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.Write 200 as a product of its prime factors, using index notation.
- 2.Work out the value of 3a − 2b when a = 5 and b = 4
- 3.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.
- 4.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.
- 5.A school recorded what 60 students chose for lunch. 35 of the students are in Year 10 and the rest are in Year 11. 20 of the Year 10 students chose a sandwich and 9 of the Year 11 students chose a sandwich. Everyone else chose a hot meal. Work out how many Year 11 students chose a hot meal.
- 6.The number of pets owned by each of 19 pupils in a class is recorded: 0 pets — 7 pupils, 1 pet — 3 pupils, 2 pets — 4 pupils, 3 pets — 5 pupils. Work out the median number of pets.
- 7.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.
- 8.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.
- 9.Write 250 g : 2 kg as a ratio in its simplest form.
- 10.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 11.A = {factors of 12} and B = {factors of 18}. Work out n(A ∩ B), the number of elements in both sets.
- 12.Work out √25 + 4² − 12 ÷ 3
- 13.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?
- 14.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.
- 15.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.
- 16.A pack contains 20 stickers. Noah gives 1/5 of the pack to his sister. Work out how many stickers he gives away.
- 17.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.
- 18.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.
- 19.Write the fraction 47/50 as a decimal.
- 20.A recipe for 4 people needs 300 g of rice. Work out how much rice is needed for 6 people, assuming the amount is in direct proportion to the number of people.
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.