Fractions, decimals and percentages — Paper 3 · IGCSE Mathematics 0580

2 (a) Complete the table of values for y = 1 + 2x – x2. For Examiner's Use x − 3 − 2 − 1 0 1 2 3 4 5 y − 14 − 7 1 − 2 − 14 [3] (b) Draw the graph of y = 1 + 2x – x2 on the grid below. y 4 2 x –3 –2 –1 0 1 2 3 4 5 –2 –4 –6 –8 –10 –12 –14 [4] (c) Use your graph to find the solutions to the equation 1 + 2x – x2 = 0. Answer (c) x = or x = [2] (d) (i) On the grid, draw the line of symmetry of the graph. [1] (ii) Write down the equation of this line of symmetry. Answer(d)(ii) [1]

11 marks

Mark scheme: 2 (a) –2 1 2 –7 3 B2 for 3 correct, B1 for 1 or 2 correct (b) 9 correct points P3 f.t. P2 f.t. for 7 or 8 correct, P1 f.t. for 5 or 6 plotted correct limit for acurracy is ½ small square smooth curve drawn C1 must go through the 9 correct points not dependent on P3 (c) –0.4 ( ± /0.1) 1 please note no f.t. on this part 2.4 ( ± 0.1) 1 (d) (i) correct line drawn 1 accept dotted/dashed line must be full length from (1, –14) to (1,2) (ii) x = 1 1 f.t. f.t. from (d)(i) if x = k any reference to y is X 11

This question in 0580/31 May/June 2005

4 (a) The table shows corresponding values of x and y for the function For Examiner's 60 Use y = (x ≠ 0). x x −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 y −12 −15 −30 60 12 10 [2] (i) Fill in the missing values of y in the table above. (ii) Plot the points on the grid below and draw the graph for −6 x −1 and 1 x 6. y 60 50 40 30 20 10 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –10 –20 –30 –40 –50 –60 [4] (b) Write down the order of rotational symmetry of the graph. Answer(b) [1] (c) Draw the lines of symmetry of the graph on the grid. [2] (d) One line of symmetry intersects the graph at two points. (i) Write down the co-ordinates of these two points. Answer(d)(i) ( , ) and ( , ) [2] (ii) Write down the equation of this line of symmetry. Answer(d)(ii) [1] (e) Find the gradient of the other line of symmetry. Answer(e) [1]

13 marks

Mark scheme: 4 (a) (i) −10, −20, −60, 30, 20, 15 B2 B1 for –20 (x = –3) or 20 (x = 3) (ii) Their 12 points plotted correctly. P3ft P2ft for 10 or 11 points correct. P1ft for 8 or 9 points or 1 quadrant correct. Smooth curves through all points. C1 Two distinct curves; no part of curves between x = –1 and x = 1 (b) 2 B1 (c) Correct lines ruled B1,B1 Minimum length from x = –3 to x = 3. (d) (i) (2.4 to 2.5, 24 to 25) B1ft ft their points of intersection (−2.4 to −2.5, −24 to −25) B1ft ft their points of intersection (ii) y = 10x oe B1 cao (e) −10 B1 cao [13] IGCSE – May/June 2007 0580/0581 03

This question in 0580/31 May/June 2007

36 , (x ≠ 0). For3 (a) Complete the table for the function y = x Examiner's Use x −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 y −7.2 −9 −18 18 9 7.2 [3] 36 (b) On the grid below, draw the graph of y = for −6 x −1 and 1 x 6. x y 40 30 20 10 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –10 –20 –30 –40 [4] (c) Use your graph to find x when y = 21. Answer(c) x = [1] (d) Complete the table for the function y = x2. For Examiner's Use x −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 y 25 16 4 1 1 4 16 25 [2] (e) On the same grid, draw the graph of y = x2 for −6 x 6. [4] 36(f) Write down the co-ordinates of the point of intersection of the graphs of y = and y = x2. x Answer(f)( , ) [1]

15 marks

Mark scheme: 3 (a) –6, –12, –36, 36, 12, 6 B3 B1 for ± 36, B1 for ± 12, B1 for ± 6 SC1 for any 3 correct (b) 12 points plotted P3 correct points ft within 1 mm P2 for 10 or 11, P1 for 8 or 9, P1 for 1 correct branch 2 curves drawn C1 must be smooth branches of rectangular hyperbola (c) 1.6 to 1.8 B1 ft (d) 36, 9, 0, 9, 36 B2 B1 for 4 correct (e) 13 points plotted P3 correct points ft within 1 mm P2 for 11 or 12 P1 for 9 or 10 curve drawn C1 must be smooth parabola (f) 3.3, 10.9 B1ft x from 3.2 to 3.4, y from 10.0 to 12.0 [15]

This question in 0580/31 Oct/Nov 2007

1 Aida, Bernado and Cristiano need $30 000 to start a business. For Examiner's 2 Use (a) (i) They borrow of this amount. 5 Show that they still need $18 000. Answer (a)(i) [1] (ii) They provide the $18 000 themselves in the ratio Aida : Bernado : Christiano = 5 : 4 : 3. Calculate the amount each of them provides. Answer(a)(ii)Aida $ Bernado $ Cristiano $ [3] (b) (i) Office equipment costs 35 % of the $30 000. Calculate the cost of the equipment. Answer(b)(i)$ [2] (ii) Office expenses cost another $6500. Write this as a fraction of $30 000. Give your answer in its lowest terms. Answer(b)(ii) [2] (iii) How much remains of the $30 000 now? Answer(b)(iii)$ [1] (c) They invest $12 500. After one year this has increased to $15 500. Calculate this percentage increase. Answer(c) % [3]

12 marks

Mark scheme: Qu Answers Mark Part Marks 1 (a) (i) 3 × 30 000 M1 Must see evidence of fractions 5 or 30 000 − 52 × 30 000 (ii) Aida $7500 5 or 4 or 3 W3 M1 for 5+ 4 + 3 × 18000 Bernado $6000 A1 for 1 correct answer Christiano $4500 (b) (i) 10 500 W2 M1 for 10035 × 30 000 or 0.35 × 30 000 (ii) 13 6500 60 W2 W1 for 30000 seen or other ‘correct’ fraction. (iii) ($)13 000 W1ft 15500 (c) 24 W3cao M1 for 15 500 − 12500 or 12500 × 100 M1 for 12500' 3000 ' × 100 or ‘124’− 100

This question in 0580/31 Oct/Nov 2008

7 y = 9x – x2. For Examiner's (a) Complete the table of values for this equation. Use x 0 1 2 3 4 5 6 7 8 9 y 8 20 20 8 0 [3] (b) On the grid below, draw the graph of y = 9x – x2 for 0 Y x Y 9. y 22 20 18 16 14 12 10 8 6 4 2 x 0 1 2 3 4 5 6 7 8 9 [4] (c) Write down the values of x and y at the highest point of the curve. For Examiner's Use Answer(c) x = y = [2] (d) (i) On the grid, draw the line y = 6 for 0 Y x Y 9. [1] (ii) Use this line to find the solutions of the equation 9x – x2 = 6. Give your answers correct to one decimal place. Answer(d)(ii) x = or x = [2]

12 marks

Mark scheme: 7 (a) x 0 1 2 3 4 5 6 7 8 9 3 W2 for 4 correct y 0 8 14 18 20 20 18 14 8 0 W1 for 3 correct (b) Their 10 points correctly plotted, within P3ft P2ft for 8 or 9 correct half a square. P1ft for 6 or 7 correct Smooth curve through the 10 correct C1 Shape must be correct and the curve goes above points y = 20. (c) (x =) 4.4 to 4.6 1cao (y =) 20.1 to 20.5 1cao (d) (i) Ruled line y = 6 1 (ii) 8.1 to 8.5 Must be to 1 decimal place 1cao SC1 for both correct but not to 1dp e.g. 8.27 and 0.5 to 0.9 Must be to 1 decimal place 1cao 0.73 IGCSE – May/June 2009 0580, 0581 03

This question in 0580/31 May/June 2009

3 For 6 (a) Complete the table of values for the function y = , x ≠ 0. Examiner's x Use x −3 −2.5 −2 −1.5 −1 −0.5 −0.3 0.3 0.5 1 1.5 2 2.5 3 y −1 −1.2 −2 −3 −6 3 2 1.5 1 [3] 3 (b) On the grid below, draw the graph of y = for −3 Y x Y −0.3 and 0.3 Y x Y 3. x y 10 9 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 –1 –2 –3 –4 –5 –6 –7 –8 –9 [5] –10 3 For (c) Use your graph to solve the equation = 7. Examiner's x Use Answer(c) x = [1] 2 x (d) Complete the table of values for y = − 1 . 3 x −3 0 3 y [2] 2 x (e) On the grid, draw the straight line y = − 1 for −3 Y x Y 3. [2] 3 2 x (f) Write down the co-ordinates of the points where the line y = − 1 intersects 3 3 the graph of y = . x Answer(f) ( , ) and ( , ) [2]

15 marks

Mark scheme: 6 (a) –1.5 –10 10 6 1.2 3 B2 for 3 or 4 correct, B1 for 2 correct (b) 14 points plotted accurately P3ft P2ft for 11, 12 or 13 points, P1ft for 8, 9 or 10 2 smooth correct curves C1 No part across y-axis B1 Indep (c) 0.4 to 0.5 1 (d) −3 −1 1 2 B1 for 2 correct (e) Ruled line from (−3, −3) to (3, 1) 2 SC1 for freehand or short ruled line – must meet curve twice or P1 for their 3 points plotted (f) (−1.5, −2) and (3, 1) 1, 1

This question in 0580/31 May/June 2010

2 Francis earns $150 per week. Examiner's He has $132 left after he pays his tax. Use (a) Calculate what percentage of his $150 he pays in tax. Answer(a) % [3] (b) He divides the $132 between expenses, savings and family in the ratio Expenses : Savings : Family = 15 : 7 : 11. Calculate his expenses. Answer(b) $ [3] (c) His rent is $24 per week. What fraction of the $132 is this? Give your answer as a fraction in its simplest form. Answer(c) [2] (d) His earnings of $150 per week increase by 8%. Calculate his new earnings. Answer(d) $ [2]

10 marks

Mark scheme: 2 (a) 12 3 Either M1 for 150 − 132 soi M1 for ‘18’ ÷ 150 × 100 or M1 for 132/150×100 M1 for 100 – ‘88’ (b) 60 3 M1 for 15 + 7 +11 M1dep for 15 ÷‘33’ × 132, 132÷‘33’×15, 4×15 SC2 for 60:28:44 (c) 11 2 cao 2 W1 for 1266 or 448 or 336 or 224 (d) ($)162 2 M1 for 108 ÷ 100 × 150 or 150 + (8 ÷ 100 × 150) IGCSE – May/June 2010 0580 32

This question in 0580/32 May/June 2010

1 A bookshop sold a total of 2750 books in January. Examiner's Use (a) The ratio hardback books sold : paperback books sold was 4 : 7. Calculate how many paperback books were sold. Answer(a) [2] (b) 24% of the 2750 books sold were non-fiction. Calculate how many non-fiction books were sold. Answer(b) [2] (c) 330 cookery books were sold. Write 330 as a fraction of 2750 in its lowest terms. Answer(c) [2] (d) In February, the bookshop sold 14% more than the 2750 books sold in January. Calculate the number of books sold in February. Answer(d) [3] (e) The total value of the books sold in January was $9480 correct to the nearest 10 dollars. Write down the lower bound for this amount. Answer(e) $ [1] (f) 35000 books were sold in a year. Write this number in standard form. Answer(f) [1]

11 marks

Mark scheme: Qu. Answers Mark Part Marks 771 (a) 1750 2 M1 × 2750 oe 4 + 7 24× 2750 (b) 660 2 M1 100 3 (c) 2 W1 for equivalent fractions 25 114 (d) 3135 cao 3 M2 × 2750 oe 100 14 If M0 then M1 for × 2750 or 385 seen 100 (e) 9475 1 cao (f) 3.5 × 104 1 cao

This question in 0580/33 May/June 2010

4 For 6 (a) Complete the table of values for y = , x ≠ 0 . Examiner's x Use x −4 −3 −2 −1 − 0.5 0.5 1 2 3 4 y −1.3 −2 −8 8 4 2 [2] 4 (b) On the grid below, draw the graph of y = , for – 4 Y x Y – 0.5 and 0.5 Y x Y 4. x y 8 7 6 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 –1 –2 –3 –4 –5 –6 –7 –8 [4] (c) Complete the following statement. For Examiner's Use 4 The point (−2.5, ) lies on the graph of y = . [1] x (d) (i) On the grid, draw the line y = 5. [1] 4 (ii) Use your graphs to solve the equation = 5 . x Answer(d)(ii) x = [1] (e) (i) On the grid, draw the straight line joining the points (− 0.5 , − 8 ) and ( 2 , 2 ). [2] (ii) Find the gradient of this line. Answer(e)(ii) [1] (iii) Write down the equation of this line in the form y = mx + c. Answer(e)(iii) y = [2]

14 marks

Mark scheme: 6 (a) –1, –4, 1.3, 1 2 B1 for –1 and 1 and B1 for –4 and 1.3 (b) 10 points plotted ½ small square P3ft P2 for 8 or 9 points, P1 for 5 or 6 or 7 points accuracy smooth correct curves not across y-axis C1 (c) –1.6 correct or ft 1ft ft from their graph (d) (i) y = 5 drawn 1 (ii) (x =) 0.8 correct or ft 1ft ft from their graph (e) (i) Ruled line drawn from (–0.5, –8) 2 B1 for ruled line drawn from either point not to (2, 2) horizontal or vertical (ii) 4 cao 1 (iii) y = 4x – 6 or 2ft B1 ft y = 4x + k or y = their (e)(ii) x + k or y = their (e)(ii) x + their intercept y = jx – 6 or y = jx + their intercept or y = 4x + their intercept

This question in 0580/31 Oct/Nov 2010

1 A drink consists of water and fruit juice. For Examiner's (a) 24% of the drink is water. Use Show that there is a total of 760 cm3 of fruit juice in one litre of the drink. Answer(a) [2] (b) What fraction of one litre of the drink is fruit juice? Give your answer in its simplest form. Answer(b) [2] (c) The 760 cm3 of fruit juice in one litre of the drink is made from apple, mango and peach in the following ratio. Apple : Mango : Peach = 6 : 15 : 17 Calculate the amount of apple juice. Answer(c) cm3 [2] (d) A shopkeeper buys bottles of the drink for 65 cents each. He sells them for 80 cents each. Calculate the percentage profit he makes on each bottle he sells. Answer(d) % [3]

9 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 0.76 × 1000 = 760 oe 2 B1 0.76 × 1000 or 1000 – 0.24 × 1000 19 760 76 38 (b) cao 2 B1 for or or 25 1000 100 50 (c) 120 2 M1 for 6 × 760 ÷ (6 + 15 + 17) or 6 ÷ (6 + 15 + 17) or 760 ÷ (6 + 15 + 17) or 20 (d) 23 or art 23.1 3 M1 for 80 – 65 (= 15) and M1 dep for ‘15’ ÷ 65 × 100

This question in 0580/32 Oct/Nov 2010

1 (a) Write twenty five million in figures. For Examiner's Answer(a) [1] Use (b) Write the following in order of size, starting with the smallest. 2 65% 0.6 3 Answer(b) I I [1] (c) In a sale a coat costing $250 is reduced to $200. Find the percentage decrease in the cost. Answer(c) % [3] (d) Basketball NOT TO SCALE 90° 150° Football Tennis 120 students are asked to choose their favourite sport. The results are shown in the pie chart. Calculate the number of students who chose (i) basketball, Answer(d)(i) [1] (ii) football. Answer(d)(ii) [2]

8 marks

Mark scheme: Qu. Answers Mark Part Marks 1 (a) 25 000 000 cao 1 2 (b) 0.6 < 65% < 1 3 their 50 (c) 20% 3 B1 for 50 seen M1 for × 100 250 or B1 for 0.8 or 80 seen M1 for 1 – their 0.8 or 100 – their 80 (d) (i) 30 1 (ii) 40 2 M1 for 360 – (90 + 150) implied by 120 seen

This question in 0580/31 Oct/Nov 2011

2 Aminata buys a business costing $23 000. For Examiner's (a) She pays part of this cost with $12 000 of her own money. Use Calculate what percentage of the $23 000 this is. Answer(a) % [1] (b) Aminata’s brother gives her 32% of the remaining $11 000. Show that $7 480 is still needed to buy the business. Answer(b) [2] (c) Aminata borrows the $7 480 at a rate of 3.5 % per year compound interest. Calculate how much money she owes at the end of 3 years. Answer(c) $ [3] (d) In the first year Aminata spent $11 000 on salaries, equipment and expenses. 2 of this money was spent on salaries, 0.45 of this money was spent on equipment and the 5 remainder was for expenses. Calculate how much of the $11 000 was spent on (i) salaries, Answer(d)(i) $ [1] (ii) equipment, Answer(d)(ii) $ [1] (iii) expenses. Answer(d)(iii) $ [1] (e) The three items in part (d) are in the ratio salaries : equipment : expenses = 0.4 : 0.45 : 0.15 . Write this ratio in its simplest form. Answer(e) : : [2]

11 marks

Mark scheme: 2 (a) 52.2(%) or 52.17… 1 (b) 11000 − (32 ÷ 100 × 11000) M1 or (68 ÷ 100 × 11000) (=) 7480 E1 Must see this for the second mark. (c) 8293 or 8290 or 8293.2 3 Either M1 for 7480 × 1.0352 oe or 8293.21 as final answer or M1 for 7480 × 1.035 = 7741.8 and their 7741.8 × 1.035 (M1 implied by 8012.76...) Then M1 dep for completion of method for the third year If zero SC1 for answer 813.(2…) (d) (i) 4 400 1 (ii) 4 950 1 (iii) 1 650 1ft 11 000 − their (d)(i) − their (d)(ii) (e) 8 : 9 : 3 cao 2 B1 for 40 : 45 : 15 oe seen or correct non-integer ratio IGCSE – October/November 2011 0580 32 ( ) (i) ( ) −2 

