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 grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.
(a)1 × 10³
(b)0.1 × 10⁻²
(c)1 × 10⁻⁴
(d)1 × 10⁻³
2.Write down the reciprocal of 0.2
(a)−0.2
(b)0.8
(c)5
(d)0.5
3.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.
(a)They are equal
(b)3²⁰ is larger
(c)2³⁰ is larger
(d)They cannot be compared without a calculator
4.Oliver drives 95 km at an average speed of 50 km/h. Work out an estimate for the time the journey takes, by rounding the distance to the nearest 100 km.
(a)1 hour 54 minutes
(b)30 minutes
(c)1 hour
(d)2 hours
5.Amelia estimates 48 × 21 by working out 50 × 20 = 1,000. Work out whether her estimate is an under-estimate or an over-estimate, and by how much.
(a)An over-estimate, by 19
(b)Neither — the estimate is exactly right
(c)An under-estimate, by 8
(d)An over-estimate, by 8
6.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
7.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.
(a)10
(b)8
(c)11
(d)12
8.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.
(a)25/2
(b)1/125
(c)4/5
(d)2/25
9.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³
(a)3.2 × 10⁴, 4.1 × 10³, 2.9 × 10⁵
(b)2.9 × 10⁵, 3.2 × 10⁴, 4.1 × 10³
(c)4.1 × 10³, 3.2 × 10⁴, 2.9 × 10⁵
(d)4.1 × 10³, 2.9 × 10⁵, 3.2 × 10⁴
10.Find the missing number: 17 × ▢ = 391
(a)23
(b)374
(c)17
(d)6647
11.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
12.Expand and simplify √3(2 + √12).
(a)6 + √6
(b)√15 + 2√3
(c)2√3
(d)6 + 2√3
13.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.
(a)200 m
(b)1050 m
(c)150 m
(d)50 m
14.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.
(a)8.15 ≤ y < 8.25
(b)8.15 < y < 8.25
(c)8.1 ≤ y < 8.2
(d)8.2 ≤ y < 8.3
15.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.
(a)3/5
(b)3/8
(c)5/3
(d)5/8

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