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 washing machine costs £320 before VAT. VAT is charged at 20%. Work out the total price including VAT.
(a)£340.00
(b)£326.40
(c)£384.00
(d)£64.00
2.A student is asked whether 3(x − 4) = 3x − 4 is an identity. Which statement gives the correct verdict and reason?
(a)It is an identity, because both sides begin with the term 3x, so they must be equivalent.
(b)It is not even an ordinary equation with a solution: expanding the left-hand side gives 3x − 12, and 3x − 12 = 3x − 4 would require −12 = −4, which is never true.
(c)It is not an identity, because the student forgot to multiply the 4 by 3 on both sides of the equation.
(d)It is not an identity, because the student needs to substitute a specific value of x before comparing the two sides.
3.A recipe for 8 muffins needs 200 g of sugar. Sam wants to make 20 muffins for a bake sale, and he already has 350 g of sugar. Work out how many more grams of sugar he needs to buy.
(a)150 g
(b)850 g
(c)0 g
(d)500 g
4.A translation is described by the column vector $(- 2 7)$ . Write down a description of this translation in words, stating the horizontal and vertical movement.
(a)7 units left and 2 units up
(b)7 units right and 2 units down
(c)7 units right and 2 units up
(d)2 units right and 7 units down
5.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
6.A scatter graph shows the mass, x kg, of a parcel and the cost, y pounds, of posting it. The line of best fit is y = 1.5x + 2. Work out the estimated cost of posting a parcel with a mass of 6 kg, using the line of best fit.
y = 1.5x + 2
(a)£13.50
(b)£11.00
(c)£12.00
(d)£9.00
7.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.
(a)12
(b)7
(c)20
(d)5
8.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.
(a)2n + 4
(b)2n
(c)2n + 2
(d)2n − 2
9.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.
(a)5:3
(b)2:5
(c)2:3
(d)3:2
10.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.
(a)28.3 cm
(b)254.3 cm
(c)113.0 cm
(d)56.5 cm
11.Two ordinary fair dice are rolled, one after the other. Work out the probability that the first dice shows a 6 and the second dice shows an even number.
(a)1/12
(b)1/36
(c)1/6
(d)1/2
12.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.
(a)−3
(b)4
(c)3
(d)2
13.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.
(a)x ≥ 30
(b)x ≤ 50
(c)x ≤ 90
(d)x ≤ 30
14.3 kg of apples cost £6. Work out the cost of 5 kg of the same apples.
(a)£3.60
(b)£10
(c)£11
(d)£30
15.A market stall sells apples at £2.40 per kilogram. Which of these expressions gives the cost, in pounds, of buying m kilograms of apples?
(a)2.40m
(b)m/2.40
(c)m − 2.40
(d)2.40 + m
16.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?
(a)3/7
(b)7/3
(c)7/10
(d)3/10
17.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.
(a)30 m
(b)11 m
(c)22 m
(d)38 m
18.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.
(a)4 hours
(b)2 hours 40 minutes
(c)3 hours
(d)5 hours 20 minutes
19.A garden has flowers, herbs and vegetables in the ratio 2 : 3 : 4. What fraction of the garden is not vegetables?
(a)4/9
(b)5/7
(c)3/4
(d)5/9
20.6 identical printers can print a batch of exam papers in 40 minutes, all working at the same rate. Working at the same rate, work out how many minutes 4 of these printers would take to print the same batch.
(a)60 minutes
(b)40 minutes
(c)26.7 minutes
(d)24 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.