ZIMSEC O Level · Mathematics · Form 1, Form 2, Form 3
Algebra uses letters to stand for numbers so that we can write general rules.
Simplifying and expanding
- Collect like terms: 3a + 5b − a + 2b = 2a + 7b.
- Expand brackets by multiplying every term inside: 3(2x − 5) = 6x − 15.
- Two brackets: (x + 3)(x − 5) = x² − 5x + 3x − 15 = x² − 2x − 15.
Factorising
- Common factor: 6x² + 9x = 3x(2x + 3).
- Difference of two squares: a² − b² = (a + b)(a − b).
- Quadratic: x² + 7x + 12 = (x + 3)(x + 4). Find two numbers that multiply to 12 and add to 7.
Changing the subject of a formula
Do the same operation to both sides, undoing the operations in reverse order.
Worked example: Make r the subject of A = πr².
Divide by π: r² = A/π. Square root: r = √(A/π).
Laws of indices
- aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ
- a⁰ = 1; a⁻ⁿ = 1/aⁿ; a^(1/n) = ⁿ√a
Worked example: Simplify 8^(2/3).
8^(1/3) = 2, so 8^(2/3) = 2² = 4.
Exam tip: When factorising, always take out the common factor first, then look for a quadratic or difference of two squares.
Check yourself
- Expand and simplify (2x − 1)(x + 4).
- Factorise completely 2x² − 18.
- Make t the subject of v = u + at.
Show answers
- 2x² + 7x − 4
- 2(x + 3)(x − 3)
- t = (v − u)/a
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