Number worksheet — GCSE Higher

1.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.

2.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.

3.Write down the reciprocal of 0.2

4.Write 0.06 as a fraction in its simplest form.

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

6.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

7.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

8.Work out 6² − 4².

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

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 plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

12.A pizza is cut into 12 equal slices. Ben eats 5 slices and Mia eats 3 slices. What fraction of the pizza is left, giving your answer in its simplest form?

13.Write 200 as a product of its prime factors, using index notation.

14.A cyclist travels 40 km, correct to the nearest 10 km, in a time of 3 hours, correct to the nearest hour. Work out the maximum possible average speed, in km/h.

15.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.