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 driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.
(a)1.4 × 10²
(b)6.4 × 10⁸
(c)5.3 × 10⁷
(d)1.2 × 10⁹
2.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?
(a)3/7
(b)7/3
(c)7/10
(d)3/10
3.Write 0.35 as a fraction in its lowest terms.
(a)7/25
(b)35/10
(c)3/10
(d)7/20
4.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
5.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.
(a)71
(b)81
(c)70
(d)64
6.A country's population is 8,340,000, and it is estimated that 1,950,000 of them live in the capital city. By rounding each number to 1 significant figure, work out an estimate for the number of people who do not live in the capital city.
(a)6,300,000
(b)8,000,000
(c)6,390,000
(d)6,000,000
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.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
9.Work out (3 × 10²) × (2 × 10⁵). Give your answer in standard form.
(a)6 × 10³
(b)5 × 10⁷
(c)6 × 10¹⁰
(d)6 × 10⁷
10.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
11.After a price increase of 10%, a laptop costs £330. Work out the original price.
(a)£3,300
(b)£300
(c)£363
(d)£297
12.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
13.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.
(a)0.625
(b)0.58
(c)0.85
(d)0.6
14.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.
(a)7 × 10⁴
(b)12 × 10⁴
(c)1.2 × 10⁴
(d)1.2 × 10⁵
15.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.
(a)12
(b)6
(c)16
(d)8

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