Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 2 (calculator)
The real Paper 2 is 1.5 hour 30 minutes and 80 marks, 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 a calculator allowed. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
CalculatorGCSE Foundation
GCSE Foundation sample Paper 2 (calculator)
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- 1.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.
- 2.A number machine multiplies its input by 3. The output is 15. Work out the input.
- 3.Map A has a scale of 1 : 25000 and Map B has a scale of 1 : 50000, both showing the same area. A real distance of 10 km is measured on each map. On which map does this distance appear as the longer length, and how long is it on that map, in centimetres?
- 4.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?
- 5.Spinner E has 4 equal sections, numbered 1 to 4. Spinner F has 6 equal sections, numbered 1 to 6. Both spinners are spun once. Work out the probability of getting at least one 3.
- 6.The times taken, in minutes, by 30 runners in a Portsmouth fun run are grouped in this table: 0 < t ≤ 20 — 5 runners, 20 < t ≤ 40 — 10 runners, 40 < t ≤ 60 — 10 runners, 60 < t ≤ 80 — 5 runners. Work out an estimate for the mean time, in minutes.
- 7.Work out (−2)³ + (−3)² − (−4)
- 8.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.
- 9.The number of pupils who walk to school is 3 times the number who cycle. Write the ratio of the number who cycle to the number who walk, in its simplest form.
- 10.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?
- 11.A Venn diagram shows two sets, P and Q, inside a universal set. n(P) = 34, n(Q) = 27, n(P ∩ Q) = 11, and n(ξ) = 90, where ξ is the universal set. Work out n((P ∪ Q)′), the number of elements in neither P nor Q.
- 12.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.
- 13.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.
- 14.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
- 15.A recipe uses 1.25 kg of flour. Work out how many grams of flour this is.
- 16.A tin of paint has a mass of 5.672 kg. Round this mass to 1 decimal place.
- 17.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.
- 18.A jug holds 2 litres. Given that 1 litre = 1000 cm³, work out the capacity of the jug in cm³.
- 19.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.
- 20.A hosepipe fills a paddling pool at a constant rate. The volume of water in the pool increases by 15 litres every 3 minutes. Write down the gradient of the graph of volume against time.
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.