5 m 35.4 m 33.3 m 31.3 m 29.2 m 27.1 m 25 m 22.9 m 18.7 m 16.7 m 14.6 m 12.5 m 10.3 m 8.3 m 9.08 s 8.62 s 8.15 s 7.69 s 7.23 s 6.76 s 6.30 s 5.84 s 5.38 s 4.92 s 4.46 s 3.99 s 3.53 s 3.06 s 2.60 s 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 KPH ReleasedPISAItems_Maths.doc  Page 39 QUESTION 1: BRAKING M215Q01 If a vehicle is travelling at 110 kph, what distance does the vehicle travel during the driver\u2019s reaction time? BRAKING 1 SCORING GUIDE Code 1: 22.9 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q03"}, {"from": "gpt", "value": "If a vehicle is travelling at 110 kph, what is the total distance travelled before the vehicle stops? BRAKING SCORING 2 Code 1: 101 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q05"}, {"from": "gpt", "value": "If a vehicle is travelling at 110 kph, how long does it take to stop the vehicle completely? BRAKING 3 SCORING GUIDE Code 1: 5.84 seconds  (units not required) Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 40 Question 4: BRAKING M215Q04 If a vehicle is travelling at 110 kph, what is the distance travelled while the brakes are being applied? BRAKING 4 SCORING GUIDE Code 1: 78.1 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to derive a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PATIO M267Q01- 0 1 2 8 9"}, {"from": "gpt", "value": "A second driver, travelling in good conditions, stops her vehicle in a total distance of 70.7 metres.  At what speed was the vehicle travelling before the brakes were applied? BRAKING 5 SCORING GUIDE Code 1: 90 kph (units not necessary) Code 0: Other responses. Code 9 : Missing. ReleasedPISAItems_Maths.doc  Page 43 M267: Patio\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about DRUG CONCENTRATIONS M307Q01 - 0 1 2 9"}, {"from": "gpt", "value": "Nick wants to pave the rectangular patio of his new house. The patio has length 5.25 metres and width 3.00 metres. He needs 81 bricks per square metre. Calculate how many bricks Nick needs for the whole patio.  PATIO SCORING 1 Full credit Code 2: 1275, 1276  or 1275.75 (unit not required). Partial credit Code 1: 15.75 (units not required) OR 1215 bricks for 5m X 3m (This score is used for students who are able to calculate the number of bricks for an integer number of square metres, but not for fractions of square metres.  See example response.) OR Error in calculating the area, but multiplied by 81 correctly OR Rounded off the area and then multiplied by 81 correctly No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 44 Example responses Code 2: \u2022 5.25 X 3 = 15.75 X 81 = 1276 Code 1: \u2022 5.25 X 3 = 15.75 \u2022 15.75 X 81 = 9000 \u2022 81 X 15 = 1215; 1215 + 21 = 1236 \u2022 5.25 X 3.0 = 15.75 m2;   so 15.75 X 1275.75 = 1376 bricks. (Here the student got the first part right, but the second part wrong.  Give credit for the first part and ignore the second part.  So score as 1)  8 1  8 1  8 1  8 1  8 1 8 1  8 1  8 1  8 1  8 1 8 1  8 1  8 1  8 1  8 1  5m 3m ReleasedPISAItems_Maths.doc  Page 45 M307: Drug Concentrations\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BUILDING BLOCKS M309Q02"}, {"from": "gpt", "value": "A woman in hospital receives an injection of penicillin.  Her body gradually breaks the penicillin down so that one hour after the injection only 60% of the penicillin will remain active. This pattern continues: at the end of each hour only 60% of the penicillin that was present at the end of the previous hour remains active. Suppose the woman is given a dose of 300 millig rams of penicillin at 8 o\u2019clock in the morning. Complete this table showing the amount of penicillin that will remain active in the woman\u2019s blood at intervals of one hour from 0800 until 1100 hours. Time 0800 0900 1000 1100 Penicillin (mg) 300  DRUG CONCENTRATIONS SCORING 1 Full credit Code 2: All three table entries correct.  Time 0800 0900 1000 1100 Penicillin (mg) 300 180 108 64.8 or 65 Partial credit Code 1: One or two table entries correct. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 46 Amount of active drug (mg) 0 1 2 3 4 5 Time (days) after taking the drug 20 40 60 80 0 Question 2: DRUG CONCENTRATIONS M307Q02 Peter has to take 80 mg of a drug to control his blood pressure. The following graph shows the initial amount of the drug, and the amount that remains active in Peter\u2019s blood after one, two, three and four days. How much of the drug remains active at the end of the first day? A   6 mg. B 12 mg. C 26 mg. D 32 mg. DRUG CONCENTRATIONS SCORING 2 Full credit Code 1: D.  32mg. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 47 Question 3: DRUG CONCENTRATIONS M307Q03 From the graph for the previous question it can be seen that each day, about the same proportion of the previous day\u2019s drug remains active in Peter\u2019s blood. At the end of each day which of the following is the approximate percentage of the previous day\u2019s drug that remains active? A 20%. B 30%. C 40%. D 80%. DRUG CONCENTRATIONS SCORING 3 Full credit Code 1: C.  40%. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 48 M309: Building Blocks  Susan likes to build blocks from small cubes like the one shown in the following diagram: Susan has lots of small cubes like this one.  She uses glue to join cubes together to make other blocks. First, Susan glues eight of the cubes together to make the block shown in Diagram A: Then Susan makes the solid blocks shown in Diagram B and Diagram C below: Diagram B Diagram C Small cube Diagram A ReleasedPISAItems_Maths.doc  Page 49 Question 1: BUILDING BLOCKS M309Q01 How many small cubes will Susan need to make the block shown in Diagram B? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 1 Full credit Code 1: 12 cubes. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BUILDING BLOCKS M309Q04"}, {"from": "gpt", "value": "How many small cubes will Susan need to make the solid block shown in Diagram C? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 2 Full credit Code 1: 27 cubes. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 50 Question 3: BUILDING BLOCKS M309Q03 Susan realises that she used more small cubes than she really needed to make a block like the one shown in Diagram C.  She realises that she could have glued small cubes together to look like Diagram C, but the block could have been hollow on the inside. What is the minimum number of cubes she needs to make a block that looks like the one shown in Diagram C, but is hollow? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 3 Full credit Code 1: 26 cubes. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about EXPORTS M438Q01 - 0 1 9"}, {"from": "gpt", "value": "Now Susan wants to make a block that looks like a solid block that is 6 small cubes long, 5 small cubes wide and 4 small cubes high.  She wants to use the smallest number of cubes possible, by leaving t he largest possible hollow space inside the block. What is the minimum number of cubes Susan will need to make this block? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 4 Full credit Code 1: 96 cubes. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 55 M432: Reaction Time In a Sprinting event, the \u2018reaction time\u2019 is the time interval between the starter\u2019s gun firing and the athlete leaving the starting block.  The \u2018final time\u2019 includes both this reaction time, and the running time. The following table gives the reaction time and the final time of 8 runners in a 100 metre sprint race. Lane Reaction time (sec) Final time (sec) 1 0.147 10.09 2 0.136 9.99 3 0.197 9.87 4 0.180 Did not finish the race 5 0.210 10.17 6 0.216 10.04 7 0.174 10.08 8 0.193 10.13  ReleasedPISAItems_Maths.doc  Page 56 Question 1: REACTION TIME  M432Q01 - 0 1 9 Identify the Gold, Silver and Bronze medallists from this race.  Fill in the table below with the medallists' lane number, reaction time and final time. Medal Lane Reaction time (secs) Final time (secs) GOLD SILVER BRONZE REACTION TIME SCORING 1 Full credit Code 1: Medal Lane Reaction time (secs) Final time (secs) GOLD 3 0.197 9.87 SILVER 2 0.136 9.99 BRONZE 6 0.216 10.04 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 57 Question 2: REACTION TIME  M432Q02 - 0 1 9 To date, no humans have been able to react to a starter\u2019s gun in less than 0.110 second. If the recorded reaction time for a runner is less than 0.110 second, then a false start is considered to have occurred because the runner must have left before hearing the gun. If the Bronze medallist had a faster reaction time, would he have had a chance to win the Silver medal?  Give an explanation to support your answer. REACTION TIME SCORING 2 Full credit Code 1: Yes, with adequate explanation. \u2022 Yes. If he had a reaction time of 0.05 sec faster, he would have equalled second place. \u2022 Y e s ,  h e  w o u l d  h a v e  a  c h a n c e  t o  w i n  t h e  S i l v e r  m e d a l  i f  h i s  r e a c t i o n  t i m e  w a s less than or equal to 0.166 sec. \u2022 Y e s ,  w i t h  t h e  f a s t e s t  p o s s i b l e  r e a c t i o n  t i m e  h e  w o u l d  h a v e  d o n e  a  9 . 9 3  w h i c h is good enough for silver medal. No credit Code 0: Other responses, including yes without adequate explanation. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 58 M438: Exports The graphics below show information about exports from Zedland, a country that uses zeds as its currency.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about WATER TANK M 4 6 5 Q 0 1"}, {"from": "gpt", "value": "What was the total value (in millions of zeds) of exports from Zedland in 1998? Answer: .................................................. EXPORTS SCORING 1 Full credit Code 1:  27.1 million zeds or 27 100 000 zeds or 27.1 (unit not required). No credit Code 0: Other responses. Code 9: Missing. Distribution of exports from Zedland in 2000 Total annual exports from Zedland in millions of zeds, 1996-2000 Year Tobacco 7% Wool 5% Cotton fabric 26% Fruit juice 9% Rice 13% Tea 5% Meat 14% Other 21% 20.4 25.4 27.1 37.9 42.6 051015202530354045 1996 1997 1998 1999 2000 ReleasedPISAItems_Maths.doc  Page 59 Question 2: EXPORTS M438Q02 What was the value of fruit juice exported from Zedland in 2000? A 1.8 million zeds. B 2.3 million zeds. C 2.4 million zeds. D 3.4 million zeds. E 3.8 million zeds. EXPORTS SCORING 2 Full credit Code 1:  E.  3.8 million zeds. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 60 M465: Water Tank\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about COLOURED CANDIES M467Q01"}, {"from": "gpt", "value": "Which of the following graphs shows how the height of the water surface changes over time? 1.5 m 1.0 m 1.5 m Water tank A water tank has shape and dimensions as shown in the diagram. At the beginning the tank is empty.  Then it is filled with water at the rate of one litre per second. Height Time Height Time D Height E Height Time Time Height Time A B C ReleasedPISAItems_Maths.doc  Page 61 WATER TANK SCORING 1 Full credit Code 1: B. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 62 M467: Coloured Candies\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SCIENCE TESTS M468Q01"}, {"from": "gpt", "value": "Robert\u2019s mother lets him pick one candy from a bag.  He can\u2019t see the candies. The number of candies of each colour in the bag is shown in the following graph. What is the probability that Robert will pick a red candy? A 10% B 20% C 25% D 50% COLOURED CANDIES SCORING 1 Full credit Code 1: B.  20%. No credit Code 0: Other responses. Code 9: Missing. 0246 8Red Orange Yellow Green Blue Pink Purple Brown ReleasedPISAItems_Maths.doc  Page 63 M468: Science Tests\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SPRING FAIR M471Q01"}, {"from": "gpt", "value": "In Mei Lin\u2019s school, her science teacher gives tests that are marked out of 100.  Mei Lin has an average of 60 marks on her first four Science tests. On the fifth test she got 80 marks. What is the average of Mei Lin\u2019s marks in Science after all five tests? Average: ................................................. SCIENCE TESTS SCORING 1 Full credit Code 1: 64. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 64 M471: Spring Fair\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SWING M472Q01"}, {"from": "gpt", "value": "A game in a booth at a spring fair involves using a spinner first.  Then, if the spinner stops on an even number, the player is allowed to pick a marble from a bag.  The spinner and the marbles in the bag are represented in the diagram below. Prizes are given when a black marble is picked.  Sue plays the game once. How likely is it that Sue will win a prize? A Impossible. B Not very likely. C About 50% likely. D Very likely. E Certain. SPRING FAIR SCORING 1 Full credit Code 1: B.  Not very likely. No credit Code 0: Other responses. Code 9: Missing. 1 4 10 8 6 2 ReleasedPISAItems_Maths.doc  Page 65 D Height of feet Time C Height of feet Time BTime Height of feet Height of feet ATime M472: Swing\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STUDENT HEIGHTS M479Q01"}, {"from": "gpt", "value": "Mohammed is sitting on a swing.  He starts to swing.  He is trying to go as high as possible. Which diagram best represents the height of his feet above the ground as he swings? ReleasedPISAItems_Maths.doc  Page 66 SWING SCORING 1 Full credit Code 1: A. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 67 M479: Student Heights\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PAYMENTS BY AREA M480Q01"}, {"from": "gpt", "value": "In a mathematics class one day, the heights of all students were measured.  The average height of boys was 160 cm, and the average height of girls was 150 cm. Alena was the tallest \u2013 her height was 180 cm.  Zdenek was the shortest \u2013 his height was 130 cm. Two students were absent from class that day , but they were in class the next day. Their heights were measured, and the averages were recalculated.  Amazingly, the average height of the girls and the average height of the boys did not change. Which of the following conclusions can be drawn from this information? Circle \u2018Yes\u2019 or \u2018No\u2019 for each conclusion. Conclusion Can this conclusion be drawn? Both students are girls. Yes / No One of the students is a boy and the other is a girl. Yes / No Both students have the same height. Yes / No The average height of all students did not change. Yes / No Zdenek is still the shortest. Yes / No  STUDENT HEIGHTS SCORING 1 Full credit Code 1: \u2018No\u2019 for all conclusions. