Number worksheet — GCSE Higher

1.Rationalise the denominator of 6/√3, giving your answer in its simplest form.

2.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.

3.Last year a company made a profit of £5,200,000. Write this amount in standard form.

4.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?

5.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.

6.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

7.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

8.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

9.4ˣ = 64. Work out the value of x.

10.The decimal 0.272727... repeats the block 27 for ever. Write 0.27 recurring as a fraction in its simplest form.

11.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

12.Work out −(−3)⁴ + (−3)³

13.Work out the value of √49 + ∛27

14.Simplify ⁴√(16a⁸b¹²)

15.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%