Mathematics 0580/42 May/June 2025: question paper and mark scheme

Question

A quadrilateral has these properties • the diagonals are the only lines of symmetry • it has rotational symmetry of order 2. Write down the mathematical name of this quadrilateral. …… [1]

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The diagram shows the net of a solid. Write down the mathematical name of this solid. …… [1] * 0000800000004 * DFD 4

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Mass of box A : Mass of box B = 4 : 7 The mass of box B is 2.4 kg more than the mass of box A. Calculate the mass of box A and the mass of box B. box A …… kg box B …… kg [3]

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D 10 cm C NOT TO 8 cm SCALE A 12 cm B ABCD is a trapezium. Work out the area of the trapezium. …… cm 2 [2]

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Scott changes $300 into pounds (£). The exchange rate is £1 = $1.20 . Calculate the amount Scott receives. …… pounds [1] * 0000800000005 * DFD 5

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A solid wooden cone has base radius 4 cm and height 12 cm. The density of the wood is 0.74 g/cm 3 . Calculate the mass of the cone. [Density = Mass ' Volume] …… g [3]

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y = mx + c Rearrange the formula to make m the subject. m = …… [2]

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Calculate. 2.1 2 - 1.9 0.5 …… [1] * 0000800000006 * DFD 6

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Solve the simultaneous equations. You must show all your working. 2w - 3y = 11 3w + y = 11 w = …… y = …… [3]

Question

A group of 12 adults and 9 children travel on a bus. The cost of an adult ticket is $n. The cost of a child ticket is $ (n - 10) . The total cost of the tickets is $277.50 . Find the cost of one adult ticket. $ …… [3] * 0000800000007 * DFD 7

Question

In a sale, the original price of a shirt is reduced by 15%. The sale price of the shirt is $23.63 . Find the original price of the shirt. $ …… [2]

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The length of a rectangle is 16 cm, correct to the nearest centimetre. The width of the rectangle is 14 cm, correct to the nearest centimetre. Calculate the lower bound of the perimeter of the rectangle. …… cm [2] * 0000800000008 * DFD 8

Question

A 12 cm P NOT TO 9 cm 6 cm SCALE B 16 cm C Q R Triangle ABC and triangle PQR are mathematically similar. (a) Calculate the length of PR. PR = ……cm [2] (b) Triangle ABC and triangle PQR are the cross-sections of two prisms. These prisms are mathematically similar. The volume of the smaller prism is 1120 cm 3. Calculate the volume of the larger prism. …… cm 3 [2]

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Factorise. 5x - 10 - ax + 2a …… [2] * 0000800000009 * DFD 9

Question

The interior angle of a regular polygon is 172°. Find the number of sides of this polygon. …… [2]

Question

On any day, the probability that the weather will be sunny is 0.7 . (a) Find the probability that on any day the weather will not be sunny. …… [1] (b) When the weather is sunny, the probability that Rohit goes for a walk is 0.9 . When the weather is not sunny, the probability that Rohit goes for a walk is 0.2 . Find the probability that on any day Rohit goes for a walk. …… [3] * 0000800000010 * DFD 10

Question

(a) Alex invests $400 at a rate of 2.3% per year simple interest. Find the total amount Alex has at the end of 5 years. $ …… [3] (b) Virat has $100 to spend. In February he spends $x . In March he spends 10% more than he spends in February. In April he spends 10% more than he spends in March. At the end of April, Virat has $33.80 remaining. Find the value of x. x = …… [3] * 0000800000011 * DFD 11 (c) Bobbie invests $500 in an account that pays compound interest each year. At the end of 17 years, the value of Bobbie’s investment is $700.13 . Find the value of Bobbie’s investment at the end of 20 years. $ …… [4] * 0000800000012 * DFD 12

Question

D z° E C NOT TO x° 26° SCALE y° 52° 125° A B A, B, C, D and E lie on a circle. Find the values of x, y and z. x = …… y = …… z = …… [4] * 0000800000013 * DFD 13

Question

f (x) = x + 1 g (x) = 5 - 2x h (x) = 2 x (a) Find f (–3) . …… [1] (b) The domain of g (x) is {–3, 0, 2}. Find the range of g (x) . { …… } [2] 1 (c) Find x when h (x) = . 32 x = …… [1] (d) Find x when h –1 (x) = 3 . x = …… [2] * 0000800000014 * DFD 14

Question

C NOT TO SCALE 10 m 56° 12 m D B 34° A The diagram shows a quadrilateral ABCD. CD = 10 m and DB = 12 m. Angle DBA = 90°, angle CDB = 56° and angle ADB = 34°. (a) Calculate the length of AB. AB = …… m [2] (b) Calculate the area of the quadrilateral ABCD. …… m 2 [3] * 0000800000015 * DFD 15 (c) Calculate the perimeter of the quadrilateral ABCD. …… m [5] (d) Calculate the shortest distance from B to the line AD. …… m [3]

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Simplify. (a) 3t 5 # 5t 3 …… [2] 5 (b) `64u 36j6 …… [2] * 0000800000016 * DFD 16

Question

% G H 8 13 7 5 % = {number of students in a class} G = {number of students who study geography} H = {number of students who study history} The Venn diagram shows information about the 33 students in a class. (a) One of the students in the class is picked at random. Find the probability that this student (i) does not study geography and does not study history …… [1] (ii) studies geography and studies history. …… [1] (b) Two of the students who study history are picked at random. Find the probability that one student also studies geography and one student does not study geography. …… [3] * 0000800000017 * DFD 17

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Simplify. h 2 + 4h h 2 - 16 …… [3]

Question

Ahmed walks 2 km at a speed of x km/h. He then walks a further 3 km at a speed of (x + 1) km/h. 1 The total time he takes to walk the 5 km is 1 hours. 4 (a) Show that 5x 2 - 15x - 8 = 0 . [5] (b) Find the value of x. Show all your working and give your answer correct to 2 decimal places. x = …… [3] * 0000800000018 * DFD 18

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P is the point (8, 0) and Q is the point (20, 6). Find the equation of the perpendicular bisector of PQ. Give your answer in the form y = mx + c . y = …… [5]

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y = ax 11 + 3x b dy = 44x 10 + 18x c dx Find the values of a, b and c. a = …… b = …… c = …… [2] * 0000800000019 * DFD 19

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P NOT TO SCALE D C A B The diagram shows a cube. Calculate the angle between the diagonal AP and the base ABCD. …… [4] * 0000800000020 * DFD 20