Number worksheet — GCSE Higher

1.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.

2.Work out the reciprocal of (2 + 3)

3.Work out (−3) × 4 + 2 × (−5)

4.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

5.A school council must choose a committee of 3 pupils from 8 volunteers. The three places on the committee are all the same, so only which pupils are chosen matters. Work out how many different committees could be formed.

6.Write 0.325 as a fraction in its simplest form.

7.Two fair six-sided dice are rolled together. One die is red and the other is blue. Work out how many different outcomes are possible.

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.Simplify √45.

10.Rationalise the denominator of 10/(4 − √6), giving your answer in its simplest form.

11.A rectangular patio measures 90 cm by 120 cm. Ben wants to cover it exactly with identical square tiles, as large as possible, with no tiles cut. Work out the side length of the largest square tile he can use.

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

14.Work out ∛(−27) + ∛8

15.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.