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 · 15 questions

MathsUKwww.geekhero.co.uk

1.A country has an area of 25,000,000 hectares. Write this area in standard form.
(a)2.5 × 10⁷
(b)2.5 × 10⁸
(c)25 × 10⁶
(d)2.5 × 10⁻⁷
2.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.
(a)300
(b)307
(c)450
(d)3,000
3.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.
(a)12.5 g
(b)25 g
(c)0.125 g
(d)300 g
4.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.
(a)31/50
(b)25/4
(c)5/8
(d)8/5
5.Which of these statements about −0.7 and −0.25 is true?
(a)−0.7 = −0.25
(b)−0.7 < −0.25
(c)−0.7 ≥ −0.25
(d)−0.7 > −0.25
6.Work out (−3) × 4 + 2 × (−5)
(a)−22
(b)50
(c)−2
(d)22
7.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.
(a)1/2
(b)1/6
(c)5/6
(d)1
8.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.
(a)9 × 10²³ seconds
(b)3 × 10⁷ seconds
(c)1 × 10⁻⁷ seconds
(d)1 × 10⁷ seconds
9.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.
(a)£6.66
(b)£8
(c)£7.60
(d)£7.40
10.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.
(a)56
(b)336
(c)24
(d)168
11.A cheetah runs at a steady speed of 25 metres per second. Work out this speed in kilometres per hour.
(a)1500 km/h
(b)90 km/h
(c)90000 km/h
(d)6.9 km/h
12.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.
(a)23/99
(b)11/45
(c)7/30
(d)23/100
13.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.
(a)700 g
(b)626 g
(c)630 g
(d)636 g
14.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.
(a)the nearest whole number
(b)it cannot be given to any degree of accuracy
(c)the nearest 0.1
(d)the nearest 10
15.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21

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