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

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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 √25 + 4² − 12 ÷ 3
(a)9
(b)17
(c)3
(d)37
2.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?
(a)y = 2x + 1
(b)y = 1/x
(c)y = x²
(d)y = x³
3.An oven is preheating. Its temperature, T °C, is plotted against time, t minutes, on a straight-line graph. The line passes through the points (2, 60) and (6, 140). Work out the gradient of the line.
(a)−20
(b)30
(c)40
(d)20
4.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
5.A fair spinner has 10 equal sections, numbered 1 to 10. The spinner is spun 150 times. Work out how many times you would expect it to land on a number greater than 7.
(a)60
(b)50
(c)45
(d)105
6.Work out the median of these six numbers: 13, 21, 22, 36, 37, 47
(a)22
(b)36
(c)34
(d)29
7.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?
(a)£4.55
(b)£4.50
(c)£4.65
(d)£4.80
8.Make a the subject of the formula b = 20 − a.
(a)a = 20 − b
(b)a = b − 20
(c)a = 20 + b
(d)a = −20 − b
9.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.
(a)£7.80
(b)£438.75
(c)£51.00
(d)£0.13
10.Two angles are complementary. One of them is 35°. Work out the size of the other angle.
(a)90°
(b)55°
(c)145°
(d)325°
11.At a gym, 45 members are surveyed. 24 use the running machines, 20 use the weights machines, and 9 use both. Work out how many of the 45 members use neither machine.
(a)15
(b)10
(c)9
(d)1
12.Work out (−2)³ + (−3)² − (−4)
(a)5
(b)−13
(c)−3
(d)21
13.Which expression means 'y squared, multiplied by 3'?
(a)3y²
(b)y³
(c)(3y)²
(d)3 + y²
14.A material has a density of 2 g/cm³. Work out the mass of 5 cm³ of this material.
(a)7 g
(b)2.5 g
(c)10 g
(d)0.4 g
15.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.
(a)7 m
(b)5 m
(c)12 m
(d)25 m
16.Work out 18 − 4 × 2
(a)12
(b)−10
(c)10
(d)28
17.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.
y = 4x − 5
(a)4
(b)−4
(c)5
(d)−5
18.A jug holds 3 litres of a drink that is 60% fruit juice. 1 litre of water is added to the jug. Work out the percentage of the new mixture that is fruit juice.
(a)60%
(b)75%
(c)45%
(d)15%
19.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
20.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
(a)9%
(b)120%
(c)20%
(d)16.7%

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.