Number worksheet — GCSE Higher

1.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.

3.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

4.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

5.Write 0.325 as a fraction in its simplest form.

6.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

7.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

8.A charity bake sale sells 187 cakes at £2.95 each. By rounding each number to 1 significant figure, work out an estimate for the total amount raised.

9.Work out the value of 2⁻²

10.Simplify 2³ × 2⁴, giving your answer as a single power of 2.

12.√700 lies between which two consecutive integers?

13.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.

14.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

15.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?