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 cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.
(a)3
(b)30
(c)25
(d)24
2.Simplify √45.
(a)9√5
(b)6√5
(c)15
(d)3√5
3.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.
(a)9 × 10¹³
(b)9 × 10⁶
(c)6.3 × 10⁷
(d)9 × 10⁷
4.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.
(a)4:3
(b)1:1
(c)3:4
(d)3:7
5.Work out the value of $1 6^{3/4}$ .
(a)12
(b)2
(c)64
(d)8
6.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
7.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.
(a)6 × 10² metres
(b)6 × 10¹⁴ metres
(c)6 × 10⁻⁴⁸ metres
(d)5 × 10² metres
8.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.
(a)11
(b)8
(c)12
(d)9
9.The density of a metal is calculated using density = mass ÷ volume. A sample has a mass of 156 g, correct to the nearest gram, and a volume of 12 cm³, correct to the nearest cm³. Work out the minimum possible density, in g/cm³.
(a)13
(b)13.52
(c)12.44
(d)12.52
10.A shape is made by joining a rectangle measuring 10 cm by 6 cm to a semicircle of diameter 6 cm along one of the rectangle's shorter sides. Work out the exact area of the shape, in terms of π.
(a)(60 + 3π) cm²
(b)(60 + 4.5π) cm²
(c)(60 + 9π) cm²
(d)(60 + 18π) cm²
11.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.
(a)8 × 10³
(b)1.28 × 10¹⁷
(c)8 × 10⁴
(d)8 × 10¹⁵
12.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.
(a)40
(b)60
(c)72
(d)120
13.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
14.£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
15.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

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