Number worksheet — GCSE Higher

1.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.

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

3.A lorry travels 105 miles in 1 hour 45 minutes. Work out its average speed in miles per hour.

4.A quarter-circle has a radius of 6 cm. Work out the exact perimeter of the quarter-circle, giving your answer in terms of π.

5.Work out 6² − 4².

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

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

8.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

9.Work out the reciprocal of (2 + 3)

10.The diameter of an artificial silk fibre is 4 × 10⁻⁶ metres. One nanometre is 10⁻⁹ metres. Work out the diameter of the fibre in nanometres.

11.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

12.Five different books are placed in a row on a shelf. Work out how many different orders the five books can be placed in.

13.Work out (−2)³ + (−3)² − (−4)

14.Work out (5 + 2) × 3²

15.A photography studio offers 4 backdrops and 3 outfits for a portrait session. The plain grey backdrop, one of the 4 backdrops, cannot be used with the formal suit outfit, one of the 3 outfits. Work out how many different backdrop-and-outfit combinations are possible.