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 bag holds 50 counters. 2/5 of them are red and the rest are blue. 5 red counters are then taken out of the bag. Work out the new ratio of red counters to blue counters. Give your answer in its simplest form.
(a)2 : 3
(b)1 : 2
(c)4 : 5
(d)2 : 1
2.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
3.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%
(a)0.55, 58%, 3/5
(b)58%, 0.55, 3/5
(c)3/5, 0.55, 58%
(d)3/5, 58%, 0.55
4.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
(a)2√3
(b)6
(c)2
(d)3√3
5.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
6.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.
(a)25
(b)−5
(c)1
(d)−35
7.Two lighthouses flash at the start of the same minute. The first lighthouse flashes every 8 minutes and the second flashes every 12 minutes. Work out how many minutes it will be until they next flash together.
(a)4
(b)24
(c)96
(d)20
8.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.
(a)to the nearest centimetre
(b)to 1 decimal place
(c)to the nearest 0.5 cm
(d)to the nearest 10 cm
9.Work out √3 × √12, giving your answer as an integer.
(a)6
(b)√15
(c)2√3
(d)36
10.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?
(a)9/10
(b)3/5
(c)4/15
(d)2/5
11.Which of these is written correctly in standard form?
(a)7.5 × 10⁴
(b)12 × 10³
(c)6.2 × 4⁵
(d)0.5 × 10⁴
12.Work out 3³ + 2⁴.
(a)35
(b)25
(c)43
(d)432
13.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
14.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.
(a)37.5
(b)27.5
(c)36.5
(d)26.5
15.Work out (−2)² − 3
(a)−7
(b)1
(c)25
(d)−1

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