Number worksheet — GCSE Higher

1.Work out 6² − 4².

2.Work out the value of (1/3)⁻²

3.Write 12 as a product of its prime factors.

4.Given that 4³ = 64 and 5³ = 125, estimate ∛100 to 1 decimal place.

5.A restaurant offers a lunch deal of one starter from 5 options, one main from 6 options and one dessert from 3 options. Work out how many different lunch deals are possible.

6.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.

7.Work out the value of 6² − 4³.

8.Write 0.36 as a fraction in its simplest form.

9.Write down the symbol that makes this statement true: −2/3 ___ −5/6

10.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

11.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.

12.Work out −(−3)⁴ + (−3)³

13.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

14.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

15.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.