Number worksheet — GCSE Higher

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

2.A garden path is measured by Jon as 12 m, correct to the nearest metre, and by Mia as 12.6 m, correct to the nearest 0.1 m. Which statement about the two measurements is correct?

3.Work out 36 ÷ (2 × 3)

4.Ava measures a metal rod and records its length as 15 cm, correct to the nearest centimetre. Ben measures the same rod and records its length as 14.8 cm, correct to the nearest 0.1 cm. Decide whether both records can be correct, and give a reason for your answer.

5.√700 lies between which two consecutive integers?

6.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.

7.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

8.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

9.Write 5/6 as a decimal, showing clearly which digit recurs.

10.A square tile has an area of 72 cm². Work out the exact perimeter of the tile, giving your answer in the form k√2 cm.

11.Write down the symbol that makes this statement true: −2/3 ___ −5/6

12.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

13.Two bags of mixed nuts are combined. Bag A has peanuts and cashews in the ratio 2 : 3. Bag B has peanuts and cashews in the ratio 1 : 4. Both bags contain the same total number of nuts. Work out the fraction of the combined mixture that is peanuts.

14.Work out the value of 2⁻²

15.A bag of flour is labelled 1.5 kg, correct to the nearest 0.1 kg. The true mass of the flour is m kg. Which inequality gives all the possible values of m?