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%.

CalculatorGCSE Higher

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

New sheet

GCSE Higher sample Paper 2 (calculator)

Maths · GCSE Higher · Paper 2 · Calculator · 20 questions

MathsUKwww.geekhero.co.uk

1.A company's turnover is 5.6 × 10⁷ pounds, spread evenly across 3.5 × 10² shops. Work out the average turnover per shop, in standard form.
(a)2.1 × 10⁵
(b)1.6 × 10⁹
(c)1.6 × 10¹⁴
(d)1.6 × 10⁵
2.Solve 3x + 14 = 8x − 6
(a)x = 15
(b)x = 2.5
(c)x = 4
(d)x = −1.6
3.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
4.In triangle OAB, OA = a and OB = b. P lies on AB such that AP is twice PB. Express the vector OP in terms of a and b.
(a)a + (2/3)b
(b)(1/2)a + (1/2)b
(c)(1/3)a + (2/3)b
(d)(2/3)a + (1/3)b
5.A fair six-sided dice is rolled 150 times. The table shows how many times each number came up: 1 came up 22 times, 2 came up 27 times, 3 came up 24 times, 4 came up 34 times, 5 came up 21 times and 6 came up 22 times. The theoretical probability of each number is 1/6. Which number is most over-represented compared with its theoretical probability?
(a)3
(b)4
(c)2
(d)6
6.A study found that people who drink more coffee tend to concentrate better at work. A coffee company says that this shows that drinking coffee improves concentration. Give the reason why this conclusion cannot be drawn.
(a)The conclusion is safe because the correlation is positive
(b)The conclusion is wrong because the correlation is negative
(c)The data show a link only; a third factor may affect both
(d)The two quantities are not linked, so nothing can be said
7.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.
(a)5.25
(b)5
(c)6
(d)7
8.f(x) = x³ − 5x − 6. Given that f(2.6) = −1.424 and f(2.7) = 0.183, work out what this shows about the equation x³ − 5x − 6 = 0.
y = x
(a)It has a solution between x = 2.6 and x = 2.7
(b)There is no root in this interval
(c)It has a solution between x = −2.6 and x = −2.7
(d)It shows that x = 2.6 is a solution of the equation
9.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
10.A solid cube has a volume of 8 cm³. Work out the length of one edge of the cube.
(a)4 cm
(b)2 cm
(c)2.83 cm
(d)8 cm
11.At a sports club, the numbers of members who play tennis and badminton are: 50 members play tennis, 40 members play badminton, and 18 members play both tennis and badminton. A member who plays tennis is chosen at random. Work out the probability that this member also plays badminton.
(a)9/25
(b)9/20
(c)1/4
(d)1/5
12.Work out the value of $8^{- 2/3}$ .
(a)4
(b)−16/3
(c)−4
(d)1/4
13.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20
14.The strength of a radio signal, in units, is inversely proportional to the square of the distance from the transmitter, in km. At a distance of 2 km the signal strength is 20 units. Construct the equation connecting signal strength S and distance d, then work out the distance at which the signal strength is 5 units.
(a)16 km
(b)20 km
(c)4 km
(d)8 km
15.A trapezium has vertices (2, 1), (6, 1), (5, 4) and (3, 4). It is rotated 180° about the vertex (2, 1). Work out the number of points on the trapezium — including its vertices, edges and interior — that are invariant under this rotation.
(a)0 points
(b)1 point
(c)2 points
(d)4 points
16.A square tile has an area of 144 cm². Work out the side length of the tile.
(a)12 cm or −12 cm
(b)72 cm
(c)12 cm
(d)36 cm
17.There are 2500 electric cars registered in a town. The number is predicted to increase by 6% each year. Work out the predicted number of electric cars after 3 years, to the nearest whole number.
(a)2978
(b)3156
(c)2809
(d)2950
18.Work out the exact value of (cos 45°)² + (sin 45°)².
(a)2
(b)√2
(c)1
(d)1/2
19.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.
(a)4n² − n − 2
(b)5n − 6
(c)2n²
(d)2n² − n − 2
20.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.
(a)6.4
(b)4
(c)5.2
(d)3.5

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.