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)
MathsUKwww.geekhero.co.uk
- 1.Work out (2/3)² + (1/2)². Give your answer as a fraction.
- 2.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.
- 3.Given that 1 mile ≈ 1.6 km, work out a speed of 55 mph in km/h.
- 4.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.
- 5.A fair six-sided dice is rolled once. Write down the probability of rolling a 6.
- 6.A sports club has 300 women members and 200 men members, 500 members in total. The club committee wants to choose a sample of 40 members that is in proportion to the club's membership. Work out how many women should be in the sample.
- 7.Write 200 as a product of its prime factors, using index notation.
- 8.Solve 3x − 1 = 8
- 9.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
- 10.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?
- 11.Isla travels to school by bus, by bike, on foot or by car, and never by more than one of these on the same day. The probability that she travels by bus is 0.2, the probability that she travels by bike is 0.3 and the probability that she travels on foot is 0.1. Work out the probability that she travels to school by bus, by bike or on foot.
- 12.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.
- 13.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.
- 14.A mortar mix is made from sand and cement in the ratio 5 : 3. Write the ratio of sand to the total mix in its simplest form.
- 15.In geometry, which of the following best describes a 'plane'?
- 16.Round 3.947 to 2 decimal places.
- 17.Which of these values of x is a solution of x² + 2x − 15 = 0?
- 18.£96 is shared between Ben, Cara and Dev in the ratio 2:3:7. Work out how much Cara receives.
- 19.Is 120 divisible by 5? Give a reason for your answer.
- 20.A charity collects donations from adults and children in the ratio 5:2. Altogether, £238 is collected. Work out how much more the adults donate than the children.
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.