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.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.
(a)1/2
(b)9/20
(c)5/11
(d)4/9
2.Solve the inequality 5x − 3 > 2x + 9.
(a)x > 4
(b)x > 2
(c)x < 4
(d)x > 36
3.The value of a delivery van, in £, is plotted against its age, in years, since it was bought. At age 2 years, the gradient of the tangent to the graph is −950. What does this tell you about the van at age 2 years?
(a)Falling at 950% per year
(b)Rising at £950 per year
(c)Falling at £950 per year
(d)Falls by £950 over the next year
4.In triangle ABC, AB = 9 cm, angle BAC = 50° and the area of the triangle is 36 cm². Work out the length of AC. Give your answer to 1 decimal place.
(a)5.2 cm
(b)12.4 cm
(c)10.4 cm
(d)6.1 cm
5.A two-way table records 150 customers at a café. 90 of the customers bought a hot drink and the rest did not. 54 of the hot-drink customers also bought a cake. 21 of the customers who did not buy a hot drink bought a cake. Work out the percentage of all 150 customers who bought a cake.
(a)60%
(b)50%
(c)36%
(d)14%
6.The times, t minutes, taken by 120 runners to finish a fun run are summarised by these cumulative frequencies: t < 20, 8 runners; t < 30, 26 runners; t < 40, 74 runners; t < 50, 110 runners; t < 60, 120 runners. Work out the number of runners who took 40 minutes or longer to finish.
(a)36
(b)74
(c)46
(d)10
7.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.
(a)6.1 < x ≤ 6.2
(b)6.2 ≤ x < 6.3
(c)6.2 ≤ x ≤ 6.3
(d)6.15 ≤ x < 6.25
8.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.
(a)x = 0, y = 3 and x = 6, y = −3
(b)x = 0, y = 3 and x = −3, y = 6
(c)x = 0, y = 3 and x = 3, y = 0
(d)x = 0, y = 3
9.The ratio of Josh's savings to Mia's savings is 4:7. Mia has £39 more than Josh. Work out Josh's savings.
(a)£39
(b)£52
(c)£91
(d)£13
10.A hexagon has interior angles of 130°, 142°, 125°, 150°, 135° and x°. Work out the value of x.
(a)142°
(b)40°
(c)38°
(d)398°
11.At a gym, 70 members are asked whether they use the pool or the sauna. 38 use the pool, 30 use the sauna, and 12 use neither. Work out n(P ∩ S), the number of members who use both the pool and the sauna.
(a)12
(b)10
(c)28
(d)68
12.Work out the value of $1 6^{3/4}$ .
(a)12
(b)2
(c)64
(d)8
13.Solve 2x² − 32 = 0.
(a)x = 8
(b)x = 4
(c)x = 16
(d)x = 4 or x = −4
14.A tangent to a curve at the point where x = 3 passes through the points (1, 4) and (5, 20). Work out the gradient of the tangent at x = 3, and hence the instantaneous rate of change of y with respect to x at that point.
(a)−4
(b)16
(c)4
(d)20
15.AT is a diameter of a circle with centre O. PT is a tangent to the circle at the point T, and P is a point on this tangent such that A, T and P form a triangle. Angle PAT = 28°. Work out the size of angle APT.
(a)118°
(b)62°
(c)28°
(d)90°
16.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.
(a)1.8
(b)72
(c)3.6
(d)6
17.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.
(a)£18.00
(b)£0.01
(c)£8.00
(d)£2.00
18.Work out the exact value of cos 0° − sin 30°.
(a)1/2
(b)−1/2
(c)3/2
(d)1
19.The graph of y = f(x) has roots at x = −1 and x = 4, and crosses the y-axis at (0, −8). Which statement about the graph of y = f(x − 3) is correct?
(a)x = 2, x = 7; y-intercept cannot be found here
(b)x = 2, x = 7; y-intercept stays at (0, −8)
(c)x = −4, x = 1; y-intercept stays at (0, −8)
(d)x = −4, x = 1; y-intercept cannot be found here
20.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.
(a)Subtracting 4x gives 3 = 10, which is never true.
(b)x would have to be negative, but x must be positive.
(c)It's true for every x, so there are infinite solutions.
(d)x = 7, since 10 − 3 = 7.

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.