Algebra opens Paper 1 every year. The format is so predictable that with 30 minutes of focused practice a week, you can bank 20+ marks before the harder topics begin.
How algebra is examined in Paper 1 (23 October 2026)
NSC Mathematics Paper 1 is written on Friday 23 October 2026 at 09:00: 3 hours for 150 marks. Algebra, equations and inequalities carry about 25 of those marks and open the paper, so a confident start here sets the pace for everything after it.
- Quadratic equations, by factorising or with the quadratic formula, often with a rounding instruction.
- Quadratic inequalities, with the answer written in the correct notation.
- Simultaneous equations with one linear and one quadratic equation.
- Surds, exponents and the nature of roots using the discriminant.
Practice 1 — Quadratic equation
Solve for x: 2x² − 5x − 3 = 0. Use factorisation, then verify with the quadratic formula. Answer: x = 3 or x = −½.
Practice 2 — Quadratic inequality
Solve for x: x² − x − 6 ≥ 0. Factorise: (x − 3)(x + 2) ≥ 0. Answer: x ≤ −2 or x ≥ 3. Common slip: writing −2 ≤ x ≤ 3.
Practice 3 — Simultaneous equations
Solve: y = x + 1 and x² + y² = 13. Substitute and you get 2x² + 2x − 12 = 0, giving x = 2 or x = −3, with matching y values 3 and −2.
Practice 4 — Surds
Solve for x: √(x + 7) = x − 5. Square both sides, solve the quadratic, then test for extraneous roots. Answer: x = 9 only.
Practice 5 — Nature of roots (discriminant)
For which value(s) of k will x² + kx + 9 = 0 have equal roots? Δ = 0 → k² − 36 = 0 → k = ±6.
Practice 6 — Exponential equation
Solve 3^(x+1) − 3ˣ = 54. Factorise: 3ˣ(3 − 1) = 54, so 3ˣ = 27 = 3³ and x = 3.
Practice 7 — Equation with a fraction
Solve x − 2/x = 1, with x ≠ 0. Multiply through by x: x² − x − 2 = 0, so (x − 2)(x + 1) = 0 and x = 2 or x = −1. Neither value is 0, so both are valid.
Want more, with full step-by-step solutions?
When a question stops you, snap it into Snap&Learn — you'll get a CAPS-aligned step-by-step explanation in seconds, and your first three AI solutions are free.