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.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.
- 2.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
- 3.The ratio of the amount Noah has saved to the amount Grace has saved is 4:5. Noah has saved £200. Work out how much they have saved altogether.
- 4.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).
- 5.On the probability scale from 0 (impossible) to 1 (certain), evens is exactly halfway. An event is 3/10 more likely than evens. Work out the probability of that event, giving your answer as a decimal.
- 6.Grace asked 12 children how many brothers and sisters they have. Her results, in order, were 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 6. Work out the median number of brothers and sisters.
- 7.Simplify x⁷ × x⁴, giving your answer as a single power of x.
- 8.Work out the equation of the straight line through the points (−3, 4) and (1, −8).
- 9.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.
- 10.A rectangular notice board measures 150 cm by 80 cm. Work out its area in m².
- 11.Spinner C has 3 equal sections, numbered 2, 3 and 5. Spinner D has 6 equal sections, numbered 1 to 6. Both spinners are spun once, and the two numbers are multiplied together. Work out the probability that the product is a multiple of 5.
- 12.Work out the highest common factor of 15 and 25.
- 13.Factorise fully 56x − 24
- 14.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.
- 15.In this question, a curved surface counts as a face. How many faces does a cone have?
- 16.Work out 35% of 180.
- 17.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.y = 0.15x + 20
- 18.A recipe for 4 people needs 300 g of rice. Work out how much rice is needed for 6 people, assuming the amount is in direct proportion to the number of people.
- 19.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.
- 20.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.
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.