Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 1 (non-calculator)
The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-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 no calculator-only items. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
Non-calculatorGCSE Foundation
GCSE Foundation sample Paper 1 (non-calculator)
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- 1.Work out ∛(−27) + ∛8
- 2.Work out the gradient of the straight line with equation 3y = 12 − 6x.
- 3.A shop buys a bike for £150 and sells it, making a profit of £45. Write the selling price as a fraction of the cost price, giving your answer in its simplest form.
- 4.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.
- 5.A grower knows that the probability that one of their seeds germinates is 0.6. The grower wants to expect 300 of the seeds to germinate. Work out how many seeds the grower should plant.
- 6.A café in York counts the number of customers in each of the nine hours it is open on one day: 4, 4, 4, 11, 13, 15, 18, 22 and 25. The owner says that a typical hour has about 4 customers, because 4 is the mode. Is the owner right? Give a reason for your answer.
- 7.Write 0.36 as a fraction in its simplest form.
- 8.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.
- 9.The number of pupils who walk to school is 3 times the number who cycle. Write the ratio of the number who cycle to the number who walk, in its simplest form.
- 10.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
- 11.A drawer contains 4 red socks and 2 blue socks. Two socks are taken out at random, one after the other, without the first being put back. Work out the probability that both socks are the same colour.
- 12.A café offers 3 types of soup and 4 types of bread roll. Work out how many different combinations of one soup and one bread roll are possible.
- 13.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.
- 14.A sofa costs £800. Its price is increased by 25%. Work out the new price of the sofa.
- 15.A line segment joins two points on the circumference of a circle, without necessarily passing through the centre. Write down the general term for this line segment.
- 16.Work out −4.5 + 2.8.
- 17.Solve the inequality 3x + 6 ≤ 0.
- 18.y is directly proportional to x. When x = 8, y = 20. Work out the value of y when x = 12.
- 19.A weather app records the temperature at three points in one day: 6 °C at noon, −2 °C at midnight, and −7 °C just before dawn. Work out the difference between the highest and lowest of these three temperatures.
- 20.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.
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.