This question in 0580/32 Oct/Nov 2011

1 (a) Vince and Wendy share $2000 in the ratio Vince : Wendy = 19 : 21. For Examiner's Calculate the amount of money that Vince receives. Use Answer(a) $ [2] (b) Wendy has $265 to spend on some chairs. The chairs cost $37 each. Work out the largest number of chairs she can buy. Answer(b) [2] (c) Wendy shares $200 between her three children Jake, Karl and Lana. 2 She gives 27% of the money to Jake and of the money to Karl. 5 Work out the amount of money she gives to Lana. Answer(c) $ [3] (d) Wendy invests $500 at a rate of 4% per year compound interest. Calculate the total amount of interest she receives at the end of 2 years. Give your answer correct to the nearest dollar. Answer(d) $ [4]

11 marks

Mark scheme: Qu. Answers Mark Part Mark 1 (a) 950 2 M1 for 2000 ÷ (19 + 21) 265 (b) 7 cao 2 M1 for seen oe e.g. adding up 37s 37 (c) 66 3 M1 for 54 seen M1 indep for 80 seen Or 33 67 M2 for × 200 or M1 for × 200 100 100 (d) 41 4 M1 for (500 × 1.04) × (1.04) oe A1 for 540.8 M1 dep for ‘their 540.8’ – 500 B1 ft for ‘their 40.8’ rounded to 41 Alt Method M1 for [500 + (500×0.04)] × 0.04 M1 dep ‘their 20’ + ‘their 20.8’ A1 for 40.8 B1 ft for ‘their 40.8’ rounded to 41

This question in 0580/31 May/June 2012

10 For 4 (a) The table shows some values of y = . Examiner's x Use x –8 –5 –4 –2 –1 1 2 4 5 8 y –1.25 –5 10 2 (i) Complete the table. [2] 10 (ii) On the grid opposite, draw the graph of y = for −8 Y x Y −1 and 1 Y x Y=8 . [4] x (b) (i) On the same grid, draw the straight line through the points (−3, −5) and (1, 3). Extend the line to the edges of the grid. [2] 10 (ii) Find the co-ordinates of the points of intersection of this line with the graph of y = . x Answer(b)(ii) ( , ) and ( , ) [2] (c) For the line in part (b)(i) (i) work out the gradient, Answer(c)(i) [2] (ii) write down the equation in the form y = mx + c . Answer(c)(ii) y = [1] y For Examiner's 10 Use 9 8 7 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10

13 marks

Mark scheme: 4 (a) (i) −2, −2.5, −10 2 B1 for 4 or 5 correct 5, 2.5, 1.25 (ii) 10 points correctly plotted 3ft B2ft for 8 or 9 points correctly plotted. B1ft for 6 or 7 points correctly plotted Smooth curve 1 (b) (i) Ruled line through both given points 2 B1 for not ruled but otherwise correct or through just 1 of the points (ii) (−2.5, −4),(2, 5) 2ft B1 for 1 correct. ft their line and their curve. (c) (i) 2 cao 2 M1 for change in y / change in x for 2 correct points (ii) (y =) 2x + 1 1ft Ft (y=) their (c)(i) x + intercept of their line in (b)(i)

This question in 0580/32 May/June 2012

9 (a) Complete the table of values for y = 8 + 3x – x2. For Examiner's Use x –3 –2 –1 0 1 2 3 4 5 6 y –10 8 10 10 –10 [3] (b) On the grid, draw the graph of y = 8 + 3x – x2 for –3 Y x Y 6 . y 12 10 8 6 4 2 x –3 –2 –1 0 1 2 3 4 5 6 –2 –4 –6 –8 –10 [4] (c) Write down the equation of the line of symmetry of the graph. Answer(c) [1] (d) (i) On the grid, draw the graph of y = 6 . [1] (ii) Use your graphs to solve the equation 8 + 3x – x2 = 6 . Answer(d)(ii) x = or x = [2]

11 marks

Mark scheme: 9 (a) y-values –2, 4, 8, 4, –2 3 B2 for 3 or 4 correct B1 for 2 correct (b) 10 correctly plotted points 3ft B2ft for 8 or 9 points B1ft for 6 or 7 points Smooth curve through 10 correct 1 Curve must pass above y = 10 points and correct shape. (c) x = 1.5 oe 1 (d) (i) Line y = 6 drawn 1 (ii) x = 3.5 to 3.7 1ft Ft their curve and their line drawn x = – 0.7 to – 0.5 1ft IGCSE – October/November 2012 0580 31

This question in 0580/31 Oct/Nov 2012

8 For 2 (a) The table shows some values of the function y = x O . Examiner's x Use x O8 O6 O5 O4 O2 O1 1 2 4 5 6 8 y O7 O4.7 O3.4 O2 7 O2 3.4 4.7 7 (i) Complete the table. [3] 8 (ii) On the grid on the opposite page, draw the graph of y = x O for x O8 Y x Y O1, 1 Y x Y 8 . [5] (iii) Write down the order of rotational symmetry of the graph. Answer(a)(iii) [1] 8 (iv) Use your graph to solve the equation x O = 0 . x Answer(a)(iv) x = or x = [2] 1 (b) (i) Write down the gradient of the line y = x + 1 . 2 Answer(b)(i) [1] 1 (ii) Complete the table below for the line y = x + 1 . 2 x O8 O4 0 4 8 y O3 3 [2] 1 (iii) On the grid, draw the line y = x + 1 for O8 Y x Y 8 . [1] 2 8 1 (c) Write down the co-ordinates of the points of intersection of y = x O and y = x + 1 . x 2 Answer(c) ( , ) and ( , ) [2] y For Examiner's 8 Use 7 6 5 4 3 2 1 x–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8

17 marks

Mark scheme: 2 (a) (i) 2 −7 2 1,1,1 (ii) 12 correctly plotted points 3ft P2ft for 10 or 11 correct. P1ft for 8 or 9 correct 2 smooth curves through 12 C1 correct points and correct shape Two separate branches not B1 crossing the y-axis (iii) 2 1 (iv) 2.7 to 3.0, 1 −3.0 to −2.7 1 IGCSE – October/November 2012 0580 32 (b) (i) 1 or 0.5 2 1 (ii) −1 1 5 2 B1 for 2 correct (iii) Correct ruled continuous line 1 drawn (c) (5.0 to 5.2, 3.5 to 3.7) 1ft Ft ± 0.1 from their intersections (−3.2 to –3.0, −0.7 to –0.5) 1ft

This question in 0580/32 Oct/Nov 2012

3 Mrs Ali sold her house for $600 000. For Examiner's Use 2 (a) She gives of the money to her son. 5 Work out how much her son receives. Answer(a)$ [1] (b) Mrs Ali gives $2400 to her grandchildren Elize, Sam and Juan in the ratio Elize : Sam : Juan = 8 : 3 : 5 . Calculate how much they each receive. Answer(b) Elize $ Sam $ Juan $ [3] (c) Mrs Ali invests $200 000 for 3 years at a rate of 4% per year compound interest. Calculate the total amount of money she will have at the end of the 3 years. Give your answer correct to the nearest dollar. Answer(c) $ [3] (d) Mrs Ali spends a total of $9000 on the following items. For Examiner's Use Amount spent ($) Angle in pie chart Holiday 4050 162° Television 90° Clothes 1800 72° Computer (i) Complete the table. [3] (ii) Complete the pie chart. Label each of your sectors. Holiday [2]

12 marks

Mark scheme: 3 (a) 240000 1 (b) 1200, 450, 750 3 SC2 for all three correct in wrong order seen SC1 for 2400 ÷ 16 implied by 150 (c) 224973 3 M2 224972.8 or 200000 × 1.043 or 224793.0(0) if M0 M1 200000 × 1.042 or 216320 SC1 for their answer correctly rounded to nearest dollar (d) (i) 2250 1,1,1 If first B0,B0 then SC1 for adding to 3150 900 36 (ii) 2 correct sectors 1 correct labels 1 Must only be 4 sectors in total

This question in 0580/33 Oct/Nov 2012

9 (a) (i) Complete the table of values for y = x2 + x . For Examiner′s Use x –3 –2 –1 0 1 2 3 y 6 0 0 6 [2] (ii) On the grid, draw the graph of y = x2 + x for –3 Ğ x Ğ 3 . y 14 13 12 11 10 9 8 7 6 5 4 3 2 1 x –3 –2 –1 0 1 2 3 –1 –2 [4] (iii) On the grid, draw the line y = 10. [1] (iv) Use both your graphs to solve x2 + x = 10 for –3 Ğ x Ğ 3 . Answer(a)(iv) x = … [1] 2 For (b) Another line, L, has the equation y = 3 x – 5 . Examiner′s Use (i) Write down the gradient of L. Answer(b)(i) … [1] (ii) Write down the equation of a straight line that is parallel to L. Answer(b)(ii) … [1] (c) y 5 K 4 3 2 1 x –2 –1 0 1 2 3 4 –1 –2 –3 –4 –5 –6 –7 Write the equation of the line, K, in the form y = mx + c . Answer(c) y = … [3] _____________________________________________________________________________________

13 marks

Mark scheme: 9 (a) (i) 2 and 2 1 all in the correct places 12 1 (ii) 7 points correctly plotted 3ft P2ft for 5 or 6 points correctly plotted P1ft for 3 or 4 points correctly plotted correct curve through the 7points 1 (iii) correct line 1 Must be ruled and continuous (iv) 2.6 – 2.8 1ft ft their curve and their line (b) (i) 2 1 3 2 (ii) y = x + c 1 c not –5 3 (c) [y =] 2x – 3 3 M2 for y = 2x + p rise or M1 for attempt at gradient i.e. run B1 for y = qx – 3 q≠0

This question in 0580/31 May/June 2013

3 (a) A shop has maps arranged in bookcases. For Examiner′s Use (i) The length of one wall in the shop is 7.35 m. Each bookcase is 120 cm wide. Work out the maximum number of bookcases that will fi t along this wall. Answer(a)(i) … [2] (ii) Each bookcase weighs 45 kg correct to the nearest 5 kg. Write down the upper bound for the weight of a bookcase. Answer(a)(ii) … kg [1] (b) During July and August the shop sells a total of 160 maps. Some of these maps are driving maps and the rest are walking maps. (i) Complete the table below. Driving maps Walking maps Total July 15 August 65 Total 40 160 [2] (ii) Write down the fraction of the total number of walking maps that are sold in July. Give your answer in its simplest form. Answer(b)(ii) … [2] (c) The shopkeeper buys each map for $5.50 . For Examiner′s He sells each map for $6.60 . Use (i) Calculate his percentage profi t. Answer(c)(i) … % [3] (ii) Each map has a price in dollars ($) and euros (€). The price is $6.60 or €3.52 . Work out the exchange rate for €1 . Answer(c)(ii) €1 = $ … [2] (d) The shop is open for 312 days each year. The shopkeeper pays 3 employees $47.66 each per day. The total annual wage bill for the three employees is given by 3 × 312 × 47.66 . (i) Rewrite this calculation so that each number is rounded to 1 signifi cant fi gure. 3 × … × … [1] (ii) Use your answer to part (d)(i) to work out an estimate for the total annual wage bill. Answer(d)(ii) $ … [1] _____________________________________________________________________________________

14 marks

Mark scheme: 3 (a) (i) 6 cao 2 M1 for 735/120 oe implied by 6.125 or SC1 for figs ‘61 … ’ (ii) 47.5 1 (b) (i) 55 ---- 70 2 M1 for 3 or 4 correct numbers ---- 25 90 120 ---- --- 3 15 3 (ii) cao 2 B1 for or seen 8 40 8 20 (c) (i) 3 B1 for 6.6 - 5.5 or better M1 for ‘their 1.1’ / 5.5 OR (an alternative method) M1 for 6.6/5.5 M1 for ‘their 1.2’ –1 oe 1.875 cao (ii) 2 M1 for 6.60/3.52, imp by 1.87 or 1.88 300, 50 (d) (i) 1 45000 (ii) 1 SC1 43200

This question in 0580/32 May/June 2013

7 (a) Complete the table of values for y = x2 – x + 2 . For Examiner′s Use x –3 –2 –1 0 1 2 3 4 y 8 2 4 [3] (b) On the grid, draw the graph of y = x2 – x + 2 for −3 Y x Ğ 4 . y 16 14 12 10 8 6 4 2 x –3 –2 –1 0 1 2 3 4 [4] (c) Write down the equation of the line of symmetry of the graph. For Examiner′s Use Answer(c) … [1] (d) (i) On the grid, draw the line y = 9 . [1] (ii) Solve the equation x2 – x + 2 = 9 . Answer(d)(ii) x = … or x = … [2] _____________________________________________________________________________________

11 marks

Mark scheme: 7 (a) 14, 4, 2, 8, 14 3 B2 for 4 correct B1 for 2 or 3 correct (b) 8 points correctly plotted P3FT P2FT for 6 or 7 points correctly plotted P1FT for 4 or 5 points correctly plotted Smooth and correct curve through all C1 correct points 1 (c) x = 0.5 or x = 1 2 (d) (i) y = 9 ruled 1 (ii) –2.15 to –2.25 1FT 3.15 to 3.25 1FT

This question in 0580/31 Oct/Nov 2013

5 Examiner′s5 (a) Complete the table of values for y = . x Use x –5 –4 –3 –2 –1 1 2 3 4 5 y –1.67 –2.5 –5 5 1.67 1.25 [2] 5 (b) On the grid, draw the graph of y = for –5 Y x Y –1 and 1 Y x Y 5. x y 6 5 4 3 2 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 [4] 5 (c) Use your graph to solve the equation = 4 . x Answer(c) x = … [1] (d) (i) On the grid, draw the line x = –3.5 . [1] (ii) On the grid, plot the point (5, –3) and label it P. [1] (iii) Draw the line that passes through P and is perpendicular to x = –3.5 . [1] _____________________________________________________________________________________

10 marks

Mark scheme: 5 (a) –1 –1.25 2.5 1 2 B1 for two correct (b) 10 correctly plotted points P3FT P2FT for 8 or 9 correctly plotted P1FT for 6 or 7 correctly plotted Two correct smooth curves through C1 all correct points and not across y-axis (c) 1.15 to 1.35 1FT (d) (i) Line x = –3.5 ruled 1 (ii) (5, –3) plotted 1 (iii) line y = –3 ruled 1FT IGCSE – October/November 2013 0580 32

This question in 0580/32 Oct/Nov 2013

86 (a) (i) Complete the table of values for y = , x ≠ 0 . x x –8 –4 –2 –1 1 2 4 8 y –2 2 [3] 8 (ii) On the grid, draw the graph of y = for –8 Ğ x Ğ –1 and 1 Ğ x Ğ 8 . x y 8 6 4 2 x –8 –6 –4 –2 0 2 4 6 8 –2 –4 –6 –8 [4] (iii) Write down the order of rotational symmetry of your graph. Answer(a)(iii) … [1] (b) (i) Complete this table of values for y = 1.5x + 3 . x –6 –4 –2 0 2 y –6 3 [2] (ii) On the grid, draw the graph of y = 1.5x + 3 . [1] 8 (c) Use your graphs to solve the equation = 1.5x + 3 . x Answer(c) x = … or x = … [2] (d) Write down the gradient of the graph of y = 1.5x + 3 . Answer(d) … [1] __________________________________________________________________________________________

14 marks

Mark scheme: 6 (a) (i) −1, −4, −8, 8, 4, 1. 3 1 for each symmetrical pair (ii) 8 points correctly plotted, within ½ square. 3FT B2FT for 6 or 7 correct Or B1 FT for 4 or 5 correct 2 smooth correct curves, not joined 1 (iii) 2 1 IGCSE – May/June 2014 0580 31 (b) (i) −3 0 6 2 B1 for two correct (ii) Correct ruled line 1 (c) 1.4 to 1.6 and −3.6 to −3.4 1FT,1FT FT from their graph ±0.1 (d) 1.5 1

This question in 0580/31 May/June 2014

1 (a) Here is a list of numbers. 2 4 5 8 9 12 Write down all the numbers from this list which are (i) odd, Answer(a)(i) … [1] (ii) square, Answer(a)(ii) … [1] (iii) cube, Answer(a)(iii) … [1] (iv) prime. Answer(a)(iv) … [1] (b) Write one of these symbols >, < or = to make each statement true. 22 π … 7 2 … 2 ^ h2 1 … 2 1 + 1 (–1)2 … –1 [2] (c) Put one pair of brackets in each statement to make it true. (i) 16 + 8 ÷ 4 – 2 = 4 [1] (ii) 16 + 8 ÷ 4 – 2 = 20 [1] (d) (i) Write 84 as a product of its prime factors. Answer(d)(i) … [2] (ii) Find the highest common factor of 84 and 24. Answer(d)(ii) … [2] (iii) Find the lowest common multiple of 84 and 24. Answer(d)(iii) … [2] (e) Here are the fi rst four terms of a sequence. 3 7 11 15 (i) Write down the next term in this sequence. Answer(e)(i) … [1] (ii) Explain how you found your answer. Answer(e)(ii) … [1] (iii) Write down an expression for the n th term of this sequence. Answer(e)(iii) … [2] (iv) Explain why 125 is not in this sequence. Answer(e)(iv) … … [1] __________________________________________________________________________________________

