Number worksheet — GCSE Higher

1.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.

2.Write these decimals in order, starting with the smallest: 0.6, 0.55, 0.601, 0.5, 0.56

3.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2

4.Work out √(4 × 9)

5.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.

6.3/5 of a 5/6 litre bottle of juice is poured out. Work out the exact volume poured out, in litres.

7.A carpenter has a plank of wood 4.8 m long. She cuts off 3 pieces, each 0.9 m long, to make shelves. Work out the length of wood remaining.

8.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.

9.A student writes 0.08 as the fraction 8/10, reading the 8 as if it stood in the tenths column and ignoring the zero. Work out the correct fraction that 0.08 is equal to, giving your answer in its simplest form.

10.A semicircle has a diameter of 8 cm. Work out the exact area of the semicircle, in terms of π.

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

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

13.A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

14.Work out ⁴√16

15.Work out (−2)³ + (−3)² − (−4)