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 68 M480: Payments by Area People living in an apartment building decide to buy the building. They will put their money together in such a way that each will pay an amount that is proportional to the size of their apartment. For example, a man living in an apartment that occupies one fifth of the floor area of all apartments will pay one fifth of the total price of the building.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BOOKSHELVES M484Q01"}, {"from": "gpt", "value": "Circle Correct or Incorrect for each of the following statements. Statement Correct / Incorrect A person living in the largest apartment will pay more money for each square metre of his apartment than the person living in the smallest apartment. Correct / Incorrect If we know the areas of two apartments and the price of one of them we can calculate the price of the second. Correct / Incorrect If we know the price of the building and how much each owner will pay, then the total area of all apartments can be calculated.  Correct / Incorrect If the total price of the building were reduced by 10%, each of the owners would pay 10% less. Correct / Incorrect  PAYMENTS BY AREA SCORING 1 Full credit Code 1: Incorrect, Correct, Incorrect, Correct, in that order. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 69 Question 2: PAYMENTS BY AREA M480Q02 - 0 1 2 9 There are three apartments in the building.  The largest, apartment 1, has a total area of 95m2.  Apartments 2 and 3 have areas of 85m2 and 70m2 respectively.  The selling price for the building is 300 000 zeds. How much should the owner of apartment 2 pay?  Show your work. PAYMENTS BY AREA SCORING 2 Full credit Code 2: 102,000 zeds, with or without the calculation shown, and unit not required. \u2022 Apartment 2: 102 000 zeds \u2022 zeds Apt 102000 30000025085:2 = \u00d7 \u2212 \u2022 1200250300000=zeds for each square metre, so Apartment 2 is 102 000. Partial credit Code 1: Correct method, but minor computational error/s. \u2022 zeds Apt 10200 30000025085:2 = \u00d7 \u2212 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 70 M484: Bookshelves\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LITTER M505Q01 - 0 1 9"}, {"from": "gpt", "value": "To complete one set of bookshelves a carpenter needs the following components: 4 long wooden panels, 6 short wooden panels, 12 small clips, 2 large clips and 14 screws. The carpenter has in stock 26 long wooden panels, 33 short wooden panels, 200 small clips, 20 large clips and 510 screws. How many sets of bookshelves can the carpenter make? Answer: .................................................. BOOKSHELVES SCORING 1 Full credit Code 1: 5. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 71 M505: Litter\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about EARTHQUAKE M509Q01"}, {"from": "gpt", "value": "For a homework assignment on the envir onment, students collected information on the decomposition time of several types of litter that people throw away: Type of Litter Decomposition time Banana peel 1\u20133 years Orange peel 1\u20133 years Cardboard boxes 0.5 year Chewing gum 20\u201325 years Newspapers A few days Polystyrene cups Over 100 years A student thinks of displaying the results in a bar graph. Give one reason why a bar graph is unsuitable for displaying these data. LITTER SCORING 1 Full credit Code 1: Reason focuses on big variance in data. \u2022 T h e  d i f f e r e n c e  i n  t h e  l e n g t h s  o f  t h e  b a rs of the bar graph would be too big. \u2022 I f  y o u  m a k e  a  b a r  w i t h  l e n g t h  1 0  c e n t i m e t r e s  f o r  p o l y s t y r e n e ,  t h e  o n e  f o r cardboard boxes would be 0.05 centimetres. O R Reason focuses on the variability of the data for some categories. \u2022 The length of the bar for \u201cpol ystyrene cups\u201d is undetermined. \u2022 Y o u  c a n n o t  m a k e  o n e  b a r  f o r  1 \u2013 3  y e a r s  o r  o n e  b a r  f o r  2 0 \u2013 2 5  y e a r s . No credit Code 0: Other responses. \u2022 B e c a u s e  i t  w i l l  n o t  w o r k . \u2022 A  p i c t o g r a m  i s  b e t t e r . \u2022 Y o u  c a n n o t  v e r i f y  t h e  i n f o . \u2022 B e c a u s e  t h e  n u m b e r s  i n  t h e  t a b l e  a r e  o n l y  a p p r o x i m a t i o n s . Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 72 M509: Earthquake\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about CHOICES M510Q01"}, {"from": "gpt", "value": "A documentary was broadcast about earthquakes and how often earthquakes occur. It included a discussion about the predictability of earthquakes. A geologist stated: \u201cIn the next twenty years, the chance that an earthquake will occur in Zed City is two out of three\u201d. Which of the following best reflects the meaning of the geologist\u2019s statement ? A 13.3 2032=\u00d7 , so between 13 and 14 years from now there will be an earthquake in Zed City. B 32 is more than 21, so you can be sure there will be an earthquake in Zed City at some time during the next 20 years. C The likelihood that there will be an earthquake in Zed City at some time during the next 20 years is higher than the likelihood of no earthquake. D You cannot tell what will happen, because nobody can be sure when an earthquake will occur. EARTHQUAKE SCORING 1 Full credit Code 1: C.  The likelihood that there will be an earthquake in Zed City at some time during the next 20 years is higher than the likelihood of no earthquake. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 73 M510: Choices\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TEST SCORES M513Q01 - 0 1 9"}, {"from": "gpt", "value": "In a pizza restaurant, you can get a basic pizza with two toppings: cheese and tomato. You can also make up your own pizza with extra  toppings. You can choose from four different extra toppings: olives, ham, mushrooms and salami. Ross wants to order a pizza with two different extra  toppings. How many different combinations can Ross choose from? Answer: ..................................................combinations. CHOICES SCORING 1 Full credit Code 1: 6. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 74 M513: Test Scores\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHOES FOR KIDS M515Q01"}, {"from": "gpt", "value": "The diagram below shows the results on a Science test for two groups, labelled as Group A and Group B. The mean score for Group A is 62.0 and the mean for Group B is 64.5.  Students pass this test when their score is 50 or above. Looking at the diagram, the teacher claims that Group B did better than Group A in this test. The students in Group A don\u2019t agree with their teacher. They try to convince the teacher that Group B may not necessarily have done better. Give one mathematical argument, using the graph, that the students in Group A could use. TEST SCORES SCORING 1 Full credit Code 1: One valid argument is given. Valid  arguments could relate to the number of students passing, the disproportionate influence of the outlier, or the number of students with scores in the highest level. \u2022 M o r e  s t u d e n t s  i n  G r o u p  A  t h a n  i n  G r o u p  B  p a s s e d  t h e  t e s t . \u2022 I f  y o u  i g n o r e  t h e  w e a k e s t  G r o u p  A  s t u d e n t ,  t h e  s t u d e n t s  i n  G r o u p  A  d o  b e t t e r than those in Group B. \u2022 M o r e  G r o u p  A  s t u d e n t s  t h a n  G r o u p  B  s t u d e n t s  s c o r e d  8 0  o r  o v e r .  Scores on a Science test 0 1 2 3 4 5 6 0 - 9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100 Score Number of students Group A Group B ReleasedPISAItems_Maths.doc  Page 75 No credit Code 0: Other responses, including responses with no mathematical reasons, or wrong mathematical reasons, or responses that simply describe differences but are not valid arguments that Group B may not have done better. \u2022 G r o u p  A  s t u d e n t s  a r e  n o r m a l l y  b e t t e r  than Group B students in science. This test result is just a coincidence. \u2022 B e c a u s e  t h e  d i f f e r e n c e  b e t w e e n  t h e  h i g h e s t  a n d  l o w e s t  s c o r e s  i s  s m a l l e r  f o r Group B than for Group A. \u2022 G r o u p  A  h a s  b e t t e r  s c o r e  r e s u l t s  i n  t h e  8 0 - 8 9  r a n g e  a n d  t h e  5 0 - 5 9  r a n g e . \u2022 G r o u p  A  h a s  a  l a r g e r  i n t e r - q u a r t i l e  r a n g e  t h a n  G r o u p  B . Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 76 M515: Shoes for Kids The following table shows the recommended Zedland shoe sizes corresponding to various foot lengths.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SKATEBOARD M520Q02"}, {"from": "gpt", "value": "Marina\u2019s feet are 163 mm long.  Use the table to determine which Zedland shoe size Marina should try on . Answer: .................................................. SHOES FOR KIDS SCORING 1 Full credit Code 1: 26. No credit Code 0: Other responses. Code 9: Missing. Conversion table for kids shoe sizes in Zedland From (in mm) To (in mm) Shoe size 107 115 18 116 122 19 123 128 20 129 134 21 135 139 22 140 146 23 147 152 24 153 159 25 160 166 26 167 172 27 173 179 28 180 186 29 187 192 30 193 199 31 200 206 32 207 212 33 213 219 34 220 226 35 ReleasedPISAItems_Maths.doc  Page 77 M520: Skateboard Eric is a great skateboard fan. He visits a shop named SKATERS to check some prices. At this shop you can buy a complete board. Or you can buy a deck, a set of 4 wheels, a set of 2 trucks and a set of hardware, and assemble your own board. The prices for the shop\u2019s products are: Product Price in zeds Complete skateboard 82 or 84  Deck 40, 60 or 65  One set of 4 Wheels  14 or 36  One set of 2 Trucks 16  One set of hardware (bearings, rubber pads, bolts and nuts) 10 or 20  ReleasedPISAItems_Maths.doc  Page 78 Question 1: SKATEBOARD M520Q01a M520Q01b Eric wants to assemble his own skateboard. What is the minimum price and the maximum price in this shop for self-assembled skateboards? (a) Minimum price: .................................zeds. (b) Maximum price: ................................zeds. SKATEBOARD SCORING 1 Full credit Code 21: Both the minimum (80) and the maximum (137) correct. Partial credit Code 11: Only the minimum (80) correct. Code 12: Only the maximum (137) correct. No credit Code 00: Other responses. Code 99: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SKATEBOARD M520Q03"}, {"from": "gpt", "value": "The shop offers three different decks, two different sets of wheels and two different sets of hardware. There is only one choice for a set of trucks. How many different skateboards can Eric construct? A 6 B 8 C 10 D 12 SKATEBOARD SCORING 2 Full credit Code 1: D.  12. ReleasedPISAItems_Maths.doc  Page 79 No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TABLE TENNIS TOURNAMENT M521Q01 - 0 1 9"}, {"from": "gpt", "value": "Eric has 120 zeds to spend and wants to buy the most expensive skateboard he can afford. How much money can Eric afford to spend on each of the 4 parts?  Put your answer in the table below. Part Amount (zeds) Deck Wheels Trucks Hardware  SKATEBOARD SCORING 3 Full credit Code 1: 65 zeds on a deck, 14 on wheels, 16 on trucks and 20 on hardware. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 80 M521: Table Tennis Tournament\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LIGHTHOUSE M523Q01"}, {"from": "gpt", "value": "Teun, Riek, Bep and Dirk have formed a practice group in a table tennis club.  Each player wishes to play against each other  player once.  They have reserved two practice tables for these matches. Complete the following match schedule; by writing the names of the players playing in each match. P r a c t i c e  T a b l e  1  P r a c t i c e  T a b l e  2 Round 1  Teun - Riek Bep - Dirk Round 2 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 Round 3 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026   ReleasedPISAItems_Maths.doc  Page 81 TABLE TENNIS TOURNAMENT SCORING 1 Full credit Code 1:  Four remaining matches correctly described and distributed over rounds 2 and 3. \u2022  E . g . Practice Table 1 Practice Table 2 Round 1 Teun - Riek Bep - Dirk Round 2 Teun - Bep Riek \u2013 Dirk Round 3 Teun - Dirk Riek - Bep No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 82 M523: Lighthouse Lighthouses are towers with a light beacon on top.  Lighthouses assist sea ships in finding their way at night when they are sailing close to the shore. A lighthouse beacon sends out light flashes with a regular fixed pattern.  Every lighthouse has its own pattern. In the diagram below you see the pattern of a certain lighthouse. The light flashes alternate with dark periods. It is a regular pattern.  After some time the pattern repeats itself.  The time taken by one complete cycle of a pattern, before it starts to repeat, is called the period.  When you find the period of a pattern, it is easy to extend the diagram for the next seconds or minutes or even hours.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LIGHTHOUSE M523Q03 - 0 1 2 9"}, {"from": "gpt", "value": "Which of the following could be the period of the pattern of this lighthouse? A 2 seconds. B 3 seconds. C 5 seconds. D 12 seconds. LIGHTHOUSE SCORING 1 Full credit Code 1: C.  5 seconds. No credit Code 0: Other responses. Code 9: Missing. light dark 0 1 2 3 4 5 6 7 8 9 10 11 12 time (sec) 13 ReleasedPISAItems_Maths.doc  Page 83 Question 2: LIGHTHOUSE M523Q02 For how many seconds does the lighthouse send out light flashes in 1 minute? A 4 B 12 C 20 D 24 LIGHTHOUSE SCORING 2 Full credit Code 1: D.  24. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about DECREASING CO 2 LEVELS M 5 2 5 Q 0 2  -  0 1 9"}, {"from": "gpt", "value": "In the diagram below, make a graph of a possible pattern of light flashes of a lighthouse that sends out light flashes for 30 seconds per minute.  The period of this pattern must be equal to 6 seconds. LIGHTHOUSE SCORING 3 Full credit Code 2: The graph shows a pattern of light and dark with flashes for 3 seconds in every 6 seconds, and with a period of 6 seconds.  This can be done in the light dark 0 1 2 3 4 5 6 7 8 9 10 11 12 time (sec) ReleasedPISAItems_Maths.doc  Page 84 following ways: - 1  o n e - s e c o n d  f l a s h  a n d  a  t w o - s e c o n d  f l a s h  ( a n d  t h i s  c a n  b e  s h o w n  i n several ways), or - 1  t h r e e - s e c o n d  f l a s h  ( w h i c h  c a n  b e  s h o w n  i n  f o u r  d i f f e r e n t  w a y s ) . If two periods are shown, the pattern must be identical for each period. Partial credit Code 1: The graph shows a pattern of light and dark with flashes for 3 seconds in every 6 seconds, but the period is not 6 seconds.  