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 plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.
- 2.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?y = 3x + 2
- 3.y is directly proportional to x. If the value of x is trebled (multiplied by 3), what happens to the value of y?
- 4.The diagram shows the plan, front elevation and side elevation of a solid. Which of these solids matches all three views?
- 5.On the probability scale from 0 (impossible) to 1 (certain), evens is exactly halfway. An event is 3/10 more likely than evens. Work out the probability of that event, giving your answer as a decimal.
- 6.A café sold 10 sandwiches on each of four days: 10, 10, 10, 10. Work out the range of the numbers sold.
- 7.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.
- 8.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.
- 9.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
- 10.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.
- 11.A fair six-sided dice is rolled 150 times. The table shows how many times each number came up: 1 came up 22 times, 2 came up 27 times, 3 came up 24 times, 4 came up 34 times, 5 came up 21 times and 6 came up 22 times. The theoretical probability of each number is 1/6. Which number is most over-represented compared with its theoretical probability?
- 12.Work out (3 × 5)²
- 13.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.
- 14.Four graphs are described below. Each shows one quantity plotted against another. Write down the description of the graph that shows two quantities in direct proportion.
- 15.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.
- 16.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.
- 17.a = 2 and b = 5. Work out the value of a²b.
- 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.A pack contains 20 stickers. Noah gives 1/5 of the pack to his sister. Work out how many stickers he gives away.
- 20.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.
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.