10 The diagram shows triangle A and triangle B. – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 – 7 – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 8 y x A B (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Triangle A is mapped onto triangle C by a rotation, 90° anticlockwise, centre (0, 0). Draw triangle C. [2] (c) Triangle A is mapped onto triangle D by an enlargement, scale factor 3, centre (5, -5). Draw triangle D. [2]

10(a) Translation 4 2     −   2 B1 for each 10(b) Triangle at (4, 2), (4, 3), (2, 3) 2 B1 for correct size and orientation but wrong position or SC1 for triangle at (–4, –2), (–2, –3), (–4, –3) 10(c) Triangle at (–1, –2), (–1, 4), (–4, –2) 2 B1 for correct size and orientation but wrong centre

13 The diagram shows triangle A and triangle B. – 7 – 6 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4 5 6 7 – 7 – 6 – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 6 7 y x A B (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Triangle A is mapped onto triangle C by an enlargement, centre (0, 1 - ) and scale factor 2. Draw triangle C. [2]

13(a) Translation 5 4 −       2 B1 for each 13(b) Vertices at (6, –1), (6, –5) and (4, –5) 2 B1 for correct size and orientation, wrong centre

15 The point A has position vector 3 7 - e o and AB 5 12 = - e o. (a) Find the coordinates of point B. ( … , … ) [2] (b) Find AB . AB = … units [2]

15(a) (–2, 5) 2 B1 for each value or for 2 5 −       seen 15(b) 13 2 M1 for (–5)² + 12² oe

16 – 6 – 5 – 4 – 3 – 2 – 1 – 1 1 2 3 4 5 6 – 2 – 3 – 4 – 5 – 6 0 1 2 3 4 5 6 y x C B A Triangles A, B and C are drawn on the grid. (a) Describe fully the single transformation that maps triangle A onto triangle B. … … [2] (b) Describe fully the single transformation that maps triangle A onto triangle C. … … [3] (c) Triangle D is the image of triangle A after an enlargement, scale factor 2, with centre of enlargement (1, 2). Draw triangle D. [2]

16(a) Reflection and x = − 1 oe 2 B1 for reflection B1 for x = − 1 oe 16(b) Rotation and 90º clockwise oe and (0,1) 3 B1 for rotation B1 for 90º clockwise oe B1 for (0,1) 16(c) Triangle D drawn in correct position with vertices (1,2) (5,2) and (5,4) 2 B1 for triangle D drawn with correct orientation but in wrong position or for triangle D drawn with vertices (1,2) (−3,2) and (−3,0)

19 On Monday, 40 adults and 20 children visit a museum. On Tuesday, 30 adults and 35 children visit the museum. The cost of an adult ticket is $2.50 and the cost of a child ticket is $2. This information can be represented by the matrices M and N. M 40 30 20 35 = e o . N 2 50 2 = e o (a) (i) Work out MN. MN = [2] (ii) Explain what the numbers in your answer to part (a)(i) represent. … … [1] (b) The museum increases the cost of tickets by 10%. Complete matrix P to show the new ticket costs. P = f p [2]

19(a)(i) 140 145       2 B1 for one element correct in a 2 by 1 matrix If 0 scored, SC1 for answer (140 145) 19(a)(ii) Total money for tickets on Monday and total money for tickets on Tuesday 1 19(b) 2.75 2.20       2 B1 for one element correct or for 2.75 oe and 2.20 oe seen If 0 scored, SC2 for answer 154 159.5       or 1.1 140 1.1 145 ×     ×   their their evaluated or SC1 for one element correct

Cambridge O Level Mathematics (Syllabus D) · 4024

O-Level Mathematics (Syllabus D) (4024) Vectors, matrices and transformations past paper questions

Revise O-Level Mathematics (Syllabus D) (4024) — Vectors, matrices and transformations with real Cambridge past-paper questions grouped by topic, each shown with its marking scheme. Working one topic at a time targets exactly the skill each question tests.

76 free questions from 2016–2021, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.

Vectors, matrices and transformations in O-Level Mathematics (Syllabus D) 4024 exams, 2020–2025

Across 2020–2025, Vectors, matrices and transformations accounted for 70 questions worth 392 marks in Cambridge O Level Mathematics (Syllabus D) (4024) papers.