If two periods are shown, the pattern must be identical for each period. \u2022 Three one-second flashes, alternating with 3 one-second dark periods. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 85 M525: Decreasing CO 2  Levels Many scientists fear that the increasing level of CO 2 gas in our atmosphere is causing climate change. The diagram below shows the CO 2 emission levels in 1990 (the light bars) for several countries (or regions), the emission levels in 1998 (the dark bars), and the percentage change in emission levels between 1990 and 1998 (the arrows with percentages). Percentage change in emission levels from 1990 to 1998. +11% -35% +10% +13% +15% -4% -16% +8% 612423218 692485236 1 209 4 208 1 213 3 040 6 0491 020 4 041 1 331 1 962 6 727 Emissions in 1990 (million tons CO 2) Emissions in 1998 (million tons CO 2) USA Russia Japan Canada Australia EU total Germany Netherlands ReleasedPISAItems_Maths.doc  Page 86 Question 1: DECREASING CO 2 LEVELS M 5 2 5 Q 0 1  -  0 1 2 9 In the diagram you can read that in the USA, the increase in CO 2 emission level from 1990 to 1998 was 11%. Show the calculation to demonstrate how the 11% is obtained. DECREASING CO 2 LEVELS SCORING 1 Full credit Code 2: Correct subtraction, and correct calculation of percentage. \u2022 6 7 2 7  \u2013  6 0 4 9  =  6 7 8 ,   11% 100%6049678\u2248\u00d7 . Partial credit Code 1: Subtraction error and percentage calculation correct, or subtraction correct but dividing by 6727. \u2022 89.9% 10067276049=\u00d7 , and 100-89.9=10.1%. No credit Code 0: Other responses, including just \u2018Yes\u2019 or \u2018No\u2019. \u2022 Y e s ,  i t  i s  1 1 % . Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q01 - 0 1 2 9"}, {"from": "gpt", "value": "Mandy analysed the diagram and claimed she discovered a mistake in the percentage change in emission levels: \u201cThe percentage decrease in Germany (16%) is bigger than the percentage decrease in the whole European Union (EU total, 4%). This is not possible, since Germany is part of the EU.\u201d Do you agree with Mandy when she says this is not possible? Give an explanation to support your answer. DECREASING CO 2 LEVELS SCORING 2 Full credit Code 1: No, with correct argumentation. \u2022 N o ,  o t h e r  c o u n t r i e s  f r o m  t h e  E U  c a n  h a ve increases e.g. the Netherlands so the total decrease in the EU can be smaller than the decrease in Germany. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 87 Question 3: DECREASING CO 2 LEVELS M 5 2 5 Q 0 3  -  0 1 2 9 Mandy and Niels discussed which country (or region) had the largest increase  of CO 2 emissions. Each came up with a different conclusion based on the diagram. Give two possible \u2018correct\u2019 answers to this question, and explain how you can obtain each of these answers. DECREASING CO 2 LEVELS SCORING 3 Full credit Code 2: Response identifies both mathematical approaches (the largest absolute increase and the largest relative increase), and names the USA and Australia. \u2022 U S A  h a s  t h e  l a r g e s t  i n c r e a s e  i n  m i l l i o n s  o f  t o n s ,  a n d  A u s t r a l i a  h a s  t h e  l a r g e s t increase in percentage. Partial credit Code 1: Response identifies or refers to both the largest absolute increase and the largest relative increase, but the countries are not identified, or the wrong countries are named. \u2022 R u s s i a  h a d  t h e  b i g g e s t  i n c r e a s e  i n  t h e  a m o u n t  o f  C O 2 (1078 tons), but Australia had the biggest pe rcentage increase (15%). No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 88 M535: Twisted Building In modern architecture, buildings often have unusual shapes. The picture below shows a computer model of a \u2018twisted building\u2019 and a plan of the ground floor.  The compass points show the orientation of the building. The ground floor of the building contains the main entrance and has room for shops. Above the ground floor there are 20 storeys containing apartments. The plan of each storey is similar to the plan of the ground floor, but each has a slightly different orientation from the stor ey below.  The cylinder contains the elevator shaft and a landing on each floor.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q02"}, {"from": "gpt", "value": "Estimate the total height of the building, in metres.  Explain how you found your answer. TWISTED BUILDING SCORING 1 Full credit Code 2:  Accept answers from 50 to 90 me tres if a correct explanation is given. \u2022 O n e  f l o o r  o f  t h e  b u i l d i n g  h a s  a  h e i g h t  o f  a b o u t  2 . 5  m e t e r s .   T h e r e  i s  s o m e extra room between floors.  Therefor e an estimate is 21 x 3 = 63 metres. \u2022 A l l o w  4  m  f o r  e a c h  s t o r y ,  s o  2 0  o f  t h e s e  g i v e s  8 0  m ,  p l u s  1 0  m  f o r  t h e  g r o u n d floor, so a total of 90 m. N S E W N S E W ReleasedPISAItems_Maths.doc  Page 89 Partial credit Code 1: Correct calculation method and explanation, but using 20 stories instead of 21. \u2022 E a c h  a p a r t m e n t  c o u l d  b e  3 . 5  m e t r e s  h i g h ,  2 0  s t o r i e s  o f  3 . 5  m e t r e s  g i v e s  a total height of 70 m. No credit Code 0: Other responses, including answer without any explanation, answers with other incorrect number of floors, and answers with unreasonable estimates of the height of each floor (4 m would be the upper limit). \u2022 Each floor is around 5 m high, so 5 \u00d7 21 equals 105 metres. \u2022 6 0  m . Code 9: Missing.  The following pictures are sideviews of the twisted building.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q03"}, {"from": "gpt", "value": "From which direction has Sideview 1 been drawn? A From the North. B From the West. C From the East. D From the South. TWISTED BUILDING SCORING 2 Full credit Code 1: C.  From the East. Sideview 1 S i d e v i e w  2 ReleasedPISAItems_Maths.doc  Page 90 No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about HEARTBEAT M537Q01 - 0 1 9"}, {"from": "gpt", "value": "From which direction has Sideview 2 been drawn? A From the North West. B From the North East. C From the South West. D From the South East. TWISTED BUILDING SCORING 3 Full credit Code 1: D.  From the South East. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 91 Question 4: TWISTED BUILDING M535Q04 - 0 1 2 9 Each storey containing apartments has a certain \u2018twist\u2019 compared to the ground floor. The top floor (the 20th floor above the ground floor) is at right angles to the ground floor. The drawing below represents the ground floor.  Draw in this diagram the plan of the 10th floor above the ground floor, showing how this floor is situated compared to the ground floor. TWISTED BUILDING SCORING 4 Full credit Code 2: A correct drawing, meaning correct rotation point and anti-clockwise rotation.  Accept angles from 40\u00b0 to 50\u00b0.  Partial credit Code 1: One of the rotation angle, the rotation point, or the rotation direction incorrect. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 92 M537: Heartbeat For health reasons people should limit their efforts, for instance during sports, in order not to exceed a certain heartbeat frequency. For years the relationship between a person\u2019s recommended maximum heart rate and the person\u2019s age was described by the following formula: Recommended maximum heart rate =  220 - age Recent research showed that this formula should be modified slightly.  The new formula is as follows: Recommended maximum heart rate =  208 \u2013 (0.7 \u00d7 age)\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SPACE FLIGHT M 5 4 3 Q 0 1"}, {"from": "gpt", "value": "A newspaper article stated: \u201cA result of using the new formula instead of the old one is that the recommended maximum number of heartbeats per minute for young people decreases slightly and for old people it increases slightly.\u201d From which age onwards does the recommended maximum heart rate increase as a result of the introduction of the new formula?  Show your work. HEARTBEAT SCORING 1 Full credit Code 1: Accept 41, or 40. \u2022 2 2 0  \u2013  age = 208 \u2013 0.7 \u00d7 age results in age = 40, so people above 40 will have a higher recommended maximum heart rate under the new formula. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 93 Question 2: HEARTBEAT M537Q02 - 0 1 9 The formula recommended maximum heart rate =  208 \u2013 (0.7 \u00d7 age) is also used to determine when physical training is most effective. Research has shown that physical training is most effective when the heartbeat is at 80% of the recommended maximum heart rate. Write down a formula for calculating the heart rate for most effective physical training, expressed in terms of age. HEARTBEAT SCORING 2 Full credit Code 1: Any formula that is the equivalent of multiplying the formula for recommended maximum heart rate by 80%. \u2022 h e a r t  r a t e  =  1 6 6  \u2013  0 . 5 6  \u00d7 age. \u2022 h e a r t  r a t e  =  1 6 6  \u2013  0 . 6  \u00d7 age. \u2022 h  =  1 6 6  \u2013  0 . 5 6  \u00d7 a. \u2022 h  =  1 6 6  \u2013  0 . 6  \u00d7 a. \u2022 h e a r t  r a t e  =  ( 2 0 8  \u2013  0 . 7 a g e )  \u00d7 0.8. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 94 M543: Space Flight Space station Mir remained in orbit for 15 years and circled Earth some 86 500 times during its time in space. The longest stay of one cosmonaut in the Mir was around 680 days.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STAIRCASE M547Q01"}, {"from": "gpt", "value": "Approximately how many times did this cosmonaut fly around Earth? A 110 B 1 100 C 11 000 D 110 000 SPACE FLIGHT SCORING 1 Full credit Code 1: C.  11 000. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 95 M547: Staircase\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about ROCK CONCERT M552Q01"}, {"from": "gpt", "value": "The diagram below illustrates a staircase with 14 steps and a total height of 252 cm: What is the height of each of the 14 steps? Height: ....................................................cm. STAIRCASE SCORING 1 Full credit Code 1:  18. No credit Code 0:  Other responses. Code 9:  Missing. Total height 252 cm Total depth 400 cm ReleasedPISAItems_Maths.doc  Page 96 M552: Rock Concert\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about NUMBER CUBES M555Q02"}, {"from": "gpt", "value": "For a rock concert a rectangular field of size 100 m by 50 m was reserved for the audience.  The concert was completely sold out and the field was full with all the fans standing. Which one of the following is likely to be the best estimate of the total number of people attending the concert? A 2 000 B 5 000 C 20 000 D 50 000 E 100 000 ROCK CONCERT SCORING 1 Full credit Code 1: C.  20 000. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 97 M555: Number Cubes\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SUPPORT FOR THE PRESIDENT M702Q01 - 0 1 2 9"}, {"from": "gpt", "value": "On the right, there is a picture of two dice. Dice are special number cubes for which the following rule applies: The total number of dots on two opposite faces is always seven. You can make a simple number cube by cutting, folding and gluing cardboard.  This can be done in many ways.  In the figure below you can see four cuttings that can be used to make cubes, with dots on the sides. Which of the following shapes can be folded together to form a cube that obeys the rule that the sum of opposite faces is 7? For each shape, circle either \u201cYes\u201d or \u201cNo\u201d in the table below. Shape Obeys the rule that the sum of opposite faces is 7? I Yes / No II Yes / No III Yes / No IV Yes / No  NUMBER CUBES SCORING 2 Full credit Code 1: No, Yes, Yes, No, in that order. No credit Code 0: Other responses. Code 9: Missing. I II IIIIV ReleasedPISAItems_Maths.doc  Page 98 M702: Support for the President\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about MOVING WALKWAYS M703Q01 - 0 1 9"}, {"from": "gpt", "value": "In Zedland, opinion polls were conducted to find out the level of support for the President in the forthcoming election.  Four newspaper publishers did separate nationwide polls.  The results for the four newspaper polls are shown below: Newspaper 1: 36.5% (poll conducted on January 6, with a sample of 500 randomly selected citizens with voting rights) Newspaper 2: 41.0% (poll conducted on January 20, with a sample of 500 randomly selected citizens with voting rights) Newspaper 3: 39.0% (poll conducted on January 20, with a sample of 1000 randomly selected citizens with voting rights) Newspaper 4: 44.5% (poll conducted on January 20, with 1000 readers phoning in to vote). Which newspaper\u2019s result is likely to be the best for predicting the level of support for the President if the election is held on January 25?  Give two reasons to support your answer. SUPPORT FOR THE PRESIDENT SCORING 1 Full credit Code 2: Newspaper 3.  The poll is more recent, with larger sample size, a random selection of the sample, and only voters were asked.  (Give at least two reasons).  Additional information (including irrelevant or incorrect information) should be ignored. \u2022 N e w s p a p e r  3 ,  b e c a u s e  t h e y  h a v e  s e l e c t e d  m o r e  c i t i z e n s  r a n d o m l y  w i t h  v o t i n g rights. \u2022 N e w s p a p e r  3  b e c a u s e  i t  h a s  a s k e d  1 0 0 0  p e o p l e ,  r a n d o m l y  s e l e c t e d ,  a n d  t h e date is closer to the election date so t he voters have less time to change their mind. \u2022 N e w s p a p e r  3  b e c a u s e  t h e y  w e r e  r a n d o m l y  s e l e c t e d  a n d  t h e y  h a d  v o t i n g rights. \u2022 N e w s p a p e r  3  b e c a u s e  i t  s u r v e y e d  m o r e  p e o p l e  c l o s e r  t o  t h e  d a t e . \u2022 N e w s p a p e r  3  b e c a u s e  t h e  1 0 0 0  p e o p l e  w e r e  r a n d o m l y  s e l e c t e d . Partial credit Code 1: Newspaper 3, with only one reason, or without explanation. \u2022 N e w s p a p e r  3 ,  b e c a u s e  t h e  p o l l  i s  c l o s e r  t o  e l e c t i o n  d a t e . \u2022 N e w s p a p e r  3 ,  b e c a u s e  m o r e  p e o p l e  w e r e  s u r v e y e d  t h a n  n e w s p a p e r s  1  a n d  2 . \u2022 N e w s p a p e r  3 . ReleasedPISAItems_Maths.doc  Page 99 No credit Code 0: Other responses. \u2022 N e w s p a p e r  4 .   M o r e  p e o p l e  m e a n s  m o r e  a c c u r a t e  r e s u l t s ,  a n d  p e o p l e  p h o n i n g in will have considered their vote better. