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.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?
(a)£4.55
(b)£4.50
(c)£4.65
(d)£4.80
2.A company's cost, in £, for producing x items is shown on a graph. The tangent to the curve at x = 50 passes through (30, 400) and (70, 800). Interpret the gradient of this tangent in the context of the company's costs.
(a)The cost decreases by about £10 per extra item
(b)The cost increases by about £400 per extra item
(c)The cost increases by about £0.10 per extra item
(d)The cost increases by about £10 per extra item
3.In one batch of shortbread, a bakery uses 240 g of butter and 160 g of sugar. Another batch, made in the same ratio, uses 90 g of sugar. Work out how much butter is needed for the second batch.
(a)240 g
(b)170 g
(c)135 g
(d)60 g
4.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?
(a)kite
(b)trapezium
(c)rhombus
(d)parallelogram
5.A bag contains beads that are exactly one of red, white or black. The probability of taking a red bead is 3/10 and the probability of taking a white bead is 1/4. Work out the probability of taking a bead that is red or white.
(a)1/2
(b)9/20
(c)11/20
(d)3/40
6.A café owner in Brighton records the midday temperature, x °C, and the number of hot chocolates sold, y, on 12 days. The temperatures recorded run from 4 °C to 18 °C, and the line of best fit is y = −3x + 74. The forecast for tomorrow gives a midday temperature of 12 °C. Work out the number the line of best fit predicts, and write down how much confidence the owner can have in it.
y = -3x + 74
(a)38, and completely certain, as the line gives exact sales
(b)110, and fairly confident, as 12 °C is inside the range
(c)38, but little confidence, as 12 °C is outside the range
(d)38, and fairly confident, as 12 °C is inside the range
7.Find the missing number: 17 × ▢ = 391
(a)23
(b)374
(c)17
(d)6647
8.Which of these statements is an equation with exactly one solution?
(a)5x − 3 = 12
(b)5x − 3 = 5x − 3
(c)5x − 3 > 12
(d)5x − 3 = 5x + 2
9.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.
(a)1.50 m
(b)16.67 m
(c)6.00 m
(d)8.00 m
10.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.
(a)65 cm²
(b)1,000 cm²
(c)500 cm²
(d)2,000 cm²
11.A bag is known to contain red, blue and green counters in equal numbers, so the theoretical probability of taking each colour is 1/3. In 90 trials with replacement, red was taken 38 times, blue was taken 26 times and green was taken 26 times. Which colour is over-represented compared with its theoretical probability?
(a)Green
(b)Blue
(c)Red
(d)None of the three colours
12.Four locations each record a temperature one winter morning. Which of these temperatures is the coldest?
(a)−4.5 °C
(b)−3.8 °C
(c)−4.05 °C
(d)2 °C
13.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.
(a)x² + y² = 18
(b)x² + y² = 81
(c)x² − y² = 81
(d)x² + y² = 9
14.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.
(a)£33.80
(b)£40
(c)£32
(d)£26
15.A trapezium has vertices (0, 2), (4, 2), (3, 5) and (1, 5). It is rotated 180° about the point (2, 2), and the image is then translated by the vector (1, −5). Work out the coordinates of the image of (0, 2).
(a)(1, −7)
(b)(5, −3)
(c)(3, 7)
(d)(4, 2)
16.f(x) = 3x − 2. Find f⁻¹(x).
y = 3x − 2
(a)(x − 2)/3
(b)(x + 2)/3
(c)3x + 2
(d)x/3 + 2
17.The width, the length and the height of a box are in the ratio 3:4:5. The length of the box is 16 cm. Work out the height of the box.
(a)20 cm
(b)80 cm
(c)4 cm
(d)12 cm
18.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?
(a)vertically opposite angles are equal
(b)corresponding angles are equal
(c)base angles of an isosceles triangle are equal
(d)angles in a triangle add up to 180°
19.Make x the subject of the formula y = 2x − 9.
y = 2x − 9
(a)x = (y + 9) / 2
(b)x = (y − 9) / 2
(c)x = 2(y + 9)
(d)x = y / 2 + 9
20.Factorise 3x² + 10x − 8.
(a)(3x − 4)(x + 2)
(b)(3x + 2)(x − 4)
(c)(x − 2)(3x + 4)
(d)(3x − 2)(x + 4)

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.