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 speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.
- 2.Solve the inequality 5 − x ≤ 2.
- 3.An architect builds a scale model of a staircase before construction. The model is mathematically similar to the real staircase, at a scale of 1 : 10. The model covers a floor area of 0.4 m² on the plan. Work out the floor area the real staircase will cover, giving your answer in m².
- 4.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?
- 5.A cinema sold 150 tickets for a Saturday screening. A frequency tree records the sales: 90 of the tickets were bought by adults and the rest by children. Of the adult tickets, 54 were for the 3D showing and the rest were for the standard showing. Work out how many adult tickets were for the standard showing.
- 6.A two-way table records whether each of 40 people at a gym in Sheffield prefers weights or cardio, and whether they are male or female. 24 of the 40 people are female. 15 of the males prefer cardio. 10 of the females prefer weights. Work out the total number of people who prefer cardio.
- 7.A paint mix is made from white paint and blue paint in the ratio 5 : 3. Priya uses 1.2 litres of blue paint and the matching amount of white paint. Work out the total volume of the mix.
- 8.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?
- 9.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.
- 10.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?
- 11.In a board game Mia moves forward by the total of two ordinary fair dice. Work out the probability that her total is 7. Give your answer as a fraction in its simplest form.
- 12.Grace buys three items costing £9.95, £19.90 and £4.99. Work out an estimate for the total cost, by rounding each price to the nearest pound.
- 13.Which expression means the same as 3 × a × b?
- 14.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².
- 15.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.
- 16.Work out 6² − 4².
- 17.Make x the subject of the formula y = x/2 − 5.y = x
- 18.A cyclist rides at a steady speed of 20 mph. Given that 1 mile ≈ 1.6 km, work out the cyclist's speed in km/h.
- 19.Work out √49
- 20.Which of these ratios is equivalent to 5 : 4?
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.