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.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.
- 2.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.y = x² − 7x + 2
- 3.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.
- 4.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.
- 5.Each turn of a game ends in a win, a draw or a loss, and no turn can end in more than one of these. The probability of a win is 1/4 and the probability of a draw is 1/3. Work out the probability of a loss.
- 6.The numbers 2, 4, 6, 8, 10 and 12 have a mean of 7 and a median of 7. The value 100 is now added to the list. Which measure is changed more by adding 100, and why?
- 7.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.
- 8.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?
- 9.A plumber charges a call-out fee plus an hourly rate. The total charge, C pounds, for a job lasting h hours is shown on a straight-line graph. The line passes through the points (2, 70) and (5, 130). Work out the call-out fee, in pounds.
- 10.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.
- 11.In a class experiment a fair six-sided dice is rolled 60 times and lands on a six 14 times. The whole school then rolls the same fair dice 3000 times. Work out the best estimate of the number of sixes the school should expect.
- 12.A concert hall has 300 seats. 20% of the seats are in the balcony. Work out how many of the seats are in the balcony.
- 13.Make x the subject of the formula y = 5x + 3.y = 5x + 3
- 14.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.
- 15.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
- 16.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.
- 17.Which of these statements is an identity?
- 18.A laptop costs £800 when new. Its value decreases by 25% of its value at the start of each year. Work out how much value the laptop loses in the second year.
- 19.Which of these numbers is a common factor of 18 and 24?
- 20.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.
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.