Number worksheet — GCSE Higher

1.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?

2.Write 0.005 in standard form.

3.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

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.

5.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.

6.To estimate the cost of buying 38.7 m of rope at £21.40 per metre, both numbers are first rounded to 1 significant figure. Work out the estimate.

7.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

8.Expand and simplify √3(2 + √12).

9.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

10.By listing systematically, work out how many two-digit multiples of 5 can be made using the digits 0, 3 and 5, if each digit can be used at most once and the number cannot start with 0.

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

12.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

13.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.

14.Four friends share a restaurant bill of £53.90 equally. A calculator gives each share as 13.475. Work out how much each friend should pay.

15.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.