Number worksheet — GCSE Higher

1.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?

2.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

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

4.A country has an area of 25,000,000 hectares. Write this area in standard form.

5.Work out an estimate for 79.3 − 24.6, by rounding each number to the nearest whole number.

6.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

7.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

9.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

10.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

11.A rope is measured as 15 m, correct to the nearest metre. Write down the error interval for the true length, l, of the rope.

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

13.Write 0.005 in standard form.

14.A sponsored walk is 36 km long. Aisha has completed 8/12 of the walk. Work out how far she has walked.

15.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.