Mathematics 0580/33 May/June 2025: question paper and mark scheme

Question

2 6 16 18 24 26 27 33 From this list, write down the number that is (a) a multiple of 12 …… [1] (b) a square number …… [1] (c) a cube number. …… [1]

Question

Shade one square so that the diagram has 1 line of symmetry. [1]

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Put one pair of brackets into this calculation to make it correct. 80 ' 8 + 2 # 3 = 24 [1] * 0000800000004 * DFD 4

Question

Tim drives home from work. The travel graph shows his journey. Work 36 30 Distance 24 from home (km) 18 12 6 Home 0 14 00 14 30 15 00 15 30 Time (a) Write down the time Tim leaves work. …… [1] (b) Tim stops on the way home. (i) Find how far Tim travels before he stops. …… km [1] (ii) Find how long Tim stops for. …… min [1]

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Calculate. 2.8 5 - 0.3 2 5 Give your answer correct to 2 decimal places. …… [2] * 0000800000005 * DFD 5

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In a bag of counters, 6 of the counters are blue. The arrow ( ↓) on the probability scale shows the probability of picking a blue counter at random. 0 0.5 1 Work out the total number of counters in the bag. …… [1] 1

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The local time in Japan is 3 hours ahead of the local time in India. 2 Find the time in Japan when it is 21 45 in India. …… [1]

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Mia changes $350 into euros. The exchange rate is $1 = 0.92 euros. Calculate the amount Mia receives. …… euros [1] * 0000800000006 * DFD 6

Question

C NOT TO SCALE 53° B D 32° y° x° A E ABC is a straight line. BD is parallel to AE. (a) Find the value of x. Give a geometrical reason for your answer. x = …… because …… [2] (b) Find the value of y. Give a geometrical reason for your answer. y = …… because…… [2] * 0000800000007 * DFD 7

Question

Solve. 4p + 11 = 25 p = …… [2]

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(a) Expand and simplify. 5 (x - 2) + 3 (x - 7) …… [2] (b) Factorise. 4a 2 + 16a …… [2] * 0000800000008 * DFD 8

Question

Kai opens his restaurant from Tuesday to Saturday each week. He counts the number of customers each day for two weeks. The bar chart shows some of the results. 70 60 50 Number of customers 40 30 20 10 0 Tue Wed Thur Fri Sat Day Key: = Week 1 = Week 2 (a) In week 1 there were 200 customers in total. Complete the bar chart. [2] (b) Write down the mode for week 2. …… [1] (c) Find the mean number of customers for the 5 days in week 2. …… [2] * 0000800000009 * DFD 9

Question

In May a shop makes a profit of $542. In June the shop makes a profit of $600. (a) Calculate the percentage increase in the profit from May to June. …… % [2] 2 (b) The shop gives of the profit from May to a charity. 5 Find the amount the shop gives to the charity. $ …… [1] (c) The shop spends 38% of the profit from June on a fridge. Find the amount the shop spends on the fridge. $ …… [1]

Question

Meg invests $2500 at a rate of 4.6% per year simple interest. Calculate the total amount of her investment at the end of 3 years. $ …… [3] * 0000800000010 * DFD 10

Question

The table gives information about the costs of hiring bikes. Type of bike Cost for first day Cost for each extra day Road $25 $20 Mountain $40 $35 Electric $70 $50 (a) Work out the cost of hiring 2 road bikes for 3 days. $ …… [2] (b) The cost, M, of hiring a mountain bike for d days can be written as M = 35d + 5 . (i) Write a formula for the cost, E, of hiring an electric bike for d days. E = …… [2] (ii) The cost of hiring an electric bike for 6 days is the same as the cost of hiring a mountain bike for d days. Find the value of d. d = …… [3] * 0000800000011 * DFD 11

Question

The scale drawing shows a path from S to P. The scale is 1 cm represents 2.5 km. North P North S Scale: 1 cm to 2.5 km (a) Work out the actual distance between S and P. …… km [2] (b) Measure the bearing of S from P. …… [1] (c) E is 20 km from P on a bearing of 070°. On the scale drawing, mark the position of E. [2] * 0000800000012 * DFD 12

Question

y 8 7 6 5 4 A 3 B 2 1 C –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 x –1 –2 –3 –4 (a) Sue describes the single transformation that maps shape A onto shape B as a translation by the 7 vector e o. 1 Explain why Sue is incorrect. …… [1] (b) On the grid, draw the image of shape A after a rotation of 90° anticlockwise about (0, 0). [2] (c) Describe fully the single transformation that maps shape A onto shape C. …… [3] * 0000800000013 * DFD 13

Question

(a) D C Points C and D lie on the circle. Write down the mathematical name for the line CD. …… [1] (b) The diagram shows a circle with centre O. O Points K, L and M lie on the circumference of the circle. Draw triangle KLM so that angle KLM = 90° . [1] * 0000800000014 * DFD 14 20

Question

(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] * 0000800000015 * DFD 15

Question

A spinner is numbered 1, 2, 3, 4 and 5. Rinesh spins the spinner many times. He works out the relative frequency that the spinner lands on each number. Number 1 2 3 4 5 Relative frequency 0.15 0.22 0.26 0.25 (a) Complete the table. [2] (b) Rinesh spins the spinner another 1500 times. Calculate the expected number of times the spinner lands on 2. …… [1] * 0000800000016 * DFD 16

Question

(a) These are the distances above the surface of the Earth of five satellites, A, B, C, D and E. Each distance is in kilometres. A B C D E 2 35 800 7.8 # 10 1.5 # 10 6 535 2 # 10 4 (i) Write these distances in order, starting with the shortest. …… , …… , …… , …… , …… [2] shortest (ii) The radius of Earth is 6370 km. Satellite A is k times further from the centre of Earth than satellite D. Show that k = 6.11 correct to 2 decimal places. [2] (b) A satellite travels at a speed of 27 000 km/h. Find the distance the satellite travels in 95 minutes. …… km [2] (c) A different satellite travels at a speed of 25 200 km/h. Convert this speed into m / s. …… m / s [2] * 0000800000017 * DFD 17

Question

The diagram shows a solid cylinder with height 10 cm. NOT TO SCALE 10 cm The volume of the cylinder is 478 cm3. (a) Find the radius of the cylinder. …… cm [3] (b) The cylinder is made from gold. The density of the gold is 19.3 g/cm3. Calculate the mass of the cylinder. mass :Density = D volume …… g [1] * 0000800000018 * DFD 18

Question

The diagram shows a right-angled triangle. 35 cm NOT TO SCALE 22 cm h cm Calculate the value of h. h = …… [2]

Question

The diagram shows a right-angled triangle. 52° NOT TO SCALE 18.4 cm y cm Calculate the value of y. y = …… [2] DFD 19 * 0000800000020 * DFD 20