Surds — KCSE Mathematics

KCSE Mathematics · 93 practice questions · 3 syllabus objectives

24 easy36 medium33 hard

What You'll Learn

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

Define rational and irrational numbers and identify surds

Simplify expressions involving surds

Rationalise denominators containing surds

Sample Questions

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easySHORT ANSWER3 marks

Rationalise the denominator of the expression 3/(2 + √5) and express your answer in the form p + q√5. (3 marks)

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Part (a) — 3 marks

Multiply numerator and denominator by the conjugate (2 - √5) (1 mk)

Calculate the new numerator: 3(2 - √5) = 6 - 3√5 (1 mk)

Calculate the new denominator: (2 + √5)(2 - √5) = 4 - 5 = -1 (1 mk)

easySHORT ANSWER4 marks

List two examples of irrational numbers and explain why each qualifies as irrational. (4 marks)

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Part (a) — 2 marks

Example 1: √2 (1 mk)

Example 2: π (1 mk)

Part (b) — 2 marks

√2 cannot be expressed as a fraction of two integers (1 mk)

π is a non-repeating, non-terminating decimal (1 mk)

easySHORT ANSWER4 marks

Identify whether the following numbers are rational or irrational: (a) √{18} (b) 5/2 (c) √{50} (d) √{16}. (4 marks)

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Part (a) — 4 marks

√{18} is irrational (1 mk)

5/2 is rational (1 mk)

√{50} is irrational (1 mk)

√{16} is rational (1 mk)

Express √{50} in its simplest surd form. (2 marks)

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Why Practise Surds?

KNEC Aligned

Questions match the KCSE syllabus objectives and exam format exactly.

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Surds — KCSE Mathematics

What You'll Learn

Sample Questions

+90 More Questions

Why Practise Surds?

KNEC Aligned

Detailed Marking Schemes

Track Your Mastery

Master Surds for KCSE