Number worksheet — GCSE Higher

1.Round 592.5 to the nearest 10.

2.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

3.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

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

5.Work out 6² − 4².

6.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.

7.Simplify x⁷ × x⁴, giving your answer as a single power of x.

8.Work out (−2)² − 3

9.Work out −(−3)⁴ + (−3)³

11.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.

12.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?

13.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

14.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

15.A spreadsheet shows that 812 − 397 = 315. Work out an estimate for 812 − 397, by rounding each number to the nearest 100, to check whether the spreadsheet's answer is reasonable.