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.A speed camera measures a car's speed as 34 mph, correct to the nearest mph. Work out the smallest possible actual speed of the car, in mph.
(a)33.5 mph
(b)33 mph
(c)34.5 mph
(d)34 mph
2.Write 12 as a product of its prime factors.
(a)2² × 3
(b)2 × 3²
(c)2 × 3
(d)2 × 6
3.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.
(a)8/5
(b)5/3
(c)3/8
(d)3/5
4.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.
(a)3⁷
(b)3³
(c)3⁻³
(d)3¹⁰
5.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
6.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
7.Write 0.325 as a fraction in its simplest form.
(a)13/40
(b)3/8
(c)8/25
(d)13/4
8.Work out the value of √49 + ∛27
(a)10
(b)34
(c)16
(d)21
9.A concrete mix is made from cement and sand in the ratio 3 : 5 by mass. A builder mixes 96 kg of concrete. Work out the mass of cement in the mix.
(a)36 kg
(b)60 kg
(c)12 kg
(d)57.6 kg
10.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.
(a)18
(b)25
(c)24
(d)28
11.A shop buys boxes of pens for £4 each. It sells each box on to a school for £3 more than it paid, and charges an extra £2 delivery fee for the whole order. A school orders 5 boxes. Work out the total cost of the order.
(a)£45
(b)£37
(c)£25
(d)£22
12.Write 0.875 as a fraction in its simplest form.
(a)7/8
(b)7/80
(c)9/10
(d)8/7
13.Work out 5⁰ + 5¹ + 5²
(a)125
(b)30
(c)31
(d)35
14.Work out 4368 ÷ 12.
(a)346
(b)364
(c)304
(d)36.4
15.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.
(a)415
(b)400
(c)300
(d)500

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