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)
MathsUKwww.geekhero.co.uk
- 1.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.
- 2.Solve x² − 2x − 24 = 0.
- 3.A plan is drawn to a scale of 1 : 500. Work out how many metres are represented by 1 cm on the plan.
- 4.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Give a reason why angle F = 58°.
- 5.Two ordinary fair dice are rolled. Work out the probability that both dice show the same score.
- 6.A café in Preston records the type of drink ordered by 20 customers one morning: tea 8, coffee 7, hot chocolate 4 and juice 1. Write down the modal drink.
- 7.Write down the reciprocal of 0.2
- 8.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.
- 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.Triangle ABC is drawn. The interior angle bisectors from vertices A and B are constructed and meet at point I inside the triangle. Which statement about point I must be true?
- 11.A grower knows that the probability that one of their seeds germinates is 0.6. The grower wants to expect 300 of the seeds to germinate. Work out how many seeds the grower should plant.
- 12.Which of these numbers lies between −4 and −1 on a number line?
- 13.Solve x² + 3x − 10 = 0.
- 14.A table shows three pairs of values: when x = 2, y = 6; when x = 5, y = 15; when x = 8, y = 24. In every pair the ratio y : x is the same. Write down a formula for y in terms of x.
- 15.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?
- 16.A train leaves Leeds at 14:35. The journey takes 1 hour 50 minutes. Work out the time the train arrives. Give your answer using the 24-hour clock.
- 17.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).
- 18.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.
- 19.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.
- 20.Three numbers are in the ratio 1:2:3. The three numbers add up to 72. Work out the largest of the three numbers.
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.