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.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?
- 2.Solve x² = 81.
- 3.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.
- 4.Work out the exact value of tan 30° + tan 30°.
- 5.In a class of 32 pupils, 19 study geography and 15 study history. 8 study both subjects. Work out n(G ∪ H), the number of pupils who study geography or history or both.
- 6.Isla wants to find out the favourite television programme of the pupils at her school. She asks only her own close group of friends. Write down what is wrong with her sample.
- 7.Work out 3.7 × 24.
- 8.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
- 9.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.
- 10.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.
- 11.At a summer fair, the probability of winning at the hoopla stall is 6/10 and the probability of winning at the coconut shy is 2/10. Work out how many times as likely a player is to win at the hoopla stall as at the coconut shy.
- 12.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.
- 13.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.
- 14.1 litre = 100 centilitres. Work out how many centilitres there are in 6 litres.
- 15.A perpendicular bisector is drawn through the midpoint of a line segment AB. Which set of points does this construction show?
- 16.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
- 17.Which expression is equivalent to 7x − 3(2x − 6)?
- 18.Two quantities are connected by the formula y = 0.8x. Write down the ratio y : x in its simplest form.y = 0.8x
- 19.A bus leaves the station at 09:47 and arrives at its destination at 11:23. Work out the journey time.
- 20.3 kg of apples cost £6. Work out the cost of 5 kg of the same apples.
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.