Sample paper · GCSE Higher · grades 4–9

GCSE Higher 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 Higher qualification — number 15%, algebra 30%, ratio, proportion and rates of change 20%, geometry and measures 20%, probability 7.5%, statistics 7.5% — with a calculator allowed. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.

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GCSE Higher sample Paper 2 (calculator)

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

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1.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
2.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x
(a)−10
(b)5x − 10
(c)2
(d)−7
3.A shop sells identical pens. The total cost, C pence, of n pens is given by C = 12n. Write the ratio n : C in its simplest form.
(a)1:13
(b)1:12
(c)12:144
(d)12:1
4.A stage designer is building a triangular platform ABC for a school play. AB = 11.5 m, AC = 8.2 m and angle BAC = 72°, the angle between them. The flooring for the platform costs £15.80 per square metre. Work out the total cost of the flooring, to the nearest pound.
(a)£994
(b)£709
(c)£1417
(d)£230
5.A market research company found that, out of 120 shoppers surveyed, 42 preferred paper bags to plastic bags. A supermarket expects 900 shoppers this week. Using this relative frequency, work out how many of the 900 shoppers would be expected to prefer paper bags.
(a)42
(b)350
(c)585
(d)315
6.A sports centre in Ipswich has 2,000 members. It wants to know what its members think of its opening hours, so it asks a random sample of 100 of them. Write down what the population is in this survey.
(a)Everybody who lives in Ipswich.
(b)All 2,000 members of the sports centre.
(c)The members who say they are unhappy with the opening hours.
(d)The 100 members who were asked.
7.A rectangular garden has a length of 12.4 m and a width of 7.5 m, each measured correct to 1 decimal place. Calculate the upper bound for the area of the garden.
(a)93.375
(b)93.9975
(c)92.0075
(d)93
8.A market stall's cost of hiring n tables is modelled by two formulas: Formula A: C = 3(2n + 5); Formula B: C = 6n + 15, where C is in pounds. A stallholder says the two formulas always give the same cost. Work out the cost given by each formula when n = 4, and use your results to decide whether the stallholder is correct.
(a)Formula A gives £39 and Formula B gives £39, but the stallholder is wrong because the two formulas use a different number of terms.
(b)Formula A gives £29 and Formula B gives £39, so the stallholder is wrong.
(c)Formula A gives £39 and Formula B gives £39, but this is only true when n = 4, so the stallholder is wrong.
(d)Formula A gives £39 and Formula B gives £39, and since 3(2n + 5) expands to 6n + 15 for every value of n, the stallholder is correct.
9.A company's turnover was £128 000 in 2023 and £176 000 in 2024. Work out the multiplier that changes the 2023 turnover into the 2024 turnover.
(a)1.375
(b)0.375
(c)0.727
(d)137.5
10.A circle has centre O and radius 13 cm. AB is a chord of the circle, and M is the midpoint of AB. OM is drawn, and OM = 5 cm. Work out the length of AB.
(a)24 cm
(b)12 cm
(c)144 cm
(d)16 cm
11.On a probability scale from 0 to 1, five descriptions are used: impossible (0), unlikely (between 0 and 0.5), evens (exactly 0.5), likely (between 0.5 and 1) and certain (1). The probability that a particular bus is late is 3/8. Which description best fits this probability?
(a)unlikely
(b)likely
(c)evens
(d)certain
12.Work out 3.7 × 24.
(a)8.88
(b)88.8
(c)888
(d)87.8
13.n is an integer. Which of these expressions is always an even number?
(a)n² + n
(b)n² − n + 1
(c)2n + 1
(d)n² + 1
14.A patient is given a dose of 200 mg of a drug. Each hour, 30% of the drug remaining in the bloodstream is eliminated, and then a further dose of 50 mg is given. Using the recurrence D_{n+1} = 0.7D_n + 50, with D_0 = 200, work out the amount of drug in the bloodstream after 2 hours.
(a)83 mg
(b)98 mg
(c)183 mg
(d)157.5 mg
15.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?
(a)SAS, right angle as included angle
(b)ASA, AB as the included side
(c)SSS, using BM = CM as a fact
(d)RHS, using AM as common side
16.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.
(a)8
(b)4
(c)2
(d)0
17.Cheng is paid an hourly rate that is proportional to the number of hours she works. She earns £52.50 for 7 hours. Work out how much she earns for 11 hours, assuming the same rate.
(a)£99
(b)£56.50
(c)£30
(d)£82.50
18.A shape is translated by the vector $(- 7 4)$ and then by the vector $(3 - 9)$ . Write down the single column vector that has the same effect as those two translations together.
(a) $(- 4 - 5)$
(b) $(- 10 13)$
(c) $(- 4 - 13)$
(d) $(- 10 - 5)$
19.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?
(a)11
(b)48
(c)15.5
(d)12
20.Work out the value of m² + 3m when m = −2
(a)−10
(b)10
(c)−14
(d)−2

How the 20 questions are shared out

Number — 3 questions (15% of the qualification)
Algebra — 6 questions (30% of the qualification)
Ratio, proportion and rates of change — 4 questions (20% of the qualification)
Geometry and measures — 4 questions (20% 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.