Number worksheet — GCSE Higher

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

2.Work out √144 − 2 × 3 + √25

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

4.Work out (−2)² − 3

5.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

6.Work out 3 × (−2)² − 5

7.Work out (2/3)² + (1/2)². Give your answer as a fraction.

8.At a swimming pool the ratio of adults to children is 3 : 5. Of the children, 2/5 are boys. What fraction of the people at the pool are boys?

9.During one night on a mountain, four hikers each recorded the temperature they felt: Ben −6 °C, Priya −2 °C, Sam −9 °C, Alex 1 °C. Work out the difference between the coldest and the warmest of these four temperatures.

10.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.

11.Work out the value of (√5)⁴

12.Given that 2⁵ = 32, work out 2⁶.

13.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

14.Write 7/12 as a decimal, showing clearly which digit is recurring.

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