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.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.
- 2.Which expression is equivalent to 7x − 3(2x − 6)?
- 3.A vegetable patch is divided between carrots, potatoes and onions in the ratio 2 : 3 : 5. Write down the fraction of the patch used for potatoes.
- 4.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.
- 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.Priya wants to find out the favourite sport of the 900 pupils at her school. She asks 5 pupils, chosen at random. Give a reason why her sample may not give a reliable result.
- 7.A bus leaves the station at 09:47 and arrives at its destination at 11:23. Work out the journey time.
- 8.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).
- 9.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.
- 10.A parallelogram has an area of 54 cm² and a base of 9 cm. Work out its perpendicular height.
- 11.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.
- 12.Work out 35% of 180.
- 13.Work out the coordinates of the point where the graph of y = 2x − 6 crosses the x-axis.y = 2x − 6
- 14.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.
- 15.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.
- 16.Work out (−36) ÷ (−6) × 2
- 17.Factorise x² − 3x − 10.
- 18.The number of calories burned, E, by a runner is plotted against the time, m minutes, on a straight-line graph. The line passes through the origin and the point (10, 80). Work out the gradient of the line.
- 19.Which of these numbers lies between −4 and −1 on a number line?
- 20.Two mathematically similar flags are made in different sizes. The length scale factor from the smaller flag to the larger flag is 5. Work out the area scale factor from the smaller flag to the larger flag.
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.