Dr John P. Magufuli Secondary School | Form Two Algebra Mastery

Comprehensive Algebra Summary - Form Two

1. Algebraic Expressions

Algebra uses letters (variables) to represent numbers. Terms: parts separated by + or −. Like terms: same variable power.
Example: 3x + 5y - 2x + y = (3x-2x) + (5y+y) = x + 6y

✏️ Example: Simplify 4a + 3b - a + 2b → 3a + 5b

2. Expansion & Factorisation

Expansion: a(b + c) = ab + ac. Factorisation: reverse process.

e.g., 3x(x - 4) = 3x² - 12x Factorise: 6x² + 9x = 3x(2x + 3)

📌 Quadratic expansion: (x + 3)(x - 2) = x² + x - 6

3. Laws of Indices (Exponents)

a^m × aⁿ = a^m+n a^m ÷ aⁿ = a^m-n (a^m)ⁿ = a^mn

🧠 Example: 2³ × 2⁴ = 2⁷ = 128

4. Linear Equations & Inequalities

Solve equations by balancing: e.g., 3x + 5 = 20 → 3x = 15 → x = 5.
Inequalities: reverse sign when multiplying/dividing by negative.

⚡ Example: Solve 2(x - 3) ≤ 10 → 2x - 6 ≤ 10 → 2x ≤ 16 → x ≤ 8

5. Simultaneous Equations (2 variables)

Substitution or elimination method.
Elimination: 2x + y = 7 and x - y = 2 → add: 3x = 9 → x = 3, then y = 1.

Solution: x=3, y=1

6. Quadratic Equations

Standard form ax² + bx + c = 0. Solve by factorisation, completing square, or quadratic formula: x = [-b ± √(b² - 4ac)] / 2a

📐 Example: x² - 5x + 6 = 0 → (x-2)(x-3)=0 → x=2 or x=3

7. Changing the Subject & Word Problems

Rearrange formulae. Translate real scenarios into algebraic equations.

🚀 Tip: Always define variables first. "Two numbers sum to 20, difference 4" → x+y=20, x-y=4 → numbers 12 and 8.

Master these topics for high performance in Form Two National Assessment!