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.Rationalise the denominator of 6/√3, giving your answer in its simplest form.
(a)2√3
(b)6
(c)2
(d)3√3
2.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.
(a)Yes — Priya's jump could have been up to 3.9 m
(b)No — their possible jump lengths do not overlap
(c)Yes — both jumps could have been 3.85 m
(d)No — a recorded jump is exactly the length jumped
3.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.
(a)2√3 + 2√6
(b)12√2
(c)36
(d)6
4.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.
(a)8 litres per minute
(b)0.125 litres per minute
(c)8.7 litres per minute
(d)10 litres per minute
5.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
6.Estimate the value of √45, giving your answer to the nearest whole number.
(a)2,025
(b)7
(c)6
(d)22.5
7.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.
(a)They are equal
(b)3²⁰ is larger
(c)2³⁰ is larger
(d)They cannot be compared without a calculator
8.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.
(a)200 m
(b)1050 m
(c)150 m
(d)50 m
9.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?
(a)2/3
(b)2/5
(c)1/3
(d)3/5
10.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².
(a)300 N/m²
(b)3000 N/m²
(c)192 N/m²
(d)30 N/m²
11.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.
(a)No, because 14.8 cm is not the same length as 15 cm
(b)Yes, because 14.8 cm rounds to 15 cm to the nearest cm
(c)No, because 14.8 cm rounds to 14 cm to the nearest cm
(d)Yes, because 14.8 cm rounds to 15.0 cm to 1 decimal place
12.Write 0.35 as a fraction in its lowest terms.
(a)7/25
(b)35/10
(c)3/10
(d)7/20
13.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.
(a)64π cm²
(b)4π cm²
(c)8π cm²
(d)16π cm²
14.Write 7/12 as a decimal, showing clearly which digit is recurring.
(a)0.588888...
(b)0.58333...
(c)0.585858...
(d)0.58
15.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.
(a)10
(b)8
(c)11
(d)12

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