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HomeCIE IGCSE MathematicsAlgebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square)
CIE · IGCSE · Mathematics

Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square)
Practice Questions

20 CIE IGCSE Mathematics questions on Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square), each with instant feedback and a full examiner-style mark scheme.

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✨ Revision guide includes key terms, worked examples and exam technique for Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square).

Try 2 sample questions on Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square)

Question 1 · 1 mark · Difficulty 1/3

Solve the equation x² - 5x + 6 = 0 by factorising.

  1. x = 2 or x = 3
  2. x = -2 or x = -3
  3. x = 1 or x = 6
  4. x = -1 or x = -6
Show answer & explanation
✓ Answer: Ax = 2 or x = 3
Award 1 mark for correct factorisation (x - 2)(x - 3) = 0 and solving. B is incorrect — this gives x² + 5x + 6 = 0 (wrong signs). C is incorrect — this gives x² - 7x + 6 = 0 (factors do not sum to -5). D is incorrect — this gives x² + 7x + 6 = 0 (wrong signs and sum).
Question 2 · 1 mark · Difficulty 2/3

A rectangular garden has length (x + 4) metres and width (x - 1) metres. The area of the garden is 54 m². Which equation represents this situation?

  1. x² + 3x - 4 = 54
  2. x² + 5x - 4 = 54
  3. x² + 3x + 4 = 54
  4. x² - 3x - 4 = 54
Show answer & explanation
✓ Answer: Ax² + 3x - 4 = 54
Award 1 mark for expanding (x + 4)(x - 1) = x² + 3x - 4 and setting equal to 54. B is incorrect — incorrect expansion (added coefficients wrongly). C is incorrect — sign error in constant term. D is incorrect — sign error in x coefficient from expansion.
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20 questions · 25 min · free

CIE IGCSE Mathematics: Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square) FAQ

How many CIE IGCSE Mathematics questions on Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square) are there on Kramizo?
Kramizo currently has 20 exam-board-aligned practice questions on Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square) for CIE IGCSE Mathematics, with new questions added every week. Each question gives you instant feedback and a full examiner-style mark scheme that tells you exactly what would earn marks on a real CIE paper. The questions span the full difficulty range — from straightforward recall (level 1) right up to multi-step reasoning and evaluation (level 3) — so the bank works for first-pass revision and final exam-week stress testing alike.
Is Kramizo free for CIE IGCSE students preparing for Mathematics?
Yes — completely free. Every student gets 45 questions a day on the free plan, with no card required and no trial countdown. That free quota works across every subject and every topic in our bank, so you can mix Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square) practice with other Mathematics topics or even switch to a totally different CIE subject without paying anything. Kramizo's optional Pro plan removes the daily cap and adds detailed progress analytics, but the free tier is the real product — used by thousands of GCSE, IGCSE and CSEC students.
Are the Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square) questions aligned to the official CIE IGCSE Mathematics syllabus?
Every question is written against the published CIE IGCSE Mathematics specification, including the exact command words (state, describe, explain, calculate, evaluate, etc.), mark allocations, and difficulty tier you'd see on a real CIE paper. Explanations are written in the style of official examiner mark schemes — they tell you what is being awarded marks and why distractors are wrong, not just whether you got it right. The bank is continually refined to match the latest syllabus updates from CIE.
How is Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square) typically tested on CIE IGCSE Mathematics papers?
Algebra and Graphs: Solving quadratic equations (factorising, quadratic formula, completing the square) appears across multiple question types on real CIE IGCSE Mathematics papers — most commonly as multiple-choice questions in the objective section, structured short-answer questions in the main paper, and occasionally as part of an extended response. Kramizo's practice bank reflects that mix: 4-option MCQs, true/false statements, fill-in-the-blank key terms, multi-select questions, and ordering questions. Working through the bank gives you exposure to every question style examiners actually use.

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