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 (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.
(a)1 × 10³
(b)2.5 × 10⁻⁶
(c)2.5 × 10⁶
(d)2.5 × 10²
2.f(x) = x² − 1 and g(x) = 3x. Work out fg(4).
y = x² − 1
(a)36
(b)143
(c)11
(d)45
3.The density of a type of solid plastic is 0.9 g/cm³. Work out the mass of 0.5 m³ of the plastic, in kilograms.
(a)0.45 kg
(b)450.00 kg
(c)4.50 kg
(d)450000.00 kg
4.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?
(a)85
(b)340
(c)170
(d)680
5.A ferry company finds that on 20% of days the sea is rough. If the sea is rough, the probability that a crossing is delayed is 0.75. If the sea is calm, the probability that a crossing is delayed is 0.1. Given that a crossing was delayed, work out the probability that the sea was rough that day.
(a)1/5
(b)3/20
(c)15/23
(d)3/4
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.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4
8.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.
(a)20 km
(b)10 km
(c)40 km
(d)3 km
9.The cost, in pounds, of hiring a minibus is modelled against the number of passengers booked. A tangent to the cost graph at 20 passengers passes through the points (16, 184) and (24, 216). Work out the instantaneous rate at which the cost increases with each extra passenger, at 20 passengers.
(a)£32
(b)£8
(c)£40
(d)£4
10.In parallelogram PQRS, angle P = 65°. Which reason correctly explains why angle R = 65°?
(a)opposite angles of a parallelogram are equal
(b)co-interior angles add up to 180°
(c)alternate angles are equal
(d)angles on a straight line add up to 180°
11.The probability that Leo wakes up before his alarm is 0.35. The probability that his younger sister wakes up before her alarm, independently of Leo, is 0.28. Work out the probability that neither of them wakes up before their alarm.
(a)0.098
(b)0.63
(c)0.532
(d)0.468
12.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.
(a)£40
(b)£192
(c)£200
(d)£120
13.A bacteria colony doubles every 4 hours and its size is recorded only every 4 hours. The recorded population 20 hours after the start is 9,600. After how many hours did the recorded population first exceed 1,000?
(a)0
(b)12
(c)20
(d)8
14.A coach journey is 372 miles in total. After a stop, the coach has travelled 217 miles. Write the distance still to travel as a fraction of the total journey. Give your answer in its simplest form.
(a)5/12
(b)5/7
(c)145/372
(d)7/12
15.A drinks company sells a novelty giant bottle that is geometrically similar to its standard 500 ml bottle, scaled up by a length factor of 1.5. Work out the capacity of the giant bottle, in ml.
(a)750 ml
(b)2250 ml
(c)1125 ml
(d)1687.5 ml
16.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
17.Simplify the ratio 12 : 18 : 30 to its simplest form.
(a)3:2:5
(b)4:6:10
(c)6:9:15
(d)2:3:5
18.A shape is reflected in the line x = 1, and the image is then reflected in the line x = 5. Which single transformation is equivalent to this combination, for every point?
(a)Reflection in the line x = 3
(b)Translation by the vector (4, 0)
(c)Translation by the vector (8, 0)
(d)Translation by the vector (−8, 0)
19.Solve the inequality x² ≥ 16, giving your answer using set notation.
(a){x : x ≤ 4}
(b){x : x ≥ 4}
(c){x : x ≤ −4} ∪ {x : x ≥ 4}
(d){x : −4 ≤ x ≤ 4}
20.Simplify (x² − 9) ÷ (x² + 5x + 6).
(a)(x + 3)/(x + 2)
(b)(x − 3)/(x + 2)
(c)x − 3
(d)−9/(5x + 6)

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.