CBC-Aligned · Kenya's Free Mathematics Resource

Master Mathematics
One Step at a Time

Clear, structured lessons in algebra, trigonometry, calculus and statistics — designed for secondary school and college students across Kenya and fully aligned to the Competency Based Curriculum (CBC) as approved by KICD, TSC, and the Ministry of Education. No account required. Always free.

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100+Worked Examples

13Core Topics

CBCAligned

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Fully Aligned to the Kenyan CBC Curriculum

KICD Kenya Institute of Curriculum Development standards

TSC Teacher Service Commission competency frameworks

MoE Kenya Ministry of Education Senior Secondary pathways

Senior Secondary STEM, Arts & Sports Science, Social Sciences pathways

B.Ed Science — Univ. of Embu

Mathematics & Computer Science

Embu County, Kenya

Meet Your Teacher

About Mwalimu Ronny

My name is Ronny Mwenda Best, a qualified Mathematics and Computer Science teacher based in Embu County, Kenya, and a B.Ed Science student at the University of Embu. I created this platform because I believe every Kenyan student — regardless of their school's resources or location — deserves access to high-quality, curriculum-aligned mathematics instruction.

Every lesson on this site is written and reviewed by me personally, following the Competency Based Curriculum (CBC) as defined by the Kenya Institute of Curriculum Development (KICD). The content maps directly to the Senior Secondary mathematics strands — covering Pure Mathematics, Applied Mathematics, and the cross-cutting competencies required under Kenya's current education framework.

My teaching philosophy is simple: no student is bad at mathematics — they simply have not yet found the right explanation. That is why every topic here is broken into numbered, logical steps with multiple worked examples, common error warnings, and practice problems that mirror the style of KCSE and Senior Secondary assessments.

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Core Curriculum · 13 Topics

All Mathematics Topics

Structured lessons from foundational concepts through to advanced applications — aligned to the Kenyan CBC Senior Secondary curriculum.

Algebra

Pure Maths

2x² + 5x − 3 = 0x = ½, −3

Linear & quadratic equations
Simultaneous equations
Logarithms & exponents
Factorisation methods

Intermediate

Explore Algebra

Trigonometry

Pure Maths

sin²θ + cos²θ=1

Sine, cosine & tangent ratios
Unit circle & identities
Sine & Cosine Rules
Trigonometric equations

Intermediate

Explore Trigonometry →

Statistics

Applied Maths

Mean[2,4,6,8]=5

Mean, median & mode
Standard deviation
Probability & distributions
Data representation

Foundational

Explore Statistics →

Limits

Calculus

lim x→0 sin(x)/x=1

Definition of a limit
One-sided limits
Continuity of functions
L'Hôpital's Rule

Advanced

Explore Limits →

Differentiation

Calculus

d/dx (x⁴)=4x³

Power, product & chain rules
Rates of change
Turning points & optimisation
Implicit differentiation

Advanced

Explore Differentiation →

Integration

Calculus

∫ 3x² dx=x³ + C

Indefinite integration
Definite integrals
Area under a curve
Integration by substitution

Advanced

Explore Integration →

Vectors

Pure Maths

|AB⃗|=√(x²+y²)

Vector addition & subtraction
Magnitude & direction
Dot product
Position vectors

Intermediate

Explore Vectors →

Matrices

Pure Maths

det(A)=ad − bc

Matrix operations
Determinants & inverses
Solving linear systems
Geometric transformations

Intermediate

Explore Matrices →

Conic Sections

Pure Maths

x²/a² + y²/b²=1

Circles & ellipses
Parabolas & hyperbolas
Standard form equations
Focus & directrix

Advanced

Explore Conics →

Sequences & Series

Pure Maths

Sn = n/2(a+l)→AP Sum

Arithmetic progressions
Geometric progressions
Sum of series
Convergence tests

Intermediate

Explore Sequences →

Complex Numbers

Pure Maths

i²=−1

Real & imaginary parts
Argand diagrams
Modulus & argument
Complex arithmetic

Advanced

Explore Complex Numbers →

Areas

Applied Maths

Area △=½ bh

Area of plane shapes
Composite figures
Surface area of solids
Sector & segment area