19 marks

Mark scheme: Qu Answers Mark Part Answers 1 (a) (i) 5 and 9 cao 1 (ii) 4 and 9 cao 1 (iii) 8 cao 1 (iv) 2 and 5 cao 1 (b) < = < > 2 B1 for 3 correct (c) (i) (16 + 8) ÷ 4 ─ 2 = 4 1 (ii) 16 + 8 ÷ (4 ─ 2) = 20 1 (d) (i) 2 × 2 × 3 × 7 2 B1 for 2, 3, 7 or 2, 2, 3, 7, or 1 × 2 × 2 × 3 × 7 (ii) 12 2 B1 for 2, 3, 4 or 6 or 2 × 2 × 3 or 22 × 3 or 4 × 3 or 2 × 6 seen as ans (iii) 168 2 B1 for any other multiple of 168 or 2 × 2 × 2 × 3 × 7 oe (e) (i) 19 1 any other terms must be correct (ii) +4 oe 1 e.g. add 4 (iii) 4n – 1 oe final answer 2 B1 for 4n + k , qn – 1 q ≠ 0 (iv) accept any correct statement 1 IGCSE – May/June 2014 0580 32

This question in 0580/32 May/June 2014

20 .6 (a) (i) Complete the table of values for y = x x –8 –5 –4 –2.5 2.5 4 5 8 y –2.5 –4 8 4 [2] 20 (ii) On the grid, draw the graph of y = for –8 Y x Y –2.5 and 2.5 Y x Y 8. x y 9 8 7 6 5 4 3 2 1 x –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 –9 [4] 20 (iii) By drawing a suitable line on your graph solve the equation = 6. x Answer(a)(iii) x = … [2] (b) x –8 0 8 y 1 (i) Complete the table for y = x – 1. [2] 2 1 (ii) On the grid, draw the graph of y = x – 1 for –8 Y x Y 8. [1] 2 1 (iii) Write down the gradient of y = x – 1. 2 Answer(b)(iii) … [1] 20 1 (c) Write down the values of x at the points of intersection of the graphs of y = and y = x – 1. x 2 Answer(c) x = … and x = … [2] __________________________________________________________________________________________

14 marks

Mark scheme: 6 (a) (i) –5 –8 5 2.5 2 B1 for 3 correct (ii) 8 points correctly plotted B3FT B2FT for 6 or 7 correct points Correct curve 1 B1FT for 4 or 5 correct points (iii) Ruled line y = 6 drawn 1 Independent marks 3.1 to 3.6 1 (b) (i) –5 –1 3 2 B1 for 2 correct (ii) Ruled correct line 1 (iii) 1 1 oe 2 (c) 7.2 to 7.6 1FT –5.2 to –5.6 1FT

This question in 0580/32 Oct/Nov 2014

1 (a) Parminder sells dresses. The pie charts show information about the colour of dresses she sold. She sold 250 dresses in 2013 and 280 dresses in 2014. Sales in 2013 Sales in 2014 Pink 12% Blue Blue Pink 30% 32% 35% Violet 40% Silver Silver 15% Violet 16% 20% (i) Write down the most popular colour of dress she sold in 2013. Answer(a)(i) … [1] (ii) Write down the fraction of dresses sold in 2014 that were either pink or silver. Answer(a)(ii) … [1] (iii) Write down the ratio of Blue : Pink dresses sold in 2013. Give your answer in its simplest form. Answer(a)(iii) … : … [2] (iv) Work out how many more pink dresses were sold in 2014 than in 2013. Answer(a)(iv) … [3] (v) Complete the table by writing True or False beside each statement. The first answer has been completed for you. Statement True or False 40% of the dresses sold in 2013 were violet. True Blue was the second most popular colour in both 2013 and 2014. One third of the dresses sold in 2014 were blue. Violet was more popular than silver in both 2013 and 2014. [2] (vi) From 2013 to 2014 the number of silver dresses sold has increased but the percentage sold has decreased. Give a reason why the percentage sold has decreased. You do not need to do any calculations. Answer(a)(vi) … … [1] (b) The table shows the number of metres of silk needed to make a dress. Height of customer to the nearest 10 cm Dress length 160 cm 170 cm 180 cm 190 cm Short 4.0 4.3 4.6 4.9 Medium 4.8 5.0 5.2 5.4 Long 5.5 5.8 6.2 6.6 Silk costs $12.50 per metre. It takes 6 hours to make one dress. The dressmaker charges $9.25 per hour. A customer orders a dress for each of her two daughters. She orders a long dress for one daughter who is 160 cm tall. She orders a short dress for her other daughter who is 176 cm tall. Calculate the total cost of the two dresses. Answer(b) $ … [4] __________________________________________________________________________________________

14 marks

Mark scheme: 1 (a) (i) Violet 1 50 (ii) oe 1 100 (iii) 8:3 2 M1 for 32:12 or better or 80:30 or better SC1 for 3:8 or 6:7 (iv) 68 3 M2 for 0.35 × 280 – 0.12 × 250 or better or M1 for 0.35 × 280 or 0.12 × 250 seen (v) True, False, True 2 B1 for 2 correct (vi) [The] percentage is [smaller but it is] 1 of a larger [total] number [of dresses] (b) 237.25 4 B1 for 5.5 and 4.6 seen M1FT for their 5.5×12.50 + their 4.6×12.50 or better M1 for 6 × 2 × 9.25 or better OR M1FT for their 5.5 × 12.50 + 6 × 9.25 M1FT for their 4.6 × 12.50 + 6 × 9.25

This question in 0580/32 Feb/March 2015

67 (a) The table shows some values of y = . x x –5 –4 –3 –2 –1 1 2 3 4 5 y –1.2 –1.5 6 2 1.5 1.2 (i) Complete the table. [2] 6 (ii) On the grid, draw the graph of y = for –5  x  –1 and 1  x  5. x y 6 5 4 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 –4 –5 –6 [4] (iii) On the same grid, draw the line y = 4. [1] 6 (iv) Find the co-ordinates of the point where the line y = 4 crosses the graph of y = . x Answer(a)(iv) ( … , … ) [1] (b) y 5 4 3 2 1 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –1 –2 –3 –4 –5 (i) On this grid, plot the point A (–1, –3). [1] (ii) Draw a line with gradient 2 through point A. [1] (iii) Write down the equation of your line in the form y = mx + c. Answer(b)(iii) y = … [2] __________________________________________________________________________________________

12 marks

Mark scheme: 7 (a) (i) –2, –3, –6, 3 2 B1 for 2 or 3 correct (ii) Correct curves 4 B3FT for 9 or 10 correctly plotted points or B2FT for 7 or 8 correctly plotted points or B1FT for 5 or 6 correctly plotted points (iii) Ruled line y = 4 1 (iv) (1.4 to 1.6, 4) 1 SC1 for (4, 1.4 to 1.6) from line x = 4 drawn (b) (i) (–1, –3) plotted 1 (ii) Correct ruled line 1FT FT line with gradient 2 through their A (iii) 2x – 1 2FT FT 2x + their y-intercept for 2 marks B1 for 2x + k or mx – 1 (m ≠ 0) or mx + their y-intercept (m ≠ 0)

This question in 0580/31 Oct/Nov 2015

1 (a) Write down in figures the number twenty one million. Answer(a) … [1] (b) Write down the four factors of 21. Answer(b) … , … , … , … [2] (c) Write 21% as a fraction. Answer(c) … [1] (d) Put brackets in this calculation to make it correct. 210 + 21 ÷ 2.1 + 21 = 10 [1] (e) Write down the first two prime numbers after 21. Answer(e) … and … [2] (f) Fill in the missing number. 21 210 = 210 ff [1] (g) Calculate 21 2 - 21 . Answer(g) … [1] (h) Work out ( 21 ) 2. Answer(h) … [1] (i) Write down the value of 210. Answer(i) … [1] (j) Write 0.0021 in standard form. Answer(j) … [1] (k) Write down the lowest common multiple (LCM) of 21 and 15. Answer(k) … [2]

14 marks

Mark scheme: Question Answer Mark Part marks 1 (a) 21 000 000 1 (b) 1, 3, 7, 21 2 M1 for 3 correct and one incorrect (or missing) or for 4 correct and one extra 21 (c) 1 100 (d) (210 + 21) ÷ (2.1+ 21) 1 (e) 23 1 If zero scored SC1 for any two other prime 29 1 numbers greater than 21 (f) 2100 1 (g) 436 or 436.4... 1 (h) 21 1 (i) 1 1 (j) 1.2 × 10 − 3 1 (k) 105 2 M1 for [1 ×] 3 × 5 × 7 or 105k or for [1], 3, 7 and [1], 3, 5 seen or for [1], 3, 5, 7 (maybe in a table) or for listing multiples of 15 and 21 to at least 105 with not more than one error

This question in 0580/32 Oct/Nov 2015

9 y l 8 7 6 5 4 3 2 1 x –4 –3 –2 –1 0 1 2 3 4 –1 –2 –3 –4 –5 –6 –7 –8 (a) Write down the equation of the line l in the form y = mx + c. Answer(a) y = … [3] 2 (b) Complete the table of values for y = . x x −4 −3 −2 −1 −0.5 −0.25 0.25 0.5 1 2 3 4 y −0.7 −4 4 0.7 [3] 2 (c) On the grid, draw the graph of y = for –4  x  –0.25 and 0.25  x  4. [4] x

10 marks

Mark scheme: 9 (a) [ y = ] 2 x + 4 3 B2 for 2 x + c or kx + 4 k ≠ 0 or 2 k rise M1 for gradient = ± or attempt at k run using a triangle or co-ordinates allowing one slip (b) –0.5, –1, –2, –8, 8, 2, 1, 0.5 3 B2 for any 6 or 7 correct or B1 for any 4 or 5 correct (c) Correct curve 4 B3FT for 11 or 12 points correctly plotted B2FT for 9 or 10 points correctly plotted B1FT for 7 or 8 points correctly plotted

This question in 0580/32 Oct/Nov 2015

2 Kylie, Rio and Choi buy a horse for $21 600. (a) They pay for the horse in the ratio Kylie : Rio : Choi = 2 : 3 : 4. Calculate the amount that they each pay. Answer(a) Kylie $ … Rio $ … Choi $ … [3] (b) It costs $14 000 to keep the horse for one year. (i) Food costs 30% of the $14 000. Calculate the cost of the food. Answer(b)(i) $ … [2] (ii) Stable fees are $8000. Write this as a fraction of the $14 000. Give your answer in its lowest terms. Answer(b)(ii) … [2] (iii) It costs $600 for vets’ fees and the rest of the $14 000 is spent on equipment. Work out how much is spent on equipment. Answer(b)(iii) $ … [2] (c) They later sell the horse for $17 280. Calculate the percentage loss on the $21 600 they paid for the horse. Answer(c) … % [3] (d) Rio invests $5500 for 3 years at a rate of 2.5% per year compound interest. Calculate how much interest he receives after the 3 years. Answer(d) $ … [3] __________________________________________________________________________________________

15 marks

Mark scheme: 2 (a) 4800 M2 for 1 correct value in correct place 7200 3 M1 for 21600 ÷ (2 + 3 + 4) or better 9600 If zero scored SC1 for all correct values in incorrect order (b) (i) 4200 2 M1 for 0.3 × 14000 oe 4 8000 (ii) cao 2 B1 for correct fraction other than 7 14000 (iii) 1200 2 FT M1FT for (14000 – their (b)(i) – 8000 – 600)

This question in 0580/33 Oct/Nov 2015

7 (a) Goat food is sold in 20 kg bags. One goat eats 25 of a bag of food each week. (i) Work out how many kilograms of food this goat eats in one week. Answer(a)(i) … kg [1] (ii) How many bags of food will the goat eat in 15 weeks? Answer(a)(ii) … [2] (b) This scale drawing shows a field. The scale is 1 centimetre represents 2 metres. A B C (i) Find the actual length of AB. Answer(b)(i) … m [1] (ii) There are two goats in the field. One goat is on a 14 m lead fastened at point B. The other goat is on a 12 m lead fastened at point C. There is a water trough positioned so that both goats can reach it. Shade the area where the trough can be positioned. [3] (iii) The trough holds 6.5 litres of water. How many millilitres is this? Answer(b)(iii) … ml [1] __________________________________________________________________________________________

8 marks

Mark scheme: 7 (a) (i) 8 1 their 8× 15 2 (ii) 6 2FT M1 for or × 15 oe 20 5 (b) (i) 30 or 29.6 to 30.4 1 (ii) Arc 7 cm from B 1 Arcs must be continuous lines and fit for purpose (intersect twice) Arc 6 cm from C 1 If 0, 0 scored then SC1 for two correct arcs that intersect once Correct area shaded 1 dep Dependent on an attempt at 2 arcs (iii) 6500 1

This question in 0580/33 Oct/Nov 2015

9 (a) Complete the table of values for y = x 2 - 3x - 1. x –2 –1 0 1 2 3 4 5 y 9 –1 [3] (b) On the grid, draw the graph of y = x 2 - 3x - 1 for – 2  x  5. y 9 8 7 6 5 4 3 2 1 x –2 –1 0 1 2 3 4 5 –1 –2 –3 –4 [4] (c) Write down the co-ordinates of the lowest point of the graph. ( … , … ) [1] (d) (i) On the grid, draw the line of symmetry of the graph. [1] (ii) Write down the equation of the line of symmetry of the graph. … [1]

10 marks

Mark scheme: 9 (a) (9), 3, (–1), –3, –3, –1, 3, 9 3 B2 for any 5 correct or B1 for any 3 or 4 correct (b) completely correct curve 4 B3FT for 7 or 8 correct plots B2FT for 5 or 6 correct plots B1FT for 3 or 4 correct plots (c) (1.5, k) where –3.5 ⩽ k < –3 1 (d) (i) ruled line x = 1.5 drawn 1 (ii) x = 1.5 oe 1

This question in 0580/32 Feb/March 2016

9 (a) Complete the table of values for y = 8 + 7x − x2. x 0 1 2 3 4 5 6 7 8 y 8 18 18 8 [3] (b) On the grid, draw the graph of y = 8 + 7x − x2 for 0 G x G 8. y 22 20 18 16 14 12 10 8 6 4 2 x 0 1 2 3 4 5 6 7 8 [4] (c) Write down the co-ordinates of the highest point of the curve. ( … , … ) [1] (d) (i) On the grid, draw the line y = 16. [1] (ii) Use your line to solve the equation 8 + 7x − x2 = 16. x = … or x = … [2]

11 marks

Mark scheme: 9 (a) … 14 … 20 20 … 14 … 0 3 B2 for 3 or 4 correct B1 for 2 correct (b) Completely correct curve 4 B3FT for 8 or 9 points correctly plotted or B2FT for 6 or 7 points correctly plotted or B1FT for 4 or 5 points correctly plotted (c) (3.5, h) 1 20 < h ⩽ 20.4 (d) (i) Correct ruled line 1 (ii) 1.4 5.6 1, 1FT FT their graph and line

This question in 0580/31 May/June 2016

16 5 (a) (i) Complete the table of values for y = , x ! 0 . x x −16 −8 −4 −2 −1 1 2 4 8 16 y −1 −2 −8 16 4 2 [2] 16 (ii) On the grid, draw the graph of y = for - 16 G x G - 1 and 1 G x G 16 . x y 16 14 12 10 8 6 4 2 x 0 –16 –14 –12 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 16 –2 –4 –6 –8 –10 –12 –14 –16 [4] (b) Write down the order of rotational symmetry of your graph. … [1] (c) One line of symmetry crosses the graph twice. (i) Draw this line of symmetry on the grid. [1] (ii) Write down the equation of this line of symmetry. … [1] 16 (d) By drawing a suitable line on the grid, solve the equation = 7 . x x = … [2]

11 marks

Mark scheme: 5 (a) (i) −4 −16 8 1 2 B1 for 3 correct (ii) Completely correct curve 4 B3FT for 9 or 10 correctly plotted B2FT for 7 or 8 correctly plotted B1FT for 5 or 6 correctly plotted (b) 2 1 (c) (i) Ruled line y = x drawn 1 Must at least intersect the graph in two places (ii) y = x oe 1 (d) Continuous ruled line y = 7 1 Must intersect the graph drawn 2.1 to 2.5 1FT

This question in 0580/33 May/June 2016

3 (a) Tariq wants to buy some orange juice. He sees these offers in a shop. Offer A Offer B Offer C 1-litre carton 2-litre carton Pack of 4 1-litre cartons $0.65 $1.25 $2.56 Work out the lowest amount Tariq could pay for 5 litres of orange juice. Show how you decide. Tariq buys … cartons. The lowest amount is $ … [3] (b) Bottle P contains 1.5 litres of lemonade. 1 Bottle Q contains 3 more lemonade than bottle P. Work out how much lemonade is in bottle Q. … litres [2] (c) Tariq makes a fruit drink. He mixes 500 ml of orange juice, 200 ml of pineapple juice and 1 litre of lemonade. (i) Write the ratio orange juice : pineapple juice : lemonade in its simplest form. … : … : … [2] (ii) Tariq makes more of this fruit drink. Work out the total amount of fruit drink he makes when he uses 2 litres of orange juice. Give your answer in litres. … litres [3] (d) Tariq pours 300 cm3 of fruit drink into a glass. The glass is in the shape of a cylinder with radius 3.5 cm. The height of the drink in the glass is h cm. NOT TO SCALE h cm 3.5 cm Work out the value of h. h = … [2] (e) The capacity of a jug is 750 ml correct to the nearest 10 ml. Write down the upper and lower bounds of the capacity of the jug. Upper bound = … ml Lower bound = … ml [2]

14 marks

Mark scheme: 3 (a) 2 B and 1 A selected, with 2 M1 for one correct cost for 5 litres at least one other or B1 for 0.625 or 0.64 combination and its value seen or 2 B and 1 A selected, with 1 Independent 0.625 and 0.64 seen 3.15 selected 1 (b) 2 2 M1 for [1.5 + ] × 1.5 oe soi by 0.5 3 (c) (i) 5 : 2 : 10 2 M1 for 500 : 200 : 1000 oe (ii) 6.8 3 B2 for answer 6800 or 2 M2 for × 17 oe or for 4 × (0.5 + 0.2 + 1) 5 or for 4 × (500 + 200 + 1000) oe 5 2000 or M1 for soi or for oe soi by 4 17 500 (d) 7.79 or 7.80 or 7.794 to 2 M1 for 300 = π × 3.52 × h or better implied by 7.795 300 (38.4to38.5) (e) 755 2 B1 for one correct or both values reversed 745

