Mathematics 0580/32 October/November 2025: question paper and mark scheme

Question

A, B and C are points on a circle, centre O. A O C B (a) Write down the mathematical name for line OC. …… [1] (b) Write down the mathematical name for line AB. …… [1]

Question

Write down all the factors of 32. …… [2]

Question

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] * 0000800000004 * DFD 4

Question

y 4 P 3 2 1 –4 –3 –2 –1 0 1 2 3 4 x –1 –2 –3 –4 (a) Write down the coordinates of point P. ( …… , …… ) [1] (b) On the grid, draw the line y = x . [1] (c) On the grid, draw the line that goes through point P and is perpendicular to the line y = x . [1]

Question

Solve. (a) 8x = 5 x = …… [1] (b) x + 8 = 5 x = …… [1] * 0000800000005 * DFD 5

Question

0 1 8 27 39 51 59 81 From the list of numbers, write down (a) a square number …… [1] (b) the value of 39 0 …… [1] (c) a prime number. …… [1]

Question

Calculate 361 + 1. …… [1]

Question

Complete these statements. 65 000 centimetres = …… metres 3.25 litres = …… millilitres [2]

Question

(a) Shape A is a quadrilateral with only one pair of parallel lines. Write down the mathematical name of shape A. …… [1] (b) Shape B is a quadrilateral with • two pairs of parallel lines • all four sides equal • no right angles. Write down the mathematical name of shape B. …… [1] * 0000800000006 * DFD 6

Question

The bar chart shows the frequency of each score on a spinner. 10 9 8 7 6 Frequency 5 4 3 2 1 0 1 2 3 4 5 Score on spinner Calculate the mean score. …… [3]

Question

Y = 3t 2 + 2m Find the value of Y when t = 6 and m = -3. Y = …… [2] * 0000800000007 * DFD 7

Question

The table shows the results of a survey about the colour of 90 cars in a car park. Colour of car Frequency Pie chart sector angle Black 16 White 34 Other 40 (a) Complete the table. [2] (b) Complete the pie chart. [2] * 0000800000008 * DFD 8

Question

Find the value of 8 5 . Give your answer correct to 3 significant figures. …… [2]

Question

(a) Ada works from Monday to Friday. Her working hours each day are 08 00 to 12 30 and 13 30 to 17 00. Find the number of hours she works in 5 days. …… hours [2] (b) Ada is paid $15.20 per hour. Work out her pay for these 5 days. $ …… [1] 1 (c) On Saturday she is paid 1 times her normal hourly rate. 2 Work out her hourly rate of pay for Saturday. $ …… [1] (d) Ada changes 370 euros into dollars. The exchange rate is $1 = 0.925 euros. Work out the amount she receives. $ …… [1] * 0000800000009 * DFD 9

Question

The scale drawing shows the position of ship A. The scale is 1 centimetre represents 40 kilometres. North A Scale : 1 cm to 40 km Ship B is 220 km from ship A on a bearing of 140°. On the scale drawing, mark the position of ship B. [2]

Question

Find 57% of $128. $ …… [1]

Question

Represent the inequality x H 3 on the number line. x −5 −4 −3 −2 −1 0 1 2 3 4 5 [1] * 0000800000010 * DFD 10

Question

A school records the marks students score in Paper 1 and Paper 2 of a subject. The scatter diagram shows the scores for twelve students. 60 50 40 Paper 2 30 20 10 0 0 10 20 30 40 50 Paper 1 (a) What type of correlation is shown in the scatter diagram? …… [1] (b) On the scatter diagram, draw a line of best fit. [1] (c) Another student scores 35 on Paper 1. Use your line of best fit to find an estimate for their score on Paper 2. …… [1] * 0000800000011 * DFD 11

Question

The diagram shows a cylinder and a cube. NOT TO SCALE x cm 12 cm x cm 5 cm x cm The cylinder has the same volume as the cube. Find the value of x. x = …… [3]

Question

A town has two cinemas, Movie Scene and Flix. The table shows the mean and range of the audience numbers. Mean Range Movie Scene 83 52 Flix 105 25 (a) Which cinema has higher audience numbers on average? Give a reason for your choice. Cinema …… because …… …… [1] (b) Which cinema has greater variation in its audience numbers? Give a reason for your choice. Cinema …… because …… …… [1] * 0000800000012 * DFD 12

Question

Calculate (5.6 # 10 -3) ' (2.4 # 10 -5) . Write your answer in standard form. …… [2]

Question

NOT TO SCALE 16 m 10 m The diagram shows a garden. The garden has a circular pond and the shaded area is grass. The width of the grass area is equal to the diameter of the pond. (a) Find the area of the pond. …… m 2 [2] (b) Find the area of the grass. …… m 2 [2] (c) Find the percentage of the garden that is grass. …… % [2] * 0000800000013 * DFD 13

Question

6 cm NOT TO 15 cm SCALE 14 cm Calculate the perimeter of this trapezium. …… cm [4]

Question

Triangles ABC and PQR are mathematically similar. Q B NOT TO 42 cm SCALE A P 12 cm C 28 cm R Calculate AB. AB = …… cm [2] * 0000800000014 * DFD 14

Question

(a) The grid shows line L. y 5 L 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 x Find the equation of line L in the form y = mx + c . y = …… [3] (b) Another line, R, has equation y =- 3x + 5 . Find the equation of the line which is parallel to R and goes through the point (1, 5). Give your answer in the form y = mx + c . y = …… [2]

Question

The diagram shows a right-angled triangle. x cm NOT TO SCALE 37° 12 cm Calculate the value of x. x = …… [2] * 0000800000015 * DFD 15 12

Question

(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. * 0000800000016 * DFD 16

Question

Ali invests $2950 in an account paying 12% compound interest. Bob invests $3000 in an account paying 12% simple interest. Show that after 3 years Ali has a larger investment than Bob. [5]