Instructions
- Answer all questions in Section A and any four questions from Section B.
- Show all working — no marks are given for a final answer alone.
- Calculators are permitted for Section B only.
Section A — Short answer (25 marks)
- Solve for x: 3x + 7 = 22 (2 marks)
- Factorize: x² − 9x + 20 (3 marks)
- Find the value of D = b² − 4ac for 2x² + 5x − 3 = 0 (3 marks)
- A triangle has angles in the ratio 2:3:4. Find each angle. (4 marks)
- Simplify: (2x²y³) ÷ (4xy²) (3 marks)
- Find the equation of a line passing through (2, 3) with gradient 4. (4 marks)
- Express 0.6666... as a fraction in lowest terms. (3 marks)
- If sin θ = 3/5, find cos θ, given θ is acute. (3 marks)
Section B — Long answer (50 marks, choose 4 of 6)
- Solve the quadratic 2x² − 4x − 6 = 0 using the quadratic formula, showing every step. (10 marks)
- A ladder 5 m long leans against a wall, its foot 3 m from the wall's base. Find the angle the ladder makes with the ground. (10 marks)
- Prove that the sum of interior angles of a hexagon is 720°, then find each angle of a regular hexagon. (10 marks)
- A cylinder has radius 7 cm and height 15 cm. Find its curved surface area and volume. Use π = 22/7. (10 marks)
- Two trains leave stations 300 km apart at the same time, travelling toward each other at 60 km/h and 40 km/h. Find when and where they meet. (10 marks)
- Sketch the graph of y = x² − 4x + 3, marking the roots, y-intercept, and vertex. (10 marks)
Marking scheme (summary)
Full marking guidance, including method marks for partially correct working, is available to download separately. As a rule of thumb: method marks are awarded even when the final numeric answer is wrong, provided the approach is valid — so always show your working.