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 student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.
- 2.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.
- 3.Simplify the ratio 45 : 30 : 75 to its simplest form.
- 4.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 5.A student is estimating the probability that a spinner lands on red. In her first 85 spins it landed on red 34 times. She then spins it 165 more times, and in those it lands on red 58 times. Work out the best estimate of the probability of red from all 250 spins. Give your answer as a decimal, correct to 3 decimal places.
- 6.A company found that the higher the price it charged for a product, the lower the satisfaction score its customers gave. The price and the satisfaction score are plotted on a scatter graph. Describe the line of best fit that would be drawn on that graph.
- 7.Work out the highest common factor of 12 and 18.
- 8.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.
- 9.A rectangular garden has its length and width in the ratio 5:3. Given that the perimeter of the garden is 64 m, work out the width of the garden.
- 10.A builder lays a low wall made from identical bricks. The diagram shows the plan of the wall's footprint on a grid, where each square is one brick. The wall is built up to a height of 4 bricks everywhere. Work out the total number of bricks used.
- 11.At a fête, a game costs £3 to play. The probability of winning is 0.1, and each win pays out £20. 150 people play the game. Work out the fête's expected profit from the game.
- 12.Which of these statements about −0.7 and −0.25 is true?
- 13.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?
- 14.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.
- 15.Write down the exact value of cos 30°.
- 16.Work out √225 ÷ 3.
- 17.Factorise fully 56x − 24
- 18.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.
- 19.A country has an area of 25,000,000 hectares. Write this area in standard form.
- 20.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.
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.