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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Number worksheet — GCSE Higher

Maths · GCSE Higher · Number · 15 questions

MathsUKwww.geekhero.co.uk

1.Work out √25 + 4² − 12 ÷ 3
(a)9
(b)17
(c)3
(d)37
2.Work out √3 × √12, giving your answer as an integer.
(a)6
(b)√15
(c)2√3
(d)36
3.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.
(a)180
(b)12
(c)10
(d)11
4.A charity raises 8 × 10⁶ pounds. This total is shared equally among 2 × 10² local projects. Work out how much each project receives, in standard form.
(a)4 × 10⁸
(b)4 × 10¹²
(c)4 × 10⁴
(d)6 × 10⁴
5.Simplify (5² × 2³)³ ÷ (5³ × 2²)²
(a)2
(b)2⁵
(c)2²
(d)2¹³
6.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21
7.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.
(a)5⁻⁶
(b)5²
(c)5⁻⁸
(d)5⁶
8.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
9.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
10.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.
(a)4,000 nanometres
(b)4 nanometres
(c)400 nanometres
(d)0.004 nanometres
11.Work out (5 × 10⁴) ÷ (2 × 10⁻²). Give your answer in standard form.
(a)1 × 10³
(b)2.5 × 10⁻⁶
(c)2.5 × 10⁶
(d)2.5 × 10²
12.Expand and simplify √3(2 + √12).
(a)6 + √6
(b)√15 + 2√3
(c)2√3
(d)6 + 2√3
13.Work out (4 × 10³) × (3 × 10¹). Give your answer in standard form.
(a)7 × 10⁴
(b)12 × 10⁴
(c)1.2 × 10⁴
(d)1.2 × 10⁵
14.Round 0.006482 to 2 significant figures.
(a)0.01
(b)0.00648
(c)0.0065
(d)0.006
15.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.
(a)6.1 < x ≤ 6.2
(b)6.2 ≤ x < 6.3
(c)6.2 ≤ x ≤ 6.3
(d)6.15 ≤ x < 6.25

Build your own mix at the worksheet builder.