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.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.
- 2.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?y = 3x + 2
- 3.The ratio of two lengths is 0.6 : 1.5. Write this ratio in its simplest whole-number form.
- 4.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.
- 5.On Amelia's walk to school there are two sets of traffic lights. The probability that the first set is green when she reaches it is 0.4. The probability that the second set is green when she reaches it is 0.5. The two sets work independently of each other. Work out the probability that both sets are green.
- 6.The mean of three numbers is 50. A fourth number, 100, is added to the set. Work out the mean of the four numbers.
- 7.Write 45,000 in standard form.
- 8.Make x the subject of the formula y = x/2 − 5.y = x
- 9.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.
- 10.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
- 11.A survey of 60 readers records: 21 read only fiction, 17 read only non-fiction, 14 read both, and the rest read neither. Work out the probability that a randomly chosen reader reads exactly one of the two types, giving your answer as a fraction in its simplest form.
- 12.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.
- 13.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.
- 14.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
- 15.All four sides of a rhombus are the same length. One side of a rhombus is 7 cm long. Work out the perimeter of the rhombus.
- 16.Work out 5⁰ + 5¹ + 5²
- 17.Write down the gradient of the line with equation y = 7x − 2.y = 7x − 2
- 18.Divide 84 in the ratio 3:4. Work out the smaller share.
- 19.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2
- 20.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.
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.