This question in 0580/32 Oct/Nov 2016

4 (a) Complete the table of values for y = x 2 - 5x + 3 . x –1 0 1 2 3 4 5 y 3 –1 –1 3 [2] (b) On the grid, draw the graph of y = x 2 - 5x + 3 for -1 G x G 5 . y 10 8 6 4 2 x –1 0 1 2 3 4 5 –2 –4 [4] (c) Write down the equation of the line of symmetry of the graph of y = x 2 - 5x + 3 . … [1] (d) Write down the co-ordinates of the point where the line y = 4 - x (i) crosses the x-axis, ( … , … ) [1] (ii) crosses the y-axis. ( … , … ) [1] (e) On the grid, draw the line y = 4 - x . [1] (f) Write down the co-ordinates of the points of intersection of the graph of y = x 2 - 5x + 3 and the line y = 4 - x . ( … , … ) ( … , … ) [2]

12 marks

Mark scheme: 4 (a) 9, –3, –3 2 B1 for 9 or –3 and –3 (b) Correct curve 4 B3FT for 6 or 7 correctly plotted points or B2FT for 4 or 5 correctly plotted points or B1FT for 2 or 3 correctly plotted points (c) x = 2.5 1 (d) (i) (4, 0) 1 (ii) (0, 4) 1

This question in 0580/32 Oct/Nov 2016

9 (a) Here is a list of ingredients to make 18 chocolate chip biscuits. butter 130 g sugar 60 g flour 180 g chocolate chips 30 g Work out how much of each ingredient you need to make 45 biscuits. butter … g sugar … g flour … g chocolate chips … g [3] (b) In a recipe for bread, 58 of the mass of bread mixture is flour. Paul uses 395 g of flour. (i) What mass of bread mixture does he make? … g [2] (ii) Write your answer to part(b)(i) in kilograms. … kg [1]

6 marks

Mark scheme: 9 (a) 325 3 B2 for 3 correct 150 or B1 for 1 or 2 correct 450 or M1 for 45 ÷ 18 soi by 2.5 75 (b) (i) 632 2 M1 for (395 × 8) ÷ 5 oe (ii) 0.632 1FT FT their (b)(i) ÷ 1000

This question in 0580/33 Oct/Nov 2016

5 A train departs from Green Hill, stops at Deep Valley for 5 minutes and then goes on to Clear Lake. The train timetable shows the times. Station Arrive Depart Green Hill - 10 30 Deep Valley 10 45 10 50 Clear Lake 11 14 - (a) (i) Complete this statement. The journey from Green Hill to Deep Valley takes … minutes. [1] (ii) Write your answer to part (a)(i) as a fraction of an hour. … [1] (b) The train travels the 18 km between Green Hill and Deep Valley at a constant speed. Calculate the speed, in km/h, for the train on this part of the journey. … km/h [1] (c) The train travels at a constant speed of 85 km/h between Deep Valley and Clear Lake. Work out the distance between Deep Valley and Clear Lake. … km [2] (d) Work out the total distance between Green Hill and Clear Lake. … km [1] (e) Complete the travel graph to show the whole journey from Green Hill to Clear Lake. 60 56 52 48 44 40 36 32 Distance (km) 28 24 20 Deep Valley 16 12 8 4 Green Hill 0 10 30 10 40 10 50 11 00 11 10 11 20 Time [3]

9 marks

Mark scheme: 5 (a) (i) 15 1 1 (ii) oe 1FT FT their (a)(i) / 60 4 (b) 72 1FT FT 18 / their (a)(ii) or 18 / their (a)(i) × 60 24 (c) 34 2 M1 for [ 85] × or 85 × 24 [ ÷60 ] or 60 85 ÷ 60 × [ 24 ] (d) 52 1FT FT is 18 + their 34 (e) ruled line from (10 30, 0) to 1 (10 45, 18) ruled line from (10 45, 18) to 1 (10 50, 18) ruled line from (10 50, 18) to 1FT FT (10 50, 18) to (11 14, their 52) (11 14, 52) 6

This question in 0580/32 Feb/March 2017

89 (a) Complete the table of values for y = . x x –8 –6 –4 –2 –1 1 2 4 6 8 y –1 –1.3 –8 2 1.3 1 [2] 8 (b) On the grid, draw the graph of y = for - 8 G x G - 1 and 1 G x G 8 . x y 8 7 6 5 4 3 2 1 x –8 –7–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 –1 –2 –3 –4 –5 –6 –7 –8 [4] 8 (c) The graph of y = has two lines of symmetry. x Write down the equation of each of these lines. … and … [2] 8 (d) Mark a point, P, on the graph of y = where the x and y co-ordinates are equal. [1] x

9 marks

Mark scheme: 9 (a) −2, −4, 8, 4 2 B1 for any 2 correct (b) completely correct curve 4 B3FT for 9 or 10 correct plots B2FT for 7 or 8 correct plots B1FT for 5 or 6 correct plots (c) y = x , y = − x oe 1,1 (d) point at (2.8, 2.8) or ( −2.8, − 2.8) 1FT FT a point on their curve lying on y = x

This question in 0580/32 Feb/March 2017

5 (a) Complete the table of values for y = x 2 + 2x - 1. x -5 -4 -3 -2 -1 0 1 2 3 y 14 2 -1 -1 2 [3] (b) On the grid, draw the graph of y = x 2 + 2x - 1 for -5 G x G 3 . y 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 x –5–5 –4–4 –3–3 –2–2 –1–1 00 11 22 33 –1 –2 –3 –4 (c) (i) On the grid, draw the line of symmetry. [1] (ii) Write down the equation of the line of symmetry. … [1] (d) (i) On the grid, plot the points (- 5 , 7) and (0, - 3) and join them with a straight line, L. [2] (ii) Write down the x co-ordinate of each point where the line L crosses the graph of y = x 2 + 2x - 1. x = … and x = … [2] (iii) Work out the gradient of the line L. … [2]

15 marks

Mark scheme: 5(a) 7 –2 7 14 3 B2 for 3 correct B1 for 2 correct 5(b) Correct smooth curve 4 B3FT for 8 or 9 correct plots or B2FT for 6 or 7 correct plots or B1FT for 4 or 5 correct plots 5(c)(i) Ruled line, x = –1, drawn 1 5(c)(ii) x = –1 oe 1 5(d)(i) Ruled line L drawn, joining 2 B1 for one of the points correct and line drawn, or (–5, 7) and (0, −3) both points correct and no or wrong line. 5(d)(ii) −3.3 to −3.5, −0.5 to −0.7 2FT B1FT for one correct. 5(d)(iii) −2 2 Rise y 2 − y1 M1FT for their from part (d)(i) or their Run x2 − x1 If zero scored, SC1 for answer 2

This question in 0580/31 May/June 2017

158 (a) Complete the table for y = . x x -5 -4 -3 -2 -1 1 2 3 4 5 y -3.75 -15 15 5 [3] 15 (b) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 15 10 5 x –5 –4 –3 –2 –1 0 1 2 3 4 5 –5 –10 –15 [4] 15 (c) Use your graph to solve the equation = 8 . x x = … [1]

8 marks

Mark scheme: 8(a) –3, –5, –7.5, 7.5, 3.75, 3 3 B2 for 4 or 5 correct B1 for 2 or 3 correct 8(b) Correct curve drawn 4 B3FT for 9 or 10 points correctly plotted or B2FT for 7 or 8 points correctly plotted or B1FT for 5 or 6 points correctly plotted 8(c) 1.8 ⩽ x < 2 1 If zero scored, then FT their graph

This question in 0580/32 May/June 2017

1 (a) Martha makes hats. Each week she makes 160 hats. (i) Work out how many hats she makes in 5 weeks. … [1] (ii) The hats are made in the ratio small : medium : large = 2 : 5 : 3. Work out how many of the 160 hats are large. … [2] (iii) She sells 3 of the 160 hats. 8 Work out how many hats she sells. … [1] (b) Nina sells T-shirts. The prices are shown in the table. Type Plain Striped Logo Price $7.50 $9.50 $10.50 (i) Sam buys 3 plain T-shirts and 2 logo T-shirts. Work out how much she pays altogether. $ … [2] (ii) One day, Nina reduces all prices by 20%. Work out the new price of a striped T-shirt. $ … [2] (c) Nina sold 300 T-shirts in September. She wants to show how many of each type she sold using a pie chart. Type Number sold Pie chart sector angle Plain 100 120° Striped 85 Logo 115 (i) Complete the table. [2] (ii) Complete the pie chart. [2] (d) Nina paid $22.50 for a dress. She sold the dress for $31.50 . Work out her percentage profit. … % [3]

15 marks

Mark scheme: Question Answer Marks Partial marks 1(a)(i) 800 1 1(a)(ii) 48 2 160 M1 for [ × 3] 2 + 5 + 3 1(a)(iii) 60 1 1(b)(i) 43.5[0] 2 M1 for 3 × 7.5[0] + 2 × 10.5[0] 1(b)(ii) 7.6[0] 2  20  M1 for 9.5  1 −  oe  100  1(c)(i) 102 2 85 115 M1 for × 360 or × 360 or 138 300 300 120 120 × 85 or × 115 oe 100 100 1(c)(ii) 3 correct sectors 2FT FT if their angles add to 240° B1FT for one correct sector 1(d) 40 3 31.50 − 22.50 M2 for × 100 or 22.50  31.50   − 1  × 100 oe  22.50  31.50 − 22.50 or M1 for or 22.50 31.50 31.50 − 1 or × 100 oe 22.50 22.50

This question in 0580/33 Oct/Nov 2017

2 (a) Fill in the missing number in each calculation. (i) 6 + 2 # … = 24 [1] (ii) (10 – … ) ÷ 3 = 2 [1] (b) Find the value of (i) .196, … [1] (ii) 163. … [1] 7. 82 - 4. 15 (c) Work out . 5.25 # 16. 4 Give your answer correct to 2 significant figures. … [2] 1 2 (d) V = a h 3 Calculate V when a = 4.5 and h = 9.6 . V = … [2] (e) Put a ring around the irrational number in the list below. 2 5 4 5 - 36 1 [1] 3 7 5 (f) Written as a product of its prime factors, T = 22 # 3 # 52 . (i) Work out the value of T. T = … [1] (ii) Write 80 as a product of its prime factors. … [2] (iii) Find the highest common factor (HCF) of T and 80. … [2]

14 marks

Mark scheme: 2(a)(i) 9 1 2(a)(ii) 4 1 2(b)(i) 1.4 1 2(b)(ii) 4096 1 2(c) [0].043 cao 2 367 M1 for 0.0426… or 8610 2(d) 64.8 2 1 2 324 M1 for × 4.5 × 9.6 or 3 5 2(e) 5 indicated 1 2(f)(i) 300 1 2(f)(ii) 24 × 5 or 2 × 2 × 2 × 2 × 5 2 M1 for 2, 2, 2, 2, 5 or 24,5 or 1 × 2 × 2 × 2 × 2 × 5 or 1 × 24 × 5 2(f)(iii) 20 2 B1 for 2 or 4 or 5 or 10 as answer or 22 × 5 as answer

This question in 0580/33 Oct/Nov 2017

127 (a) (i) Complete the table of values for y = . x x –6 –4 –2 –1 1 2 4 6 y –2 –12 12 2 [2] 12 (ii) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 12 10 8 6 4 2 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –2 –4 –6 –8 –10 –12 [4] (iii) On the grid, draw the line y =- 5 . [1] 12 (iv) Use your graph to solve the equation =- 5 . x x = … [1] (b) Line L is drawn on the grid. y 5 4 L 3 2 1 x 0 –4 –3 –2 –1 1 2 3 4 5 –1 (i) Find the gradient of line L. … [2] (ii) Find the equation of line L in the form y = mx + c. y = … [1] (iii) Line M is parallel to line L. Line M passes through the point (0, 3). Write down the equation of line M. y = … [2]

13 marks

Mark scheme: 7(a)(i) –3 –6 6 3 2 B1 for 2 or 3 values correct 7(a)(ii) Correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points 7(a)(iii) Ruled line y = –5 1 7(a)(iv) –2.5 to –2.3 1FT FT intersection of their line with their curve 7(b)(i) –0.5 oe 2 rise M1 for run 7(b)(ii) y = –0.5x + 2 oe 1FT FT their gradient 7(b)(iii) y = –0.5x + 3 oe 2FT B1FT for y = –0.5x + k oe, k ≠ 2 or B1 for y = mx + 3 oe, m ≠ –0.5 or 0

This question in 0580/33 Oct/Nov 2017

2 (a) Write down (i) the number twenty seven million, three hundred and sixty thousand and forty five in figures, … [1] (ii) the six factors of 20, … , … , … , … , … , … [2] 7 (iii) a fraction that is equivalent to , 9 … [1] (iv) a prime number between 30 and 40. … [1] (b) For each statement, insert one pair of brackets to make it correct. (i) 17 - 3 # 5 - 3 = 11 [1] (ii) 3 + 2 2 - 4 = 21 [1] (c) Find 3 4913 . … [1]

8 marks

Mark scheme: 2(a)(i) 27 360 045 1 2(a)(ii) 1, 2, 4, 5, 10, 20 2 B1 for 4 or 5 correct factors 2(a)(iii) 7 k 1 where k ≠ 1 9 k 2(a)(iv) 31 or 37 1 2(b)(i) 17 – 3 × (5 – 3) = 11 1 2(b)(ii) (3 + 2)2 – 4 = 21 1 2(c) 17 1

This question in 0580/31 May/June 2018

4 (a) Complete the table of values for y = 5x − x2. x −1 0 1 2 3 4 5 6 y 0 6 6 −6 [2] (b) On the grid, draw the graph of y = 5x − x2 for - 1 G x G 6. y 8 7 6 5 4 3 2 1 x –1 0 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 –7 –8 [4] (c) Write down the equation of the line of symmetry of the graph. … [1] (d) (i) Complete the table of values for y = 1.5x − 2. x 0 2 5 y [2] (ii) On the grid, draw the graph of y = 1.5x − 2 for - 1 G x G 6. [2] (iii) Use your graphs to write down the solutions to the equation 1.5x − 2 = 5x − x2. x = … or x = … [2]

13 marks

Mark scheme: 4(a) −6 4 4 0 2 B1 for 2 or 3 correct 4(b) Correct smooth curve 4 B3FT for 7 or 8 correct plots or B2FT for 5 or 6 correct plots or B1FT for 3 or 4 correct plots 4(c) x = 2.5 cao 1 4(d)(i) −2 1 5.5 2 B1 for 2 correct 4(d)(ii) Correct continuous ruled line from 2 B1FT for 2 or 3 correct plots x = −1 to x = 6 4(d)(iii) [x =] −0.6 to −0.4 and 3.9 to 4.1 2 B1FT for each

This question in 0580/32 May/June 2018

66 (a) Complete the table of values for y = , x =Y 0 . x x - 6 - 4 - 3 - 2 - 1 1 2 3 4 6 y - .15 - 3 3 1.5 [3] 6 (b) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 6 5 4 3 2 1 x – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 – 1 – 2 – 3 – 4 – 5 – 6 [4] (c) On the grid, draw the line y =- 5 . [1] 6 (d) Use your graph to solve the equation =- 5 . x x = … [1]

9 marks

Mark scheme: 6(a) –1 … –2 … –6 … 6 … 2 … 1 3 B2 for 4 or 5 correct or B1 for 2 or 3 correct 6(b) correct smooth curves 4 B3FT for 9 or 10 points plotted correctly B2FT for 7 or 8 points plotted correctly B1FT for 5 or 6 points plotted correctly FT their table 6(c) correct continuous ruled line 1 6(d) –1.2 oe 1 or FT their line and their graph

This question in 0580/33 May/June 2018

2 (a) Write down all the factors of 18. … [2] (b) Write down a prime number between 40 and 50. … [1] 7. 85 . (c) Calculate 1.09 + 6.21 - 4.37 Give your answer correct to 1 decimal place. … [2] (d) Find the value of (i) .2 89, … [1] (ii) 143, … [1] (iii) 4–2. … [1] (e) (i) 126 = 2 # 32 # k Find the value of k. k = … [1] (ii) Write 90 as the product of its prime factors. … [2] (iii) Find the lowest common multiple (LCM) of 90 and 126. … [2]

13 marks

Mark scheme: 2(a) 1, 2, 3, 6, 9, 18 2 B1 for four or more correct and no extras or six correct and one extra 2(b) 41 or 43 or 47 1 2(c) 5.4 2 B1 for 5.35[6…] or 5.36 2(d)(i) 1.7 1 2(d)(ii) 2744 1 2(d)(iii) 1 1 0.0625 or 16 2(e)(i) 7 1 2(e)(ii) 2 × 32 × 5 or 2 × 3 × 3 × 5 2 M1 for a complete factor tree or 2, 3, 3, 5 clearly identified as factors or B1 for a correct product that equals 90 2(e)(iii) 630 2 B1 for 630k, where k ⩾ 2 or for list of multiples of 90 and 126 to at least 630

This question in 0580/31 Oct/Nov 2018

3 (a) The table gives some information about the numbers of visitors at a leisure centre one day. Adult Child Total Male 144 240 Female 129 260 Total 225 275 500 (i) Complete the table. [1] (ii) Work out how many more child visitors than adult visitors there are. … [1] (iii) Write down the fraction of visitors that are adults. Give your answer in its lowest terms. … [2] (iv) Write the ratio number of males : number of females. Give your answer in its simplest form. … : … [2] (v) One of these visitors is selected at random. Find the probability that this visitor is a male child. … [1] (b) The number of people in each of 150 cars entering the leisure centre car park is recorded. The table shows the results. Number of people 1 2 3 4 5 Frequency 44 43 30 25 8 (i) Write down the mode. … [1] (ii) Calculate the mean. … [3] (c) In a survey of 50 visitors to the leisure centre, 18 used the gym. One day, 1500 people visited the leisure centre. Calculate an estimate for the number of people who used the gym on this day. … [2]

