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.A wall is tiled in rows, and every row uses the same number of tiles. One row uses 10 tiles, two rows use 20 tiles and three rows use 30 tiles. Work out how many tiles are needed for 7 rows.
- 3.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.
- 4.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?
- 5.Four bags each contain counters, some of which are winning counters. The probability of taking a winning counter is 5/12 from the red bag, 3/8 from the blue bag, 7/24 from the green bag and 1/3 from the yellow bag. Work out which bag has the smallest probability of giving a winning counter.
- 6.A dual bar chart shows how many boys and how many girls are in a class. The bar for boys stands at 14 and the bar for girls stands at 16. Work out how many pupils are in the class altogether.
- 7.Write down the symbol that makes this statement true: 3/10 ___ 0.3
- 8.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
- 9.y is directly proportional to x, so y = kx. When x = 2, the value of y is 10. Work out the value of k.
- 10.In a phone game, a character starts at the point (−5, 2) on a grid. It moves by the vector to collect a coin. The player now wants the character's next single move to finish at the point (3, 0). Write down the column vector of that second move.
- 11.A survey asks 40 people whether they own a cat, a dog, both, or neither. 12 people own only a cat, 15 own only a dog, 5 own both, and 8 own neither. Work out the probability that a randomly chosen person owns a cat or a dog (or both). Give your answer as a fraction in its simplest form.
- 12.Work out 3 + 4 × (−2).
- 13.Solve the inequality x + 5 < 12.
- 14.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.
- 15.Vector A is and vector B is . Write down how vector B compares to vector A.
- 16.Round 0.0759 to 2 decimal places.
- 17.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.y = x² + 1
- 18.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 19.Write down the fraction, in its simplest form, that is equal to 0.6
- 20.Simplify the ratio 12 : 18 : 30 to 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.