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.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.
(a)9 × 10²³ seconds
(b)3 × 10⁷ seconds
(c)1 × 10⁻⁷ seconds
(d)1 × 10⁷ seconds
2.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.
(a)2/5
(b)3/5
(c)2/3
(d)1/2
3.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
4.£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
5.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
6.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.
(a)£48
(b)£72
(c)£75
(d)£12
7.Write 0.875 as a fraction in its simplest form.
(a)7/8
(b)7/80
(c)9/10
(d)8/7
8.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
9.Work out the value of $1 6^{3/4}$ .
(a)12
(b)2
(c)64
(d)8
10.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.
(a)7
(b)0.07
(c)70
(d)0.7
11.Write 0.36 as a fraction in its simplest form.
(a)36/10
(b)9/25
(c)9/50
(d)3/10
12.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.
(a)0.625
(b)0.58
(c)0.85
(d)0.6
13.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
14.A café is planning its lunch menu. It will offer one soup from 3 choices and one sandwich from 4 choices, but the mushroom soup, one of the 3 soups, will only be served with the cheese sandwich, one of the 4 sandwiches, on a normal day. Work out how many different soup-and-sandwich combinations are available on a normal day.
(a)11
(b)8
(c)12
(d)9
15.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.
(a)36
(b)6
(c)108
(d)216

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