Number worksheet — GCSE Higher

1.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.

2.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

3.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.

4.Write 60 as a product of its prime factors, using index notation.

6.In standard form, 2,000 is written as 2 × 10ⁿ. Write down the value of n.

7.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

8.Work out how many factors 36 has.

9.A box stands on a table. The box exerts a force of 240 N on the table, and the base of the box has an area of 0.8 m². Work out the pressure the box exerts on the table, in N/m².

10.Write 0.36 as a fraction in its simplest form.

11.Work out the value of (1/3)⁻²

12.Work out 3.7 × 24.

13.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?

14.Which of these is written correctly in standard form?

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