Lemmara logoLemmaraWorked solution

4024/21 May/Jun 2022, Question 5: Plotting Curves from a Table of Values

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Complete a table for y = x³ − 4x + 3, draw its graph for −3 ≤ x ≤ 3, then use a straight line to solve x³ − 4x − 2 = 0.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Fill in the missing y value in the table for y = x³ − 4x + 3 at the given x values.

  1. 1x = −3: y = (−3)³ − 4(−3) + 3 = −27 + 12 + 3
  2. 2y = −12

Answer−12

Part (b) · 3 marks

Plot the graph of y = x³ − 4x + 3 over −3 ≤ x ≤ 3 on the grid.

  1. 1Plot (−3, −12), (−2, 3), (−1, 6), (0, 3), (1, 0), (2, 3), (3, 18)
  2. 2Join the points with a smooth curve

AnswerCorrect smooth curve

Part (c) · 3 marks

Sketch the curve, add a suitable straight line, and use it to find the solutions of x³ − 4x − 2 = 0.

  1. 1x³ − 4x − 2 = 0 is the same as x³ − 4x + 3 = 5
  2. 2Draw the line y = 5 and read the x-values where it crosses the curve
  3. 3x ≈ −1.7, x ≈ −0.5, x ≈ 2.2

Answer−1.8 to −1.5, −0.6 to −0.3, 2.1 to 2.5

Stuck on a step? Read the free lesson: Plotting Curves from a Table of Values

Practise more plotting curves from a table of values questions

Real 4024 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on plotting curves from a table of values

Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 5.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.