Number worksheet — GCSE Higher

1.Estimate the value of √45, giving your answer to the nearest whole number.

2.Work out the value of √(16 + 9)

3.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

4.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.

5.Work out √144 − 2 × 3 + √25

6.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

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.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

9.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.

10.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

11.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

12.A grain of fine sand has a mass of 0.001 grams. Write this mass in standard form.

13.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

14.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.

15.A recipe needs 0.485 kg of flour per cake. A bakery estimates its flour order by rounding this amount to 1 significant figure, then multiplying by the 60 cakes it plans to bake. Work out the bakery's estimate for the total flour needed, in kg.