Number worksheet — GCSE Higher

1.A choir has sopranos, altos and tenors in the ratio 6 : 4 : 5. What fraction of the choir is not tenors?

2.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.

3.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

4.Petrol costs £1.48 per litre. Sam buys 35 litres and pays with three £20 notes. Work out his change.

5.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

6.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.

7.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

8.Simplify (x⁻²)³, giving your answer as a fraction.

9.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

10.Given that 2⁵ = 32, work out 2⁶.

11.By first working out 2.9², then squaring your result, estimate 2.9⁴ to 2 significant figures.

12.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

13.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

14.Write 60 as a product of its prime factors, using index notation.

15.Work out 3 + 4 × (−2).