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.Write ∛(x²) as a single power of x.
(a)x⁽¹⁄⁶⁾
(b)x⁶
(c)x⁽²⁄³⁾
(d)x⁽³⁄²⁾
2.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.
(a)23/99
(b)11/45
(c)7/30
(d)23/100
3.Estimate the value of √45, giving your answer to the nearest whole number.
(a)2,025
(b)7
(c)6
(d)22.5
4.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.
(a)2, 3, 4, 5
(b)3, 4, 5
(c)1, 2, 3, 4, 5
(d)2, 3, 4, 5, 6
5.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.
(a)2/9
(b)4/9
(c)2/5
(d)4/7
6.Ten athletes run in a final. Gold, silver and bronze medals are awarded to the first three athletes to finish, and there are no ties. Work out how many different ways the three medals can be awarded.
(a)30
(b)1000
(c)120
(d)720
7.A charity raises money from a raffle and a cake sale in the ratio 5 : 3. Altogether the charity raises £320. Work out how much money the cake sale raised.
(a)£40
(b)£192
(c)£200
(d)£120
8.Simplify (3a²)² × (2a)³
(a)17a⁷
(b)72a¹²
(c)36a⁷
(d)72a⁷
9.Work out √(4 × 9)
(a)5
(b)18
(c)36
(d)6
10.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%
(a)7/20, 32%, 0.3
(b)0.3, 32%, 7/20
(c)0.3, 7/20, 32%
(d)32%, 0.3, 7/20
11.Work out the value of $1 0^{- 3}$ .
(a)1000
(b)−1000
(c)0.001
(d)−0.001
12.A car manufacturer offers a car in 6 colours and 4 trim levels. Two colour-and-trim combinations are not available: red with sport trim, and white with sport trim. Work out how many different colour-and-trim combinations are available.
(a)18
(b)23
(c)22
(d)24
13.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?
(a)0.0485
(b)0.052
(c)0.0479
(d)0.04
14.Which statement about the number 91 is correct?
(a)91 is not prime, because 91 = 7 × 13.
(b)91 is prime, because it is not divisible by 2, 3 or 5.
(c)91 is not prime, because it is divisible by 3.
(d)91 is prime, because it is an odd number ending in 1.
15.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

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