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
- 1.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.
- 2.Solve x² − x − 12 = 0.
- 3.Order these three values from smallest to largest: 3/8, 0.43, 41%.
- 4.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?
- 5.An ordinary pack of 52 playing cards contains 13 hearts. One card is taken at random from the pack. Work out the probability that the card is not a heart. Give your answer as a percentage.
- 6.In a vertical line chart of test results, the tallest line stands for 40 pupils. The same results are to be shown in a pie chart of all 100 pupils. Work out the angle at the centre of the sector that will stand for those 40 pupils.
- 7.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.
- 8.Which of these is a formula, rather than an expression, an equation, or an identity?
- 9.In one batch of shortbread, a bakery uses 240 g of butter and 160 g of sugar. Another batch, made in the same ratio, uses 90 g of sugar. Work out how much butter is needed for the second batch.
- 10.Work out the exact value of (sin 30°)² + (cos 30°)².
- 11.Kwame flips a fair coin three times and writes down what it lands on each time. Work out the probability that it lands on heads all three times.
- 12.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.
- 13.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.
- 14.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.
- 15.A recipe uses 0.75 kg of sugar. Work out how many grams of sugar this is.
- 16.Which one of these statements about negative numbers is true?
- 17.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?
- 18.A watering can holds 4500 cm³ of water. Given that 1 litre = 1000 cm³, work out the capacity of the watering can in litres.
- 19.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.
- 20.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.
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.