Printable · GCSE Higher · ages 14-16

Number worksheet — GCSE Higher

Fifteen questions across the number statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Number worksheet — GCSE Higher

Maths · GCSE Higher · Number · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Work out (−2)² − 3
(a)−7
(b)1
(c)25
(d)−1
2.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.
(a)5
(b)20/9
(c)5/3
(d)2
3.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.
(a)36
(b)6
(c)108
(d)216
4.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.
(a)20
(b)19
(c)17
(d)200
5.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.
(a)4
(b)24
(c)96
(d)20
6.Work out (2/3)² + (1/2)². Give your answer as a fraction.
(a)7/3
(b)49/36
(c)25/36
(d)5/13
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.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.
(a)18 minutes
(b)54 minutes
(c)3 minutes
(d)15 minutes
9.A padlock code is formed from 3 different digits chosen from 1, 2, 3, 4, 5 and 6 (no digit may be used twice in the same code). Work out how many different codes can be made.
(a)120
(b)216
(c)15
(d)20
10.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.
(a)7
(b)4 + 5√3
(c)7 + 4√3
(d)5 + 4√3
11.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.
(a)6
(b)12
(c)36
(d)21
12.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.
(a)4 + √6
(b)4
(c)4 − √6
(d)4 + 10√6
13.Write 0.005 in standard form.
(a)5 × 10³
(b)5 × 10⁻²
(c)5 × 10⁻³
(d)0.5 × 10⁻²
14.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56
(a)0.5, 0.55, 0.56, 0.6, 0.601
(b)0.5, 0.56, 0.55, 0.6, 0.601
(c)0.5, 0.6, 0.55, 0.56, 0.601
(d)0.601, 0.6, 0.56, 0.55, 0.5
15.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.
(a)18
(b)25
(c)24
(d)28

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