Number worksheet — GCSE Higher

1.Jack buys 3 books, each costing £4.25, and pays with a £20 note. Work out how much change he receives.

2.Work out the value of √(16 + 9)

3.Work out how many factors 100 has.

4.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

5.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

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

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

8.Four students each estimate √70 without a calculator. Ben says: '8² = 64 and 9² = 81, and 70 is about a third of the way from 64 to 81, so √70 ≈ 8.3.' Chloe says: '8.5² = 72.25, which is close to 70 but a little too big, so I'll bring it down slightly to √70 ≈ 8.4.' Dan says: '9² = 81 is closer to 70 than 8² = 64 is, so √70 ≈ 8.9.' Ella says: '8² = 64 and 9² = 81, so I'll just take the midpoint of 8 and 9: √70 ≈ 8.5.' Given that √70 = 8.3666... to 4 decimal places, whose estimate is closest?

9.A shop assistant says that 7.2 × 3.9 = 56.16. Work out an estimate for 7.2 × 3.9, by rounding each number to the nearest whole number, to show that the assistant’s answer cannot be correct.

10.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09

11.Simplify (x⁻²)³, giving your answer as a fraction.

12.A jacket normally costs £65. In a sale it is reduced by 20%, and the shop then takes a further £5 off at the till. Work out the final price.

13.A flight departs at 21:35 and lands at 06:10 the following morning. Work out the total flight time.

14.Work out the value of (1/3)⁻²

15.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.