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)
MathsUKwww.geekhero.co.uk
- 1.In a chess club, 3/8 of the members are girls and the rest are boys. Write down the ratio of girls to boys.
- 2.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
- 3.y is directly proportional to x, and y = 3x. Work out the value of y when x = 4.y = 3x
- 4.Triangle ABC has angle A = 40°, angle B = 65° and AB = 10 cm. Triangle DEF has angle D = 40°, angle E = 65° and DE = 10 cm. Which condition proves the two triangles are congruent?
- 5.A fair coin is flipped and an ordinary fair dice is rolled. Every possible result is listed in a table. Work out how many different results the table contains altogether.
- 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.A circle has a radius of 5 cm. Work out the exact circumference of the circle, in terms of π.
- 8.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.
- 9.A recipe for 8 people needs 320 g of rice. Sanjay scales the recipe down to serve 5 people, then wants to scale his new amount back up to serve 8 people again. Work out the multiplier he should use to scale his amount for 5 people back up to the amount for 8 people.
- 10.A birthday cake is a cylinder of radius 10 cm and height 8 cm, with a thin ribbon fixed exactly once around the curved side, at half the height, and joined with no overlap. Work out the length of ribbon needed. Use π = 3.14.
- 11.An ordinary fair dice is rolled twice. Work out the probability of getting at least one 5.
- 12.Write down the value of 7⁰
- 13.y = 3x − 2. Work out the value of y when x = 4.y = 3x − 2
- 14.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.
- 15.Point B is at (3, 5). It is reflected in the line y = 2. Work out the coordinates of the image of point B.
- 16.A rectangular field measures 19.6 m by 48.3 m. Work out an estimate for the area of the field, by rounding each length to 1 significant figure.
- 17.How many turning points does the graph of y = x² − 7x + 10 have?y = x² − 7x + 10
- 18.Order these three values from smallest to largest: 3/8, 0.43, 41%.
- 19.Simplify x⁷ × x⁴, giving your answer as a single power of x.
- 20.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.
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.