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.Work out an estimate for 113 + 491, by rounding each number to the nearest 100.
- 2.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
- 3.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.
- 4.Write down the exact value of sin 60°.
- 5.The probability that Oliver's train is delayed on any morning is 0.3. Work out the probability that his train is not delayed.
- 6.In a scatter graph of the age, in years, and the wingspan, in cm, of 20 birds of the same species, all the points lie close to a rising line of best fit except one, which lies a long way below the line. That bird was later found to have a damaged wing. Give a reason why this point should not be used when drawing the line of best fit.
- 7.Grace buys three items costing £9.95, £19.90 and £4.99. Work out an estimate for the total cost, by rounding each price to the nearest pound.
- 8.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.
- 9.A market stall sells apples at a fixed price per kilogram. Priya buys 3 kg for £5.40. Write the ratio of the mass in kilograms to the cost in pounds, in its simplest form.
- 10.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?
- 11.The probability that a spinner lands on blue is 2/5. Write this probability as a percentage.
- 12.Write down the fraction, in its simplest form, that is equal to 0.6
- 13.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.
- 14.A bag contains 7 red counters and 15 blue counters. Write down the ratio of red counters to blue counters in its simplest form.
- 15.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
- 16.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.
- 17.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.
- 18.A glass holds 250 ml of squash. Work out how many of these glasses are needed to fill a 1 litre bottle.
- 19.Work out the total cost of 3 pens at 45p each and one notebook at £2.35. Give your answer in pounds.
- 20.A beaker holds 500 g of a salt solution of concentration 12%. Pure water is added until the concentration falls to 8%. Work out the mass of water added.
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.