Number worksheet — GCSE Higher

1.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

2.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.

3.Write 60 as a product of its prime factors, using index notation.

4.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

5.Sam compares 0.6 and 5/8 by comparing the digit 6 with the digit 5, and says that 0.6 is the larger number. Convert 5/8 to a decimal to find the correct larger value.

6.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.

7.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

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

10.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

11.Work out (−3) × 4 + 2 × (−5)

12.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

13.Work out an estimate for 6.4 × 3.9, by rounding each number to the nearest whole number.

14.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

15.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.