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 space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.
(a)600
(b)750,000,000
(c)7,500,000,000
(d)0.000000075
2.Work out (−2)³ + (−3)² − (−4)
(a)5
(b)−13
(c)−3
(d)21
3.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.
(a)4π cm²
(b)8π cm²
(c)16π cm²
(d)32π cm²
4.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.
(a)1/10
(b)1/9
(c)1/11
(d)11/100
5.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
6.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
7.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.
(a)28.8 km/h
(b)0.48 km/h
(c)2.22 km/h
(d)28 800 km/h
8.A tank contains 120 litres of water. Water is drained out at a rate of 8 litres per minute for 6 minutes, and then a hose adds 15 litres. Work out how much water is left in the tank.
(a)121 litres
(b)57 litres
(c)87 litres
(d)72 litres
9.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
10.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.
(a)0.11 g/cm³
(b)9 g/cm³
(c)480 g/cm³
(d)32400 g/cm³
11.Write these numbers in order, starting with the largest: 7/8, 0.8, 78%, 17/20
(a)7/8, 17/20, 0.8, 78%
(b)7/8, 0.8, 17/20, 78%
(c)78%, 0.8, 17/20, 7/8
(d)17/20, 7/8, 0.8, 78%
12.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
13.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
14.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.
(a)7.5 m
(b)2.1 m
(c)3.0 m
(d)2.7 m
15.A jug holds 1.8 litres of juice. Priya pours out 3/4 of a litre to fill a glass. Work out how much juice is left in the jug, in millilitres.
(a)1725 ml
(b)50 ml
(c)2550 ml
(d)1050 ml

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