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%.

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GCSE Foundation sample Paper 1 (non-calculator)

Maths · GCSE Foundation · Paper 1 · Non-calculator · 20 questions

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1.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.
(a)56
(b)21
(c)35
(d)28
2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?
(a)An identity, true for every value of x
(b)A formula, relating two expressions
(c)An equation, because it has an equals sign
(d)An equation, solved by one value of x
3.A parcel has a mass of 2400 g. Given that 1 kg = 1000 g, work out the mass of the parcel in kilograms.
(a)2.4 kg
(b)24 kg
(c)240 kg
(d)0.24 kg
4.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?
(a)A smaller circle
(b)A triangle
(c)The same size circle as the base
(d)An ellipse
5.The probability that Priya scores with a netball shot is 3/4. She takes two shots, and the shots are independent. Work out the probability that she scores with her first shot but misses her second shot.
(a)3/4
(b)9/16
(c)3/16
(d)1/2
6.A scatter graph shows the midday temperature, x °C, and the number of ice creams sold at a seaside kiosk, y. The line of best fit is y = 3x − 20. Give a reason why the y-intercept of this line of best fit is not a sensible estimate of the number of ice creams sold.
y = 3x − 20
(a)x = 0 gives y = −20: a negative number sold
(b)x = 0 gives y = 3, so 3 ice creams still sell
(c)Sales rise without limit as temperature rises
(d)y = −20 means 20 ice creams were given away
7.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.
(a)25
(b)9
(c)20
(d)10
8.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.
(a)12 km/h
(b)8 km/h
(c)6 km/h
(d)4 km/h
9.Write 1/5 as a percentage.
(a)20%
(b)5%
(c)50%
(d)25%
10.A trundle wheel has a diameter of 0.5 m. It is rolled along the ground and makes 20 complete turns. Using π = 3.14, work out the total distance rolled, in metres.
(a)31.4
(b)62.8
(c)3.14
(d)15.7
11.A two-way table records how 80 students travel to school. 45 of the students are boys and the rest are girls. 27 of the boys walk to school. Work out the probability, as a fraction, that a student chosen at random from the boys walks to school.
(a)27/80
(b)2/5
(c)27/35
(d)3/5
12.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.
(a)3.84 × 10⁵
(b)3.84 × 10⁶
(c)3.84 × 10⁻⁵
(d)38.4 × 10⁴
13.Solve x² + 3x − 10 = 0.
(a)x = 2 or x = 5
(b)x = −2 or x = 5
(c)x = −5 or x = −2
(d)x = 2 or x = −5
14.A bottle contains 1.5 litres of juice. Given that 1 litre = 1000 ml, work out the capacity of the bottle in millilitres.
(a)1500 ml
(b)150 ml
(c)1.5 ml
(d)15000 ml
15.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.
(a)−10
(b)47.5
(c)25
(d)20
16.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20
(a)7/8, 17/20, 0.8, 78%
(b)7/8, 0.8, 17/20, 78%
(c)78%, 0.8, 17/20, 7/8
(d)17/20, 7/8, 0.8, 78%
17.Solve x² + 7x = 0.
(a)x = 0 or x = 7
(b)x = 0 or x = −14
(c)x = 0 or x = −7
(d)x = −7
18.A car uses 6 litres of petrol to travel 90 km. Write the ratio of the distance travelled in km to the amount of petrol used in litres, in its simplest form.
(a)15:1
(b)5:2
(c)14:1
(d)1:15
19.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.
(a)7
(b)3
(c)1
(d)6
20.£5000 is invested in an account paying 4% compound interest each year. Work out the total interest earned after 3 years.
(a)£600.00
(b)£408.00
(c)£624.32
(d)£5624.32

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.