Sample paper · GCSE Foundation · grades 1–5

GCSE Foundation sample Paper 2 (calculator)

The real Paper 2 is 1.5 hour 30 minutes and 80 marks, 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 a calculator allowed. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.

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GCSE Foundation sample Paper 2 (calculator)

Maths · GCSE Foundation · Paper 2 · Calculator · 20 questions

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1.A number line runs from 0 to 1 and is divided into 4 equal parts. Which mark on the line represents 1/4?
(a)the third mark after 0
(b)the second mark after 0
(c)the fourth mark after 0
(d)the first mark after 0
2.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?
(a)It has an = sign, and equations always use =.
(b)3x + 5 cannot be simplified, so it must be an equation.
(c)Only x = 5 satisfies 3x + 5 = 20, not every value of x.
(d)A number on the right-hand side makes it an equation.
3.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.
(a)d + t
(b)d × t
(c)t ÷ d
(d)d ÷ t
4.Which of the following correctly describes what it means for two lines to be perpendicular?
(a)Two lines equal in length
(b)Two lines crossing at any angle
(c)Two lines that never meet
(d)Two lines that cross at right angles
5.Four pupils each flip the same coin a number of times and record the results. Sam flips it 40 times and gets 24 heads. Priti flips it 25 times and gets 10 heads. Leo flips it 20 times and gets 9 heads. Fatima flips it 15 times and gets 6 heads. Combine all four pupils' results to estimate the probability that the coin lands on heads.
(a)0.60
(b)0.49
(c)0.40
(d)0.46
6.Harry counted the coins he found on each of six days: 5, 7, 8, 9, 11, 30. Write down the outlier.
(a)30
(b)8.5
(c)11
(d)5
7.Write down the symbol that makes this statement true: 0.45 ___ 0.5
(a)>
(b)=
(c)<
(d)≥
8.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.
(a)y = 3x + 9
(b)y = 12x
(c)y = 9x + 3
(d)y = 9x
9.Write 350 ml : 1.4 l as a ratio in its simplest form.
(a)2:8
(b)25:1
(c)4:1
(d)1:4
10.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
(a)£24.00
(b)£2.94
(c)£29.40
(d)£2940.00
11.A phone network sends automatic text alerts to customers. On average, 1,500 alerts are sent each day, and the probability that a customer replies 'STOP' to an alert is 0.18. Work out how many replies of 'STOP' the network should expect over a 30-day month.
(a)270
(b)8,100
(c)810
(d)5
12.Which of these statements about −0.7 and −0.25 is true?
(a)−0.7 = −0.25
(b)−0.7 < −0.25
(c)−0.7 ≥ −0.25
(d)−0.7 > −0.25
13.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.
(a)£13.20
(b)£15.50
(c)£34.20
(d)£16.70
14.Three friends share a raffle prize of £360 in the ratio 2:3:4. Work out the share of the friend whose part of the ratio is 3.
(a)£160
(b)£40
(c)£80
(d)£120
15.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
(a)65 cm²
(b)1,000 cm²
(c)500 cm²
(d)2,000 cm²
16.A car is hired from 10:00 on Monday until 16:00 on Thursday. Work out the total length of the hire, in hours.
(a)54 hours
(b)78 hours
(c)66 hours
(d)96 hours
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.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%
19.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.
(a)55
(b)54
(c)59
(d)54.7
20.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

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.