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 + 2) × 3²
(a)147
(b)63
(c)23
(d)441
2.Two expressions are 4(x + 3) and 4x + 3. A student checks whether they are equivalent by substituting x = 2. Which statement correctly interprets the result?
(a)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, so the two expressions are not equivalent, because the bracket means the 3 must be added before multiplying by 4.
(b)4(x + 3) = 11 and 4x + 3 = 11 when x = 2, since the bracket has no effect on the multiplication, so the two expressions are equivalent.
(c)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, but the two expressions are equivalent because both involve the same terms, 4x and 3.
(d)4(x + 3) = 20 and 4x + 3 = 11 when x = 2, so the two expressions are not equivalent, but they would become equal for some larger value of x.
3.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.
(a)1.3
(b)−1.3
(c)7.7
(d)14.4
4.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.
(a)0.2 hours
(b)25 hours
(c)5 hours
(d)125 hours
5.A machine produces bolts. In a sample of 250 bolts, 15 are faulty. Work out the relative frequency of a bolt being faulty, giving your answer as a fraction in its simplest form.
(a)50/3
(b)3/47
(c)1/10
(d)3/50
6.A two-way table records the favourite subject, Maths or Art, of 60 pupils in Year 10, and whether each pupil is left-handed or right-handed. 9 of the 60 pupils are left-handed, and 6 of those left-handed pupils prefer Art. In total, 24 of the 60 pupils prefer Art. A pupil is chosen at random from the 60. Work out the probability that the pupil is right-handed and prefers Art.
(a)3/10
(b)1/10
(c)2/5
(d)17/20
7.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
8.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.
(a)8
(b)4
(c)1
(d)3
9.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.
(a)27.6 km
(b)1800 km
(c)30 km
(d)19.2 km
10.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.
(a)94.2 cm³
(b)90 cm³
(c)282.6 cm³
(d)1130.4 cm³
11.At a fun run, each runner finishes, retires or is disqualified, and cannot do more than one of these. The probability that a runner finishes is 68.5% and the probability that a runner retires is 24.75%. Work out the probability, as a percentage, that a runner is disqualified.
(a)6.75%
(b)93.25%
(c)75.25%
(d)31.50%
12.Work out (8 × 10⁻⁵) × (5 × 10³). Give your answer in standard form.
(a)4 × 10⁻⁸
(b)4 × 10⁻¹⁵
(c)4 × 10⁻¹
(d)40 × 10⁻²
13.A point has coordinates (x, y). In which two quadrants is the product x × y positive?
(a)the first and the fourth
(b)the first and the third
(c)the second and the fourth
(d)the first and the second
14.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.
(a)4:3
(b)2:3
(c)3:4
(d)1:2
15.Two circles are drawn with the same centre but different radii. Write down the term used to describe this pair of circles.
(a)Congruent circles
(b)Tangential circles
(c)Similar circles
(d)Concentric circles
16.Write down the gradient of the line with equation y = −x + 3.
y = −x + 3
(a)−3
(b)−1
(c)3
(d)1
17.A mobile phone tariff is shown on a straight-line graph with the monthly cost, C pounds, on the vertical axis and the amount of data used, g gigabytes, on the horizontal axis. The line passes through (0, 10) and (8, 26). Work out the gradient and say what it represents.
(a)3.25, the cost in pounds of each extra gigabyte
(b)2, the cost in pounds of each extra gigabyte
(c)10, the cost in pounds of each extra gigabyte
(d)2, the fixed monthly charge in pounds
18.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.
(a)−10
(b)47.5
(c)25
(d)20
19.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.
(a)−2
(b)19
(c)−17
(d)18
20.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.
(a)40
(b)11
(c)20
(d)80

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.