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.Work out how many factors 100 has.
(a)8
(b)4
(c)9
(d)10
2.Simplify x⁶ ÷ x²
(a)x¹²
(b)x³
(c)x⁸
(d)x⁴
3.Work out ∛(−27) + ∛8
(a)5
(b)−5
(c)−1
(d)−6
4.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.
(a)2/9
(b)4/9
(c)2/5
(d)4/7
5.Work out 1 − 1/2 − 1/4 − 1/8 − 1/16. Give your answer as a fraction.
(a)1/16
(b)1/8
(c)15/16
(d)3/16
6.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.
(a)9 × 10²³ seconds
(b)3 × 10⁷ seconds
(c)1 × 10⁻⁷ seconds
(d)1 × 10⁷ seconds
7.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.
(a)23/99
(b)11/45
(c)7/30
(d)23/100
8.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.
(a)5 or −3
(b)4 or −4
(c)3 or −5
(d)3 only
9.Work out the value of √(16 + 9)
(a)5
(b)12
(c)7
(d)−5
10.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.
(a)7
(b)4 + 5√3
(c)7 + 4√3
(d)5 + 4√3
11.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.
(a)25/2
(b)1/125
(c)4/5
(d)2/25
12.Without using a calculator, estimate √20 × √12, giving your answer to the nearest whole number.
(a)240
(b)12
(c)8
(d)15
13.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?
(a)Ben's estimate
(b)Chloe's estimate
(c)Ella's estimate
(d)Dan's estimate
14.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?
(a)1/3
(b)2/3
(c)1/2
(d)7/12
15.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

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