5 Simplify a a a 3 2 - + . … [1]

5 4a final answer 1 To earn the mark, you must simplify the expression correctly to 4a as the final answer.

7 (a) Evaluate 40 . … [1] (b) Simplify m m 3 5 # . … [1]

7(a) 1 1 7(b) m8 1 For part (a), you must state the value 1. For part (b), you must simplify the expression to m^8.

8 (a) Simplify x x 6 15 2 8 + - + . … [1] (b) Expand and simplify ( ) x 5 2 - . … [2]

8(a) 4x + 23 final answer 1 8(b) x² − 10x + 25 final answer 2 M1 for x² − 5x − 5x + 25 or three of these terms correct For part (a), you must provide the fully simplified expression. For part (b), you must provide the fully expanded and simplified expression; one mark is awarded for correctly expanding to show three correct terms or all four terms before simplification.

11 Solve the simultaneous equations. Show your working. x y x y 5 2 7 2 3 18 + = - = x = … y = … [4]

11 Correctly equating one set of coefficients or correct rearrangement of one equation M1 Correct method to eliminate one variable M1 x = 3 y = – 4 nfww A2 A1 for x = 3 or y = – 4 nfww or after A0, SC1 for a pair of values that satisfy either equation or for correct answers with no working To earn marks, you must first correctly equate coefficients or rearrange an equation, then correctly eliminate one variable. Full marks are awarded for both correct answers (x=3, y=-4) with working, with partial credit for one correct answer or for correct answers without working.

12 (a) Lara goes for a cycle ride. The distance–time graph shows her journey. 10 00 Distance (km) 0 5 10 15 20 25 10 30 11 00 11 30 Time of day Calculate Lara’s average speed, in kilometres per hour, for the whole journey. … km/h [3] (b) A car travels at a constant speed of 10 m/s for 80 seconds. It then decelerates at a constant rate of 0.5 m/s2 until it stops. On the grid, draw the speed–time graph for this journey. 0 20 40 10 5 20 15 0 60 Time (s) Speed (m/s) 80 100 120 [2]

12(a) 16 nfww 3 B1 for [total distance = ] 24 used or [total time = ] 1.5 hours oe used M1 for figs 24 ÷ their total time 12(b) Correct graph 2 B1 for line from (0, 10) to (80, 10) B1FT for line from their (80, 10) with gradient –0.5 (a) To earn marks, you must calculate Lara's average speed by dividing the total distance by the total time; partial credit is given for correctly identifying the total distance or total time. (b) You earn marks by drawing the correct speed-time graph, with partial credit for drawing the initial constant speed segment or the deceleration segment with the correct gradient.

Cambridge O Level Mathematics (Syllabus D) · 4024

O-Level Mathematics (Syllabus D) (4024) Algebra and graphs past paper questions

Revise O-Level Mathematics (Syllabus D) (4024) — Algebra and graphs 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.

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

Algebra and graphs in O-Level Mathematics (Syllabus D) 4024 exams, 2020–2025

Across 2020–2025, Algebra and graphs accounted for 283 questions worth 1,531 marks in Cambridge O Level Mathematics (Syllabus D) (4024) papers.