Number worksheet — GCSE Higher

1.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.

2.Simplify √8 + √18, giving your answer in the form k√2.

3.4ˣ = 64. Work out the value of x.

4.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.

5.Work out the value of 2⁻⁴

6.A jumper is reduced by 15% in a sale to a price of £42.50. Work out the original price.

7.Work out (−6) + (−4) × 3

8.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

9.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

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

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

12.Put these numbers in order, starting with the smallest: 3.2 × 10⁴, 2.9 × 10⁵, 4.1 × 10³

13.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

14.A recipe uses 160 g of flour. Sam wants to increase the amount by 1/4. Work out the new amount of flour.

15.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.