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 100 time Distance from the start of the moving walkway A person walking on the ground A person walking on the moving walkway time Distance from the start of the moving walkway A person walking on the ground A person walking on the moving walkway A person standing still on the moving walkway M703: Moving Walkways\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about THE BEST CAR M704Q01"}, {"from": "gpt", "value": "On the right is a photograph of moving walkways. The following Distance-Time graph shows a comparison between \u201cwalking on the moving walkway\u201d and \u201cwalking on the ground next to the moving walkway.\u201d Assuming that, in the above graph, the walking pace is about the same for both persons, add a line to the graph that would represent the distance versus time for a person who is standing still on the moving walkway. MOVING WALKWAYS SCORING 1 Full credit Code 1: Accept a line below the two lines, but it must be closer to the line of \u201cA person walking on the ground\u201d than to the baseline.  ReleasedPISAItems_Maths.doc  Page 101 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 102 M704: The Best Car A car magazine uses a rating system to evaluate new cars, and gives the award of \u201cThe Car of the Year\u201d to the car with the highest total score.  Five new cars are being evaluated, and their ratings are shown in the table. Car Safety Features (S) Fuel Efficiency (F)External Appearance(E)Internal Fittings (T) Ca 3 1 2 3 M2 2 2 2 2 Sp 3 1 3 2 N1 1 3 3 3 KK 3 2 3 2 The ratings are interpreted as follows: 3  p o i n t s  =  E x c e l l e n t 2  p o i n t s  =  G o o d 1  p o i n t  =  F a i r\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STEP PATTERN M806Q01"}, {"from": "gpt", "value": "To calculate the total score for a car, the car magazine uses the following rule, which is a weighted sum of the individual score points: T o t a l  S c o r e  =  ( 3  x  S )  +  F  +  E  +  T Calculate the total score for Car \u201cCa\u201d.  Write your answer in the space below. Total score for \u201cCa\u201d: ............................... THE BEST CAR SCORING 1 Full credit Code 1: 15 points. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 103 Question 2: THE BEST CAR M704Q02 The manufacturer of car \u201cCa\u201d thought the rule for the total score was unfair. Write down a rule for calculating the total score so that Car \u201cCa\u201d will be the winner. Your rule should include all four of the variables, and you should write down your rule by filling in positive numbers in the four spaces in the equation below. Total score = \u2026\u2026\u2026 \u00d7 S + \u2026\u2026\u2026\u00d7 F + \u2026\u2026\u2026\u00d7 E + \u2026\u2026\u2026\u00d7 T. THE BEST CAR SCORING 2 Full credit Code 1: Correct rule that will make \u201cCa\u201d the winner. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 104 M806: Step Pattern\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q01"}, {"from": "gpt", "value": "Robert builds a step pattern using squares. Here are the stages he follows. As you can see, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3. How many squares should he use for the fourth stage? Answer: ..................................................squares. STEP PATTERN SCORING 1 Full credit Code 1: 10. No credit Code 0: Other responses. Code 9: Missing. Stage 1 Stage 2 Stage 3 ReleasedPISAItems_Maths.doc  Page 105 M836: Postal Charges The postal charges in Zedland are based on the weight of the items (to the nearest gram), as shown in the table below: Weight (to nearest gram) Charge Up to 20 g 0.46 zeds 21 g \u2013 50 g 0.69 zeds 51 g \u2013 100 g 1.02 zeds 101 g \u2013 200 g 1.75 zeds 201 g \u2013 350 g 2.13 zeds 351 g \u2013 500 g 2.44 zeds 501 g \u2013 1000 g 3.20 zeds 1001 g \u2013 2000 g 4.27 zeds 2001 g \u2013 3000 g 5.03 zeds\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q02 - 0 1 9"}, {"from": "gpt", "value": "Which one of the following graphs is the best representation of the postal charges in Zedland?  (The horizontal axis shows the weight in grams, and the vertical axis shows the charge in zeds.) 0123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 00123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 0123456 20 50 100 200 350 500 1000 2000 30000123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0A C D B ReleasedPISAItems_Maths.doc  Page 106 POSTAL CHARGES SCORING 1 Full credit Code 1: C. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q02 - 0 1 9"}, {"from": "gpt", "value": "Jan wants to send two items, weighing 40 grams and 80 grams respectively, to a friend. According to the postal charges in Zedland, decide whether it is cheaper to send the two items as one parcel, or send the items as two separate parcels.  Show your calculations of the cost in each case. POSTAL CHARGES SCORING 2 Full credit Code 1: It will be cheaper to send the items as two separate parcels.  The cost will be 1.71 zeds for two separate parcels, and 1.75 zeds for one single parcel containing both items. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 107 Source Publications for Released Items  OECD Sources  (available www.pisa.oecd.org) Test Questions (1) Interactive Web examples: http://pisa-sq.acer.edu.au (2) PISA 2003 sample question files: http://www.pisa.oecd.org Follow the links: What PISA Produces > PISA 2003 > Test questions Publications (3) OECD (Organisation for Economic Co-operation and Development ) (2002), Sample Tasks from the PISA 2000 Assessment: Reading,  Mathematical and Scientific Literacy , OECD, Paris. (4) OECD  (2000), Measuring Student Knowledge and Skills - The PISA 2000 Assessment of Reading, Mathematical and Scientific Literacy , OECD, Paris. (5) OECD  (2003), The PISA 2003 Assessment Framework - Mathematics, Reading, Science and Problem Solving Knowledge and Skills, OECD, Paris.  Unit S o u r c e Code Title (1) Interactive Web Examples (2) PISA 2003 Web Samples (3) PISA 2000 Sample Tasks (4) PISA 2000 Measuring Student K&S (5) PISA 2003 Assessment Framework M037 Farms \u0085 \u0085 ; M047 Lichen ; \u0085 \u0085 ; M124 Walking \u0085 ; M136 Apples \u0085 \u0085 ; M143 Coins ; \u0085 \u0085 ; M143 Cubes \u0085 ; M148 Continent Area \u0085 \u0085 ; M150 Growing Up \u0085 ; M154 Pizzas ; \u0085 \u0085 ; M158 Shapes ; \u0085 \u0085 ; M159 Speed of Racing Car \u0085 \u0085 ; M161 Triangles \u0085 \u0085 ; M179 Robberies \u0085 ; M215 Braking ; \u0085 \u0085 ; M266 Carpenter \u0085 ; M267 Patio ; \u0085 \u0085 ; M307 Drug Concentrations \u0085 \u0085 \u0085 \u0085 ; M309 Building Blocks \u0085 \u0085 \u0085 \u0085 ; M402 Internet Relay Chat \u0085 ; M413 Exchange Rate \u0085 ; ReleasedPISAItems_Maths.doc  Page 108 Unit S o u r c e Code Title (1) Interactive Web Examples (2) PISA 2003 Web Samples (3) PISA 2000 Sample Tasks (4) PISA 2000 Measuring Student K&S (5) PISA 2003 Assessment Framework M432 Reaction Time \u0085 \u0085 \u0085 \u0085 ; M438 Exports \u0085 ; M465 Water Tank \u0085 \u0085 \u0085 \u0085 ; M467 Coloured Candies \u0085 ; M468 Science Tests \u0085 ; M471 Spring Fair \u0085 ; M472 Swing \u0085 \u0085 \u0085 \u0085 ; M479 Student Heights \u0085 \u0085 \u0085 \u0085 ; M480 Payments by Area \u0085 \u0085 \u0085 \u0085 ; M484 Bookshelves \u0085 ; M505 Litter \u0085 ; M509 Earthquake \u0085 ; M510 Choices \u0085 ; M513 Test Scores \u0085 ; M515 Shoes for Kids \u0085 ; M520 Skateboard \u0085 ; M521 Table Tennis Tournament \u0085 ; M523 Lighthouse \u0085 \u0085 \u0085 \u0085 ; M525 Decreasing CO 2 Levels \u0085 ; M535 Twisted Building \u0085 \u0085 \u0085 \u0085 ; M537 Heartbeat \u0085 \u0085 \u0085 \u0085 ; M543 Space Flight \u0085 ; M547 Staircase \u0085 ; M552 Rock Concert \u0085 \u0085 \u0085 \u0085 ; M555 Number Cubes \u0085 ; M702 Support for the President \u0085 ; M703 Moving Walkways \u0085 \u0085 \u0085 \u0085 ; M704 The Best Car \u0085 ; M806 Step Pattern \u0085 ; M836 Postal Charges \u0085 \u0085 \u0085 \u0085 ;\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LICHEN M047Q02- 0 1 2 8 9"}, {"from": "gpt", "value": "Using the formula, calculate the diameter of the lichen, 16 years after the ice disappeared. Show your calculation. LICHEN SCORING 1 Full credit Code 2: 14mm (units not required).  Code 2 should be given as long as the correct answer is 14 whether working out is shown or not. Partial credit Code 1: Partial responses including: \u2022 C o r r e c t  s u b s t i t u t i o n  o f  v a l u e  i n  t h e  f o r m u l a  b u t  i n c o r r e c t  a n s w e r  O r  m i s s i n g answer. \u2022 I n c o m p l e t e  a n s w e r s  ( e g ,   7 \u221a4). No credit Code 0: Other responses. Code 9: Missing. Example responses Code 2: 1412160.7 =\u2212\u00d7= dd 14mm 14  ReleasedPISAItems_Maths.doc  Page 8 years ddd 144 0.712 16 0.7 =\u00d7=\u2212\u00d7= (Note that here the calculations are all correct, but the unit is wrong. We will assume for now that it is the slip of the pen) Code 1: 1612160.7 =\u2212\u00d7= dd (wrong answer but correct substitution) 47121607 =\u2212\u00d7= dd . (incomplete answer)  Code 0: 16\n\nThis question is designed to test: To elicit student's  ability to apply a given formula."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about COINS M143Q01-0 1 8 9"}, {"from": "gpt", "value": "Ann measured the diameter of some lichen and found it was 35 millimetres. How many years ago did the ice disappear at this spot? Show your calculation. LICHEN SCORING 2 Full credit Code 2: 37 years (unit not required) whether working out is shown or not. Partial credit Code 1: Correct substitution of values in the formula but incorrect answer or missing answer. OR 36 years or 38 years. (Students may arrive at these answers using the trial and error method) No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 9 Example responses Code 2: 3712 2512 512 7 35 =\u2212=\u2212=\u2212\u00d7= tttt  years373771225 725 7575735\u2234\u00d7=+\u00d7=\u00d7=\u00d7=\u00f7   37 122525 557/35 2 =+== (Strictly incorrect algebraic repres entation, but we know what the student is trying to do)  t = 15  d = 12.1 t = 25  d = 25.2 t = 40  d = 37.0 t = 35  d = 33.6 t = 37  d = 35 So 37 years after the ice disappeared (Note that here the answer 37 is embedded in an equation that is correct)  756 = 35 = 7X \u221a(37-12) = 7X \u221a25 = 7X5 = 35 Code 1: 251237 4912 7 3512 0.7 35 2 2 ==\u2212\u00d7=\u2212\u00d7= tttt  1312 2512 512 0.7 35 2 2 =\u2212=\u2212=\u2212\u00d7= tttt  !12 512 512 0.7 35 hardToottt \u2212=\u2212=\u2212\u00d7=  Code 0: 79612 78412 2812 0.7 35 =\u2212=\u2212=\u2212\u00d7= tttt  40 years   ReleasedPISAItems_Maths.doc  Page 17 M143: Coins You are asked to design a new set of coins. All coins will be circular and coloured silver, but of different diameters.  Researchers have found out that an ideal coin system meets the following requirements: \u2022 d i a m e t e r s  o f  c o i n s  s h o u l d  n o t  b e  s m a l l e r  t h a n  1 5  m m  a n d  n o t  b e  l a r g e r  t h a n  4 5 mm. \u2022 g i v e n  a  c o i n ,  t h e  d i a m e t e r  o f  t h e  n e x t  c o i n  m u s t  b e  a t  l e a s t  3 0 %  l a r g e r . \u2022 t h e  m i n t i n g  m a c h i n e r y  c a n  o n l y  p r o d u c e  c o i n s  w i t h  d i a m e t e r s  o f  a  w h o l e  n u m b e r of millimetres (e.g. 17 mm is allowed, 17.3 mm is not).\n\nThis question is designed to test: To elicit student's  ability to apply a given formula."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PIZZAS M154Q01- 0 1 2 8 9"}, {"from": "gpt", "value": "You are asked to design a set of coins that satisfy the above requirements. You should start with a 15 mm coin and your set should contain as many coins as possible. What would be the diameters of the coins in your set? COINS SCORING 1 calculations. Code 1: 15 \u2013 20 \u2013 26 \u2013 34 \u2013 45. It is possible that the response could  be presented as actual drawings of the coins of the correct diameters.  This should be coded as 1 as well. Code 8: Gives a set of coins that satisfy the three criteria, but not the set that contains as many coins as possible, eg., 15 \u2013 21 \u2013 29 \u2013 39, or 15 \u2013 30 \u2013 45 OR The first three diameters correct, the last two incorrect (15 \u2013 20 \u2013 26 - ) OR The first four diameters correct, the last one incorrect (15 \u2013 20 \u2013 26 \u2013 34 - ) Code 0: Other responses. Code 9 : Missing. ReleasedPISAItems_Maths.doc  Page 27 M154: Pizzas A pizzeria serves two round pizzas of the same thickness in different sizes. The smaller one has a diameter of 30 cm and costs 30 zeds. The larger one has a diameter of 40 cm and costs 40 zeds.\n\nThis question is designed to test: Understanding and use of complicated information to do"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHAPES M158Q01- 0 1 8 9"}, {"from": "gpt", "value": "Which pizza is better value for money? Show your reasoning. PIZZAS SCORING 1 comparison Code 2: Gives general reasoning that the surface area of pizza increases more rapidly than the price of pizza to conclude that the larger pizza is better value. \u2022 The diameter of the pizzas is the same  number as their price, but the amount of pizza you get is found using diameter2 , so you will get more pizza per zeds from the larger one Code 1: Calculates the area and amount per zed for each pizza to conclude that the larger pizza is better value. \u2022 A r e a  o f  s m a l l e r  p i z z a  i s  0 . 2 5  x  \u03c0 x 30 x 30 = 225 \u03c0; amount per zed is 23.6 cm2 area of larger pizza is 0.25 x \u03c0 x 40 x 40 = 400 \u03c0; amount per zed is 31.4 cm2 so larger pizza is better value Code 8: They are the same value for money.  (This incorrect answer is coded separately, because we would like to keep track of how many students have this misconception). Code 0: Other incorrect responses OR a correct answer without correct reasoning. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 28 M158: Shapes   A  B  C\n\nThis question is designed to test: Applies understanding of area to solving a value for money"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHAPES M158Q03- 0 1 8 9"}, {"from": "gpt", "value": "Which of the figures has the largest area? Explain your reasoning. SHAPES SCORING 1 Code 1: Shape B, supported with plausible reasoning. \u2022 I t \u2019 s  t h e  l a r g e s t  a r e a  b e c a u s e  the others will fit inside it. Code 8: Shape B, without plausible support. Code 0: Other responses. Code 9: Missing. Example responses Code 1: \u2022 B .  