Every algebra formula on the Grade 12 CAPS information sheet — quadratic formula, discriminant, exponent and surd laws — with notes on when to use each in NSC Paper 1.
Algebra formulas appear in almost every NSC Paper 1 question. The official Department of Basic Education information sheet only gives you the quadratic formula, so the exponent laws, surd rules and factorising identities below must be memorised.
| Formula | Expression | Note |
|---|---|---|
| Quadratic formula | x = (−b ± √(b² − 4ac)) / 2a | Use when the quadratic does not factorise. Round only in the final step. |
| Discriminant (nature of roots) | Δ = b² − 4ac | Δ > 0 two real roots, Δ = 0 one real root, Δ < 0 non-real roots, Δ a perfect square means rational roots. |
| Difference of two squares | a² − b² = (a − b)(a + b) | First factorising check in every simplification question. |
| Sum and difference of cubes | a³ ± b³ = (a ± b)(a² ∓ ab + b²) | Common in simplify-and-solve questions worth 3–4 marks. |
| Exponent laws | aᵐ · aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ | Write every base as a prime before applying the laws. |
| Rational exponents | aᵐ/ⁿ = ⁿ√(aᵐ) | Converting surds to exponent form makes simplification faster. |
Some are printed on the official information sheet, but not all. Treat every formula on this page as examinable and learn it with a worked example so you recognise when to use it.
Algebra & Equations is examined in Paper 1 of the NSC Mathematics examination.
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