Number worksheet — GCSE Higher

1.Work out the value of 6² − 4³.

2.The decimal 0.2333... has one non-recurring digit (the 2) followed by a single recurring digit (the 3), so it can be written as 0.2 recurring 3. Let x = 0.2333... . Work out x as a fraction in its simplest form.

3.Work out ⁴√81

4.Work out 3 1/5 + 1 2/3. Give your answer as a mixed number in its simplest form.

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

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

7.Work out ∛(−27) + ∛8

8.In a school, 3/5 of the students study French. Of these students, 2/3 also study Spanish. What fraction of all the students study both French and Spanish?

9.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

10.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.

11.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?

13.Write 200 as a product of its prime factors, using index notation.

14.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

15.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.