Number worksheet — GCSE Higher

1.Chloe wants to work out 3 1/4 − 1 2/3. She converts both mixed numbers to twelfths, then subtracts the whole numbers and the fraction parts separately, without checking whether she needs to exchange first. Work out the correct value of 3 1/4 − 1 2/3, giving your answer as a mixed number in its simplest form.

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

3.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

4.Work out 5⁰ + 5¹ + 5²

5.Postage on a parcel is calculated as £4.60, correct to the nearest 20p. Which of these could not be the actual cost of the postage?

6.Simplify √45.

7.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

8.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.

9.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

10.Write 5/6 as a decimal, showing clearly which digit recurs.

11.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

12.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

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.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

15.Which of these statements about −0.7 and −0.25 is true?