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 (−36) ÷ (−6) × 2
(a)3
(b)6
(c)12
(d)−12
2.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.
(a)30 cm
(b)360 cm
(c)15 cm
(d)10 cm
3.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³
(a)3.2 × 10⁴, 4.1 × 10³, 2.9 × 10⁵
(b)2.9 × 10⁵, 3.2 × 10⁴, 4.1 × 10³
(c)4.1 × 10³, 3.2 × 10⁴, 2.9 × 10⁵
(d)4.1 × 10³, 2.9 × 10⁵, 3.2 × 10⁴
4.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.
(a)No — 493 kg is only an estimate, so it may be over 500 kg
(b)Cannot be decided without the exact total
(c)Yes — the greatest possible total is 493.5 kg, under 500 kg
(d)No — the true total could be as high as 498 kg
5.Work out (−2)² − 3
(a)−7
(b)1
(c)25
(d)−1
6.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.
(a)3/10
(b)27/100
(c)3/11
(d)2/9
7.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.
(a)2/5
(b)3/5
(c)3/10
(d)1/5
8.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.
(a)8
(b)12
(c)6
(d)2
9.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.
(a)27/20
(b)17/50
(c)27/5
(d)27/80
10.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.
(a)5/4
(b)3/4
(c)3/2
(d)3/8
11.Work out √144 − 2 × 3 + √25
(a)35
(b)11
(c)1
(d)7
12.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?
(a)3/5
(b)9/10
(c)2/5
(d)3/4
13.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.
(a)18
(b)4
(c)24
(d)36
14.A measuring jug shows a volume of 340 ml, correct to the nearest 20 ml. Work out the smallest possible volume in the jug.
(a)330 ml
(b)320 ml
(c)335 ml
(d)350 ml
15.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.
(a)1 × 10³
(b)0.1 × 10⁻²
(c)1 × 10⁻⁴
(d)1 × 10⁻³

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