I t  d o e s n \u2019 t  h a v e  i n d e n t s  i n  i t  w h i c h decreases the area.  A and C have gaps. \u2022 B ,  b e c a u s e  i t \u2019 s  a  f u l l  c i r c l e ,  a n d  t h e  o t h e rs are like circles with bits taken out. \u2022 B, because it has no open areas:  Code 8: \u2022 B. because it has the largest surface area \u2022 T h e  c i r c l e .   I t \u2019 s  p r e t t y  o b v i o u s . \u2022 B ,  b e c a u s e  i t  i s  b i g g e r . Code 0: \u2022 They are all the same. ReleasedPISAItems_Maths.doc  Page 29 Question 2: SHAPES M158Q02- 0 1 8 9 Describe a method for estimating the area of figure C. SHAPES SCORING 2 irregular shapes. Code 1: Reasonable method: \u2022 D r a w  a  g r i d  o f  s q u a r e s  o v e r  t h e  s h ape and count the squares that are more than half filled by the shape. \u2022 C u t  t h e  a r m s  o f f  t h e  s h a p e  a n d  r e a r r a n g e  t he pieces so that they fill a square then measure the side of the square. \u2022 Build a 3D model based on the shape and fill it with water. Measure the amount of water used and the depth of the water in the model.  Derive the area from the information. Code 8: Partial answers: \u2022 The student suggests to find the area of the circle and subtract the area of the cut out pieces.  However, the student does not mention about how to find out the area of the cut out pieces. \u2022 A d d  u p  t h e  a r e a  o f  e a c h  i n dividual arm of the shape Code 0:  Other responses. Code 9: Missing. NOTE: The key point for this question is whether the student offers a METHOD for determining the area.  The coding schemes (1, 8, 0) is a hierarchy of the extent to which the student describes a METHOD. Example responses Code 1: \u2022 You could fill the shape with lots of ci rcles, squares and ot her basic shapes so there is not a gap.  Work out the area of all of the shapes and add together. \u2022 Redraw the shape onto graph paper and count all of the squares it takes up. \u2022 D r a w i n g  a n d  c o u n t i n g  e q u a l  s i z e  b o x e s .   S m a l l e r  b o x e s  =  b e t t e r  a c c u r a c y (Here the student\u2019s description is brief, but we will be lenient about student\u2019s writing skills and regard the method offered by the student as correct) \u2022 M a k e  i t  i n t o  a  3 D  m o d e l  a n d  f i l l i n g  i t  w i t h  e x a c t l y  1 c m  o f  w a t e r  a n d  t h e n measure the volume of water required to fill it up. Code 8: \u2022 F i n d  t h e  a r e a  o f  B  t h e n  f i n d  t h e  a r e a s  o f  the cut out pieces and subtract them from the main area. \u2022 M i n u s  t h e  s h a p e  f r o m  t h e  c i r c l e \u2022 A d d  u p  t h e  a r e a  o f  e a c h  i n d i v i d u a l  p i e c e  e . g . , \u2022 Use a shape like that and pour a liquid into it. \u2022 U s e  g r a p h \u2022 H a l f  o f  t h e  a r e a  o f  s h a p e  B \u2022 F i g u r e  o u t  h o w  m a n y  m m2 are in one little leg things and times it by 8. ReleasedPISAItems_Maths.doc  Page 30 Code 0: \u2022 U s e  a  s t r i n g  a n d  m e a s u r e  t h e  p e r i m e t e r  o f  the shape.  Stretch the string out to a circle and measure the area of the circle using \u03c0 r2. (Here the method described by the student is wrong)\n\nThis question is designed to test: To assess students\u2019 strategies for measuring areas of"}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q01"}, {"from": "gpt", "value": "Describe a method for estimating the perimeter of figure C. SHAPES SCORING 3 irregular shapes Code 1: Reasonable method: \u2022 Lay a piece of string over the outline of the shape then measure the length of string used. \u2022 C u t  t h e  s h a p e  u p  i n t o  s h o r t ,  n e a r l y  s t r a i ght pieces and join them together in a line, then measure the length of the line. \u2022 M e a s u r e  t h e  l e n g t h  o f  s o m e  o f  t h e  arms to find an average arm length then multiply by 8 (number of arms) X 2. Code 0: Other responses. Code 9: Missing. Example responses Code 1: \u2022 W o o l  o r  s t r i n g ! ! ! (Here although the answer is brief, the student did offer a METHOD for measuring the perimeter) \u2022 C u t  t h e  s i d e  o f  t h e  s h a p e  i n t o  s e c t i o n s .   M e a s u r e  e a c h  t h e n  a d d  t h e m together. (Here the student did not explicitly  say that each section needs to be approximately straight, but we will give t he benefit of the doubt,  that is, by offering the METHOD of cutting the shape into pieces, each piece is assumed to be easily measurable) Code 0: \u2022 M e a s u r e  a r o u n d  t h e  o u t s i d e . (Here the student did not suggest any METHOD of measuring. Simply saying \u201cmeasure it\u201d is not offering any method of how to go about measuring it) \u2022 S t r e t c h  o u t  t h e  s h a p e  t o  m a k e  i t  a  c i r c l e . (Here although a method is offered by the student, the method is wrong) ReleasedPISAItems_Maths.doc  Page 38 M215: Braking The approximate distance to stop a moving vehicle is the sum of: \u2022 t h e  d i s t a n c e  c o v e r e d  d u r i n g  t h e  t i m e  t h e  d r i v e r  t a k e s  t o  b e g i n  t o  a p p l y  t h e brakes (reaction-time distance) \u2022 t h e  d i s t a n c e  t r a v e l l e d  w h i l e  t h e  b r a k e s  a r e  a p p l i e d  ( b r a k i n g  d i s t a n c e ) The \u2018snail\u2019 diagram below gives the theoretical stopping distance for a vehicle in good braking conditions (a particularly alert driver, brakes and tyres in perfect condition, a dry road with a good surface) and how much the stopping distance depends on speed. 20.8 m245.5 m Distance to stop a vehicle. Time to stop the vehicle. Distance travelled during the braking time. Distance travelled during the driver\u2019s reaction time. 219 m 197.6 m 175.4 m 152.2 m 135.6 m 118 m 101 m 85.4 m 70.7 m 57.7 m 46 m 35.7 m 26.5 m 18.6 m 37.5 m 35.4 m 33.3 m 31.3 m 29.2 m 27.1 m 25 m 22.9 m 18.7 m 16.7 m 14.6 m 12.5 m 10.3 m 8.3 m 9.08 s 8.62 s 8.15 s 7.69 s 7.23 s 6.76 s 6.30 s 5.84 s 5.38 s 4.92 s 4.46 s 3.99 s 3.53 s 3.06 s 2.60 s 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 KPH ReleasedPISAItems_Maths.doc  Page 39 QUESTION 1: BRAKING M215Q01 If a vehicle is travelling at 110 kph, what distance does the vehicle travel during the driver\u2019s reaction time? BRAKING 1 SCORING GUIDE Code 1: 22.9 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q03"}, {"from": "gpt", "value": "If a vehicle is travelling at 110 kph, what is the total distance travelled before the vehicle stops? BRAKING SCORING 2 Code 1: 101 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BRAKING M215Q05"}, {"from": "gpt", "value": "If a vehicle is travelling at 110 kph, how long does it take to stop the vehicle completely? BRAKING 3 SCORING GUIDE Code 1: 5.84 seconds  (units not required) Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 40 Question 4: BRAKING M215Q04 If a vehicle is travelling at 110 kph, what is the distance travelled while the brakes are being applied? BRAKING 4 SCORING GUIDE Code 1: 78.1 metres (units not required) Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to derive a information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PATIO M267Q01- 0 1 2 8 9"}, {"from": "gpt", "value": "A second driver, travelling in good conditions, stops her vehicle in a total distance of 70.7 metres.  At what speed was the vehicle travelling before the brakes were applied? BRAKING 5 SCORING GUIDE Code 1: 90 kph (units not necessary) Code 0: Other responses. Code 9 : Missing. ReleasedPISAItems_Maths.doc  Page 43 M267: Patio\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about DRUG CONCENTRATIONS M307Q01 - 0 1 2 9"}, {"from": "gpt", "value": "Nick wants to pave the rectangular patio of his new house. The patio has length 5.25 metres and width 3.00 metres. He needs 81 bricks per square metre. Calculate how many bricks Nick needs for the whole patio.  PATIO SCORING 1 Full credit Code 2: 1275, 1276  or 1275.75 (unit not required). Partial credit Code 1: 15.75 (units not required) OR 1215 bricks for 5m X 3m (This score is used for students who are able to calculate the number of bricks for an integer number of square metres, but not for fractions of square metres.  See example response.) OR Error in calculating the area, but multiplied by 81 correctly OR Rounded off the area and then multiplied by 81 correctly No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 44 Example responses Code 2: \u2022 5.25 X 3 = 15.75 X 81 = 1276 Code 1: \u2022 5.25 X 3 = 15.75 \u2022 15.75 X 81 = 9000 \u2022 81 X 15 = 1215; 1215 + 21 = 1236 \u2022 5.25 X 3.0 = 15.75 m2;   so 15.75 X 1275.75 = 1376 bricks. (Here the student got the first part right, but the second part wrong.  Give credit for the first part and ignore the second part.  So score as 1)  8 1  8 1  8 1  8 1  8 1 8 1  8 1  8 1  8 1  8 1 8 1  8 1  8 1  8 1  8 1  5m 3m ReleasedPISAItems_Maths.doc  Page 45 M307: Drug Concentrations\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BUILDING BLOCKS M309Q02"}, {"from": "gpt", "value": "A woman in hospital receives an injection of penicillin.  Her body gradually breaks the penicillin down so that one hour after the injection only 60% of the penicillin will remain active. This pattern continues: at the end of each hour only 60% of the penicillin that was present at the end of the previous hour remains active. Suppose the woman is given a dose of 300 millig rams of penicillin at 8 o\u2019clock in the morning. Complete this table showing the amount of penicillin that will remain active in the woman\u2019s blood at intervals of one hour from 0800 until 1100 hours. Time 0800 0900 1000 1100 Penicillin (mg) 300  DRUG CONCENTRATIONS SCORING 1 Full credit Code 2: All three table entries correct.  Time 0800 0900 1000 1100 Penicillin (mg) 300 180 108 64.8 or 65 Partial credit Code 1: One or two table entries correct. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 46 Amount of active drug (mg) 0 1 2 3 4 5 Time (days) after taking the drug 20 40 60 80 0 Question 2: DRUG CONCENTRATIONS M307Q02 Peter has to take 80 mg of a drug to control his blood pressure. The following graph shows the initial amount of the drug, and the amount that remains active in Peter\u2019s blood after one, two, three and four days. How much of the drug remains active at the end of the first day? A   6 mg. B 12 mg. C 26 mg. D 32 mg. DRUG CONCENTRATIONS SCORING 2 Full credit Code 1: D.  32mg. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 47 Question 3: DRUG CONCENTRATIONS M307Q03 From the graph for the previous question it can be seen that each day, about the same proportion of the previous day\u2019s drug remains active in Peter\u2019s blood. At the end of each day which of the following is the approximate percentage of the previous day\u2019s drug that remains active? A 20%. B 30%. C 40%. D 80%. DRUG CONCENTRATIONS SCORING 3 Full credit Code 1: C.  40%. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 48 M309: Building Blocks  Susan likes to build blocks from small cubes like the one shown in the following diagram: Susan has lots of small cubes like this one.  She uses glue to join cubes together to make other blocks. First, Susan glues eight of the cubes together to make the block shown in Diagram A: Then Susan makes the solid blocks shown in Diagram B and Diagram C below: Diagram B Diagram C Small cube Diagram A ReleasedPISAItems_Maths.doc  Page 49 Question 1: BUILDING BLOCKS M309Q01 How many small cubes will Susan need to make the block shown in Diagram B? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 1 Full credit Code 1: 12 cubes. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BUILDING BLOCKS M309Q04"}, {"from": "gpt", "value": "How many small cubes will Susan need to make the solid block shown in Diagram C? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 2 Full credit Code 1: 27 cubes. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 50 Question 3: BUILDING BLOCKS M309Q03 Susan realises that she used more small cubes than she really needed to make a block like the one shown in Diagram C.  She realises that she could have glued small cubes together to look like Diagram C, but the block could have been hollow on the inside. What is the minimum number of cubes she needs to make a block that looks like the one shown in Diagram C, but is hollow? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 3 Full credit Code 1: 26 cubes. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about EXPORTS M438Q01 - 0 1 9"}, {"from": "gpt", "value": "Now Susan wants to make a block that looks like a solid block that is 6 small cubes long, 5 small cubes wide and 4 small cubes high.  She wants to use the smallest number of cubes possible, by leaving t he largest possible hollow space inside the block. What is the minimum number of cubes Susan will need to make this block? Answer: ..................................................cubes. BUILDING BLOCKS SCORING 4 Full credit Code 1: 96 cubes. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 55 M432: Reaction Time In a Sprinting event, the \u2018reaction time\u2019 is the time interval between the starter\u2019s gun firing and the athlete leaving the starting block.  The \u2018final time\u2019 includes both this reaction time, and the running time. The following table gives the reaction time and the final time of 8 runners in a 100 metre sprint race. Lane Reaction time (sec) Final time (sec) 1 0.147 10.09 2 0.136 9.99 3 0.197 9.87 4 0.180 Did not finish the race 5 0.210 10.17 6 0.216 10.04 7 0.174 10.08 8 0.193 10.13  ReleasedPISAItems_Maths.doc  Page 56 Question 1: REACTION TIME  M432Q01 - 0 1 9 Identify the Gold, Silver and Bronze medallists from this race.  Fill in the table below with the medallists' lane number, reaction time and final time. Medal Lane Reaction time (secs) Final time (secs) GOLD SILVER BRONZE REACTION TIME SCORING 1 Full credit Code 1: Medal Lane Reaction time (secs) Final time (secs) GOLD 3 0.197 9.87 SILVER 2 0.136 9.99 BRONZE 6 0.216 10.04 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 57 Question 2: REACTION TIME  M432Q02 - 0 1 9 To date, no humans have been able to react to a starter\u2019s gun in less than 0.110 second. If the recorded reaction time for a runner is less than 0.110 second, then a false start is considered to have occurred because the runner must have left before hearing the gun. If the Bronze medallist had a faster reaction time, would he have had a chance to win the Silver medal?  