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.Zoe worked out 3/8 + 1/8 by adding the numerators and the denominators, and got 4/16. Work out the correct value of 3/8 + 1/8, giving your answer in its simplest form.
- 2.Write down the gradient of the line with equation y = 7x − 2.y = 7x − 2
- 3.A graph shows two quantities, x and y, in direct proportion. Write down which statement about the graph must be true.
- 4.A square tile has sides of length 6 cm. Work out the area of the tile.
- 5.Ellie drops a bottle top and records whether it lands open end up. In her first 20 drops it lands open end up 13 times. She carries on, and after 200 drops in total it has landed open end up 84 times. Work out the best estimate of the probability that the bottle top lands open end up.
- 6.A table shows the time each of four pupils took to run 100 m: Oliver 12 seconds, Grace 15 seconds, Ethan 10 seconds, Freya 14 seconds. Write down the name of the fastest runner and the time taken.
- 7.Work out the value of ∛8.
- 8.Work out the equation of the straight line through the points (−3, 4) and (1, −8).
- 9.A table shows three pairs of values: when x = 2, y = 6; when x = 5, y = 15; when x = 8, y = 24. In every pair the ratio y : x is the same. Write down a formula for y in terms of x.
- 10.Write down the exact value of tan 60°.
- 11.Four bags each contain counters, some of which are winning counters. The probability of taking a winning counter is 5/12 from the red bag, 3/8 from the blue bag, 7/24 from the green bag and 1/3 from the yellow bag. Work out which bag has the smallest probability of giving a winning counter.
- 12.A bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.
- 13.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.
- 14.Two straight-line graphs represent y = 2x and y = 5x. For the same value of x, where x ≠ 0, write down the ratio of the y-value on the first graph to the y-value on the second graph, in its simplest form.y = 2xy = 5x
- 15.A water tank holds 2.5 m³. Work out this volume in cm³.
- 16.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.
- 17.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.
- 18.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
- 19.A circle has a radius of 5 cm. Work out the exact circumference of the circle, in terms of π.
- 20.It takes 2 identical pumps 10 hours to empty a flooded basement. Working at the same rate, work out how many hours 5 of these pumps would take to empty the same basement.
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.