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.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%
- 2.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.
- 3.A cyclist travels 45 km in 3 hours at a constant speed. Work out the cyclist's average speed, in km/h.
- 4.A construction for the perpendicular bisector of AB begins by opening a pair of compasses to more than half the length of AB, then drawing an arc centred at A. What is the next step?
- 5.A spinner lands on red, on blue or on green, and it cannot land on more than one colour at a time. The probability that it lands on red is 0.3 and the probability that it lands on blue is 0.5. Work out the probability that it lands on red or on blue.
- 6.A vet records the masses, m kg, of 30 dogs at a clinic in Preston: 0 < m ≤ 10 — 11 dogs, 10 < m ≤ 20 — 5 dogs, 20 < m ≤ 30 — 5 dogs, 30 < m ≤ 40 — 9 dogs. Work out an estimate for the mean mass, in kg, using the midpoint of each class interval.
- 7.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56
- 8.Priya says that x = 6 is the solution of the equation 4x + 8 = 24. Priya is wrong. Work out the correct value of x.
- 9.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.
- 10.Write down the column vector, from the options given, that would move a point to the right and downwards.
- 11.The universal set is {1, 2, 3, ..., 30}. Set A is the set of multiples of 4 between 1 and 30. Work out n(A′), the number of elements not in A.
- 12.Simplify 2³ × 2⁴, giving your answer as a single power of 2.
- 13.A cyclist's journey is shown on a distance–time graph. The graph is a straight line from (0 minutes, 0 km) to (40 minutes, 12 km). Work out her speed in kilometres per hour.
- 14.A metal block has a mass of 270 g and a volume of 30 cm³. Work out the density of the block, in g/cm³.
- 15.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.
- 16.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.
- 17.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).
- 18.The number of biscuits, b, that each guest at a party receives is inversely proportional to the number of guests, g. Which equation could show this relationship?
- 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.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.
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.