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)
MathsUKwww.geekhero.co.uk
- 1.Find the missing number: 17 × ▢ = 391
- 2.Which expression means 'add 3 to n, then multiply the result by 4'?
- 3.A scale drawing states '1 cm represents 25 m'. Which of these is the correct way to write this scale in the form 1 : n?
- 4.Write down the exact value of tan 0°.
- 5.Priya and Ben each want to estimate the probability that a coin lands on heads. Priya flips the coin 50 times and works out her relative frequency. Ben flips the same coin 500 times and works out his relative frequency. Whose relative frequency is more likely to be close to the true probability? Give a reason for your answer.
- 6.A vet records the weights, in kilograms, of 7 dogs, in the order she weighs them: 18, 12, 50, 10, 20, 14, 16. Work out the median weight.
- 7.Work out √49
- 8.Write down the expression that means 5 more than half of n.
- 9.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
- 10.A cyclist rides around a perfectly circular track with centre O. At every moment of the ride, the distance from O to the cyclist is exactly the same. Which term names this fixed distance?
- 11.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.
- 12.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56
- 13.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.
- 14.A crate exerts a force of 84 N on the floor through a base with an area of 2.4 m². Work out the pressure on the floor, in N/m².
- 15.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?
- 16.Work out the value of 2⁻²
- 17.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.
- 18.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.y = 3x
- 19.In a box of counters the ratio of red counters to blue counters is 4 : 5. What fraction of the counters are blue?
- 20.Isla and her brother share £60 in the ratio 1:2. Work out Isla's share.
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.