Number worksheet — GCSE Higher

1.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?

2.Work out (−2)² − 3

3.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?

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

5.Write these three numbers in order, starting with the smallest: 7/20, 0.3, 32%

6.Work out 3 + 4 × (−2).

7.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

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

9.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.

10.£60 is shared between Amir, Bo and Chen in the ratio 1:2:3. Work out the fraction of the £60 that Amir and Bo receive together.

11.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

12.√700 lies between which two consecutive integers?

13.Work out ⁴√81

14.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.

15.Estimate the value of √45, giving your answer to the nearest whole number.