13 marks

Mark scheme: 3(a)(i) 96 144 240 1 both correct 129 131 260 225 275 500 3(a)(ii) 50 1 3(a)(iii) 9 2 225 45 B1 for or or 0.45 20 500 100 3(a)(iv) 12 : 13 2 B1 for 240 : 260 oe If 0 scored, SC1 for answer 13 : 12 3(a)(v) 144 1 oe 500 3(b)(i) 1 1 3(b)(ii) 2.4 3 M1 for 44 × 1 + 43 × 2 + 30 × 3 + 25 × 4 + 5 × 8 M1dep for their 360 ÷ 150 3(c) 540 2 18 1500 M1 for [× 1500 ] or [× 18] 50 50

This question in 0580/31 Oct/Nov 2018

4 (a) (i) Complete the table of values for y = x 2 - 5x . x –1 0 1 2 3 4 5 6 y –4 –6 –6 –4 0 [2] (ii) On the grid, draw the graph of y = x 2 - 5x for -1 G x G 6 . y 7 6 5 4 3 2 1 0 x –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 –7 [4] (iii) Write down the co-ordinates of the lowest point of your graph. ( … , … ) [1] (iv) Use your graph to solve the equation x 2 - 5x = 3 . x = … or x = … [2] (b) y 5 L 4 3 2 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 x –1 –2 –3 –4 –5 Line L is drawn on the grid. (i) Find the equation of line L in the form y = mx + c. y = … [3] (ii) Line P is parallel to line L and passes through the point (0, -1). On the grid above, draw line P for -5 G x G 5 . [2]

14 marks

Mark scheme: 4(a)(i) 6, 0, 6 2 B1 for two correct 4(a)(ii) Correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points 4(a)(iii) (2.5, –6.4 to –6.1) 1 4(a)(iv) –0.7 to –0.4, 5.4 to 5.7 2 FT their curve B1 for each 4(b)(i) 1 3 1 y = − x + 2 oe M2 for gradient = − oe soi 2 2 1 or M1 for rise / run or gradient = 2 and B1 for y = mx + 2, m ≠ 0 4(b)(ii) Correct ruled line for –5 ⩽ x ⩽ 5 2 B1 for line through (0, –1) or line parallel to line L or correct short line at least from (–4, 1) to (4, –3)

This question in 0580/31 Oct/Nov 2018

7 (a) Write in figures the number eight million and twenty three thousand. … [1] (b) Write these in order of size, starting with the smallest. 3 7 42% 0.45 7 17 … 1 … 1 … 1 … [2] smallest (c) 25 64 2.9 97 39 47 4.63 111 1.5 × 106 13 Write down a number from this list that is (i) prime, … [1] (ii) a multiple of 13, … [1] (iii) irrational. … [1] (d) The number, n, is given as 5300, correct to 2 significant figures. Complete this statement about the value of n. … G n 1 … [2] 3 2(e) Without using a calculator, work out 1 # 1 . 4 7 Show all your working and give your answer as a mixed number in its simplest form. … [3]

11 marks

Mark scheme: 7(a) 8 023 000 1 7(b) 7 3 2 B1 for converting to decimals or percentages 42% 0.45 e.g. [0].428 … or [0].429, [0].42, (.45), [0].41.. 17 7 7(c)(i) 47 1 7(c)(ii) 39 1 7(c)(iii) 97 1 7(d) 5250 5350 2 B1 for each If 0 scored SC1 for both correct but reversed 7(e) 7 9 B1 either fraction seen or 4 7 7 9 9 63 M1 or equivalent improper fractions × = or 4 7 4 28 7 k 9 m 9 n × = 4 k 7 m 4 n 2 14 cao A1

This question in 0580/32 Oct/Nov 2018

8 (a) Complete the table of values for y = 8x - x 2 . x 0 1 2 3 4 5 6 7 8 y 0 12 15 15 12 [3] (b) On the grid, draw the graph of y = 8x - x 2 for 0 G x G 8 . y 18 16 14 12 10 8 6 4 2 0 x 1 2 3 4 5 6 7 8 [4] (c) Write down the equation of the line of symmetry of this graph. … [1] (d) Use the graph to solve 8x - x 2 = 10 . x = … or x = … [2]

10 marks

Mark scheme: 8(a) 7 16 7 0 3 B2 for 2 or 3 correct B1 for 1 correct 8(b) Correct curve 4 B3FT for 8 or 9 points plotted correctly or B2FT for 6 or 7 points plotted correctly or B1FT for 4 or 5 points plotted correctly 8(c) x = 4 1 8(d) 1.45 to 1.65 and 6.35 to 6.55 2 B1 for each or both correct as co-ordinates

This question in 0580/32 Oct/Nov 2018

67 (a) Complete the table of values for y = . x x –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 y –1 –2 –3 –6 6 3 2 1.2 1 [2] 6 (b) On the grid, draw the graph of y = for -6 G x G -1 and 1 G x G 6 . x y 6 5 4 3 2 1 0 x –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 [4] 6 (c) Use your graph to solve the equation = 4. 5 . x x = … [1] (d) (i) On the grid, draw the line y = x. [1] 6 (ii) Write down the co-ordinates of the points of intersection of y = and y = x. x ( … , … ) and ( … , … ) [2]

10 marks

Mark scheme: 7(a) −1.2, −1.5, 1.5 2 B1 for 2 correct 7(b) Correct curve 4 B3FT for 11 or 12 points correctly plotted or B2FT for 9 or 10 points correctly plotted or B1FT for 6, 7 or 8 points correctly plotted 7(c) 1.2 to 1.4 1 FT their (b) 7(d)(i) Correct ruled line 1 7(d)(ii) (−2.6 to −2.3, −2.6 to −2.3,) and 2 FT y = x drawn and their curve (2.3 to 2.6, 2.3 to 2.6) B1FT for one correct, or both x values correct or both y values correct

This question in 0580/33 Oct/Nov 2018

2 (a) Write down the fraction of the rectangle that is shaded. Give your answer in its simplest form. … [2] 7 (b) Write down a fraction that is equivalent to . 12 … [1] (c) Write down a fraction that completes this calculation. 13 … # = 1 11 … [1] (d) Find a fraction that makes this statement true. 7 … 8 1 1 9 9 … [1] (e) Write these numbers in order, starting with the smallest. -1 4 .57 # 10 .033 57.2% 7 … 1 … 1 … 1 … [2] smallest

7 marks

Mark scheme: 2(a) 4 2 8 cao M1 for 15 30 2(b) 7 k 1 k ≠ 1 12 k 2(c) 11k 1 13k 2(d) Any correct fraction 1 2(e) 1 4 2 B1 for 3 in correct order 5.7 × 10− , , 57.2% , 0.33 M1 for 3 of 0.57, 0.571[….], 0.574[….], 7 0.572

This question in 0580/32 Feb/March 2019

2 (a) Work out 48 ' 3 - 5 # 2 . … [1] (b) Insert one pair of brackets to make this statement correct. 3 + 2 # 12 - 4 = 19 [1] (c) Write the following in order, starting with the smallest. 3 11 0.749 76% 4 15 … 1 … 1 … 1 … [2] smallest (d) Find the value of (i) 265.69, … [1] (ii) 83. … [1] (e) Write down the smallest prime number. … [1] (f) Write down all the factors of 18. … [2] (g) Write down a common factor of 16 and 72 that is greater than 2. … [1] 28(h) Write as a fraction in its simplest form. 140 … [1] (i) Jeff and his friends win a prize. 5 Jeff’s share is $160 which is of the prize. 11 Work out the value of the prize. $ … [2]

13 marks

Mark scheme: 2(a) 6 1 2(b) 3 + 2 × (12 – 4) = 19 1 2(c) 15 11 [0].749 34 76[%] 2 B1 for 3 in the correct order or 0.75, (0.749) , 0.76, 0.73… or 75%, 74.9%, (76%), 73….% 2(d)(i) 16.3 1 2(d)(ii) 512 1 2(e) 2 1 2(f) 1 2 3 6 9 18 2 B1 for 4 or 5 correct factors only or 6 correct factors with one extra or 1 × 18, 2 × 9, 3 × 6 2(g) 4 or 8 1 2(h) 1 5 cao 1 2(i) 352 2 M1 for 160 ÷ 5 [ × 11]

This question in 0580/31 May/June 2019

1 (a) (i) Write 26% as a decimal. … [1] (ii) Write 0.48 as a fraction. … [1] (b) Write down 5 (i) a fraction that is equivalent to , 9 … [1] (ii) the 7th odd positive number, … [1] (iii) a decimal number that is larger than 0.0467 but smaller than 0.0468 . … [1] (c) Find the value of (i) 3 512 , … [1] 6 8 (ii) 6 , 2 … [1] (iii) 70. … [1] (d) Find the first even multiple of seven that is greater than 100. … [2] - 1 - 3 7 (e) 6 10 .897 # 10 64 5 From the list, write down the irrational number. … [1]

11 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 0.26 cao 1 1(a)(ii) 48 1 or equivalent fraction 100 1(b)(i) 5k 1 where k ≠ 1 9k 1(b)(ii) 13 1 1(b)(iii) Any decimal between 0.0467 and 1 0.0468 1(c)(i) 8 1 1(c)(ii) 26 244 1 1(c)(iii) 1 1 1(d) 112 2 B1 for any multiple of 7 greater than 100 seen 1(e) 10 1

This question in 0580/32 May/June 2019

1 (a) Write this number in figures. One million three hundred and two thousand five hundred and ninety-six. … [1] (b) (i) Two numbers are added together to give the number in the box immediately above. 2 5 – 3 – 4 Complete the diagram. [2] (ii) Two numbers are multiplied together to give the number in the box immediately above. 5 – 3 – 4 Complete the diagram. [3] (c) Write these in order of size, starting with the smallest. 5 -1 18.4% .183 # 10 5-1 27 … 1 … 1 … 1 … [2] smallest (d) Work out 142 as a percentage of 304. … % [1] (e) (i) Find the highest common factor (HCF) of 28 and 98. … [2] (ii) Find the lowest common multiple (LCM) of 28 and 98. … [2] (f) The average distance from Earth to Mars is .225 # 108 km. A space ship travels from Earth to Mars at an average speed of .58 # 104 km/h. Find how long, in hours, the journey takes. … hours [2]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1 302 596 1 1(b)(i) −5 2 B1 for −7 −7 B1FT for 2 + their −7 1(b)(ii) −180 3 B1 for −15 −15 12 B1 for 12 and B1FT for their −15 × their 12 1(c) 5 2 M1 for 3 in correct order or for 1.83 × 10−1 18.4% 5−1 27 5 three of [ =]0.185 … , [18.4% =] 0.184, 27 [1.83 × 10−1 =] 0.183, [5−1=] 0.2 1(d) 46.7 or 46.71... 1 1(e)(i) 14 2 B1 for answer of 2 or 7 or 2 × 7 or 2 × 2 × 7 and 2 × 7 × 7 or list (28 =) 2, 2, 7 and (98 =)2, 7, 7 1(e)(ii) 196 2 B1 for 28, 56, 84, 112,… and 98, 196 or [1 ×]2 × 2 × 7 × 7 or 196k 1(f) 3880 or 3879[⋅…] 2 M1 for 2.25 × 108 ÷ 5.8 × 104 oe or 3.88(0...) × 103 or 3.879… × 103 or figs (388 or 3879…) as the answer

This question in 0580/33 May/June 2019

4 (a) Complete the table of values for y = 5 + 2 x - x 2 . x -2 -1 0 1 2 3 4 y 2 5 6 -3 [2] (b) On the grid, draw the graph of y = 5 + 2x - x 2 for - 2 G x G 4 . y 7 6 5 4 3 2 1 0 –2 –1 1 2 3 4 x –1 –2 –3 [4] (c) (i) On the grid, draw the line of symmetry. [1] (ii) Write down the equation of the line of symmetry. … [1] (d) Use your graph to find the solutions of the equation 5 + 2x - x 2 = 4 . x = … or x = … [2] (e) (i) On the grid, draw a line from (- 1, 2) to (1, 6) . [1] (ii) Find the equation of this line in the form y = mx + c . y = … [3]

14 marks

Mark scheme: 4(a) −3 5 2 2 B1 for 2 correct 4(b) Correct curve 4 B3FT for 6 or 7 points correct B2FT for 4 or 5 points correct B1FT for 2 or 3 points correct 4(c)(i) Ruled line x = 1 drawn 1 4(c)(ii) x = 1 1 4(d) −0.5 to −0.3 and 2.3 to 2.5 2 B1 for each If 0 scored, B1 for y = 4 drawn 4(e)(i) Correct ruled continuous line 1 4(e)(ii) [y =] 2x + 4 3 B2 for [y =] 2x + k rise or M1 for run B1 for kx + 4 , k ≠ 0, or c = 4

This question in 0580/33 May/June 2019

11 (a) Write as a decimal. 4 … [1] 36 (b) Write as a fraction in its lowest terms. 124 … [1] 5 (c) Work out of 128. 8 … [1] (d) Write down all the factors of 24. … [2] (e) Find the highest common factor (HCF) of 24 and 108. … [2] (f) Write down an irrational number between 3 and 9. … [1] (g) Write down the value of 250. … [1] (h) $8400 is invested for 2 years at a rate of 3.5% per year compound interest. Work out the total amount of interest earned by the end of the 2 years. $ … [3] 1 4(i) Without using a calculator, work out 2 + . 3 5 You must show all your working and give your answer as a mixed number in its simplest form. … [3]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) [0].25 1 1(b) 9 1 cao 13 1(c) 80 1 1(d) 1, 2, 3, 4, 6, 8, 12, 24 2 B1 for 6 or 7 correct factors and no extras or 8 correct factors and at most one extra 1(e) 12 2 B1 for 2, 3, 4 or 6 as final answer or 2 × 2 × 3 or for 2 × 2 × 2 × 3 and 2 × 2 × 3 × 3 × 3 1(f) Accept any irrational number between 1 3 and 9 1(g) 1 1 1(h) 598.29 cao 3 2  3.5  M2 for 8400 × 1 + oe    100  OR  3.5  2 M1 for 8400 ×  1 +  oe  100  A1 for 8998.29 1(i) 5 12 35 B1 allow denominators with multiples of 15 or or 35k 5 k 15 15 15 e.g. , 15k 15 k 5 12 35 12 M1 allow other common denominators [ 2 ] [+] or [+] 15 15 15 15 [2]17 or 47 leading to 2 cao A1 with no errors or omissions seen 15 15 315

This question in 0580/33 Oct/Nov 2019

9 (a) By rounding each number correct to 1 significant figure, show that an estimate for this calculation is 20. 9. 78 + 31. 562 0.381 # 5 .09 [2] (b) Write these numbers in order, smallest first. 22 333 3.142 3.1416 7 106 … 1 … 1 … 1 … [2] smallest (c) The length, p cm, of a pencil is 9.8 cm, correct to 2 significant figures. Complete the statement about the value of p. … G p 1 … [2] 5 2163 (d) Calculate .3142 - . 16 604 Give your answer in standard form correct to 2 significant figures. … [2]

8 marks

Mark scheme: 9(a) 10 + 30 M1 [ 0 ] .4 × 5 40 A1 [= 20] 2 9(b) 333 22 2 B1 for 3.1428[…] or 3.143 and 3.1416 3.142 3.1415[…] 106 7 or for 3 in the correct order 9(c) 9.75 9.85 2 B1 for one correct or both correct and reversed 9(d) 4.1 × 10–4 cao 2 B1 for 4.07[6…] × 10-4 or 4.08× 10-4 or figs 41

This question in 0580/33 Oct/Nov 2019

4 (a) Complete the table of values for y = 7 + 2 x - x 2 . x -2 -1 0 1 2 3 4 y -1 8 7 -1 [2] (b) On the grid, draw the graph of y = 7 + 2x - x 2 for - 2 G x G 4 . y 9 8 7 6 5 4 3 2 1 – 2 – 1 0 1 2 3 4 x – 1 – 2 [4] (c) Write down the equation of the line of symmetry of the graph. … [1] (d) Use your graph to solve the equation 7 + 2x - x 2 = 0 . x = … or x = … [2]

9 marks

Mark scheme: 4(a) 4 7 4 2 B1 for one correct 4(b) Correct curve 4 B3FT for 6 or 7 points correct or B2FT for 4 or 5 points correct or B1FT for 2 or 3 points correct 4(c) x = 1 oe 1 4(d) −1.9 to −1.7 and 3.7 to 3.9 2 B1 for each

This question in 0580/31 May/June 2020

5 (a) Write one hundred and twenty thousand and twenty in figures. … [1] (b) Find the value of 3481. … [1] (c) (i) Write down the fraction of the rectangle that is shaded. … [1] (ii) Find the percentage of the rectangle that is not shaded. … % [1] (d) Write these numbers in order, starting with the smallest. 5 7 27% 0.268 17 29 … 1 … 1 … 1 … [2] smallest (e) Write 0.3728 correct to 1 decimal place. … [1] (f) Write down the value of 190. … [1] (g) The height, h metres, of a tower is 128 m, correct to the nearest metre. Complete the statement about the value of h. … G h 1 … [2] (h) Find the highest common factor (HCF) of 126 and 180. … [2] (i) Write down an irrational number with a value between 6 and 7. … [1]