Give an explanation to support your answer. REACTION TIME SCORING 2 Full credit Code 1: Yes, with adequate explanation. \u2022 Yes. If he had a reaction time of 0.05 sec faster, he would have equalled second place. \u2022 Y e s ,  h e  w o u l d  h a v e  a  c h a n c e  t o  w i n  t h e  S i l v e r  m e d a l  i f  h i s  r e a c t i o n  t i m e  w a s less than or equal to 0.166 sec. \u2022 Y e s ,  w i t h  t h e  f a s t e s t  p o s s i b l e  r e a c t i o n  t i m e  h e  w o u l d  h a v e  d o n e  a  9 . 9 3  w h i c h is good enough for silver medal. No credit Code 0: Other responses, including yes without adequate explanation. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 58 M438: Exports The graphics below show information about exports from Zedland, a country that uses zeds as its currency.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about WATER TANK M 4 6 5 Q 0 1"}, {"from": "gpt", "value": "What was the total value (in millions of zeds) of exports from Zedland in 1998? Answer: .................................................. EXPORTS SCORING 1 Full credit Code 1:  27.1 million zeds or 27 100 000 zeds or 27.1 (unit not required). No credit Code 0: Other responses. Code 9: Missing. Distribution of exports from Zedland in 2000 Total annual exports from Zedland in millions of zeds, 1996-2000 Year Tobacco 7% Wool 5% Cotton fabric 26% Fruit juice 9% Rice 13% Tea 5% Meat 14% Other 21% 20.4 25.4 27.1 37.9 42.6 051015202530354045 1996 1997 1998 1999 2000 ReleasedPISAItems_Maths.doc  Page 59 Question 2: EXPORTS M438Q02 What was the value of fruit juice exported from Zedland in 2000? A 1.8 million zeds. B 2.3 million zeds. C 2.4 million zeds. D 3.4 million zeds. E 3.8 million zeds. EXPORTS SCORING 2 Full credit Code 1:  E.  3.8 million zeds. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 60 M465: Water Tank\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about COLOURED CANDIES M467Q01"}, {"from": "gpt", "value": "Which of the following graphs shows how the height of the water surface changes over time? 1.5 m 1.0 m 1.5 m Water tank A water tank has shape and dimensions as shown in the diagram. At the beginning the tank is empty.  Then it is filled with water at the rate of one litre per second. Height Time Height Time D Height E Height Time Time Height Time A B C ReleasedPISAItems_Maths.doc  Page 61 WATER TANK SCORING 1 Full credit Code 1: B. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 62 M467: Coloured Candies\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SCIENCE TESTS M468Q01"}, {"from": "gpt", "value": "Robert\u2019s mother lets him pick one candy from a bag.  He can\u2019t see the candies. The number of candies of each colour in the bag is shown in the following graph. What is the probability that Robert will pick a red candy? A 10% B 20% C 25% D 50% COLOURED CANDIES SCORING 1 Full credit Code 1: B.  20%. No credit Code 0: Other responses. Code 9: Missing. 0246 8Red Orange Yellow Green Blue Pink Purple Brown ReleasedPISAItems_Maths.doc  Page 63 M468: Science Tests\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SPRING FAIR M471Q01"}, {"from": "gpt", "value": "In Mei Lin\u2019s school, her science teacher gives tests that are marked out of 100.  Mei Lin has an average of 60 marks on her first four Science tests. On the fifth test she got 80 marks. What is the average of Mei Lin\u2019s marks in Science after all five tests? Average: ................................................. SCIENCE TESTS SCORING 1 Full credit Code 1: 64. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 64 M471: Spring Fair\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SWING M472Q01"}, {"from": "gpt", "value": "A game in a booth at a spring fair involves using a spinner first.  Then, if the spinner stops on an even number, the player is allowed to pick a marble from a bag.  The spinner and the marbles in the bag are represented in the diagram below. Prizes are given when a black marble is picked.  Sue plays the game once. How likely is it that Sue will win a prize? A Impossible. B Not very likely. C About 50% likely. D Very likely. E Certain. SPRING FAIR SCORING 1 Full credit Code 1: B.  Not very likely. No credit Code 0: Other responses. Code 9: Missing. 1 4 10 8 6 2 ReleasedPISAItems_Maths.doc  Page 65 D Height of feet Time C Height of feet Time BTime Height of feet Height of feet ATime M472: Swing\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STUDENT HEIGHTS M479Q01"}, {"from": "gpt", "value": "Mohammed is sitting on a swing.  He starts to swing.  He is trying to go as high as possible. Which diagram best represents the height of his feet above the ground as he swings? ReleasedPISAItems_Maths.doc  Page 66 SWING SCORING 1 Full credit Code 1: A. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 67 M479: Student Heights\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about PAYMENTS BY AREA M480Q01"}, {"from": "gpt", "value": "In a mathematics class one day, the heights of all students were measured.  The average height of boys was 160 cm, and the average height of girls was 150 cm. Alena was the tallest \u2013 her height was 180 cm.  Zdenek was the shortest \u2013 his height was 130 cm. Two students were absent from class that day , but they were in class the next day. Their heights were measured, and the averages were recalculated.  Amazingly, the average height of the girls and the average height of the boys did not change. Which of the following conclusions can be drawn from this information? Circle \u2018Yes\u2019 or \u2018No\u2019 for each conclusion. Conclusion Can this conclusion be drawn? Both students are girls. Yes / No One of the students is a boy and the other is a girl. Yes / No Both students have the same height. Yes / No The average height of all students did not change. Yes / No Zdenek is still the shortest. Yes / No  STUDENT HEIGHTS SCORING 1 Full credit Code 1: \u2018No\u2019 for all conclusions. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 68 M480: Payments by Area People living in an apartment building decide to buy the building. They will put their money together in such a way that each will pay an amount that is proportional to the size of their apartment. For example, a man living in an apartment that occupies one fifth of the floor area of all apartments will pay one fifth of the total price of the building.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about BOOKSHELVES M484Q01"}, {"from": "gpt", "value": "Circle Correct or Incorrect for each of the following statements. Statement Correct / Incorrect A person living in the largest apartment will pay more money for each square metre of his apartment than the person living in the smallest apartment. Correct / Incorrect If we know the areas of two apartments and the price of one of them we can calculate the price of the second. Correct / Incorrect If we know the price of the building and how much each owner will pay, then the total area of all apartments can be calculated.  Correct / Incorrect If the total price of the building were reduced by 10%, each of the owners would pay 10% less. Correct / Incorrect  PAYMENTS BY AREA SCORING 1 Full credit Code 1: Incorrect, Correct, Incorrect, Correct, in that order. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 69 Question 2: PAYMENTS BY AREA M480Q02 - 0 1 2 9 There are three apartments in the building.  The largest, apartment 1, has a total area of 95m2.  Apartments 2 and 3 have areas of 85m2 and 70m2 respectively.  The selling price for the building is 300 000 zeds. How much should the owner of apartment 2 pay?  Show your work. PAYMENTS BY AREA SCORING 2 Full credit Code 2: 102,000 zeds, with or without the calculation shown, and unit not required. \u2022 Apartment 2: 102 000 zeds \u2022 zeds Apt 102000 30000025085:2 = \u00d7 \u2212 \u2022 1200250300000=zeds for each square metre, so Apartment 2 is 102 000. Partial credit Code 1: Correct method, but minor computational error/s. \u2022 zeds Apt 10200 30000025085:2 = \u00d7 \u2212 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 70 M484: Bookshelves\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LITTER M505Q01 - 0 1 9"}, {"from": "gpt", "value": "To complete one set of bookshelves a carpenter needs the following components: 4 long wooden panels, 6 short wooden panels, 12 small clips, 2 large clips and 14 screws. The carpenter has in stock 26 long wooden panels, 33 short wooden panels, 200 small clips, 20 large clips and 510 screws. How many sets of bookshelves can the carpenter make? Answer: .................................................. BOOKSHELVES SCORING 1 Full credit Code 1: 5. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 71 M505: Litter\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about EARTHQUAKE M509Q01"}, {"from": "gpt", "value": "For a homework assignment on the envir onment, students collected information on the decomposition time of several types of litter that people throw away: Type of Litter Decomposition time Banana peel 1\u20133 years Orange peel 1\u20133 years Cardboard boxes 0.5 year Chewing gum 20\u201325 years Newspapers A few days Polystyrene cups Over 100 years A student thinks of displaying the results in a bar graph. Give one reason why a bar graph is unsuitable for displaying these data. LITTER SCORING 1 Full credit Code 1: Reason focuses on big variance in data. \u2022 T h e  d i f f e r e n c e  i n  t h e  l e n g t h s  o f  t h e  b a rs of the bar graph would be too big. \u2022 I f  y o u  m a k e  a  b a r  w i t h  l e n g t h  1 0  c e n t i m e t r e s  f o r  p o l y s t y r e n e ,  t h e  o n e  f o r cardboard boxes would be 0.05 centimetres. O R Reason focuses on the variability of the data for some categories. \u2022 The length of the bar for \u201cpol ystyrene cups\u201d is undetermined. \u2022 Y o u  c a n n o t  m a k e  o n e  b a r  f o r  1 \u2013 3  y e a r s  o r  o n e  b a r  f o r  2 0 \u2013 2 5  y e a r s . No credit Code 0: Other responses. \u2022 B e c a u s e  i t  w i l l  n o t  w o r k . \u2022 A  p i c t o g r a m  i s  b e t t e r . \u2022 Y o u  c a n n o t  v e r i f y  t h e  i n f o . \u2022 B e c a u s e  t h e  n u m b e r s  i n  t h e  t a b l e  a r e  o n l y  a p p r o x i m a t i o n s . Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 72 M509: Earthquake\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about CHOICES M510Q01"}, {"from": "gpt", "value": "A documentary was broadcast about earthquakes and how often earthquakes occur. It included a discussion about the predictability of earthquakes. A geologist stated: \u201cIn the next twenty years, the chance that an earthquake will occur in Zed City is two out of three\u201d. Which of the following best reflects the meaning of the geologist\u2019s statement ? A 13.3 2032=\u00d7 , so between 13 and 14 years from now there will be an earthquake in Zed City. B 32 is more than 21, so you can be sure there will be an earthquake in Zed City at some time during the next 20 years. C The likelihood that there will be an earthquake in Zed City at some time during the next 20 years is higher than the likelihood of no earthquake. D You cannot tell what will happen, because nobody can be sure when an earthquake will occur. EARTHQUAKE SCORING 1 Full credit Code 1: C.  The likelihood that there will be an earthquake in Zed City at some time during the next 20 years is higher than the likelihood of no earthquake. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 73 M510: Choices\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TEST SCORES M513Q01 - 0 1 9"}, {"from": "gpt", "value": "In a pizza restaurant, you can get a basic pizza with two toppings: cheese and tomato. You can also make up your own pizza with extra  toppings. You can choose from four different extra toppings: olives, ham, mushrooms and salami. Ross wants to order a pizza with two different extra  toppings. How many different combinations can Ross choose from? Answer: ..................................................combinations. CHOICES SCORING 1 Full credit Code 1: 6. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 74 M513: Test Scores\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SHOES FOR KIDS M515Q01"}, {"from": "gpt", "value": "The diagram below shows the results on a Science test for two groups, labelled as Group A and Group B. The mean score for Group A is 62.0 and the mean for Group B is 64.5.  Students pass this test when their score is 50 or above. Looking at the diagram, the teacher claims that Group B did better than Group A in this test. The students in Group A don\u2019t agree with their teacher. They try to convince the teacher that Group B may not necessarily have done better. Give one mathematical argument, using the graph, that the students in Group A could use. TEST SCORES SCORING 1 Full credit Code 1: One valid argument is given. Valid  arguments could relate to the number of students passing, the disproportionate influence of the outlier, or the number of students with scores in the highest level. \u2022 M o r e  s t u d e n t s  i n  G r o u p  A  t h a n  i n  G r o u p  B  p a s s e d  t h e  t e s t . \u2022 I f  y o u  i g n o r e  t h e  w e a k e s t  G r o u p  A  s t u d e n t ,  t h e  s t u d e n t s  i n  G r o u p  A  d o  b e t t e r than those in Group B. \u2022 M o r e  G r o u p  A  s t u d e n t s  t h a n  G r o u p  B  s t u d e n t s  s c o r e d  8 0  o r  o v e r .  Scores on a Science test 0 1 2 3 4 5 6 0 - 9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100 Score Number of students Group A Group B ReleasedPISAItems_Maths.doc  Page 75 No credit Code 0: Other responses, including responses with no mathematical reasons, or wrong mathematical reasons, or responses that simply describe differences but are not valid arguments that Group B may not have done better. \u2022 G r o u p  A  s t u d e n t s  a r e  n o r m a l l y  b e t t e r  than Group B students in science. This test result is just a coincidence. \u2022 B e c a u s e  t h e  d i f f e r e n c e  b e t w e e n  t h e  h i g h e s t  a n d  l o w e s t  s c o r e s  i s  s m a l l e r  f o r Group B than for Group A. \u2022 G r o u p  A  h a s  b e t t e r  s c o r e  r e s u l t s  i n  t h e  8 0 - 8 9  r a n g e  a n d  t h e  5 0 - 5 9  r a n g e . \u2022 G r o u p  A  h a s  a  l a r g e r  i n t e r - q u a r t i l e  r a n g e  t h a n  G r o u p  B . Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 76 M515: Shoes for Kids The following table shows the recommended Zedland shoe sizes corresponding to various foot lengths.