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.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.
(a)18
(b)30
(c)90
(d)14
2.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.
(a)x = 14, y = −4
(b)x = 7, y = 3
(c)x = 5, y = 5
(d)x = 7, y = 4
3.A car travels at a constant speed. It travels 150 miles in 3 hours. At the same speed, work out how far it travels in 5 hours.
(a)90 miles
(b)200 miles
(c)250 miles
(d)300 miles
4.In this question, a curved surface counts as a face. How many faces does a cone have?
(a)2
(b)1
(c)3
(d)0
5.120 people took a driving theory test. A frequency tree records the results. The first pair of branches splits the 120 people into 70 men and 50 women. On the men's branch, 45 passed and the rest failed. On the women's branch, 38 passed and the rest failed. Work out how many of the 120 people failed the test.
(a)12
(b)37
(c)25
(d)83
6.Four pairs of variables are listed below. Write down the pair that you would expect to show no correlation.
(a)Outdoor temperature and woolly hats sold in a day
(b)A person's shoe size and their favourite colour
(c)Distance a car travels and the fuel it uses
(d)Hours of revision a pupil does and their score
7.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.
(a)18
(b)25
(c)24
(d)28
8.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.
(a)39
(b)192
(c)768
(d)256
9.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?
(a)x = 6, y = 27
(b)x = 6, y = 13
(c)x = 6, y = 3
(d)x = 6, y = 24
10.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
(a)vertically opposite angles are equal
(b)corresponding angles are equal
(c)base angles of an isosceles triangle are equal
(d)angles in a triangle add up to 180°
11.A raffle at a school fair sells 500 tickets. Mia buys 25 of the tickets. One ticket is drawn at random to win the prize. Work out the probability that Mia wins the raffle. Give your answer as a fraction in its simplest form.
(a)19/20
(b)1/25
(c)1/10
(d)1/20
12.Write the fraction 47/50 as a decimal.
(a)0.094
(b)4.7
(c)0.94
(d)0.47
13.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.
(a)20
(b)81
(c)100
(d)1000
14.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
(a)75%
(b)133%
(c)25%
(d)18%
15.A crane's hook starts at the point (3.4, 9.5) on a construction site plan measured in metres. It moves along the vector $(- 4.5 - 1.2)$ to pick up a beam, then along the vector $(- 2.5 0.8)$ to place it. Work out the single column vector that describes the hook's overall movement from its start position to where it places the beam.
(a) $(- 2 - 2)$
(b) $(- 7 - 0.4)$
(c) $(7 - 0.4)$
(d) $(- 7 2)$
16.Write these numbers in order, starting with the smallest: 5, −8, 0, −3, 2
(a)−8, −3, 2, 0, 5
(b)−3, −8, 0, 2, 5
(c)5, 2, 0, −3, −8
(d)−8, −3, 0, 2, 5
17.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.
(a)3n − 2
(b)3n + 1
(c)3n + 4
(d)n + 3
18.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.
(a)8 : 125
(b)4 : 25
(c)4 : 5
(d)2 : 5
19.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.
(a)121 litres
(b)57 litres
(c)87 litres
(d)72 litres
20.A coach travels 210 miles at an average speed of 70 mph. Work out how long the journey takes.
(a)14700 hours
(b)140 hours
(c)3 hours
(d)280 hours

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.