13 marks

Mark scheme: 5(a) 120 020 1 5(b) 59 1 5(c)(i) 5 1 8 5(c)(ii) 37.5 1 5(d) 7 5 2 B1 for 3 in the correct order 0.268 27% or M1 for .27 .29… [.268] .24… 29 17 5(e) 0.4 1 5(f) 1 1 5(g) 127.5 128.5 2 B1 for each or SC1 for both correct but reversed 5(h) 18 2 B1 for an answer of 2 or 3 or 6 or 9 or 2 × 3 × 3 or 2 × 32 as final answer or for [126 =] 2 × 3 × 3 × 7 or 2 × 32 × 7 and [180 =] 2 × 2 × 3 × 3 × 5 or 22 × 32 × 5 or for complete correct list of factors for 126 and 180 5(i) Any irrational number between 6 and 7 1

This question in 0580/31 Oct/Nov 2020

159 (a) Complete the table of values for y = . x x - 5 - 3 - 2 - 1 1 2 3 5 y - 15 15 [3] 15 (b) On the grid, draw the graph of y = for - 5 G x G - 1 and 1 G x G 5 . x y 16 14 12 10 8 6 4 2 0 x – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 – 2 – 4 – 6 – 8 – 10 – 12 – 14 – 16 [4] (c) On the grid, draw the line y = 6 . [1] 15 (d) Use your graph to solve = 6 . x x = … [1]

9 marks

Mark scheme: 9(a) −3 −5 −7.5 7.5 5 3 3 B2 for 4 or 5 correct or B1 for 2 or 3 correct 9(b) Correct curve 4 B3FT for 7 or 8 points plotted correctly or B2FT for 5 or 6 points plotted correctly or B1FT for 3 or 4 points plotted correctly 9(c) Correct ruled line 1 9(d) 2.5 or 2.4 to 2.6 1 FT their line (y = k) and their curve

This question in 0580/31 Oct/Nov 2020

6 (a) Write 60 025 in words. … [1] (b) Write 849.481 correct to 1 decimal place. … [1] (c) Write down (i) all the factors of 21, … [2] (ii) a prime number between 40 and 50. … [1] 2 (d) Write as a decimal. 5 … [1] (e) Find the value of (i) 3 2744 , … [1] (ii) 70. … [1] (f) Gino invests $6000 for 5 years at a rate of 1.2% per year compound interest. Calculate the value of his investment at the end of the 5 years. Give your answer correct to the nearest dollar. $ … [3]

11 marks

Mark scheme: 6(a) Sixty thousand [and] twenty five 1 6(b) 849.5 cao 1 6(c)(i) 1, 3, 7, 21 2 B1 for 3 factors and no extras or 4 correct and 1 extra 6(c)(ii) 41, 43 or 47 1 6(d) 0.4 cao 1 6(e)(i) 14 1 6(e)(ii) 1 1 6(f) 6369 cao 3  1.2  5 M1 for 6000 ×  1 +  or better  100  A1 for 6368.7 … , or 6368 or 6370 If A0 scored, SC1 for correctly rounding their decimal answer

This question in 0580/32 Oct/Nov 2020

10 (a) Complete the table of values for y = x 2 - 4x - 3 . x - 2 - 1 0 1 2 3 4 5 y 2 - 3 - 6 - 6 - 3 2 [2] (b) On the grid, draw the graph of y = x 2 - 4x - 3 for - 2 G x G 5 . y 10 8 6 4 2 – 2 – 1 0 1 2 3 4 5 x – 2 – 4 – 6 – 8 [4] (c) Use your graph to solve the equation x 2 - 4 x - 3 = 0 . x = … or x = … [2]

8 marks

Mark scheme: 10(a) 9 –7 2 B1 for each 10(b) Correct curve 4 B3FT for 7 or 8 points correctly plotted B2FT for 5 or 6 points correctly plotted B1FT for 3 or 4 points correctly plotted 10(c) – 0.8 to –0.5 and 4.5 to 4.8 2 B1 for each

This question in 0580/32 Oct/Nov 2020

1 (a) Strawberries cost $4.20 per kilogram and cream costs $8.56 per litre. Venus buys 1.2 kg of strawberries and 125 ml of cream. Work out the total cost. $ … [3] (b) Ravi has $20. A pineapple costs $1.45 . Work out the largest number of pineapples Ravi can buy and the change he receives. Number of pineapples … Change $ … [3] (c) Abraham has a box of 72 biscuits. 2 He gives of the biscuits to his grandmother. 9 3 He then gives of the biscuits that are left to his cousin. 7 Work out how many biscuits Abraham has now. … [3] (d) Flo makes 84 cakes. She sells 35 of these cakes. Calculate the percentage of the cakes that she sells. … % [1] (e) A bag contains 132 sweets. The sweets are shared between Beatrix and Volker in the ratio Beatrix : Volker = 5 : 7. Work out the number of sweets they each receive. Beatrix … Volker … [2] (f) Jed sells desserts for $24 each. Each dessert costs $12.80 to make. (i) Work out his percentage profit. … % [2] (ii) The cost to make each dessert increases to $13.60 . Jed wants to make the same percentage profit. Work out the new selling price. $ … [2]

16 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6.11 3 M2 for 1.2 × 4.2 + 0.125 × 8.56 oe or M1 for 1.2 × 4.2 oe or figs125 × 8.56 or B1 for 0.125 1(b) 13 1.15 3 20 M1 for 1.45 M1 for 20 − 1.45 × k where k integer ⩽13 1(c) 32 3 7 4 M2 for × × 72 9 7 OR 2 7 M1 for 9× 72 or 9 × 72 4 and M1dep for × their 56 7 3 or × their 56 7 1(d) 41.7 or 41.66 to 41.67 1 1(e) 55 77 2 132 M1 for × k oe where k is 1 or 5 or 5 + 7 7 1(f)(i) 87.5 2 24 M1 for × 100 [ − 100 ] or 12.8 24 − 12.8 24 [× 100 ] or − 1[ × 100 ] 12.8 12.8 1(f)(ii) 25.5[0] nfww 2 FT their (f)(i)  their ( f )( i )  M1 for 13.6 ×  1 +  oe  100  or B1FT for 11.90 13.6 12.8 or M1 for = or better x 24

This question in 0580/31 May/June 2021

74 (a) Put a ring around the fraction that is equivalent to . 12 35 20 49 82 64 62 36 84 144 110 [1] (b) Write these numbers in order, starting with the smallest. 7 8 2 0.6 58% 12 13 3 … 1 … 1 … 1 … 1 … [2] smallest (c) Write 0.724 as a fraction in its simplest form. … [1] (d) The mass, m grams, of a ball is 415 g, correct to the nearest 5 grams. Complete the statement about the value of m. … G m 1 … [2] (e) Ruth uses three-quarters of a bag of flour to make one cake. Work out the number of bags of flour she needs to buy to make 7 cakes. … [3] (f) A tin of soup costs $t and a packet of biscuits costs $p. (i) 3 tins of soup and 2 packets of biscuits cost $15.50 . Complete the equation. 3t + 2p = … [1] (ii) 5 tins of soup and 4 packets of biscuits cost $28.50 . Write down another equation in terms of t and p. … [1] (iii) Solve the two simultaneous equations. You must show all your working. t = … p = … [3]

14 marks

Mark scheme: 4(a) 49 1 84 4(b) 7 8 2 2 B1 for 4 in correct order 58% 0.6 or M1 for 0.583[...], [0.6], 0.58, 0.615[…] 12 13 3 or 0.61 or 0.62, 0.66[...] or 0.67 or 0.667 or 0.7 oe 4(c) 181 1 cao 250 4(d) 412.5 417.5 2 B1 for each If 0 scored, SC1 for both correct but reversed 4(e) 6 3 3 M1 for 7 × oe 4 1 A1 for 5.25 or 5 4 4(f)(i) 15.5[0] 1 4(f)(ii) 5t + 4p = 28.5[0] 1 4(f)(iii) For correct method to eliminate one M1 FT their two linear equations variable [t =] 2.5 A1 [p =] 4 A1 If 0 scored, SC1 for 2 values satisfying one of the correct equations or their (f)(i) or (f)(ii) or SC1 if no working shown, but 2 correct answers

This question in 0580/32 May/June 2021

185 (a) Complete the table of values for y = . x x -8 -6 -4 -3 -2 2 3 4 6 8 y -3 -6 6 3 [3] 18 (b) On the grid, draw the graph of y = for -8 G x G - 2 and 2 G x G 8 . x y 1010 88 66 44 22 x –– 88 –– 66 –– 44 – 2 0 22 44 66 88 – 2 – 4 – 6 – 8 – 10 (c) Write down the order of rotational symmetry of the graph. … [1] (d) (i) On the grid, plot and join the points (-8, -3) and (6, 4). [2] 18 (ii) Write down the values of x where this line intersects the graph of y = . x x = … and x = … [2] (iii) Find the equation of this line in the form y = mx + c . y = … [2]

14 marks

Mark scheme: 5(a) −2.25 −4.5 −9 9 4.5 2.25 3 B2 for 4 or 5 correct or B1 for 2 or 3 correct 5(b) Correct curve 4 B3FT for 9 or 10 points correctly plotted or B2FT for 7 or 8 points correctly plotted or B1FT for 5 or 6 points correctly plotted 5(c) 2 1 5(d)(i) (−8, −3) and (6, 4) plotted and joined in a 2 B1 for one point correctly plotted or both ruled line correctly plotted but not joined, or ruled 5(d)(ii) −7.3 to −6.9 and 4.9 to 5.3 2 B1FT for each 5(d)(iii) 1 2 1 [y =] x + 1 oe final answer B1 for x + c (c ≠ +1) or 2 2  1  kx + 1  k ≠ 0 or   2  or B1FT for (their m)x + c or kx + their intercept (k ≠ 0)

This question in 0580/32 May/June 2021

6 (a) Write these in order, starting with the smallest. 11 17 0.5806 58% 19 29 … 1 … 1 … 1 … [2] smallest (b) Write 0.004 973 correct to (i) 3 decimal places, … [1] (ii) 2 significant figures. … [1] (c) The height of a flag pole, h metres, is measured as 37.84 metres, correct to 2 decimal places. Complete this statement about the value of h. … G h 1 … [2] (d) The population of Nigeria is 201 000 000, correct to 3 significant figures. Write this population in standard form. … [1] (e) The table shows the populations of some countries given in standard form, correct to 3 significant figures. Country Population Brazil .212 # 108 China .142 # 109 Eritrea .531 # 106 France .655 # 107 Maldives .452 # 105 New Zealand .479 # 106 Use the information in this table to find (i) the country with the smallest population, … [1] (ii) the country with the population that is nearest to 5 million, … [1] (iii) the difference between the population of Brazil and the population of France, … [1] (iv) the value of k, correct to 2 significant figures, where the population of China = k # the population of Eritrea. k = … [2]

12 marks

Mark scheme: 6(a) 11 17 2 M1 for 58% 0.5806 [0.5806] [0].57… [0].586… [0].58 19 29 or B1 for 3 in the correct order 6(b)(i) 0.005 cao 1 6(b)(ii) 0.0050 cao 1 6(c) 37.835 37.845 2 B1 for each If 0 scored, SC1 for both correct but reversed 6(d) 2.01 × 108 1 6(e)(i) Maldives 1 6(e)(ii) New Zealand 1 6(e)(iii) 146 500 000 or 1.465 × 108 1 6(e)(iv) 270 cao 2 M1 for (1.42 × 109) ÷ (5.31 × 106) oe or 267[. …] oe

This question in 0580/32 Oct/Nov 2021

10 (a) Complete the table of values for y = x 2 - 5x - 2 . x - 2 - 1 0 1 2 3 4 5 6 y 4 - 2 - 8 - 8 - 2 4 [2] (b) On the grid, draw the graph of y = x 2 - 5x - 2 for - 2 G x G 6 . y 14 12 10 8 6 4 2 – 2 – 1 0 1 2 3 4 5 6 x – 2 – 4 – 6 – 8 – 10 [4] (c) On the grid, draw the line y = 2 . [1] (d) Use your graph to solve the equation x 2 - 5 x - 2 = 2 . x = … or x = … [2]

9 marks

Mark scheme: 10(a) 12 −6 −6 2 B1 for 1 or 2 correct 10(b) Correct curve 4 B3FT for 8 or 9 points correctly plotted or B2FT for 6 or 7 points correctly plotted or B1FT for 4 or 5 points correctly plotted 10(c) Ruled line y = 2 drawn 1 10(d) −0.9 to −0.5 2 FT y = 2 and their curve B1 for each 5.5 to 5.9

This question in 0580/32 Oct/Nov 2021

7 (a) Write the number six hundred and three thousand eight hundred and twenty-one in figures. … [1] (b) Pens cost 47 cents each. Aroha buys 8 pens. How much change does she receive from $5? $ … [2] (c) Find the value of (i) 81, … [1] (ii) 63, … [1] (iii) 30. … [1] (d) Write 130 as a product of its prime factors. … [2] (e) A tower has two bells, A and B. Bell A rings every 12 minutes. Bell B rings every 14 minutes. Both bells ring at 09 30. Find the next time both bells ring together. … [3]

11 marks

Mark scheme: 7(a) 603 821 1 7(b) 1.24 2 M1 for 5 – (0.47 × 8) oe 7(c)(i) 9 1 7(c)(ii) 216 1 7(c)(iii) 1 1 7(d) 2 × 5 × 13 2 B1 for 2, 5, 13 or M1 for correct factor tree/diagram/list/ table 7(e) 1054 3 B2 for 84 or 1 hr 24 mins or M1 for 84k or 2 × 2 × 3 × 7 or [12 =] 2 × 2 × 3 and [14 =] 2 × 7 or 2 correct factor trees / tables of both 12 and 14 OR M2 for listing times/multiples of both 12 and 14 to at least 1054 or 84 or M1 for listing at least 3 of each or one full list

This question in 0580/33 Oct/Nov 2021

5 (a) A closed box, in the shape of a cuboid, has length 5 cm, width 4 cm and height 2 cm. (i) Draw a net of the box on the 1cm2 grid. [3] (ii) A container is a cube with volume 1m3. Work out the maximum number of these boxes that can be packed into this container. … [3] (b) A shop sells three different sized boxes of rice. The boxes all have the same cost per kilogram. NOT TO SCALE Box A Box B Box C 80 rupees $3.50 750 g 1.35 kg (i) Work out the cost in rupees of box B. … rupees [2] (ii) $1 = 64 rupees. Calculate the mass of box C. Give your answer in kilograms. … kg [3] (c) Change 75cm3into litres. Give your answer in standard form. … litres [2]

13 marks

Mark scheme: 5(a)(i) Correct ruled net 3 B2 for 4 or 5 correct rectangles drawn in correct positions relative to each other or B1 for one correct face drawn 5(a)(ii) 25 000 3 100 × 100 × 100 M2 for oe 2 × 4 × 5 or M1 for 100 × 100 × 100 or 0.02×0.04×0.05 or 2×4×5 or 50, 25, 20 If 0 scored, SC1 for final answer figs 25 5(b)(i) 144 2 figs135 1.35 80 750 M1 for or or or 750 figs750 750 80 oe or B1 for 1350 or 0.75[0] 5(b)(ii) 2.1 3 3.5 × 64 × figs75 M2 for oe 80 80 or M1 for 3.5× 64 or 64 5(c) 7.5 × 10−2 cao 2 75 M1 for oe 1000 If 0 scored, SC1 for correctly converting their number to standard form, provided their number is <1

This question in 0580/32 Feb/March 2022

3 Sachin, his wife and three children go on a coach holiday. (a) Each adult ticket costs $375 and each child ticket costs $194. Work out the total cost of the tickets. $ … [2] (b) A meal costs $110 plus a service charge of 18%. Calculate the total cost of the meal. $ … [2] (c) One day, the temperature at midday is 16 °C. At midnight the temperature has fallen by 23 °C. Work out the temperature at midnight. … °C [1] (d) Sachin spends $768 on holiday. 3 He spends of this amount on presents. 8 Find how much he spends on presents. $ … [1] (e) There are 604 passengers on the holiday. (i) The coach company uses coaches which can carry 46 passengers. Work out the number of coaches needed. … [2] (ii) 268 of the 604 passengers are women. Find the percentage of the passengers that are women. … % [1] (f) A coach travels at an average speed of 54 km/h. Find how long, in hours and minutes, this coach takes to travel 126 km. … h … min [3]

12 marks

Mark scheme: 3(a) 1332 2 M1 for 2  375 + 3  194 oe 3(b) 129.8[0] 2 M1 for 110  (1  10018 ) oe or B1 for 19.8[0] 3(c) −7 1 3(d) 288 1 3(e)(i) 14 2 M1 for 604 ÷ 46 or 13.1[3…] 3(e)(ii) 44.4 or 44.37… 1 3(f) 2 (h) 20 (min) 3 M1 for 126 ÷ 54 A1 for 2.33… or 140 mins If A0 scored, SC1 for their (decimal time) correctly changed to hours and minutes

This question in 0580/31 May/June 2022

129 (a) Complete the table of values for y = , x ! 0 . x x -6 -4 -3 -2 -1 1 2 3 4 6 y -3 -6 6 3 [3] 12 (b) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 12 10 8 6 4 2 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 2 – 4 – 6 – 8 – 10 – 12 [4] (c) On the grid, draw the line y = 5 . [1] 12 (d) Use your graph to solve the equation = 5 . x x = … [1]

9 marks

Mark scheme: 9(a) −2 … −4 … −12 12 … 4 … 2 3 B2 for 4 or 5 correct B1 for 2 or 3 correct 9(b) Correct curve 4 B3FT for 9 or 10 points plotted correctly B2FT for 7 or 8 points plotted correctly B1FT for 5 or 6 points plotted correctly 9(c) Correct ruled line drawn 1 9(d) 2.4 1 FT their graph and y = 5

