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 the value of 6² − 4³.
- 2.A number machine adds 5 to its input. Work out the output when the input is 0.
- 3.Two mathematically similar picture frames have perimeters 30 cm and 45 cm. The area of the smaller frame is 40 cm². Work out the area of the larger frame.
- 4.A diameter divides a circle into two equal halves. Write down the special name given to each of these two halves.
- 5.A seed company tests germination using results from three greenhouses. Greenhouse 1 plants 200 seeds and 172 germinate. Greenhouse 2 plants 150 seeds and 126 germinate. Greenhouse 3 plants 250 seeds and 212 germinate. Using the combined results from all three greenhouses, work out the best estimate of the number of seeds, out of a new batch of 4000 seeds, that would be expected to germinate.
- 6.The masses of eight school bags, in kilograms, are 3, 4, 4, 5, 6, 7, 8 and 11. Work out the median mass.
- 7.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.
- 8.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.
- 9.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.
- 10.Work out the distance between the points (−3, 4) and (5, −2).
- 11.120 members of a sports club were asked whether they play football or netball; each member plays exactly one of the two sports. 70 of the members are male. 45 of the male members play football. 38 of the female members play netball. Work out how many female members play football.
- 12.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.
- 13.Write down the y-intercept of the line with equation y = 3x + 8.y = 3x + 8
- 14.Two mathematically similar garden ponds have surface areas of 12 m² and 27 m². The fencing needed to go around the smaller pond costs £96. Assuming the cost of fencing is proportional to the perimeter of the pond, work out the cost of fencing the larger pond.
- 15.Write down the exact value of tan 60°.
- 16.A circle has a radius of 5 cm. Work out the exact circumference of the circle, in terms of π.
- 17.Solve 2x² − 32 = 0.
- 18.A plan of a garden is drawn to a scale of 1 : 200. A path measures 3 cm on the plan. Work out the real length of the path, in centimetres.
- 19.Round 0.006482 to 2 significant figures.
- 20.A cookery class lasts 45 minutes. A double lesson at school lasts 2 hours. Write the length of the cookery class as a fraction of the length of the double lesson. Give your answer in its simplest form.
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.