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.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.

3.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

4.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

5.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

6.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.

7.Simplify 5⁻² × 5⁴, giving your answer as a single power of 5.

8.Work out the reciprocal of (2 + 3)

9.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

10.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

11.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.

12.Three-digit numbers are made using the digits 2, 3, 4, 6, 8 and 9. No digit may be used twice in the same number. Work out how many of these three-digit numbers are odd.

13.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

14.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

15.Work out 3 × (−2)² − 5