0580/21 Oct/Nov 2024, Question 22: Solving Equations by Graphical Methods
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Given the graph of y = (x + 2)(x − 1)², expand it to a cubic and use a straight line on the graph to solve 2x³ − 5x = 0.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
Expand (x + 2)(x − 1)² and simplify to show it equals x³ − 3x + 2.
- 1(x − 1)² = x² − 2x + 1
- 2(x + 2)(x² − 2x + 1) = x³ − 2x² + x + 2x² − 4x + 2
- 3y = x³ − 3x + 2
AnswerA correct unsimplified expansion e.g. x³ + 2x² − x² − 2x − x² − 2x + x + 2 leading to y = x³ − 3x + 2
Part (b) · 4 marks
Draw a suitable straight line on the grid and use it to solve 2x³ − 5x = 0.
- 12x³ − 5x = 0 → x³ = 2.5x
- 2x³ − 3x + 2 = 2 − 0.5x, so draw y = 2 − 0.5x, through (0, 2) and (2, 1)
- 3Read the x-values where the line meets the curve (check: x = 0 or x² = 2.5)
- 4x ≈ −1.58, x = 0, x ≈ 1.58
Answer−1.5 to −1.6, 0, 1.5 to 1.6
Stuck on a step? Read the free lesson: Solving Equations by Graphical Methods
Practise more solving equations by graphical methods questions
Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on solving equations by graphical methods
Also searched as: 0580/21/O/N/24 · 0580_w24_qp_21 · 0580 w24 21 · question 22.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.