Number worksheet — GCSE Higher

1.Work out how many factors 36 has.

2.Write 5,000,000 in standard form.

3.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.

4.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.

5.In a music collection, the ratio of pop albums to rock albums is 5 : 3. Work out the number of rock albums as a fraction of the number of pop albums.

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

7.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

8.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.

9.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

10.The recurring decimal 0.181818... can be written as 0.18 recurring, where both digits repeat forever. Let x = 0.18 recurring. Work out x as a fraction in its simplest form.

11.Simplify (y³)⁴, giving your answer as a single power of y.

12.Simplify x⁶ ÷ x²

13.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

14.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

15.Work out the value of (√5)⁴