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 recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.
(a)31/50
(b)25/4
(c)5/8
(d)8/5
2.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
3.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
4.Work out ⁴√16
(a)4
(b)8
(c)64
(d)2
5.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.
(a)9/8
(b)2/3
(c)2
(d)1/2
6.Work out ⁴√81
(a)3
(b)20.25
(c)4.5
(d)9
7.Estimate the value of √45, giving your answer to the nearest whole number.
(a)2,025
(b)7
(c)6
(d)22.5
8.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2
(a)1/2, 3/5, 2/3, 5/6
(b)5/6, 2/3, 3/5, 1/2
(c)1/2, 3/5, 5/6, 2/3
(d)1/2, 2/3, 3/5, 5/6
9.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.
(a)4π cm²
(b)8π cm²
(c)16π cm²
(d)32π cm²
10.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.
(a)4 + √6
(b)4
(c)4 − √6
(d)4 + 10√6
11.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.
(a)Yes, the true mass is at least 847.5 kg and at most 850 kg
(b)No, the true mass could be as high as 852.5 kg
(c)Yes, the display reads 850 kg, which is not above the limit
(d)No, 850 kg on the display rounds up to 855 kg
12.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.
(a)56
(b)21
(c)35
(d)28
13.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.
(a)£160
(b)£220
(c)£213.25
(d)£200
14.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.
(a)19
(b)20
(c)16
(d)17
15.Simplify (x⁻²)³, giving your answer as a fraction.
(a)x⁶
(b)1/x⁵
(c)1/x⁶
(d)−x⁶

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