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.Work out (−6) + (−4) × 3
(a)−30
(b)−18
(c)18
(d)6
2.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?
(a)It does not cross, since the minimum lies below the axis.
(b)It crosses the x-axis, since the minimum is below it.
(c)It touches the x-axis once, at (3, −4).
(d)It is impossible to tell without the full equation.
3.A metal alloy is made from copper and tin in the ratio 7:3. Work out the mass of tin in 250 g of the alloy.
(a)125 g
(b)75 g
(c)25 g
(d)175 g
4.How many vertices does a cylinder have?
(a)2
(b)4
(c)1
(d)0
5.A fair six-sided dice is rolled 300 times. Work out how many more times you would expect it to land on an even number than on a six.
(a)50
(b)150
(c)100
(d)200
6.A charity shop in Bath holds 2,000 books. Volunteer A checks a random sample of 50 books and finds 35 paperbacks. Volunteer B checks a different random sample of 50 books and finds 31 paperbacks. Work out the estimate each sample gives for the whole stock, and write down what the shop should do next.
(a)1,400 and 1,240, so combine the samples for one estimate
(b)1,400 and 1,240, so keep 1,400 as the larger estimate
(c)1,400 and 1,240, so one volunteer must have miscounted
(d)1,750 and 1,550, so the larger estimate must be right
7.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.
(a)−56/15
(b)3/25
(c)−4/3
(d)4/3
8.A vertical line passes through the point (4, 7). Write down the equation of this line.
(a)y = 7
(b)x = 4
(c)x = 7
(d)y = 4x
9.Zara is paid £9 per hour. Her wage is directly proportional to the number of hours she works. Work out her wage for working 6 hours.
(a)£54
(b)£63
(c)£1.50
(d)£15
10.Work out the exact value of sin 45° × cos 45°.
(a)√2
(b)1
(c)1/2
(d)√2/2
11.A fair coin is flipped and a fair three-sided spinner, labelled X, Y and Z, is spun. Every outcome is listed as a pair, such as (H, X). Work out the probability that the outcome is a head and Z.
(a)1/2
(b)1/6
(c)1/3
(d)1/5
12.Write down the value of 7⁰
(a)1/7
(b)1
(c)7
(d)0
13.Solve 5x + 2 = 17.
(a)3
(b)3.8
(c)15
(d)1.4
14.£120 is shared between three cousins in the ratio 3:4:5. Work out the largest share.
(a)£10
(b)£50
(c)£30
(d)£40
15.Shape S is enlarged by a scale factor of 3, centre the origin. A vertex of S is at (2, 1). Work out the coordinates of the image of this vertex.
(a)(6, 1)
(b)(6, 3)
(c)(2, 3)
(d)(5, 4)
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.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
18.A straight-line graph shows the cost, C pounds, of hiring a small van for m miles driven. The line passes through the origin and the point (25, 20). Work out the gradient of the line.
(a)0.8
(b)20
(c)5
(d)1.25
19.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.
(a)4π cm²
(b)8π cm²
(c)16π cm²
(d)32π cm²
20.Work out the time taken to travel 120 km at an average speed of 60 km/h.
(a)180 minutes
(b)0.5 hours
(c)2 hours
(d)2 minutes

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.