Foundational

Explore Areas →

Volumes

Applied Maths

V = πr²h→Cylinder

Prisms & cylinders
Pyramids & cones
Spheres & hemispheres
Composite solids

Foundational

Explore Volumes →

Featured Lesson · CBC Senior Secondary

Solving Quadratic Equations — Three Methods

Quadratic equations appear across all three Senior Secondary pathways in the CBC curriculum. Mastering all three solution methods — factorisation, the quadratic formula, and completing the square — is essential for both internal assessments and the KCSE examination.

Standard Form

ax² + bx + c = 0 (a ≠ 0)

A quadratic equation is any polynomial equation of degree 2. The term "quadratic" comes from the Latin quadratus, meaning "square." In the CBC curriculum, quadratic equations first appear in Grade 9 under the Algebra strand and deepen in Senior Secondary under Pure Mathematics. They model real-world situations such as projectile motion, profit optimisation, and area problems.

Method 01

Factorisation

Best used when the equation has small integer coefficients and factors neatly. Always check that the right-hand side equals zero before factorising.

Example: Solve x² + 5x + 6 = 0

The equation is already in standard form (right side = 0).
Find two numbers that multiply to c = 6 and add to b = 5. Those numbers are 2 and 3 (because 2 × 3 = 6, and 2 + 3 = 5).
Rewrite as a product of two brackets: (x + 2)(x + 3) = 0
Apply the Zero Product Property: if A × B = 0, then A = 0 or B = 0.
Solve each factor: x + 2 = 0 → x = −2 x + 3 = 0 → x = −3

x = −2 or x = −3

✓ Check: (−2)² + 5(−2) + 6 = 4 − 10 + 6 = 0 ✔

Method 02

Quadratic Formula

The most reliable method — works for every quadratic equation, including those that cannot be factorised over the integers.

Example: Solve 2x² − 4x − 6 = 0

Identify the coefficients: a = 2, b = −4, c = −6
Compute the discriminant: Δ = b² − 4ac = (−4)² − 4(2)(−6) = 16 + 48 = 64
Since Δ > 0, there are two distinct real roots.
Apply the formula: x = (−b ± √Δ) / 2a = (4 ± √64) / 4 = (4 ± 8) / 4
x = (4 + 8)/4 = 12/4 = 3 or x = (4 − 8)/4 = −4/4 = −1

x = 3 or x = −1

✓ Check: 2(3)² − 4(3) − 6 = 18 − 12 − 6 = 0 ✔

Method 03

Completing the Square

This method transforms the quadratic into a perfect square, making it easy to solve. It also derives the quadratic formula and is essential for graphing parabolas.

Example: Solve x² + 6x + 5 = 0

Move the constant to the right: x² + 6x = −5
Take half of the coefficient of x: (6/2)² = 9
Add 9 to both sides: x² + 6x + 9 = −5 + 9 = 4
Write the left side as a perfect square: (x + 3)² = 4
Take square roots: x + 3 = ±2
x = −3 + 2 = −1 or x = −3 − 2 = −5

x = −1 or x = −5

✓ Check: (−1)² + 6(−1) + 5 = 1 − 6 + 5 = 0 ✔

Understanding the Discriminant (Δ = b² − 4ac)

Δ > 0 Two distinct real roots e.g. x² − 5x + 6 = 0 → x = 2, 3

Δ = 0 One repeated real root e.g. x² − 4x + 4 = 0 → x = 2 (twice)

Δ < 0 No real roots (complex roots) e.g. x² + x + 1 = 0 → complex roots

⚠ Common Errors to Avoid

Not rearranging to standard form (= 0) before solving
Sign errors when substituting negative values of b into the formula
Writing only one solution when ± gives two answers
In completing the square, forgetting to add the same value to both sides
Confusing "no real roots" (Δ < 0) with "no solution" — complex roots still exist

Full Algebra Lesson →

Quick Reference · Exam-Style

Worked Examples Across Topics

Short, exam-style problems worked step by step — the same format used in KCSE and CBC Senior Secondary assessments.

