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.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
- 2.Solve the inequality 6x ≥ 18.
- 3.Jamal is paid £54 for working 6 hours. Work out his rate of pay, in £ per hour.
- 4.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
- 5.A biased six-sided dice is rolled once. The probability that it lands on 6 is 0.25. The other five scores are all equally likely. Work out the probability that it lands on 3.
- 6.A town council wants to find out about the eating habits of the people who live in the town. It asks only the members of a local sports club. Give a reason why this sample is biased.
- 7.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.
- 8.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.
- 9.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.
- 10.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.
- 11.A two-way table records how 80 students travel to school. 45 of the students are boys and the rest are girls. 27 of the boys walk to school. Work out the probability, as a fraction, that a student chosen at random from the boys walks to school.
- 12.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.
- 13.a = 2 and b = 5. Work out the value of ab².
- 14.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.
- 15.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.
- 16.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.
- 17.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.
- 18.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.
- 19.Work out 0.6 × 0.04.
- 20.Two broadband providers show their monthly cost on straight-line graphs, with the cost in pounds on the vertical axis and the data used in gigabytes on the horizontal axis. Provider X's line passes through (0, 15) and (100, 35). Provider Y's line passes through (0, 5) and (100, 45). Work out which provider is cheaper for a customer who uses 40 gigabytes in a month.
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.