Mathematics 0580/31 October/November 2025: question paper and mark scheme

Question

A B (a) Measure the length of line AB in centimetres. …… cm [1] (b) Draw a line that is perpendicular to the line AB. [1]

Question

Complete this shopping bill. 3.4 kg of flour at $4.60 per kg = $ …… 2.75 kg of sugar at $ …… per kg = $ 9. 90 Total = $ …… [3]

Question

Total cost of a journey = number of litres of fuel used # cost of fuel per litre. A journey uses 128 litres of fuel. The cost of fuel is $1.52 per litre. Calculate the total cost of this journey. $ …… [1] * 0000800000004 * DFD 4 6 1 16 10 5

Question

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

Question

Find the value of (a) (i) 1.96 …… [1] (ii) 17 3 …… [1] (iii) -0.8 # - 1.2 . …… [1] (b) Write these numbers in order, starting with the smallest. 11 27 58% 0.574 19 47 …… 1 …… 1 …… 1 …… [2] smallest

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17 4 25 18 14 6 3 18 12 Find (a) the mode …… [1] (b) the range. …… [1] * 0000800000005 * DFD 5

Question

A bag contains 6 red balls, 4 green balls and 2 blue balls. Zia takes a ball from the bag at random. The diagram shows a probability scale. A B C D E F G 0 1 Which arrow shows the probability that, (a) Zia takes a green ball …… [1] (b) Zia takes a yellow ball …… [1] (c) Zia does not take a blue ball. …… [1]

Question

Solve. (a) 8x = 32 x = …… [1] (b) 6x - 3 = 12 x = …… [2] (c) Represent the inequality -4 G x 1 2 on the number line. –5 –4 –3 –2 –1 0 1 2 3 4 x [2] * 0000800000006 * DFD 6

Question

(a) Write down the mathematical name for this type of angle. …… [1] (b) ABC is a triangle. C 102° NOT TO SCALE 54° x° A B Lily says x is 34. Give a geometrical reason why Lily is not correct. …… [1] (c) D 126° C A 48° x° NOT TO E SCALE 75° B ABCD is a quadrilateral. DCE is a straight line. Calculate the value of x. x = …… [2] * 0000800000007 * DFD 7

Question

Anna and Bruno share some money in the ratio Anna : Bruno = 3 : 7. Bruno receives $36 more than Anna. Calculate the total amount of money they share. $ …… [2]

Question

(a) Naz pays $76.25 per day to hire a car. He hires this car for 7 days. He also pays $146 for fuel. Calculate the total amount Naz pays. $ …… [2] (b) Li pays $1400 to hire a car. $364 of this is insurance. Calculate the insurance as a percentage of the $1400. …… % [1] * 0000800000008 * DFD 8 12 300 students choose where to go on a trip. The students choose either a zoo, a museum, an art gallery or a sports stadium. Zoo Museum (a) Show that 75 students choose the museum. [1] (b) 45 students choose the art gallery and 120 students choose the sports stadium. Complete the pie chart to show this information. [2] * 0000800000009 * DFD 9

Question

In the question paper above.

Question

(a) The surface area of a solid cube is 121.5 cm 2 . Calculate the length of the side of the cube. …… cm [3] (b) 10 cm NOT TO h SCALE 15 cm The area of the trapezium is 106.25 cm 2 . (i) Calculate the height of the trapezium. …… cm [2] (ii) Convert 106.25 cm 2 into m 2 . …… m 2 [1]

Question

A bag contains red, yellow, blue and green cards. The table shows the probability of taking a red card and a yellow card. The probability of taking a blue card or a green card is in the ratio blue : green = 5 : 2 . Complete the table. Colour red yellow blue green Probability 0.53 0.19 [3] * 0000800000010 * DFD 10

Question

Shapes A and B are shown on the grid. y 5 4 3 2 1 –5 –4 –3 –2 –1 0 1 2 3 4 5 x –1 –2 B –3 A –4 –5 –6 (a) Describe fully the single transformation that maps shape A onto shape B. …… [3] 6 (b) On the grid, draw the image of shape A after a translation by the vector e o. [2] 7 * 0000800000011 * DFD 11

Question

Bob travels from town A to town B. The travel graph shows his journey. 600 500 400 Distance from town A (km) 300 200 100 0 08 00 09 00 10 00 11 00 12 00 13 00 14 00 15 00 Time (a) Between which two times did Bob stop for a rest? Explain how you know. …… and …… because …… …… [2] (b) Calculate Bob’s average speed, in km/h, for the whole journey. …… km/h [3] * 0000800000012 * DFD 12

Question

Factorise. 21x - 7xy …… [2]

Question

(a) The nth term of a sequence is n 2 - 4 . Find the first 3 terms of this sequence. …… , …… , …… [2] (b) These are the first four terms of a different sequence. 5 2 -1 -4 Find the nth term. …… [2]

Question

Jo invests $500 at a rate of 2% per year compound interest. Calculate the amount of interest earned at the end of 7 years. $ …… [3] * 0000800000013 * DFD 13

Question

(a) Work out the size of one interior angle of a regular 8-sided polygon. …… [2] (b) D NOT TO C SCALE x° B 71° O E A A, B and C lie on the circumference of the circle, centre O. AB is a diameter. DBE is a tangent to the circle at B. Find the value of x. Give a geometrical reason for your answer. …… because …… …… [2] * 0000800000014 * DFD 14

Question

The line L is shown on the grid. y 18 L 16 14 12 10 8 6 4 2 –4 –3 –2 –1 0 1 2 3 4 x –2 –4 Find the equation of the line L. Give your answer in the form y = mx + c . y = …… [3] * 0000800000015 * DFD 15

Question

(a) A train to town P leaves a station every 20 minutes. A train to town Q leaves the same station every 35 minutes. Both trains leave at 09 30. Find the next time both trains leave together. …… [3] (b) The distance, d km, between town P and town Q is 97 km, correct to the nearest kilometre. Complete the statement about the value of d. …… G d 1 …… [2] 4.6 # 10 3

Question

Calculate . 1.84 # 10 5 Give your answer in standard form. …… [2] Question 24 is printed on the next page * 0000800000016 * DFD 16

Question

A 32 cm C NOT TO SCALE 27° B ABC is a right-angled triangle. Calculate BC.