Algebra

Solve: 3x − 7 = 2x + 5

Collect x terms: 3x − 2x = 5 + 7

Simplify: x = 12

x = 12

Trigonometry

Find sin 60° exactly

Use the 30-60-90 special triangle

Opposite = √3, Hypotenuse = 2

sin 60° = √3 / 2

Differentiation

Differentiate y = 5x³ − 2x

Apply power rule: multiply by power, reduce power by 1

d/dx(5x³) = 15x² · d/dx(−2x) = −2

dy/dx = 15x² − 2

Statistics

Median of: 3, 7, 9, 11, 15

Data already in ascending order

5 values → middle = 3rd value

Median = 9

Integration

Find ∫(4x³ + 6x) dx

Increase power by 1, divide by new power

∫4x³ dx = x⁴ · ∫6x dx = 3x²

= x⁴ + 3x² + C

Vectors

If a = (3, 4), find |a|

Magnitude formula: √(x² + y²)

= √(3² + 4²) = √(9 + 16) = √25

|a| = 5

Learning Pathway

How to Use This Site Effectively

A recommended study pathway that mirrors how CBC competencies are built — from foundational understanding through to examination readiness.

Read the Lesson

Start with the theory section of each topic page. Every concept is explained in plain English with real-world context. Understanding why a rule works is the CBC approach — not just memorising formulas.
Study the Worked Examples

Each lesson contains multiple fully worked examples that mirror KCSE and Senior Secondary exam questions. Read each step carefully — notice how each line follows logically from the one before it.
Attempt Practice Problems

Visit the Practice Problems page and attempt questions on the topic you just studied. Close your notes and work independently — this is how real learning happens.
Check Your Work

Review your answers and identify where you went wrong. Common errors are highlighted in every lesson. Understanding your mistake is more valuable than getting the answer right on the first try.
Ask Mwalimu if Stuck

If you are stuck on a concept or a specific question, post it on Ask Mwalimu. Mwalimu Ronny responds with a clear, step-by-step explanation tailored to your question.

Why Ronny Best Mathematics

Everything a Maths Student Needs

Step-by-Step Methods

Every solution is broken into clearly numbered steps, showing exactly how to move from the problem to the answer — no gaps, no leaps of logic.

CBC-Aligned Content

All lessons follow the current KICD Mathematics curriculum for Senior Secondary schools in Kenya. Topics map to the Pure Mathematics and Applied Mathematics strands.

Ask Mwalimu

Stuck on a specific problem? Post your question on Ask Mwalimu and receive a direct, expert response from Mwalimu Ronny — no account or registration needed.

Progress Tracking

Your learning journey is tracked automatically. See your accuracy, topic mastery, and activity history on your personal progress dashboard, stored securely on your device.

Brain Games

Reinforce mathematical thinking through engaging, curriculum-linked brain games that make practice enjoyable. A great way to review concepts without the pressure of a formal test.

Achievements & Badges

Earn badges as you hit milestones — from your first solved problem to full topic mastery. A rewarding and motivating way to track your growing mathematical confidence.

Frequently Asked Questions

Common Questions from Students

Is this site really free? Do I need to create an account?

Which Kenyan curriculum does this site follow?

Can this site help me prepare for KCSE mathematics?

I am a teacher — can I use these materials in class?

How do I use the Ask Mwalimu feature?

Ready to Improve Your Mathematics?

Begin with structured CBC-aligned lessons, sharpen your skills through practice, and ask Mwalimu Ronny anything — all completely free, no account required.

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