Number worksheet — GCSE Higher

1.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

2.Work out 3³ + 2⁴.

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

4.The error interval for the mass of a suitcase, m kg, is given as 22.5 ≤ m < 23.5. Write down the mass of the suitcase, correct to the nearest whole number.

5.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?

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

7.3/5 of the students in a year group walk to school. 90 students walk to school. Work out the total number of students in the year group.

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

9.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

10.A florist has 5 different flowers. Freya picks 3 of them to make a small bunch, and the order in which she picks them does not matter. Work out how many different bunches she could make.

11.Which statement about the number 91 is correct?

12.A plank has length a = 12 cm and a second plank has length b = 7 cm, each correct to the nearest centimetre. Work out the upper bound of a + b.

13.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

14.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

15.The length of a pencil is 8.4 cm, correct to 1 decimal place. Using L for the length of the pencil in centimetres, write down the error interval for L.