Lemmara logoLemmaraWorked solution

4024/13 May/Jun 2025, Question 23: Recognising and Sketching Graph Shapes

Cambridge O Level Mathematics 4024 · Paper 13 (Non-calculator) · Non-calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Multiply out and simplify the product of three linear factors, then draw the cubic curve and mark where it meets the axes.

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

Part (a) · 3 marks

Multiply out the three brackets (x − 3)(2x + 5)(x + 2) and collect like terms to give a simplified cubic.

  1. 1(x − 3)(2x + 5) = 2x² + 5x − 6x − 15 = 2x² − x − 15
  2. 2(2x² − x − 15)(x + 2) = 2x³ + 4x² − x² − 2x − 15x − 30
  3. 3= 2x³ + 3x² − 17x − 30

Answer2x³ + 3x² − 17x − 30

Part (b) · 4 marks

Draw y = (x − 3)(2x + 5)(x + 2) on axes, labelling the x-intercepts and the y-intercept.

  1. 1Crosses the x-axis where (x − 3)(2x + 5)(x + 2) = 0: x = 3, x = −2.5, x = −2
  2. 2Crosses the y-axis at x = 0: y = −3 × 5 × 2 = −30
  3. 3Positive cubic (2x³): rises from bottom left, turns between −2.5 and −2, turns again between −2 and 3, rises to top right
  4. 4Label −2.5, −2 and 3 on the x-axis and −30 on the y-axis

AnswerCorrect sketch with values −2.5, −2 and 3 labelled at x-intercepts and −30 labelled at y-intercept

Stuck on a step? Read the free lesson: Recognising and Sketching Graph Shapes

Practise more recognising and sketching graph shapes 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 recognising and sketching graph shapes

Also searched as: 4024/13/M/J/25 · 4024_s25_qp_13 · 4024 s25 13 · question 23.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.