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.A circle has a diameter of 10 cm. Work out the exact circumference of the circle, in terms of π.
- 2.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).
- 3.An adult cinema ticket costs £15 and a child ticket costs £9. Write the ratio of the adult price to the child price in its simplest form.
- 4.A water tank holds 2.5 m³. Work out this volume in cm³.
- 5.A factory checked 400 items. A frequency tree splits them into 250 items made by machine A and 150 items made by machine B. On machine A's branch, 15 of the items were faulty. On machine B's branch, 5 of the items were faulty. One of the 400 items is picked at random. Work out the probability that it is faulty. Give your answer as a fraction in its simplest form.
- 6.A pie chart is divided into 10 equal sectors. 6 of those sectors stand for the people who chose purple. Altogether 120 people were asked. Work out how many of them chose purple.
- 7.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.
- 8.Which expression is equivalent to 5x − (x + 3)?
- 9.A box holds 80 chocolates. 75% of them are milk chocolates. Work out how many milk chocolates are in the box.
- 10.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.
- 11.At a tombola stall, each ticket wins a toy, wins a sweet or wins nothing, and no ticket can win more than one of these. The probability that a ticket wins a toy is 0.15 and the probability that it wins a sweet is 0.4. Work out the probability that a ticket wins neither a toy nor a sweet.
- 12.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.
- 13.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
- 14.A charity receives £360 in donations in January and £480 in donations in February. Write the amount received in January as a fraction of the amount received in February, giving your answer in its simplest form.
- 15.Two angles are complementary. One of them is 35°. Work out the size of the other angle.
- 16.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.
- 17.Make x the subject of the formula y = 5x + 3.y = 5x + 3
- 18.Write the ratio 20 : 30 in its simplest form.
- 19.Which of these is written correctly in standard form?
- 20.The width, the length and the height of a box are in the ratio 3:4:5. The length of the box is 16 cm. Work out the height of the box.
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.