Number worksheet — GCSE Higher

1.Two-digit numbers are made using the digits 1, 2, 3 and 4, and no digit may be used twice in the same number. Work out how many different two-digit numbers can be made.

2.Write 0.325 as a fraction in its simplest form.

3.Work out √225 ÷ 3.

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

5.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.

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

7.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

8.Write 60 as a product of its prime factors, using index notation.

9.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

10.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

11.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

12.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.

13.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

14.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

15.Round 0.006482 to 2 significant figures.