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.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.
(a)£27.00
(b)£15.00
(c)£9.00
(d)£33.00
2.Solve 2x + 7 = x + 13
(a)x = 2
(b)x = 20
(c)x = −6
(d)x = 6
3.The length of ribbon A is 5/12 of the length of ribbon B. Write the length of ribbon B as a fraction of the length of ribbon A.
(a)12/5
(b)5/12
(c)12/7
(d)7/12
4.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
(a)(3, 3)
(b)(4, 0)
(c)(4, 3)
(d)(3.5, 3)
5.An ordinary pack of 52 playing cards contains 13 hearts. One card is taken at random from the pack. Work out the probability that the card is not a heart. Give your answer as a percentage.
(a)39%
(b)50%
(c)25%
(d)75%
6.A sports centre in Newcastle asks 60 members which activity they prefer: swimming 15 members, football 25 members, badminton 12 members and other activities 8 members. Work out the angle at the centre of the pie chart sector that represents badminton.
(a)150°
(b)20°
(c)72°
(d)90°
7.Work out 35% of 180.
(a)45
(b)63
(c)145
(d)126
8.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.
y = x
(a)(0, 4)
(b)(4, 0)
(c)(0, 0)
(d)(0, −4)
9.y is inversely proportional to x², and x is positive. When x = 2, y = 45. Construct the equation connecting x and y, then work out the value of x when y = 5.
(a)6
(b)36
(c)18
(d)30
10.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.
(a)20 litres
(b)20000 litres
(c)0.02 litres
(d)30 litres
11.A = {factors of 12} and B = {factors of 18}. Work out n(A ∩ B), the number of elements in both sets.
(a)3
(b)8
(c)6
(d)4
12.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0
13.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.
(a)2x
(b)x² + 49
(c)x² − 14x − 49
(d)x² − 49
14.A car travels 180 miles in 3 hours. A lorry travels 160 miles in 4 hours. Write the car's average speed as a fraction of the lorry's average speed, giving your answer in its simplest form.
(a)3/2
(b)3/4
(c)9/8
(d)2/3
15.A, B and C are points on a circle with centre O, and AB is a diameter. Prove that angle ACB = 90°, using the fact that triangle OAC and triangle OBC are both isosceles. In the proof, angle OAC = angle OCA = x and angle OBC = angle OCB = y. Which equation correctly expresses the angle sum of triangle ABC in terms of x and y, and leads to the required proof?
(a)x + y = 180°
(b)2x + 2y = 180°
(c)2x + 2y = 360°
(d)2x + y = 180°
16.Which of these statements is an identity?
(a)x + 4 = 2x
(b)2(x + 4) = 20
(c)2(x + 4) ≡ 2x + 8
(d)2(x + 4) = 2x + 4
17.The mass of a length of copper pipe is proportional to its length. A pipe of length 4.5 m has a mass of 12.6 kg. Work out the mass of a pipe of the same type of length 9.5 m.
(a)12.6
(b)3.4
(c)17.6
(d)26.6
18.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?
(a)A cylinder
(b)A pyramid
(c)A cone
(d)A prism
19.A circular pond has equation x² + y² = 20, with lengths in metres from the centre of the garden. A straight path runs along the line y = 2x, entering the pond and leaving it again. Work out the coordinates of the two points where the path meets the edge of the pond.
y = 2x
(a)(2, 4)
(b)(2, 4) and (−2, −4)
(c)(2, 1) and (−2, −1)
(d)(2, −4) and (−2, 4)
20.The point (20, 21) lies on the circle x² + y² = 841, which has centre O(0, 0). The tangent to the circle at (20, 21) crosses the x-axis at P and the y-axis at Q. Work out the area of triangle OPQ, correct to 1 decimal place.
(a)842.0
(b)2.0
(c)1684.0
(d)580.7

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.