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.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.
- 2.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?
- 3.A printer prints pages at a constant rate. It prints 45 pages in 6 minutes. Work out how many pages it prints in 10 minutes.
- 4.In a construction, a point P is marked at the foot of the perpendicular drawn from point X to a straight line. Which statement correctly compares the distance XP with the distance from X to any other point on the line?
- 5.The probability that a component is faulty is 1/10. Two components are tested independently. Work out the probability that at least one of the two components is faulty.
- 6.Ben and Chloe each sat five maths tests. Ben's marks were 62, 64, 65, 66 and 68. Chloe's marks were 40, 52, 65, 78 and 90. Both pupils have a mean mark of 65. Their teacher says the mean on its own does not describe the two sets of marks well. Give a reason why the teacher is right.
- 7.Write '3.2 million' as a number in figures.
- 8.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
- 9.6 identical taps fill a paddling pool in 20 minutes. Each tap fills at the same steady rate. Work out how long 3 of these taps would take to fill the same pool.
- 10.A zip-wire is fixed at an angle of 60° to the horizontal ground. The zip-wire is 12 m long. Using the exact value of cos 60°, work out the exact horizontal distance it covers.
- 11.On Amelia's walk to school there are two sets of traffic lights. The probability that the first set is green when she reaches it is 0.4. The probability that the second set is green when she reaches it is 0.5. The two sets work independently of each other. Work out the probability that both sets are green.
- 12.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.
- 13.Solve the inequality 2(3x − 1) ≥ 4x + 8.
- 14.Write the ratio 4x : 6x in its simplest form, where x is a positive number.
- 15.A solid rubber ball has a radius of 3 cm. Work out the volume of the ball. Use π = 3.14.
- 16.Work out 18 − 4 × 2
- 17.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?
- 18.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
- 19.Write the fraction 47/50 as a decimal.
- 20.The number of calories burned, E, by a runner is plotted against the time, m minutes, on a straight-line graph. The line passes through the origin and the point (10, 80). Work out the gradient of the line.
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.