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.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.
- 2.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?
- 3.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.
- 4.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?
- 5.A bag contains 3 yellow counters and 2 green counters. Sophie takes one counter at random and does not put it back. She then takes a second counter at random. Work out the probability that the first counter is yellow and the second is green.
- 6.A shop records the colour of every car that uses its car park one Tuesday. Its frequency table reads: black 44, silver 37, blue 26, red 18, white 12. Write down the frequency of black cars.
- 7.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.
- 8.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?
- 9.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.
- 10.A treasure map has a scale of 1 cm to 4 m. A path from the start to a rock is drawn as two straight sections, measuring 3 cm and 2.5 cm. Work out the total real distance from the start to the rock, in metres.
- 11.Two fair four-sided dice, numbered 1 to 4, are rolled and the two scores are added together. Work out the probability that the total is 5.
- 12.Work out ((−3) + 5) × (−4) − (−6) ÷ 2
- 13.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).
- 14.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.
- 15.In triangle ABC the base BC is 10 cm long and the sloping side AB is 13 cm long. The perpendicular height from A down to BC is 12 cm. Work out the area of triangle ABC.
- 16.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.
- 17.Solve 3x − 1 = 8
- 18.A recipe uses flour and sugar in the ratio 4 : 1 by mass. The mass of sugar is s grams and the mass of flour is f grams. Write down a formula for f in terms of s.
- 19.Work out an estimate for 89 + 52, by rounding each number to the nearest 10.
- 20.A shop's profit, P pounds, is in direct proportion to the number of items sold, n. When 15 items are sold, the profit is £45. Write down the ratio n : P in its simplest form for this shop.
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.