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.Round 3.947 to 2 decimal places.
- 2.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.
- 3.Triangle A and triangle B are mathematically similar. A side of triangle A is 5 cm long, and the corresponding side of triangle B is 15 cm long. Write the ratio of the length in triangle A to the length in triangle B in its simplest form.
- 4.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.
- 5.At a youth club, 65 members are asked which sports they play. 27 play football, 21 play basketball, and 9 play both. Work out the number of members who play neither sport.
- 6.The daily high temperatures, in °C, in Leeds over five days were 14, 16, 18, 19 and 23. In York over the same five days they were 15, 17, 17, 18 and 18. Write a sentence comparing Leeds and York using both the median and the range.
- 7.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.
- 8.Solve the inequality 2(x − 1) ≤ 8.
- 9.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².
- 10.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
- 11.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.
- 12.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.
- 13.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.
- 14.A scale drawing of a park has a scale of 1 : 2500. On the drawing, the distance between the entrance and the lake is 4.4 cm. A jogger runs from the entrance to the lake and then back to the entrance. Work out the total distance the jogger runs, in kilometres.
- 15.A jug holds 750 ml of water. Work out what fraction of a litre this is.
- 16.Write 200 as a product of its prime factors, using index notation.
- 17.Solve (3x + 2)/5 = (x + 4)/3
- 18.A statue exerts a downward force of 68.4 N on its base, which has an area of 2.85 m². Work out the pressure that the statue exerts on its base, in N/m².
- 19.Write 45,000 in standard form.
- 20.A company's profit this year is 130% of last year's profit. Last year's profit was £40,000. Work out this year's profit.
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.