Number worksheet — GCSE Higher

1.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

2.Which one of these statements is true?

3.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.

4.Work out (2/3)² + (1/2)². Give your answer as a fraction.

5.Last year a company made a profit of £5,200,000. Write this amount in standard form.

6.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

7.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.

8.Work out 5⁰ + 5¹ + 5²

9.A cake recipe needs 3/4 of a kilogram of sugar. Aisha wants to make half the recipe. Work out how much sugar she needs, giving your answer as a fraction of a kilogram in its simplest form.

10.A gardener has 42 tulip bulbs and 56 daffodil bulbs. She plants them in rows, with every row containing the same number of tulip bulbs and the same number of daffodil bulbs, and no bulbs left over. Work out the greatest number of rows she can plant.

11.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

12.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

13.Work out √225 ÷ 3.

14.Simplify x⁷ × x⁴, giving your answer as a single power of x.

15.p = 24 and q = 6, each correct to the nearest integer. Work out the greatest degree of accuracy to which p ÷ q can be guaranteed correct.