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

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1.Work out −4.5 + 2.8.
(a)1.7
(b)−7.3
(c)−2.3
(d)−1.7
2.Write 0.325 as a fraction in its simplest form.
(a)13/40
(b)3/8
(c)8/25
(d)13/4
3.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.
(a)1/16
(b)1/8
(c)15/16
(d)3/16
4.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.
(a)£18
(b)£8
(c)£138
(d)£12
5.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.
(a)−56/15
(b)3/25
(c)−4/3
(d)4/3
6.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.
(a)1 3/4
(b)2 5/12
(c)8
(d)1 7/12
7.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
8.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.
(a)30, which is not prime
(b)31, which is not prime because 31 = 1 × 31
(c)31, which is not prime because it is a multiple of 3
(d)31, which is prime
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.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.
(a)14 and 15
(b)4 and 5
(c)3 and 4
(d)5 and 6
11.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.
(a)8 × 10²
(b)8 × 10⁸
(c)6 × 10²
(d)8 × 10⁻¹⁵
12.Simplify (5² × 2³)³ ÷ (5³ × 2²)²
(a)2
(b)2⁵
(c)2²
(d)2¹³
13.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
(a)2√3
(b)6
(c)2
(d)3√3
14.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
15.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.
(a)36 kg
(b)60 kg
(c)12 kg
(d)57.6 kg

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