This question in 0580/31 May/June 2022

1 Antonio has a shop near the beach. (a) (i) He makes a tally of the number of ice creams he sells on Friday. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Work out the number of ice creams he sells on Friday. … [1] (ii) 15 of the ice creams he sells on Friday are vanilla. Work out the fraction of ice creams he sells on Friday that are vanilla. Give your answer in its simplest form. … [1] (iii) He buys tubs of ice cream for his shop in the ratio vanilla : chocolate = 11 : 7. He buys 28 tubs of chocolate ice cream. Work out how many tubs of vanilla ice cream he buys. … [2] (b) Antonio records the number of chairs his shop hires out on each day for a week. 123 98 116 45 67 165 156 (i) Work out the range. … [1] (ii) Find the median. … [2] (iii) Calculate the mean. … [2] (c) (i) Antonio buys beach balls for $2.50 each and sells them for $4.20 each. Work out the percentage profit he makes on each beach ball. … % [2] (ii) A beach ball is a sphere with radius 15 cm. Calculate the volume of the beach ball. Give the units of your answer. 4 3 [The volume, V, of a sphere with radius r is V = rr .] 3 … … [3] (d) The shop sells sun cream in bottles A, B and C. NOT TO SCALE Bottle A Bottle B Bottle C 160 ml 200 ml 240 ml $3.75 $4.75 $6.50 Work out which bottle is the best value. You must show all your working. Bottle … [3]

17 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 48 1 1(a)(ii) 5 1 FT their (a)(i) provided simplification required and cao answer given in its simplest form 16 1(a)(iii) 44 nfww 2 28 M1 for  11 oe 7 1(b)(i) 120 1 1(b)(ii) 116 2 M1 for at least first four or last four correctly ordered 1(b)(iii) 110 2 123  98  116  45  67  165  156 M1 for oe 7 1(c)(i) 68 2 4.2  2.5 M1 for  100  oe 2.5 4.2 or  100   100  oe 2.5  4.2  oe or   1   100   2.5  1(c)(ii) 14 100 or 14 140 2 4 3 M1 for  π  15 oe or 14 137 to 14 139 3 cm3 1 1(d) A 3 M2 for 3 correct comparable values, or for a correct With correct comparisons method to compare 3 bottles shown but not evaluated to made of the 3 bottles with enough accuracy suitable accuracy shown or M1 for 2 correct comparable values or for a correct method to compare 3 bottles but not evaluated

This question in 0580/32 May/June 2022

- 62 (a) (i) Complete the table of values for y = . x x -6 -4 -3 -2 -1.5 -1 1 1.5 2 3 5 6 y 1 2 3 6 -6 -3 -2 -1 [3] - 6 (ii) On the grid, draw the graph of y = for - 6 G x G - 1 and 1 G x G 6 . x y 6 5 4 3 2 1 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 x – 1 – 2 – 3 – 4 – 5 – 6 [4] (iii) Write down the order of rotational symmetry of the graph. … [1] (iv) Write down the equation of each line of symmetry of the graph. … and … [2] (v) On the grid, draw the line y = 2.5 . [1] - 6 (vi) Use your graph to solve the equation = 2 .5 . x x = … [1] (b) L P Draw a line that passes through the point P and is perpendicular to line L. [1] (c) Find the equation of the straight line that • is parallel to the line y = 3x + 5 and • passes through the point (1, 7). Give your answer in the form y = mx + c . y = … [2]

15 marks

Mark scheme: 2(a)(i) 1.5 4 –4 –1.2 3 B2 for 3 correct or B1 for 1 or 2 correct 2(a)(ii) Correct graph drawn 4 B3FT for 12 or 11 correct plots B2FT for 10 or 9 correct plots B1FT for 8,7 or 6 correct plots 2(a)(iii) 2 1 2(a)(iv) y  x oe y  x oe 2 B1 for each 2(a)(v) Correct ruled line 1 2(a)(vi) 2.4 1 FT their graph and y  2.5 2(b) Correct ruled line 1 2(c)  y  3 x  4 cao 2 B1 for final answer  y   3 x  k , k  5 or  y   jx  4 , j ≠ 0

This question in 0580/32 May/June 2022

7 (a) Shade some squares so that both shapes have the same fraction shaded. [2] (b) Here is a pattern. ………. ……….. Position number 1 is a . Position number 2 is a . (i) Draw the next two shapes in this pattern. [1] (ii) What do the position numbers of the shape have in common? … [1] (iii) Pierre says that the shape in position number 99 is a . Explain why he is correct. … … [2] (c)  = { , , , , , , , , , , , } This universal set has twelve elements. Each shape is: • a circle, C, or a triangle, T, or a rectangle, R • large, L, or small, S • black, B, or white, W. (i) B C The triangles and rectangles are drawn in the Venn diagram. (a) Draw the four circles to complete the Venn diagram. [1] (b) Find n ( B , C ) . … [1] (ii) Six of the twelve shapes are drawn in another Venn diagram. … … Complete the Venn diagram by: • labelling the sets and • drawing the shapes , , , , and . [3]

11 marks

Mark scheme: 7(a) 15 squares shaded 2 15 B1 for 15 or 36 5 k or M1 for  oe 12 36 7(b)(i) 1 7(b)(ii) Divisible by 4 oe 1 7(b)(iii) Justifies why Pierre is correct 2 B1 for e.g. 100th term is a e.g. 4  25=100 so the 100th term is a the 99th term is the term before since is always before , Pierre is correct. 7(c)(i)(a) 1 7(c)(i)(b) 8 1 FT their (c)(i)(a) 7(c)(ii) 3 B1 for correct labelling L B B2 for 6 shapes placed correctly or B1 for 4 or 5 shapes placed correctly

This question in 0580/32 May/June 2022

5 (a) Work out the number of days in seven weeks. … days [1] (b) The summit of Mount Everest is 8848 metres above sea level. Ayding Lake is 154 metres below sea level. Work out the difference in height between these places. … m [1] (c) Find two integers that have a sum of - 12 and a product of 32. … and … [1] 3 (d) Write as 8 (i) a decimal, … [1] (ii) a percentage. … % [1] (e) Write down the reciprocal of 1. 9 … [1] (f) Find the value of (i) 45, … [1] (ii) 3 512 . … [1] (g) (i) Write 587 000 in standard form. … [1] (ii) Calculate 4.9 # 10 - 3 + 8.1 # 10 - 4 . Give your answer in standard form. … [1] (h) The height, h metres, of a fence post is 2.43 m, correct to the nearest centimetre. Complete the statement about the value of h. … G h 1 … [2]

12 marks

Mark scheme: 5(a) 49 1 5(b) 9002 1 5(c) −8 and −4 1 5(d)(i) [0].375 1 5(d)(ii) 37.5 1 5(e) 9 1 5(f)(i) 1024 1 5(f)(ii) 8 1 5(g)(i) 5.87 × 105 cao 1 5(g)(ii) 5.71 × 10−3 cao 1 5(h) 2.425 2.435 2 B1 for each If zero scored, SC1 for 242.5 ⩽ h < 243.5 or for both correct but reversed

This question in 0580/33 May/June 2022

157 (a) Complete the table of values for y = , x ≠ 0. x x - 15 - 10 - 5 - 3 - 2 - 1 1 2 3 5 10 15 y - .15 - 5 - 15 15 5 [3] 15 (b) On the grid, draw the graph of y = for - 15 G x G - 1 and 1 G x G 15 . x y 16 14 12 10 8 6 4 2 x – 16 – 14 – 12 – 10 – 8 – 6 – 4 – 2 0 2 4 6 8 10 12 14 16 – 2 – 4 – 6 – 8 – 10 – 12 – 14 – 16 [4] (c) Write down the order of rotational symmetry of the graph. … [1] (d) (i) On the grid, draw the lines of symmetry of the graph. [2] (ii) Write down the equation of the line of symmetry that does not intersect the graph. … [1] 15(e) Use your graph to solve the equation =- 6 . x x = … [1]

12 marks

Mark scheme: 7(a) −1 −3 −7.5 7.5 3 1.5 1 3 B2 for 5 or 6 correct B1 for 3 or 4 correct 7(b) Correct curve 4 B3FT for 11 or 12 points correctly plotted B2FT for 9 or 10 points correctly plotted B1FT for 6, 7 or 8 points correctly plotted 7(c) 2 1 7(d)(i) Lines y = x and y = −x drawn 2 B1 for each 7(d)(ii) y = −x oe 1 7(e) −2.5 1 FT their intersection of y = –6 with their graph

This question in 0580/33 May/June 2022

4 (a) Find (i) a multiple of 3 between 70 and 80, … [1] (ii) a factor of 63 between 5 and 10, … [1] (iii) a cube number between 60 and 90, … [1] (iv) the reciprocal of 7. … [1] 2 (b) Work out of 84. 7 … [1] (c) Find the value of (i) 3 3375 , … [1] (ii) 120. … [1] (d) Rana hires a car. The cost is $74 per day plus a delivery cost of $17.50 . Rana pays a total of $461.50 . Calculate the number of days that Rana hires the car. … days [2] (e) A train to town A leaves a station every 25 minutes. A train to town B leaves the same station every 45 minutes. Both trains leave at 08 00. Find the next time both trains leave together. … [3]

12 marks

Mark scheme: 4(a)(i) 72 or 75 or 78 1 4(a)(ii) 7 or 9 1 4(a)(iii) 64 1 4(a)(iv) 1 1 or 0.143 or 0.142[8..] 7 4(b) 24 1 4(c)(i) 15 1 4(c)(ii) 1 1 4(d) 6 nfww 2 ( 461.5 –17.5 ) M1 for oe 74 4(e) 11 45 3 B2 for 225 or 3 hr 45 mins or M1 for 225k or 3  3  5  5 or [25 =] 5  5 and [45 =] 3  3  5 or two correct factor trees/tables of both 25 and 45 OR M2 for listing times/multiples of both 25 and 45 to at least 11 45 or 225 or M1 for listing at least 3 consecutive times/multiples of each correctly or one full list

This question in 0580/31 Oct/Nov 2022

9 (a) Write down the reciprocal of 1. 3 … [1] (b) Write down the value of 30. … [1] 3 4 (c) Find a fraction between and . 25 25 … [1] (d) Find the difference in temperature between −5 °C and 9 °C. … °C [1] (e) Write in standard form. (i) 5 600 000 … [1] (ii) 0.000 072 … [1] (f) Calculate ( 5.2 # 10 6 ) # (3 .8 # 10 -2 ) . Give your answer in standard form. … [1]

7 marks

Mark scheme: 9(a) 3 1 9(b) 1 1 9(c) Correct fraction e.g. 507 1 9(d) 14 1 9(e)(i) 5.6 × 106 1 9(e)(ii) 7.2 × 10-5 1 9(f) 1.976 × 105 1

This question in 0580/32 Oct/Nov 2022

1 (a) List all the factors of 68. … [2] (b) Put one pair of brackets into each calculation to make it correct. (i) 7 + 3 # 5 - 1 = 19 [1] (ii) 12 + 16 ' 2 + 5 = 19 [1] (c) Find (i) the reciprocal of 2, 7 … [1] (ii) the value of 100. … [1] (d) Calculate. (i) 3 2 + 3 4 … [1] (ii) 3 # 12 … [1] (iii) 5 -3 … [1] (e) Write these numbers in order of size, starting with the smallest. 22 10 .3142 .182 r 7 … 1 … 1 … 1 … 1 … [2] smallest (f) By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 136 + 47.2 . 62.9 ' 18.1 You must show all your working. … [2] (g) Write .473 # 106 as an ordinary number. … [1] (h) Write down a prime number between 30 and 40. … [1]

15 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 1, 2, 4, 17, 34, 68 2 B1 for 4 or 5 correct and no extras or 6 correct and one extra 1(b)(i) 7 + 3  (5 – 1) = 19 1 1(b)(ii) (12 + 16) ÷ 2 + 5 = 19 1 1(c)(i) 7 1 1 or 3.5 or 3 2 2 1(c)(ii) 1 1 1(d)(i) 90 1 1(d)(ii) 6 1 1(d)(iii) 1 1 or 0.008 125 1(e) 22 2 B1 for 4 in correct order π, 3.142, , 10 , 1.82 7 or M1 for [ 10 =] 3.16…, [1.82=] 3.24, 22 [π =] 3.141…, [ =] 3.1428 to 3.1429 or 7 3.143 1(f) 100 + 50 M1 60  20 50 cao nfww A1 If 0 scored, SC1 for 3 correct roundings or for all correct but with any trailing zeros 1(g) 4 730 000 1 1(h) 31 or 37 1

This question in 0580/33 Oct/Nov 2022

9 (a) Alvian has a bag containing 35 counters. 6 are pink, 8 are blue and the rest are either green or yellow. He picks one counter at random. The probability that Alvian picks a green counter is 2. 7 Find the number of yellow counters in the bag. … [3] (b) Mateo has a box containing 15 counters, of which 7 are red and 8 are brown. He picks one counter at random, notes the colour and replaces it in the box. He then picks another counter at random. First counter Second counter Red … Red 7 15 Brown … Red … … Brown Brown … (i) Complete the tree diagram. [2] (ii) Calculate the probability that Mateo picks two brown counters. … [2]

7 marks

Mark scheme: 9(a) 11 3 2 M2 for 35 – 6 – 8 –  35 oe 7 2 or M1 for  35 oe 7 if 0 scored SC1 for answer of 15 9(b)(i) 7 2 8 M1 for in first column 15 15 8 or two correct values in diagram for counter 2 15 7 15 8 8 15 15 9(b)(ii) 64 2 FT their tree diagram oe 225 8 8 M1 for their  their 15 15

This question in 0580/33 Oct/Nov 2022

4 (a) Write 6479 correct to the nearest 100. … [1] (b) Write down the multiple of 13 that is between 100 and 110. … [1] (c) Find the reciprocal of 0.6 . … [1] (d) Work out. 3 + 4 # 2 … [1] (e) Write down an irrational number with a value between 15 and 20. … [1] (f) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 423.8 - 78.4 . 23.5 You must show all your working. … [2]

7 marks

Mark scheme: 4(a) 6500 1 4(b) 104 1 4(c) 2 1 13 oe 4(d) 11 1 4(e) Any irrational number between 15 and 20 1 4(f) 400 − 80 M1 20 16 nfww A1 If 0 scored, SC1 for 2 correct roundings or all correct but with trailing zeros

This question in 0580/32 Feb/March 2023

1 (a) Write the number forty thousand and thirty-three in figures. … [1] (b) Find the value of 3 729 . … [1] 7 (c) Find the reciprocal of . 9 Give your answer as a decimal, correct to 3 decimal places. … [2] (d) Find the value of 6 5 ' 3 4 . … [2] (e) Work out ( - 9 ) # ( - 7 ) ' ( - 3) . … [1] (f) Work out. (i) 11 + 9 # 5 - 4 … [1] (ii) ( 11 + 9) # 5 - 4 … [1] 5(g) - 0 .67 123 49 3 .142 9 From this list, write down an irrational number. … [1] (h) (i) Find the lowest common multiple (LCM) of 24 and 104. … [2] (ii) Find the highest common factor (HCF) of 24 and 104. … [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 40 033 1 1(b) 9 1 1(c) 1.286 cao 2 B1 for 97 or 1.29 or 1.285 or 1.285…… 1(d) 96 2 B1 for 7776 or 81 1(e) −21 1 1(f)(i) 52 1 1(f)(ii) 96 1 1(g) √123 1 1(h)(i) 312 2 B1 for 312k as final answer or M1 for [24 =] 2 × 2 × 2 × 3 or 23 × 3 and [104 =] 2 × 2 × 2 × 13 or 23 × 13 or 2 correct factor trees or tables or a list of multiples of both 24 and 104 with at least 3 of each or 2 × 2 × 2 × 3 × 13 oe 1(h)(ii) 8 2 B1 for 2 or 4 or 2 × 2 × 2 or 23 as final answer, or for a complete list of factors of 24 and 104

This question in 0580/31 May/June 2023

1 (a) Write the number three hundred thousand and three in figures. … [1] (b) Write 15 896 correct to (i) the nearest thousand … [1] (ii) the nearest ten. … [1] (c) By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of 28.9 # 5.49 . 0.472 + 0.97 You must show all your working. … [2] (d) Find the value of (i) 1849 … [1] (ii) 5 0 - 5 -1 … [1] 5 sin 30 - 8 (iii) . 11 … [1] (e) A cyclist travels at a constant speed of 8.5 metres per second. (i) Work out how long the cyclist takes to travel a distance of 5.27 kilometres. Give your answer in minutes and seconds. … min … s [4] (ii) The cyclist increases speed from 8.5 m/s to 10.2 m/s. Work out the percentage increase in speed. … % [2]

14 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 300 003 1 1(b)(i) 16 000 1 1(b)(ii) 15 900 1 1(c) 30  5 M1 0.5  1 100 A1 If 0 scored, SC1 for three correct from 30, 5, [0].5 and 1 or if all correct but with trailing zeros 1(d)(i) 43 1 1(d)(ii) 0.8 1 1(d)(iii) −0.5 1 1(e)(i) 10 (min) 20 (s) 4 B3 for 620 or 10.3… or 0.172… OR B1 for 5270 or 0.0085 or 510 or 30600 or 0.51 or 30.6 M1 for figs 527÷ figs 85 (imp by figs 62) or figs 527 ÷ figs 510 (imp by figs 103…) or figs 527 ÷ figs 306 (imp by figs172 … ) B1 for their time seen (assume time is in seconds unless units stated) and converted correctly to minutes and seconds (seconds must be correct to 3sf or better) 1(e)(ii) 20 2 10.2 8.5 M1 for [×100] oe 8.5 or (10.2  100 ) [–100 ] oe 8.5 or (10.2 )1 [×100] oe 8.5

