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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Work out √225 ÷ 3.
(a)8.7
(b)5
(c)75
(d)45
2.Work out −(−3)⁴ + (−3)³
(a)−108
(b)54
(c)−54
(d)108
3.Work out the value of (1/3)⁻²
(a)6
(b)9
(c)1/9
(d)−9
4.Work out √3 × √12, giving your answer as an integer.
(a)6
(b)√15
(c)2√3
(d)36
5.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.
(a)8.35 ≤ L < 8.45
(b)8.4 ≤ L < 8.5
(c)8.3 ≤ L < 8.5
(d)8.35 < L ≤ 8.45
6.Simplify (y³)⁴, giving your answer as a single power of y.
(a)y¹²
(b)12y
(c)y⁷
(d)y⁸¹
7.Simplify ⁴√(16a⁸b¹²)
(a)2a²b³
(b)2a⁴b⁶
(c)4a²b³
(d)2a²b⁴
8.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
9.Work out the value of √(16 + 9)
(a)5
(b)12
(c)7
(d)−5
10.Work out (−3) × 4 + 2 × (−5)
(a)−22
(b)50
(c)−2
(d)22
11.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
(a)2√3
(b)6
(c)2
(d)3√3
12.Write 5,000,000 in standard form.
(a)50 × 10⁵
(b)5 × 10⁷
(c)5 × 10⁶
(d)5 × 10⁻⁶
13.Write down the symbol that makes this statement true: −2/3 ___ −5/6
(a)<
(b)≤
(c)>
(d)=
14.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.
(a)30, which is not prime
(b)31, which is not prime because 31 = 1 × 31
(c)31, which is not prime because it is a multiple of 3
(d)31, which is prime
15.Work out the value of 6² − 4³.
(a)100
(b)28
(c)−28
(d)0

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