Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 1 (non-calculator)
The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Foundation qualification — number 25%, algebra 20%, ratio, proportion and rates of change 25%, geometry and measures 15%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
Non-calculatorGCSE Foundation
GCSE Foundation sample Paper 1 (non-calculator)
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- 1.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.
- 2.Work out the value of m² + 3m when m = −2
- 3.Three friends share a raffle prize of £360 in the ratio 2:3:4. Work out the share of the friend whose part of the ratio is 3.
- 4.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.
- 5.A red dice and a blue dice are rolled. Both dice are ordinary and fair. Work out the probability of getting a 1 on the red dice and a 2 on the blue dice.
- 6.A study found that people who drink more coffee tend to concentrate better at work. A coffee company says that this shows that drinking coffee improves concentration. Give the reason why this conclusion cannot be drawn.
- 7.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.
- 8.p = 4. Work out the value of 2p³.
- 9.Write £3.60 : £2.40 as a ratio in its simplest form.
- 10.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.
- 11.Two events are independent. The first has probability 2/5 and the second has probability 1/3. Work out the probability that both events happen.
- 12.Write 0.0038 in standard form.
- 13.Work out the y-intercept of the graph of y = x² + 3x − 10.y = x² + 3x − 10
- 14.Two mathematically similar hexagonal tiles have areas 18 cm² and 50 cm². Work out the ratio of the side length of the smaller tile to the side length of the larger tile, in simplest form.
- 15.p is the column vector with top number 4 and bottom number −3. Work out 2p, giving your answer as a column vector in the form (top, bottom).
- 16.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.
- 17.The diagram shows part of the graph of a reciprocal function of the form , passing through the labelled point. Work out the value of k.
- 18.Work out 25% of 200.
- 19.Work out −4.5 + 2.8.
- 20.Three business partners share a profit of £48,000 in the ratio 3:5:4. Work out how much the partner with 5 parts receives.
How the 20 questions are shared out
- Number — 5 questions (25% of the qualification)
- Algebra — 4 questions (20% of the qualification)
- Ratio, proportion and rates of change — 5 questions (25% of the qualification)
- Geometry and measures — 3 questions (15% of the qualification)
- Probability — 2 questions (7.5% of the qualification)
- Statistics — 1 question (7.5% of the qualification)
Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.