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Quadratic expressions and equations — KCSE Mathematics

KCSE Mathematics · 105 practice questions · 4 syllabus objectives

36 easy42 medium27 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Factorise quadratic expressions of the form ax² + bx + c; solve quadratic equations by factorisation

Apply the quadratic formula x = (–b ± √(b² – 4ac)) / 2a to solve quadratic equations and determine the nature of roots using the discriminant

Solve quadratic equations by completing the square; form a quadratic equation from given roots

Quadratic expressions and equations

Sample Questions

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1
easySHORT ANSWER3 marks

State how to solve the quadratic equation 2x² - 8x + 6 = 0 by completing the square. (3 marks)

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Part (a) — 3 marks
Divide the entire equation by 2 to simplify it (1 mk)
Rearrange to form (x - 4)² = 4 (1 mk)
Solve for x by taking the square root and isolating x (1 mk)
2
easySHORT ANSWER2 marks

Given the quadratic equation x² + 6x + 9 = 0, use the discriminant to determine the nature of its roots. (2 marks)

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Part (a) — 1 mark
Correctly identified and calculated the discriminant (b² - 4ac = 0) (1 mk)
Part (b) — 1 mark
The roots are real and equal (1 mk)
3
easySHORT ANSWER4 marks

Solve the quadratic equation 2x² - 4x - 6 = 0 using the quadratic formula and state the nature of its roots. (4 marks)

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Part (a) — 3 marks
Substituted values into the quadratic formula correctly (1 mk)
Calculated the discriminant (b² - 4ac) correctly (1 mk)
Obtained the correct roots (x = 3 or x = -1) from the formula (1 mk)
Part (b) — 1 mark
The roots are real and distinct (1 mk)
4

Explain how to factorise the quadratic equation x² - 5x + 6 = 0. (4 marks)

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Why Practise Quadratic expressions and equations?

KNEC Aligned

Questions match the KCSE syllabus objectives and exam format exactly.

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Master Quadratic expressions and equations for KCSE

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