Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 2 (calculator)
The real Paper 2 is 1.5 hour 30 minutes and 80 marks, 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 a calculator allowed. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
CalculatorGCSE Foundation
GCSE Foundation sample Paper 2 (calculator)
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- 1.Josh buys 7 pencils at 85p each. He pays with a £10 note. Work out his change.
- 2.Factorise fully 12x² + 18x.
- 3.A coach travels the 54 miles from London to Brighton in 1 hour 30 minutes. Work out the average speed of the coach, in mph.
- 4.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?
- 5.A quality inspector tests 145 light bulbs and finds that 33 are faulty. Work out the relative frequency of a bulb being faulty, as a percentage correct to 1 decimal place.
- 6.A scatter graph has 12 plotted points. Four pupils each draw a line of best fit on the same graph and count how many of the 12 points lie above their line and how many lie below it: Amir — 10 above, 2 below. Priya — 6 above, 6 below. Kofi — 2 above, 10 below. Leah — 0 above, 12 below. Write down the name of the pupil whose line was drawn correctly, so that the points are roughly balanced above and below it.
- 7.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.
- 8.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.
- 9.A colony of bacteria has 400 bacteria. The number increases by 15% each hour. Work out the number of bacteria after 1 hour.
- 10.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.
- 11.The probability that a plant grown from a seed packet germinates is 7/10. Work out the probability that it does not germinate.
- 12.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.
- 13.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.
- 14.Which of these ratios is already written in its simplest form?
- 15.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.
- 16.The length of a nail is 12 cm, correct to the nearest centimetre. Using L for the length of the nail in centimetres, write down the error interval for L.
- 17.Solve 3(2x − 1) = 27
- 18.The length of ribbon A is 5/12 of the length of ribbon B. Write the length of ribbon B as a fraction of the length of ribbon A.
- 19.Work out (2/3)² + (1/2)². Give your answer as a fraction.
- 20.Write 250 g : 2 kg as a ratio 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.