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.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.
- 2.Solve the inequality 3x − 1 ≤ 11.
- 3.40% of a number is 12 more than 25% of the same number. Work out the number.
- 4.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.
- 5.A fair six-sided dice is rolled once. Work out the probability that the score is an odd number. Give your answer as a decimal.
- 6.Ben and Chloe each sat five maths tests. Ben's marks were 62, 64, 65, 66 and 68. Chloe's marks were 40, 52, 65, 78 and 90. Both pupils have a mean mark of 65. Their teacher says the mean on its own does not describe the two sets of marks well. Give a reason why the teacher is right.
- 7.Work out 0.6 × 0.04.
- 8.A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.
- 9.A room is drawn on a plan with a scale of 1 : 200. On the plan the room has an area of 12 cm². Work out the real area of the room, in square metres.
- 10.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².
- 11.A two-way table records how 130 pupils travel to school. 70 of the pupils are girls and the rest are boys. 42 of the girls walk to school and the rest of the girls cycle. 33 of the boys walk to school. Work out what fraction of the girls walk to school.
- 12.Write 0.0038 in standard form.
- 13.Solve (2x + 1)/3 = 5
- 14.A block of wood has a mass of 60 g and a volume of 100 cm³. Work out the density of the block, in g/cm³.
- 15.A courier drone delivers a parcel. It starts at the point (2, 1) on a map grid measured in kilometres. It flies by the vector to a warehouse, then by the vector to the delivery address. Work out the coordinates of the delivery address.
- 16.Work out √(4 × 9)
- 17.Work out the value of 3b − 4 when b = 6
- 18.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.
- 19.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.
- 20.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
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.