Number worksheet — GCSE Higher

1.Rice is sold in a 400 g bag for £1.12 and in a 1.5 kg bag for £3.90. Work out how much less the rice in the larger bag costs per kilogram.

2.Hannah works out 3.1 × 19.6 on her calculator and writes down 6.076. Work out an estimate for 3.1 × 19.6, by rounding each number to 1 significant figure.

3.Write 0.06 as a fraction in its simplest form.

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

5.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

6.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.

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

8.Work out 35% of 180.

9.The decimal 0.111... has the digit 1 repeating for ever. Write 0.1 recurring as a fraction in its simplest form.

10.Given that 2⁵ = 32, work out 2⁶.

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

12.Which of these statements about −0.7 and −0.25 is true?

13.Simplify √45.

14.4ˣ = 64. Work out the value of x.

15.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?