This question in 0580/32 May/June 2023

1 (a) Claudia asks some students to choose their favourite science from biology, chemistry and physics. The pie chart shows the results. Biology 45° Chemistry 225° Physics (i) Find the percentage of students who choose chemistry. … % [1] (ii) Find the fraction of students who choose physics. Give your answer in its simplest form. … [2] (iii) For the number of students choosing each subject, find the ratio biology : chemistry : physics. Give your answer in its simplest form. … : … : … [2] (iv) Marcus says: ‘I do not know how many people choose chemistry, but I do know it is an even number.’ Explain how Marcus knows this. … [1] (v) Claudia now tells Marcus that 26 students choose chemistry. Work out how many students choose physics. … [2] (b) The Venn diagram shows information about the number of students in a class who study geography (G) and history (H). G H 5 9 10 4 (i) Work out the number of students in the class. … [1] (ii) Find n ( G ) . … [1] (iii) One of the students is chosen at random. Find the probability that this student studies geography and history. … [1] (iv) One of the students who studies geography and history stops studying history. Complete this Venn diagram to show this change. G H [1]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 25 1 1(a)(ii) 5 2 225 cao M1 for oe 8 360 1(a)(iii) 1:2:5 2 B1 for 45 : 90 : 225 oe or better 1(a)(iv) Correct explanation 1 eg if chemistry has an odd number then biology would not be a whole number of students 1(a)(v) 65 2 90 225 M1 for  oe or better 26 x or M1FT their (a)(iii) for their 5  26 their 2 1(b)(i) 28 1 1(b)(ii) 14 1 1(b)(iii) 9 1 9 oe FT 28 their(b)(i) 1(b)(iv) 6, 8, 10, 4 1

This question in 0580/33 May/June 2023

3 (a) Write the number fourteen thousand and ninety-seven in figures. … [1] (b) Write down a common multiple of 17 and 5. … [1] (c) Write 0.25 as a percentage. … % [1] (d) Find the value of (i) 75 … [1] (ii) 80. … [1] 5 (e) Ranjit buys some plants and sells of them. 11 He sells 190 plants. Work out how many plants he buys. … [2] (f) Factorise completely. 15x 3 y - 3x … [2] (g) Make n the subject of the formula V = 3n + t . n = … [2] (h) 7 15 ' 7 x = 7 9 Find the value of x. x = … [1]

12 marks

Mark scheme: 3(a) 14 097 1 3(b) Any correct multiple i.e. 85k 1 3(c) 25 1 3(d)(i) 16 807 1 3(d)(ii) 1 1 3(e) 418 2 M1 for 190 ÷ 5 soi by 38 3(f) 3x(5x2y – 1) final answer 2 B1 for 3(5x3y – x) or for x(15x2y – 3) or correct answer spoilt 3(g) V − t 2 V t oe final answer M1 for V – t =3n or = n + 3 3 3 3(h) 6 1

This question in 0580/32 Oct/Nov 2023

1 (a) Tom has a restaurant bill. Soup $ … Pasta $ 13.30 Ice cream $ 4.80 Drinks $ 3.81 Total cost $ 25.40 (i) Complete the bill to show the cost of soup. [2] (ii) Find the cost of drinks as a percentage of the total cost. … % [1] 2 (b) (i) Work out of $2400. 5 $ … [1] (ii) Decrease $3450 by 18%. $ … [2] (c) Amelia invests $14 000 at a rate of 1.6% per year compound interest. Calculate the value of her investment at the end of 5 years. Give your answer correct to the nearest dollar. $ … [3] (d) This conversion graph can be used to change between dollars and Swiss francs. 200 160 120 Swiss francs 80 40 00 40 80 120 160 200 Dollars (i) Use the graph to change (a) $80 to Swiss francs … Swiss francs [1] (b) 108 Swiss francs to dollars. $ … [1] (ii) Explain how you can use the graph to change $360 to Swiss francs. … … [1]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a)(i) 3.49 2 M1 for 25.4[0] – (13.3[0] + 4.8[0] + 3.81) oe 1(a)(ii) 15 1 1(b)(i) 960 1 1(b)(ii) 2829 2  18  M1 for 3450 ×  1 −  oe  100  or B1 for 621 1(c) 15156 cao 3 5  1.6  M1 for 14000 ×  1 +  oe  100  A1 for 15156.4…, or 15156 or 15160 or 15200 If A0 scored, SC1 for correctly rounding their decimal answer to the nearest dollar 1(d)(i)(a) 72 1 1(d)(i)(b) 120 1 1(d)(ii) Correct explanation, using any correct 1 combination of values between 0 and 200 to reach 360 oe

This question in 0580/33 Oct/Nov 2023

4 (a) A company makes glass using silica, soda, lime and magnesia. The table gives information about the proportions used. Percentage of total mass Pie chart sector angle Silica 75 270° Soda 15 Lime and magnesia 10 (i) Complete the table. [2] (ii) Complete the pie chart to show this information. 270° Silica [1] (iii) The masses of lime and magnesia used are in the ratio lime : magnesia = 3 : 2. Find the percentage of the total mass of glass that is magnesia. … % [1] (iv) The company uses 8.25 kg of soda to make some glass. Work out how many kilograms of silica they use. … kg [2] (b) The company uses the formula M = 2 .5 # A # T to find the mass of a sheet of glass. M is the mass in kilograms. A is the area in square metres. T is the thickness in millimetres. Use the formula to calculate the mass of a rectangular sheet of glass that is 1.9 m long, 0.6 m wide and 8 mm thick. … kg [2] (c) In one year, 130 000 000 tonnes of glass were produced worldwide. Write this number in standard form. … [1] (d) The company sets targets to recycle its waste materials. The bar chart shows the target rate and the actual rate for some of its recycling. Key: Metal Target rate Actual rate Paper & cardboard Glass Plastic Wood 0 10 20 30 40 50 60 70 80 90 100 Percentage recycling rate (i) The target rate for recycling glass was 55%. The actual rate for recycling glass was 70%. Complete the bar chart. [2] (ii) Which materials did the company recycle at more than double their target rate? … [2]

13 marks

Mark scheme: 4(a)(i) 54 2 B1 for each 36 360 270 If 0 scored M1 for or or 3.6 100 75 4(a)(ii) Correct pie chart 1 FT dep on their 54and their 36 adding to 90 4(a)(iii) 4 1 4(a)(iv) 41.25 2 8.25  75 M1 for oe 15 4(b) 22.8 2 M1 for 1.9 × 0.6 [× 2.5] [× 8] oe soi or B1 for figs 228 as answer 4(c) 1.3 × 108 1 4(d)(i) Correct bars drawn 2 B1 for shaded bar 55% or unshaded bar 70% or both bars of correct length 4(d)(ii) Plastic 2 B1 for 1 correct and none incorrect or 2 Wood correct and 1 incorrect

This question in 0580/33 Oct/Nov 2023

4 (a) A shop sells 58 televisions in one week. The bar chart shows the number of televisions that the shop sells on five of the days. 16 14 12 10 Number of 8 televisions 6 4 2 0 Monday Tuesday Wednesday Thursday Friday Saturday Sunday (i) Write down the number of televisions that the shop sells on Monday. … [1] (ii) Find the fraction of the televisions that the shop sells on Sunday. … [1] (iii) The number of televisions that the shop sells on the other two days is in the ratio Wednesday : Friday = 2 : 3. Complete the bar chart. [4] (iv) Write down the mode. … [1] (b) A television has a price of $550. This price is reduced by 4%. Calculate the new price of this television. $ … [2] (c) The scatter diagram shows the prices of different sized televisions. Price Television size Write down the type of correlation shown in the scatter diagram. … [1] (d) Hemang buys two televisions. The probability that a television is faulty is 0.02 . 1st television 2nd television faulty … faulty 0.02 not faulty … faulty … … not faulty not faulty … (i) Complete the tree diagram. [2] (ii) Find the probability that Hemang buys two faulty televisions. … [2] (iii) The shop sells 4150 televisions in one year. Calculate the expected number of faulty televisions. … [1]

15 marks

Mark scheme: 4(a)(i) 3 1 4(a)(ii) 11 1 cao 58 4(a)(iii) Completely correct bar chart 4 B3 for a bar height 8 drawn for Wednesday or a bar height 12 drawn for Friday. or 58 −−3 4 − 4 − 16 − 11 M2 for  k , 2 + 3 k = 1,2 or 3 or M1 for 58 −−−−3 4 4 16 − 11 oe If 0 scored SC1 for 2 bars drawn correctly from their identified values in working 4(a)(iv) Saturday 1 4(b) 528 2  4  M1 for 550   1 −  oe  100  or B1 for 22 4(c) Positive 1 4(d)(i) 0.02 2 B1 for 0.98 correctly placed once on tree 0.98 or for 0.02 correctly placed twice on tree. 0.98 0.02 0.98 oe 4(d)(ii) 0.0004 oe 2 M1 for 0.02 × 0.02 4(d)(iii) 83 1

This question in 0580/32 Feb/March 2024

8 The table shows some values for y = x 2 - x - 3 . x - 3 - 2 - 1 0 1 2 3 4 y - 1 - 1 9 (a) Complete the table. [3] (b) On the grid, draw the graph of y = x 2 - x - 3 for - 3 G x G 4 . y 9 8 7 6 5 4 3 2 1 x – 3 – 2 – 1 0 1 2 3 4 – 1 – 2 – 3 – 4 [4] (c) Write down the coordinates of the lowest point on the graph. ( … , … ) [1] (d) Use your graph to solve the equation x 2 - x - 3 = 7 . x = … or x = … [2]

10 marks

Mark scheme: 8(a) 9, 3, 3, 3, 3 3 B2 for 3 or 4 correct or B1 for 1 or 2 correct 8(b) Completely correct curve 4 B3FT for 7 or 8 correctly plotted points or B2FT for 5 or 6 correctly plotted points or B1FT for 3 or 4 correctly plotted points 8(c)  0.5,k  3.6  k 3 1 8(d) 3.7  2.7 2 B1FT for each

This question in 0580/31 May/June 2024

4 (a) Write down the value of the 8 in the number 39 829. … [1] (b) Write down all the factors of 18. … [2] (c) Show that 57 is not a prime number. [1] (d) x = 64 Find the value of x. x = … [1] (e) Find the first multiple of 40 that is greater than 620. … [1] (f) Find the reciprocal of 2. 3 … [1] 1(g) Find a fraction between and 1. 5 4 … [1] (h) Write down an irrational number with a value between 9 and 10. … [1] (i) Find the highest common factor (HCF) of 72 and 180. … [2]

11 marks

Mark scheme: 4(a) 800 1 4(b) 1 2 3 6 9 18 2 B1 for 4 or 5 correct no extras or 6 correct and 1 extra or for 1×18 and 2×9 and 3×6 4(c) [57 =] 3× 19 oe 1 4(d) 4096 1 4(e) 640 1 4(f) 1 12 or 1.5 1 4(g) Any correct fraction 1 4(h) Any correct irrational number 1 4(i) 36 2 B1 for any of 2, 3, 4, 6, 9, 12, 18 as answer or M1 for 2×2×3×3 oe as answer or [72 = ] 2×2×2 ×3×3 and [180 = ] 2×2 ×5× 3×3 or a complete list of factors of 72 and 180 or 2 correct factor trees or tables or Venn diagram

This question in 0580/33 May/June 2024

1 (a) Write the number six million and thirty in figures. … [1] (b) Write 7.896 correct to 2 decimal places. … [1] (c) 8 24 25 36 39 41 48 From this list of numbers, write down (i) a multiple of 16 … [1] (ii) a factor of 24 … [1] (iii) a cube number … [1] (iv) a prime number. … [1] (d) Put one pair of brackets into this calculation to make it correct. 10 - 12 ' 4 + 2 = 8 [1] (e) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 596 # 0.047 . 8.65 You must show all your working. … [2] (f) Calculate ( 8 # 10 6 ) # ( 3 # 10 -2) . Give your answer in standard form. … [2] (g) 216 = 2 3 # 3 3 Write 2160 as a product of its prime factors. … [1]

12 marks

Mark scheme: Question Answer Marks Partial Marks 1(a) 6 000 030 1 1(b) 7.90 cao 1 1(c)(i) 48 1 1(c)(ii) 8 or 24 1 1(c)(iii) 8 1 1(c)(iv) 41 1 1(d) 10 – 12 ÷ (4 + 2) 1 1(e) 600  0.05 M1 9 10 A1 If 0 scored SC1 for 2 correct roundings or for all correct but with any trailing zeros 1(f) 2.4 × 105 2 B1 for correct value but not in standard form 1(g) 24 × 33 × 5 1

This question in 0580/31 Oct/Nov 2024

2 (a) Write the number 845 024 in words. … [1] (b) Write these numbers in order, starting with the smallest. 7 15 39% 0.388 18 40 … 1 … 1 … 1 … [2] smallest (c) Find the value of (i) 45 … [1] (ii) 60 … [1] (iii) 16 # 49 . … [1] (d) Solve. 6x + 5 = 29 x = … [2] (e) By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 2.7 # 42.4 . 8.6 - 4.3 You must show all your working. … [2] (f) 3 5 # 3 x = 3 20 Find the value of x. x = … [1] (g) Simplify ( x4 ) 3. … [1] (h) A boat to town A leaves a port every 16 minutes. A boat to town B leaves the same port every 34 minutes. Both boats leave the port at 07 30. Work out the next time both boats leave the port together. … [3]

15 marks

Mark scheme: 2(a) Eight hundred and forty five thousand 1 and twenty four 2(b) 15 7 2 0.388 39% 40 18 B1 for 3 in the correct order Or M1 for 0.389 or 0.3888 or 0.3889 and 0.39 and 0.375 2(c)(i) 1024 1 2(c)(ii) 1 1 2(c)(iii) 28 1 2(d) 4 2 5 29 M1 for 6x = 29 – 5 or x + = oe 6 6 2(e) 3  40 M1 9 – 4 24 A1 If 0 scored SC1 for 3 correct from 3, 40, 9 and 4 or for all correct but with trailing zeros 2(f) 15 1 2(g) x12 1 2(h) 12 02 3 B2 for 272 or 4 h 32 mins or M1 for 272k or 2  2  2  2  17 oe or [16 = ] 2  2  2  2 and [34 = ] 2  17 or 2 correct factor trees/tables of both 16 and 34 OR M2 for listing times/multiples of both 16 and 34 to at least 1202 or 272 or M1 for listing at least the next 2 of each or 1 full list

This question in 0580/33 Oct/Nov 2024

10 3 0.41 17 42% 7 41 Write these numbers in order, starting with the smallest. … < … < … < … [2] smallest

2 marks

Mark scheme: 10 17 3 2 B1 for three in the correct order 0.41 42% or M1 for conversion to common 41 7 format e.g. 0.428…or 0.429 [0.41] 0.414…or 0.415 0.42 42.8…% or 42.9% 41% 41.4…% or 41.5% [42%]

This question in 0580/31 May/June 2025

20 19 (a) Complete the table of values for y = . x x 1 2 3 4 5 y 20 10 4 [2] 20 (b) On the grid, draw the graph of y = for 1 G x G 5 . x y 25 20 15 10 5 0 x 0 1 2 3 4 5 6 [3] 20 (c) Use your graph to solve the equation = 8 . x x = … [1]

6 marks

Mark scheme: 19(a) [20], [10], 6.67, 5, [4] 2 B1 for each 19(b) Correct graph 3 B2FT for 4 points correctly plotted or B1FT for 2 points correctly plotted 19(c) 2.45 to 2.55 1 FT their curve

This question in 0580/33 May/June 2025

6 1 16 10 5 4 15 10 80 25 2 2 Draw a ring around the fractions which are not equivalent to 5. [2]

2 marks

Mark scheme: 4 1 16 5 2 B1 for 2 correct and no incorrect or all 3 correct and 1 incorrect 10 80 2

This question in 0580/31 Oct/Nov 2025

3 Write one of the symbols 1, 2 or = in each statement to make it correct. 2 … 0.667 3 1 … 12.5% 8 7 71 … 8 80 [2]

2 marks

Mark scheme: 3 < 2 B1 for 2 correct = <

This question in 0580/32 Oct/Nov 2025

12 27 (a) Complete the table of values for y = . x x -4 -3 -2 -1 1 2 3 4 y -4 -6 6 4 [2] 12 (b) On the grid, draw the graph of y = for - 4 G x G -1 and 1 G x G 4 . x y 12 10 8 6 4 2 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 2 – 4 – 6 – 8 – 10 – 12 [4] 12 (c) Use your graph to write down the solution of the equation = 10 . x x = … [1] Question 28 is printed on the next page.

7 marks

Mark scheme: 27(a) −3 −12 12 3 2 B1 for 2 correct 27(b) Correct curve 4 B3FT for 7 points correctly plotted B2FT for 5 points correctly plotted B1FT for 3 points correctly plotted 27(c) 1.1 to 1.3 1 FT their curve

This question in 0580/32 Oct/Nov 2025

3 (a) Write 0.25 as a fraction. … [1] 1 (b) Write as a percentage. 2 … % [1] (c) Write 7% as a decimal. … [1]

3 marks

Mark scheme: 3(a) 1 1 or equivalent fraction 4 3(b) 50 1 3(c) 0.07 cao 1

This question in 0580/33 Oct/Nov 2025

22 (a) Complete the table of values for y = x 2 - 4 . x –4 –3 –2 –1 0 1 2 3 4 y 12 0 –3 –3 0 12 [2] (b) On the grid, draw the graph of y = x 2 - 4 for - 4 G x G 4 . y 12 11 10 9 8 7 6 5 4 3 2 1 – 4 – 3 – 2 – 1 0 1 2 3 4 x – 1 – 2 – 3 – 4 – 5 [4]

6 marks

Mark scheme: 22(a) 5 – 4 5 2 B1 for 2 correct 22(b) Correct curve 4 B3FT for 8 points correctly plotted B2FT for 6 points correctly plotted B1FT for 4 points correctly plotted

This question in 0580/33 Oct/Nov 2025