Mathematics 0580/13 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 parallel to line AB. [1]

Question

(a) Write the number 83 042 in words. …… [1] (b) Write down the value of the 7 in the number 346 709. …… [1] (c) Write 8453 correct to (i) the nearest hundred …… [1] (ii) the nearest ten. …… [1] * 0000800000004 * DFD 4

Question

a (a) Measure angle a. …… [1] (b) Write down the mathematical name of this type of angle. …… [1]

Question

Ben records the favourite sport of each of 20 students. Football Cricket Hockey Rugby Football Tennis Rugby Football Football Rugby Tennis Football Rugby Football Cricket Football Rugby Football Cricket Cricket Complete the frequency table. You may use the tally column to help you. Sport Tally Frequency Cricket Football Hockey Rugby Tennis [2] * 0000800000005 * DFD 5

Question

The diagram shows quadrilateral ABCD on a 1 cm 2 grid. y 4 3 B C 2 1 –4 –3 –2 –1 0 1 2 3 4 x –1 –2 A D –3 –4 (a) Write down the coordinates of point B. (…… , ……) [1] (b) Write down the mathematical name of quadrilateral ABCD. …… [1] (c) Find the area of quadrilateral ABCD. …… cm 2 [1] (d) On the grid, plot the point E at (–3, 2) . [1]

Question

Anna thinks of a number, she multiplies it by 2 and then finds the square root. The answer is 12. What number did Anna think of? …… [2] * 0000800000006 * DFD 6

Question

A journey starts at 10 55 and ends at 16 10. Find how long the journey takes. Give your answer in hours and minutes. …… h …… min [1]

Question

These are the masses, in kg, of each of 11 bags. 23 16 8 10 27 19 4 17 13 4 14 (a) Complete the stem-and-leaf diagram to show this information. 0 1 2 Key: 2 | 7 represents 27 kg [2] (b) Find the median. …… kg [1]

Question

Find the value of (a) 2 5 …… [1] (b) 6 0 . …… [1] * 0000800000007 * DFD 7

Question

x° 40° NOT TO SCALE y° The diagram shows an isosceles triangle between a pair of parallel lines. (a) Find the value of x. x = …… [2] (b) Find the value of y. Give a geometrical reason for your answer. y = …… because …… …… [2]

Question

(a) Sam buys 3 apples at 40 cents each. He also buys 5 peaches. The total cost is $3.45 . Find the cost of 1 peach. …… cents [3] (b) Pears cost 55 cents each. Bananas cost 36 cents each. Write an expression, in cents, for the cost of x pears and y bananas. …… [2] * 0000800000008 * DFD 8

Question

(a) Simplify. 3y - 4y + 2y …… [1] (b) Solve. (i) x + 5 = 19 x = …… [1] (ii) 6x - 5 = 7 x = …… [2]

Question

x –6 –5 –4 –3 –2 –1 0 1 2 3 Write down the inequality represented on the number line. …… [2] * 0000800000009 * DFD 9

Question

Victoria invests $2000 at a rate of 5% per year simple interest. Calculate the value of her investment after 4 years. $ …… [3]

Question

Complete each statement. (a) 0.0000047 m 2 = …… cm 2 . [1] (b) 8500 cm 3 = …… litres. [1]

Question

Kai, Jo and Liz share some money in the ratio Kai : Jo : Liz = 4 : 7 : 13. Jo receives $1400. Find the total amount of money they share. $ …… [3] * 0000800000010 * DFD 10

Question

(a) k x # k 5 = k 20 Find the value of x. x = …… [1] (b) Expand and simplify. (x + 5) (x - 4) …… [2] (c) Factorise. 21r 3 - 7r …… [2]

Question

The diameter of a circle is 16 cm. Find the area of the circle. Leave your answer in terms of r. …… cm 2 [2]

Question

Find the number of sides of a regular polygon with interior angle 160°. …… [2] * 0000800000011 * DFD 11

Question

The height, h cm, of a door is 180 cm, correct to the nearest centimetre. Complete this statement about the value of h. …… G h 1 …… [2]

Question

These are the first four terms of a sequence. –6 1 8 15 (a) Write down the next term. …… [1] (b) Write down the term-to-term rule. …… [1] (c) (i) Find the nth term. …… [2] (ii) Is 688 a term in this sequence? Explain how you decide. …… because …… …… [2] * 0000800000012 * DFD 12

Question

The diagram shows triangles A and B. y 10 9 8 7 B 6 5 4 3 2 A 1 0 1 2 3 4 5 6 7 8 9 10 x Describe fully the single transformation that maps triangle A onto triangle B. …… [3] * 0000800000013 * DFD 13

Question

(a) % A B Use set notation to describe the shaded region. …… [1] (b) % = {people in a club} T = {people who play tennis} S = {people who go swimming} There are 60 people in the club. 36 people go swimming. % T S 30 10 (i) Complete the Venn diagram. [2] (ii) Find n (T l) . …… [1] * 0000800000014 * DFD 14

Question

(a) The scale on a map is 1 cm represents 12 km. Write this in the ratio 1 : n . 1 : …… [1] (b) The bearing of B from A is 070°. Find the bearing of A from B. …… [2]

Question

Work out. 3 2 #1 4 3 Give your answer as a mixed number in its simplest form. …… [3] * 0000800000015 * DFD 15

Question

There are 2 sets of traffic lights on Li’s journey to work. The probability he stops at the first set of traffic lights is 0.4 . The probability he stops at the second set of traffic lights is 0.7 . First set of traffic lights Second set of traffic lights …… Stops Stops 0.4 Does not stop …… Stops Does not stop Does not stop (a) Complete the tree diagram. [2] (b) Work out the probability that Li does not stop at both sets of traffic lights. …… [2] Question 27 is printed on the next page. * 0000800000016 * DFD 16

Question

Sam writes 851 000 in standard form as 85.1 # 10 4 . Explain why 85.1 # 10 4 is not a number in standard form. …… [1]