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Integration — KCSE Mathematics

KCSE Mathematics · 92 practice questions · 3 syllabus objectives

32 easy28 medium32 hard

What You'll Learn

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

Interpret integration as the reverse process of differentiation and integrate polynomials

Evaluate definite integrals and apply integration in finding the area under a curve

Apply integration in kinematics to find displacement and velocity from acceleration

Sample Questions

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1
easySHORT ANSWER3 marks

A vehicle accelerates from rest with an acceleration given by a(t) = 3t - 2. Determine the expression for the velocity v after time t. (3 marks)

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Part (a) — 3 marks
Integrate: v = 3t²/2 - 2t + c (1 mk)
At t = 0, v = 0: c = 0 (1 mk)
Velocity expression: v = 3t²/2 - 2t (1 mk)
2
easySHORT ANSWER3 marks

Evaluate the definite integral: ∫ from 1 to 3 (4x + 2) dx and interpret the result in the context of finding the area under the curve. (3 marks)

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Part (a) — 2 marks
Integrate: 2x² + 2x; (1 mk)
Evaluate at upper limit x = 3 and lower limit x = 1; (1 mk)
Part (b) — 1 mark
The result represents the area under the curve from x = 1 to x = 3. (1 mk)
3
easySHORT ANSWER3 marks

Define the integral of the polynomial function f(x) = 4x^3 - 2x^2 + 5. (3 marks)

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Part (a) — 3 marks
Integrate 4x^3 to get x^4; result is x^4 (1 mk)
Integrate -2x^2 to get -2/3x^3; result is -2/3x^3 (1 mk)
Integrate 5 to get 5x; result is 5x + C (1 mk)
4

State the integral of the polynomial function 5x^3 - 4x^2 + 2 with respect to x. (3 marks)

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Why Practise Integration?

KNEC Aligned

Questions match the KCSE syllabus objectives and exam format exactly.

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