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.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.
- 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 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.
- 4.A trundle wheel has a diameter of 0.5 m. It is rolled along the ground and makes 20 complete turns. Using π = 3.14, work out the total distance rolled, in metres.
- 5.120 people took a driving theory test. A frequency tree records the results. The first pair of branches splits the 120 people into 70 men and 50 women. On the men's branch, 45 passed and the rest failed. On the women's branch, 38 passed and the rest failed. Work out how many of the 120 people failed the test.
- 6.Four books have 120, 200, 160 and 80 pages. Work out the mean number of pages.
- 7.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.
- 8.Work out the value of 2x² when x = −3
- 9.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.
- 10.In an isosceles triangle each of the two base angles is 46°. Work out the size of the angle at the apex.
- 11.A train company runs 25 trains a day, every day. The probability that any one train is late is 0.08. Work out how many late trains the company should expect over a period of 4 weeks.
- 12.Work out (−6) + (−4) × 3
- 13.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.
- 14.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.
- 15.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?
- 16.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20
- 17.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?
- 18.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
- 19.In a choir, 2/9 of the members are boys and the rest are girls. Write down the ratio of girls to boys, in its simplest form.
- 20.A market stall sells apples at a fixed price per kilogram. Priya buys 3 kg for £5.40. Write the ratio of the mass in kilograms to the cost in pounds, in its simplest form.
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.