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SKATEBOARD M520Q02"}, {"from": "gpt", "value": "Marina\u2019s feet are 163 mm long.  Use the table to determine which Zedland shoe size Marina should try on . Answer: .................................................. SHOES FOR KIDS SCORING 1 Full credit Code 1: 26. No credit Code 0: Other responses. Code 9: Missing. Conversion table for kids shoe sizes in Zedland From (in mm) To (in mm) Shoe size 107 115 18 116 122 19 123 128 20 129 134 21 135 139 22 140 146 23 147 152 24 153 159 25 160 166 26 167 172 27 173 179 28 180 186 29 187 192 30 193 199 31 200 206 32 207 212 33 213 219 34 220 226 35 ReleasedPISAItems_Maths.doc  Page 77 M520: Skateboard Eric is a great skateboard fan. He visits a shop named SKATERS to check some prices. At this shop you can buy a complete board. Or you can buy a deck, a set of 4 wheels, a set of 2 trucks and a set of hardware, and assemble your own board. The prices for the shop\u2019s products are: Product Price in zeds Complete skateboard 82 or 84  Deck 40, 60 or 65  One set of 4 Wheels  14 or 36  One set of 2 Trucks 16  One set of hardware (bearings, rubber pads, bolts and nuts) 10 or 20  ReleasedPISAItems_Maths.doc  Page 78 Question 1: SKATEBOARD M520Q01a M520Q01b Eric wants to assemble his own skateboard. What is the minimum price and the maximum price in this shop for self-assembled skateboards? (a) Minimum price: .................................zeds. (b) Maximum price: ................................zeds. SKATEBOARD SCORING 1 Full credit Code 21: Both the minimum (80) and the maximum (137) correct. Partial credit Code 11: Only the minimum (80) correct. Code 12: Only the maximum (137) correct. No credit Code 00: Other responses. Code 99: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SKATEBOARD M520Q03"}, {"from": "gpt", "value": "The shop offers three different decks, two different sets of wheels and two different sets of hardware. There is only one choice for a set of trucks. How many different skateboards can Eric construct? A 6 B 8 C 10 D 12 SKATEBOARD SCORING 2 Full credit Code 1: D.  12. ReleasedPISAItems_Maths.doc  Page 79 No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TABLE TENNIS TOURNAMENT M521Q01 - 0 1 9"}, {"from": "gpt", "value": "Eric has 120 zeds to spend and wants to buy the most expensive skateboard he can afford. How much money can Eric afford to spend on each of the 4 parts?  Put your answer in the table below. Part Amount (zeds) Deck Wheels Trucks Hardware  SKATEBOARD SCORING 3 Full credit Code 1: 65 zeds on a deck, 14 on wheels, 16 on trucks and 20 on hardware. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 80 M521: Table Tennis Tournament\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LIGHTHOUSE M523Q01"}, {"from": "gpt", "value": "Teun, Riek, Bep and Dirk have formed a practice group in a table tennis club.  Each player wishes to play against each other  player once.  They have reserved two practice tables for these matches. Complete the following match schedule; by writing the names of the players playing in each match. P r a c t i c e  T a b l e  1  P r a c t i c e  T a b l e  2 Round 1  Teun - Riek Bep - Dirk Round 2 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 Round 3 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026 \u2026\u2026\u2026\u2026\u2026 - \u2026\u2026\u2026\u2026\u2026   ReleasedPISAItems_Maths.doc  Page 81 TABLE TENNIS TOURNAMENT SCORING 1 Full credit Code 1:  Four remaining matches correctly described and distributed over rounds 2 and 3. \u2022  E . g . Practice Table 1 Practice Table 2 Round 1 Teun - Riek Bep - Dirk Round 2 Teun - Bep Riek \u2013 Dirk Round 3 Teun - Dirk Riek - Bep No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 82 M523: Lighthouse Lighthouses are towers with a light beacon on top.  Lighthouses assist sea ships in finding their way at night when they are sailing close to the shore. A lighthouse beacon sends out light flashes with a regular fixed pattern.  Every lighthouse has its own pattern. In the diagram below you see the pattern of a certain lighthouse. The light flashes alternate with dark periods. It is a regular pattern.  After some time the pattern repeats itself.  The time taken by one complete cycle of a pattern, before it starts to repeat, is called the period.  When you find the period of a pattern, it is easy to extend the diagram for the next seconds or minutes or even hours.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about LIGHTHOUSE M523Q03 - 0 1 2 9"}, {"from": "gpt", "value": "Which of the following could be the period of the pattern of this lighthouse? A 2 seconds. B 3 seconds. C 5 seconds. D 12 seconds. LIGHTHOUSE SCORING 1 Full credit Code 1: C.  5 seconds. No credit Code 0: Other responses. Code 9: Missing. light dark 0 1 2 3 4 5 6 7 8 9 10 11 12 time (sec) 13 ReleasedPISAItems_Maths.doc  Page 83 Question 2: LIGHTHOUSE M523Q02 For how many seconds does the lighthouse send out light flashes in 1 minute? A 4 B 12 C 20 D 24 LIGHTHOUSE SCORING 2 Full credit Code 1: D.  24. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about DECREASING CO 2 LEVELS M 5 2 5 Q 0 2  -  0 1 9"}, {"from": "gpt", "value": "In the diagram below, make a graph of a possible pattern of light flashes of a lighthouse that sends out light flashes for 30 seconds per minute.  The period of this pattern must be equal to 6 seconds. LIGHTHOUSE SCORING 3 Full credit Code 2: The graph shows a pattern of light and dark with flashes for 3 seconds in every 6 seconds, and with a period of 6 seconds.  This can be done in the light dark 0 1 2 3 4 5 6 7 8 9 10 11 12 time (sec) ReleasedPISAItems_Maths.doc  Page 84 following ways: - 1  o n e - s e c o n d  f l a s h  a n d  a  t w o - s e c o n d  f l a s h  ( a n d  t h i s  c a n  b e  s h o w n  i n several ways), or - 1  t h r e e - s e c o n d  f l a s h  ( w h i c h  c a n  b e  s h o w n  i n  f o u r  d i f f e r e n t  w a y s ) . If two periods are shown, the pattern must be identical for each period. Partial credit Code 1: The graph shows a pattern of light and dark with flashes for 3 seconds in every 6 seconds, but the period is not 6 seconds.  If two periods are shown, the pattern must be identical for each period. \u2022 Three one-second flashes, alternating with 3 one-second dark periods. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 85 M525: Decreasing CO 2  Levels Many scientists fear that the increasing level of CO 2 gas in our atmosphere is causing climate change. The diagram below shows the CO 2 emission levels in 1990 (the light bars) for several countries (or regions), the emission levels in 1998 (the dark bars), and the percentage change in emission levels between 1990 and 1998 (the arrows with percentages). Percentage change in emission levels from 1990 to 1998. +11% -35% +10% +13% +15% -4% -16% +8% 612423218 692485236 1 209 4 208 1 213 3 040 6 0491 020 4 041 1 331 1 962 6 727 Emissions in 1990 (million tons CO 2) Emissions in 1998 (million tons CO 2) USA Russia Japan Canada Australia EU total Germany Netherlands ReleasedPISAItems_Maths.doc  Page 86 Question 1: DECREASING CO 2 LEVELS M 5 2 5 Q 0 1  -  0 1 2 9 In the diagram you can read that in the USA, the increase in CO 2 emission level from 1990 to 1998 was 11%. Show the calculation to demonstrate how the 11% is obtained. DECREASING CO 2 LEVELS SCORING 1 Full credit Code 2: Correct subtraction, and correct calculation of percentage. \u2022 6 7 2 7  \u2013  6 0 4 9  =  6 7 8 ,   11% 100%6049678\u2248\u00d7 . Partial credit Code 1: Subtraction error and percentage calculation correct, or subtraction correct but dividing by 6727. \u2022 89.9% 10067276049=\u00d7 , and 100-89.9=10.1%. No credit Code 0: Other responses, including just \u2018Yes\u2019 or \u2018No\u2019. \u2022 Y e s ,  i t  i s  1 1 % . Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q01 - 0 1 2 9"}, {"from": "gpt", "value": "Mandy analysed the diagram and claimed she discovered a mistake in the percentage change in emission levels: \u201cThe percentage decrease in Germany (16%) is bigger than the percentage decrease in the whole European Union (EU total, 4%). This is not possible, since Germany is part of the EU.\u201d Do you agree with Mandy when she says this is not possible? Give an explanation to support your answer. DECREASING CO 2 LEVELS SCORING 2 Full credit Code 1: No, with correct argumentation. \u2022 N o ,  o t h e r  c o u n t r i e s  f r o m  t h e  E U  c a n  h a ve increases e.g. the Netherlands so the total decrease in the EU can be smaller than the decrease in Germany. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 87 Question 3: DECREASING CO 2 LEVELS M 5 2 5 Q 0 3  -  0 1 2 9 Mandy and Niels discussed which country (or region) had the largest increase  of CO 2 emissions. Each came up with a different conclusion based on the diagram. Give two possible \u2018correct\u2019 answers to this question, and explain how you can obtain each of these answers. DECREASING CO 2 LEVELS SCORING 3 Full credit Code 2: Response identifies both mathematical approaches (the largest absolute increase and the largest relative increase), and names the USA and Australia. \u2022 U S A  h a s  t h e  l a r g e s t  i n c r e a s e  i n  m i l l i o n s  o f  t o n s ,  a n d  A u s t r a l i a  h a s  t h e  l a r g e s t increase in percentage. Partial credit Code 1: Response identifies or refers to both the largest absolute increase and the largest relative increase, but the countries are not identified, or the wrong countries are named. \u2022 R u s s i a  h a d  t h e  b i g g e s t  i n c r e a s e  i n  t h e  a m o u n t  o f  C O 2 (1078 tons), but Australia had the biggest pe rcentage increase (15%). No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 88 M535: Twisted Building In modern architecture, buildings often have unusual shapes. The picture below shows a computer model of a \u2018twisted building\u2019 and a plan of the ground floor.  The compass points show the orientation of the building. The ground floor of the building contains the main entrance and has room for shops. Above the ground floor there are 20 storeys containing apartments. The plan of each storey is similar to the plan of the ground floor, but each has a slightly different orientation from the stor ey below.  The cylinder contains the elevator shaft and a landing on each floor.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q02"}, {"from": "gpt", "value": "Estimate the total height of the building, in metres.  Explain how you found your answer. TWISTED BUILDING SCORING 1 Full credit Code 2:  Accept answers from 50 to 90 me tres if a correct explanation is given. \u2022 O n e  f l o o r  o f  t h e  b u i l d i n g  h a s  a  h e i g h t  o f  a b o u t  2 . 5  m e t e r s .   T h e r e  i s  s o m e extra room between floors.  Therefor e an estimate is 21 x 3 = 63 metres. \u2022 A l l o w  4  m  f o r  e a c h  s t o r y ,  s o  2 0  o f  t h e s e  g i v e s  8 0  m ,  p l u s  1 0  m  f o r  t h e  g r o u n d floor, so a total of 90 m. N S E W N S E W ReleasedPISAItems_Maths.doc  Page 89 Partial credit Code 1: Correct calculation method and explanation, but using 20 stories instead of 21. \u2022 E a c h  a p a r t m e n t  c o u l d  b e  3 . 5  m e t r e s  h i g h ,  2 0  s t o r i e s  o f  3 . 5  m e t r e s  g i v e s  a total height of 70 m. No credit Code 0: Other responses, including answer without any explanation, answers with other incorrect number of floors, and answers with unreasonable estimates of the height of each floor (4 m would be the upper limit). \u2022 Each floor is around 5 m high, so 5 \u00d7 21 equals 105 metres. \u2022 6 0  m . Code 9: Missing.  The following pictures are sideviews of the twisted building.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about TWISTED BUILDING M535Q03"}, {"from": "gpt", "value": "From which direction has Sideview 1 been drawn? A From the North. B From the West. C From the East. D From the South. TWISTED BUILDING SCORING 2 Full credit Code 1: C.  From the East. Sideview 1 S i d e v i e w  2 ReleasedPISAItems_Maths.doc  Page 90 No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about HEARTBEAT M537Q01 - 0 1 9"}, {"from": "gpt", "value": "From which direction has Sideview 2 been drawn? A From the North West. B From the North East. C From the South West. D From the South East. TWISTED BUILDING SCORING 3 Full credit Code 1: D.  From the South East. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 91 Question 4: TWISTED BUILDING M535Q04 - 0 1 2 9 Each storey containing apartments has a certain \u2018twist\u2019 compared to the ground floor. The top floor (the 20th floor above the ground floor) is at right angles to the ground floor. The drawing below represents the ground floor.  Draw in this diagram the plan of the 10th floor above the ground floor, showing how this floor is situated compared to the ground floor. TWISTED BUILDING SCORING 4 Full credit Code 2: A correct drawing, meaning correct rotation point and anti-clockwise rotation.  Accept angles from 40\u00b0 to 50\u00b0.  Partial credit Code 1: One of the rotation angle, the rotation point, or the rotation direction incorrect. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 92 M537: Heartbeat For health reasons people should limit their efforts, for instance during sports, in order not to exceed a certain heartbeat frequency. For years the relationship between a person\u2019s recommended maximum heart rate and the person\u2019s age was described by the following formula: Recommended maximum heart rate =  220 - age Recent research showed that this formula should be modified slightly.  The new formula is as follows: Recommended maximum heart rate =  208 \u2013 (0.7 \u00d7 age)\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SPACE FLIGHT M 5 4 3 Q 0 1"}, {"from": "gpt", "value": "A newspaper article stated: \u201cA result of using the new formula instead of the old one is that the recommended maximum number of heartbeats per minute for young people decreases slightly and for old people it increases slightly.\u201d From which age onwards does the recommended maximum heart rate increase as a result of the introduction of the new formula?  Show your work. HEARTBEAT SCORING 1 Full credit Code 1: Accept 41, or 40. \u2022 2 2 0  \u2013  age = 208 \u2013 0.7 \u00d7 age results in age = 40, so people above 40 will have a higher recommended maximum heart rate under the new formula. