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.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.
(a)The tape can only give the length to the nearest centimetre
(b)A length in metres must be written to 2 decimal places
(c)A length in metres must be rounded to the nearest metre
(d)The tape can only give the length to the nearest millimetre
2.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?
(a)Ben's estimate
(b)Chloe's estimate
(c)Ella's estimate
(d)Dan's estimate
3.Work out 10% of 30% of £200.
(a)£60
(b)£80
(c)£20
(d)£6
4.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.
(a)£283.33
(b)£36.13
(c)£48.88
(d)£50.00
5.Work out 6² − 4².
(a)2
(b)52
(c)20
(d)4
6.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.
(a)7
(b)3
(c)1
(d)6
7.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
8.Round 0.006852 to 2 significant figures.
(a)0.0069
(b)0.0068
(c)0.007
(d)0.00685
9.Which of these is written correctly in standard form?
(a)7.5 × 10⁴
(b)12 × 10³
(c)6.2 × 4⁵
(d)0.5 × 10⁴
10.Work out (−36) ÷ (−6) × 2
(a)3
(b)6
(c)12
(d)−12
11.£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
12.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56
(a)0.5, 0.55, 0.56, 0.6, 0.601
(b)0.5, 0.56, 0.55, 0.6, 0.601
(c)0.5, 0.6, 0.55, 0.56, 0.601
(d)0.601, 0.6, 0.56, 0.55, 0.5
13.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.
(a)120
(b)12
(c)1440
(d)60
14.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.
(a)180
(b)12
(c)10
(d)11
15.A 3-character PIN starts with one letter chosen from A, B, C, D and E, followed by two different digits chosen from 1 to 9 (no digit may be used twice in the same PIN). Work out how many different PINs are possible.
(a)180
(b)22
(c)360
(d)405

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