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.Work out an estimate for 397 ÷ 21, by rounding each number to 1 significant figure.
- 2.Solve 6x + 4 = 28
- 3.Two mathematically similar flags are made in different sizes. The length scale factor from the smaller flag to the larger flag is 5. Work out the area scale factor from the smaller flag to the larger flag.
- 4.A tank holds 3.2 m³ of water. Work out this volume in litres.
- 5.Two ordinary fair dice are rolled. Work out the probability that both dice show the same score.
- 6.A scatter graph shows the number of guests, x, at a wedding and the length of buffet table needed, y metres. The line of best fit is y = 0.5x + 2. Write down what the 2 in this equation tells you about the buffet table.y = 0.5x + 2
- 7.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.
- 8.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.
- 9.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.
- 10.A solid cone has a base radius of 6 cm and a vertical height of 10 cm. Work out the volume of the cone. Use π = 3.14 and give your answer correct to 1 decimal place.
- 11.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.
- 12.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.
- 13.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.y = 12x + 20
- 14.In a school choir the ratio of boys to girls is 3:4. When 6 more boys join the choir, the ratio of boys to girls becomes 1:1. Work out how many girls are in the choir.
- 15.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?
- 16.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.
- 17.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.
- 18.A rectangle has its height and its width in the ratio 3:2. The height of the rectangle is 18 cm. Work out the width of the rectangle.
- 19.Work out √144
- 20.In a fruit bowl, the ratio of apples to oranges is 5 : 3. Work out what percentage of the fruit in the bowl is 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.