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 93 Question 2: HEARTBEAT M537Q02 - 0 1 9 The formula recommended maximum heart rate =  208 \u2013 (0.7 \u00d7 age) is also used to determine when physical training is most effective. Research has shown that physical training is most effective when the heartbeat is at 80% of the recommended maximum heart rate. Write down a formula for calculating the heart rate for most effective physical training, expressed in terms of age. HEARTBEAT SCORING 2 Full credit Code 1: Any formula that is the equivalent of multiplying the formula for recommended maximum heart rate by 80%. \u2022 h e a r t  r a t e  =  1 6 6  \u2013  0 . 5 6  \u00d7 age. \u2022 h e a r t  r a t e  =  1 6 6  \u2013  0 . 6  \u00d7 age. \u2022 h  =  1 6 6  \u2013  0 . 5 6  \u00d7 a. \u2022 h  =  1 6 6  \u2013  0 . 6  \u00d7 a. \u2022 h e a r t  r a t e  =  ( 2 0 8  \u2013  0 . 7 a g e )  \u00d7 0.8. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 94 M543: Space Flight Space station Mir remained in orbit for 15 years and circled Earth some 86 500 times during its time in space. The longest stay of one cosmonaut in the Mir was around 680 days.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STAIRCASE M547Q01"}, {"from": "gpt", "value": "Approximately how many times did this cosmonaut fly around Earth? A 110 B 1 100 C 11 000 D 110 000 SPACE FLIGHT SCORING 1 Full credit Code 1: C.  11 000. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 95 M547: Staircase\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about ROCK CONCERT M552Q01"}, {"from": "gpt", "value": "The diagram below illustrates a staircase with 14 steps and a total height of 252 cm: What is the height of each of the 14 steps? Height: ....................................................cm. STAIRCASE SCORING 1 Full credit Code 1:  18. No credit Code 0:  Other responses. Code 9:  Missing. Total height 252 cm Total depth 400 cm ReleasedPISAItems_Maths.doc  Page 96 M552: Rock Concert\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about NUMBER CUBES M555Q02"}, {"from": "gpt", "value": "For a rock concert a rectangular field of size 100 m by 50 m was reserved for the audience.  The concert was completely sold out and the field was full with all the fans standing. Which one of the following is likely to be the best estimate of the total number of people attending the concert? A 2 000 B 5 000 C 20 000 D 50 000 E 100 000 ROCK CONCERT SCORING 1 Full credit Code 1: C.  20 000. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 97 M555: Number Cubes\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about SUPPORT FOR THE PRESIDENT M702Q01 - 0 1 2 9"}, {"from": "gpt", "value": "On the right, there is a picture of two dice. Dice are special number cubes for which the following rule applies: The total number of dots on two opposite faces is always seven. You can make a simple number cube by cutting, folding and gluing cardboard.  This can be done in many ways.  In the figure below you can see four cuttings that can be used to make cubes, with dots on the sides. Which of the following shapes can be folded together to form a cube that obeys the rule that the sum of opposite faces is 7? For each shape, circle either \u201cYes\u201d or \u201cNo\u201d in the table below. Shape Obeys the rule that the sum of opposite faces is 7? I Yes / No II Yes / No III Yes / No IV Yes / No  NUMBER CUBES SCORING 2 Full credit Code 1: No, Yes, Yes, No, in that order. No credit Code 0: Other responses. Code 9: Missing. I II IIIIV ReleasedPISAItems_Maths.doc  Page 98 M702: Support for the President\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about MOVING WALKWAYS M703Q01 - 0 1 9"}, {"from": "gpt", "value": "In Zedland, opinion polls were conducted to find out the level of support for the President in the forthcoming election.  Four newspaper publishers did separate nationwide polls.  The results for the four newspaper polls are shown below: Newspaper 1: 36.5% (poll conducted on January 6, with a sample of 500 randomly selected citizens with voting rights) Newspaper 2: 41.0% (poll conducted on January 20, with a sample of 500 randomly selected citizens with voting rights) Newspaper 3: 39.0% (poll conducted on January 20, with a sample of 1000 randomly selected citizens with voting rights) Newspaper 4: 44.5% (poll conducted on January 20, with 1000 readers phoning in to vote). Which newspaper\u2019s result is likely to be the best for predicting the level of support for the President if the election is held on January 25?  Give two reasons to support your answer. SUPPORT FOR THE PRESIDENT SCORING 1 Full credit Code 2: Newspaper 3.  The poll is more recent, with larger sample size, a random selection of the sample, and only voters were asked.  (Give at least two reasons).  Additional information (including irrelevant or incorrect information) should be ignored. \u2022 N e w s p a p e r  3 ,  b e c a u s e  t h e y  h a v e  s e l e c t e d  m o r e  c i t i z e n s  r a n d o m l y  w i t h  v o t i n g rights. \u2022 N e w s p a p e r  3  b e c a u s e  i t  h a s  a s k e d  1 0 0 0  p e o p l e ,  r a n d o m l y  s e l e c t e d ,  a n d  t h e date is closer to the election date so t he voters have less time to change their mind. \u2022 N e w s p a p e r  3  b e c a u s e  t h e y  w e r e  r a n d o m l y  s e l e c t e d  a n d  t h e y  h a d  v o t i n g rights. \u2022 N e w s p a p e r  3  b e c a u s e  i t  s u r v e y e d  m o r e  p e o p l e  c l o s e r  t o  t h e  d a t e . \u2022 N e w s p a p e r  3  b e c a u s e  t h e  1 0 0 0  p e o p l e  w e r e  r a n d o m l y  s e l e c t e d . Partial credit Code 1: Newspaper 3, with only one reason, or without explanation. \u2022 N e w s p a p e r  3 ,  b e c a u s e  t h e  p o l l  i s  c l o s e r  t o  e l e c t i o n  d a t e . \u2022 N e w s p a p e r  3 ,  b e c a u s e  m o r e  p e o p l e  w e r e  s u r v e y e d  t h a n  n e w s p a p e r s  1  a n d  2 . \u2022 N e w s p a p e r  3 . ReleasedPISAItems_Maths.doc  Page 99 No credit Code 0: Other responses. \u2022 N e w s p a p e r  4 .   M o r e  p e o p l e  m e a n s  m o r e  a c c u r a t e  r e s u l t s ,  a n d  p e o p l e  p h o n i n g in will have considered their vote better. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 100 time Distance from the start of the moving walkway A person walking on the ground A person walking on the moving walkway time Distance from the start of the moving walkway A person walking on the ground A person walking on the moving walkway A person standing still on the moving walkway M703: Moving Walkways\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about THE BEST CAR M704Q01"}, {"from": "gpt", "value": "On the right is a photograph of moving walkways. The following Distance-Time graph shows a comparison between \u201cwalking on the moving walkway\u201d and \u201cwalking on the ground next to the moving walkway.\u201d Assuming that, in the above graph, the walking pace is about the same for both persons, add a line to the graph that would represent the distance versus time for a person who is standing still on the moving walkway. MOVING WALKWAYS SCORING 1 Full credit Code 1: Accept a line below the two lines, but it must be closer to the line of \u201cA person walking on the ground\u201d than to the baseline.  ReleasedPISAItems_Maths.doc  Page 101 No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 102 M704: The Best Car A car magazine uses a rating system to evaluate new cars, and gives the award of \u201cThe Car of the Year\u201d to the car with the highest total score.  Five new cars are being evaluated, and their ratings are shown in the table. Car Safety Features (S) Fuel Efficiency (F)External Appearance(E)Internal Fittings (T) Ca 3 1 2 3 M2 2 2 2 2 Sp 3 1 3 2 N1 1 3 3 3 KK 3 2 3 2 The ratings are interpreted as follows: 3  p o i n t s  =  E x c e l l e n t 2  p o i n t s  =  G o o d 1  p o i n t  =  F a i r\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about STEP PATTERN M806Q01"}, {"from": "gpt", "value": "To calculate the total score for a car, the car magazine uses the following rule, which is a weighted sum of the individual score points: T o t a l  S c o r e  =  ( 3  x  S )  +  F  +  E  +  T Calculate the total score for Car \u201cCa\u201d.  Write your answer in the space below. Total score for \u201cCa\u201d: ............................... THE BEST CAR SCORING 1 Full credit Code 1: 15 points. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 103 Question 2: THE BEST CAR M704Q02 The manufacturer of car \u201cCa\u201d thought the rule for the total score was unfair. Write down a rule for calculating the total score so that Car \u201cCa\u201d will be the winner. Your rule should include all four of the variables, and you should write down your rule by filling in positive numbers in the four spaces in the equation below. Total score = \u2026\u2026\u2026 \u00d7 S + \u2026\u2026\u2026\u00d7 F + \u2026\u2026\u2026\u00d7 E + \u2026\u2026\u2026\u00d7 T. THE BEST CAR SCORING 2 Full credit Code 1: Correct rule that will make \u201cCa\u201d the winner. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 104 M806: Step Pattern\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q01"}, {"from": "gpt", "value": "Robert builds a step pattern using squares. Here are the stages he follows. As you can see, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3. How many squares should he use for the fourth stage? Answer: ..................................................squares. STEP PATTERN SCORING 1 Full credit Code 1: 10. No credit Code 0: Other responses. Code 9: Missing. Stage 1 Stage 2 Stage 3 ReleasedPISAItems_Maths.doc  Page 105 M836: Postal Charges The postal charges in Zedland are based on the weight of the items (to the nearest gram), as shown in the table below: Weight (to nearest gram) Charge Up to 20 g 0.46 zeds 21 g \u2013 50 g 0.69 zeds 51 g \u2013 100 g 1.02 zeds 101 g \u2013 200 g 1.75 zeds 201 g \u2013 350 g 2.13 zeds 351 g \u2013 500 g 2.44 zeds 501 g \u2013 1000 g 3.20 zeds 1001 g \u2013 2000 g 4.27 zeds 2001 g \u2013 3000 g 5.03 zeds\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q02 - 0 1 9"}, {"from": "gpt", "value": "Which one of the following graphs is the best representation of the postal charges in Zedland?  (The horizontal axis shows the weight in grams, and the vertical axis shows the charge in zeds.) 0123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 00123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 0123456 20 50 100 200 350 500 1000 2000 30000123456 01 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0A C D B ReleasedPISAItems_Maths.doc  Page 106 POSTAL CHARGES SCORING 1 Full credit Code 1: C. No credit Code 0: Other responses. Code 9: Missing.\n\nThis question is designed to test: Ability to read information from a diagram."}]}
-{"messages": [{"from": "system", "value": "You are a tutor for PISA mathematics questions. You provide questions and evaluate student responses."}, {"from": "human", "value": "Please provide a math question about POSTAL CHARGES M836Q02 - 0 1 9"}, {"from": "gpt", "value": "Jan wants to send two items, weighing 40 grams and 80 grams respectively, to a friend. According to the postal charges in Zedland, decide whether it is cheaper to send the two items as one parcel, or send the items as two separate parcels.  Show your calculations of the cost in each case. POSTAL CHARGES SCORING 2 Full credit Code 1: It will be cheaper to send the items as two separate parcels.  The cost will be 1.71 zeds for two separate parcels, and 1.75 zeds for one single parcel containing both items. No credit Code 0: Other responses. Code 9: Missing. ReleasedPISAItems_Maths.doc  Page 107 Source Publications for Released Items  OECD Sources  (available www.pisa.oecd.org) Test Questions (1) Interactive Web examples: http://pisa-sq.acer.edu.au (2) PISA 2003 sample question files: http://www.pisa.oecd.org Follow the links: What PISA Produces > PISA 2003 > Test questions Publications (3) OECD (Organisation for Economic Co-operation and Development ) (2002), Sample Tasks from the PISA 2000 Assessment: Reading,  Mathematical and Scientific Literacy , OECD, Paris. (4) OECD  (2000), Measuring Student Knowledge and Skills - The PISA 2000 Assessment of Reading, Mathematical and Scientific Literacy , OECD, Paris. (5) OECD  (2003), The PISA 2003 Assessment Framework - Mathematics, Reading, Science and Problem Solving Knowledge and Skills, OECD, Paris.  Unit S o u r c e Code Title (1) Interactive Web Examples (2) PISA 2003 Web Samples (3) PISA 2000 Sample Tasks (4) PISA 2000 Measuring Student K&S (5) PISA 2003 Assessment Framework M037 Farms \u0085 \u0085 ; M047 Lichen ; \u0085 \u0085 ; M124 Walking \u0085 ; M136 Apples \u0085 \u0085 ; M143 Coins ; \u0085 \u0085 ; M143 Cubes \u0085 ; M148 Continent Area \u0085 \u0085 ; M150 Growing Up \u0085 ; M154 Pizzas ; \u0085 \u0085 ; M158 Shapes ; \u0085 \u0085 ; M159 Speed of Racing Car \u0085 \u0085 ; M161 Triangles \u0085 \u0085 ; M179 Robberies \u0085 ; M215 Braking ; \u0085 \u0085 ; M266 Carpenter \u0085 ; M267 Patio ; \u0085 \u0085 ; M307 Drug Concentrations \u0085 \u0085 \u0085 \u0085 ; M309 Building Blocks \u0085 \u0085 \u0085 \u0085 ; M402 Internet Relay Chat \u0085 ; M413 Exchange Rate \u0085 ; ReleasedPISAItems_Maths.doc  Page 108 Unit S o u r c e Code Title (1) Interactive Web Examples (2) PISA 2003 Web Samples (3) PISA 2000 Sample Tasks (4) PISA 2000 Measuring Student K&S (5) PISA 2003 Assessment Framework M432 Reaction Time \u0085 \u0085 \u0085 \u0085 ; M438 Exports \u0085 ; M465 Water Tank \u0085 \u0085 \u0085 \u0085 ; M467 Coloured Candies \u0085 ; M468 Science Tests \u0085 ; M471 Spring Fair \u0085 ; M472 Swing \u0085 \u0085 \u0085 \u0085 ; M479 Student Heights \u0085 \u0085 \u0085 \u0085 ; M480 Payments by Area \u0085 \u0085 \u0085 \u0085 ; M484 Bookshelves \u0085 ; M505 Litter \u0085 ; M509 Earthquake \u0085 ; M510 Choices \u0085 ; M513 Test Scores \u0085 ; M515 Shoes for Kids \u0085 ; M520 Skateboard \u0085 ; M521 Table Tennis Tournament \u0085 ; M523 Lighthouse \u0085 \u0085 \u0085 \u0085 ; M525 Decreasing CO 2 Levels \u0085 ; M535 Twisted Building \u0085 \u0085 \u0085 \u0085 ; M537 Heartbeat \u0085 \u0085 \u0085 \u0085 ; M543 Space Flight \u0085 ; M547 Staircase \u0085 ; M552 Rock Concert \u0085 \u0085 \u0085 \u0085 ; M555 Number Cubes \u0085 ; M702 Support for the President \u0085 ; M703 Moving Walkways \u0085 \u0085 \u0085 \u0085 ; M704 The Best Car \u0085 ; M806 Step Pattern \u0085 ; M836 Postal Charges \u0085 \u0085 \u0085 \u0085 ;\n\nThis question is designed to test: Ability to read information from a diagram."}]}