x̄ - > KCSE Mathematics Topical Review — Core Concepts (1996 to 2024)

Numbers & Operations

Sample KCSE 2017 – Paper 1 – Question:

Evaluate (-12) × (-3) × 4 – (-20) ÷ (-6) × 6 ÷ 3 + (-6)

(-12)×(-3)=36 → 36×4=144 → (-20)÷(-6)=3.33 → 3.33×6=20 → 20÷3=6.67 → 144–6.67+(–6)=131.33

Algebra

Sample KCSE 2020 – Paper 2 – Question:

Simplify: 3a + 2b – (a – b)

3a + 2b – a + b = (3a – a) + (2b + b) = 2a + 3b

Linear Equations

Sample KCSE 2005 – Paper 1 – Question:

Solve for x: 2x + 3 = 7

2x = 4 → x = 2

Quadratic Equations

Sample KCSE 2013 – Paper 2 – Question:

Solve: x² – 5x + 6 = 0

(x – 2)(x – 3) = 0 → x = 2 or x = 3

Geometry – Area & Perimeter

Sample KCSE 2018 – Paper 1 – Question:

A rectangle has width x cm. Its length is 3 cm longer than its width. If area is 28 cm², find its width.

x(x+3)=28 → x²+3x–28=0 → (x+7)(x–4)=0 → x=4 (width=4 cm)

Probability

Sample KCSE 2022 – Paper 1 – Question:

A box contains 3 red, 2 green, 5 yellow balls. Two balls picked, what’s probability both green?

P = 2/10 × 1/9 = 1/45

Vectors

Sample KCSE 2015 – Paper 2 – Question:

In triangle OAB, OA=3i+4j, OB=2i–j. Find AB.

AB = OB – OA = (2i–j) – (3i+4j) = –i – 5j

Trigonometry

Sample KCSE 2018 – Paper 2 – Question:

Triangle sides: 7cm, 8cm, 9cm. Find largest angle.

Use Cosine rule: cos C = (7² + 8² – 9²)/(2×7×8) = 0.446 → C = 63.5°

Transformations

Sample KCSE 2016 – Paper 2 – Question:

Draw the image of triangle ABC after translation by vector (2,–3).

Move each point A, B, C by (2,–3).

Statistics

Sample KCSE 2019 – Paper 1 – Question:

Mean score of class: 4, 6, 8, 10, 12.

Mean = (4+6+8+10+12)/5 = 8

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Part II: Advanced Topics (Mensuration – Calculus)

Mensuration (Surface Area & Volume)

Sample KCSE 2017 – Paper 2 – Question: Find the surface area of a cylinder of radius 7 cm and height 10 cm.

Surface area = 2πr(h + r) = 2π×7×(10+7) = 238π = 748 cm²

Sample KCSE 2018 – Paper 2 – Question: Find volume of a cone of base radius 3.5 cm and height 12 cm.

V = ⅓πr²h = ⅓×π×3.5²×12 = 154 cm³

Matrices

Sample KCSE 2014 – Paper 2 – Question: Find inverse of matrix A = [[2,1],[1,1]].

det(A)=1; A⁻¹ = 1/(2×1–1×1)[[1,–1],[–1,2]] = [[1,–1],[–1,2]]

Sequences & Series

Sample KCSE 2019 – Paper 2 – Question: The 3rd term of an arithmetic sequence is 11, the 7th is 23. Find the first term and common difference.

a+2d=11, a+6d=23 → subtract: 4d=12 → d=3, then a=5.

Surds & Indices

Sample KCSE 2020 – Paper 1 – Question: Simplify: (√18 + √8) / √2

(√(9×2)+√(4×2))/√2 = (3√2+2√2)/√2 = 5

Logarithms

Sample KCSE 2016 – Paper 1 – Question: Solve for x: log₁₀x + log₁₀(x–3) = 1

log₁₀[x(x–3)] = 1 → x²–3x=10 → x²–3x–10=0 → (x–5)(x+2)=0 → x=5 (valid)

Coordinate Geometry

Sample KCSE 2018 – Paper 1 – Question: Find the equation of line through (2,3) and (6,7).

Gradient m = (7–3)/(6–2)=1 → y–3=1(x–2) → y=x+1

Linear Programming

Sample KCSE 2015 – Paper 2 – Question: Maximize P=3x+2y subject to x≥0, y≥0, x+y≤6, x+2y≤8.

Corner points (0,0), (0,4), (4,2), (6,0). P max at (4,2): P=16.

Calculus (Differentiation & Integration)

Sample KCSE 2021 – Paper 2 – Question: Differentiate y=3x²+4x–5.

dy/dx = 6x + 4.

Sample KCSE 2023 – Paper 2 – Question: Find ∫(2x + 3) dx.

∫(2x + 3)dx = x² + 3x + C.

KCSE Mathematics Topical Question Bank (1996–2024)
Compiled for teachers and learners preparing for KCSE Mathematics Revision.