Number worksheet — GCSE Higher

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

2.Decide which of 2³⁰ and 3²⁰ is the larger number, and write down the correct statement.

3.Work out 3 × (−2)² − 5

4.Work out ∛64.

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

6.Estimate the value of √45, giving your answer to the nearest whole number.

7.Given that 2⁵ = 32, work out 2⁶.

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

9.Work out (−2)³ + (−3)² − (−4)

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

11.Work out ((−3) + 5) × (−4) − (−6) ÷ 2

12.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

13.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.

14.Work out the value of (√5)⁴

15.Write 90 as a product of its prime factors.