Number worksheet — GCSE Higher

1.The mass of a radioactive sample, in grams, n years after it was first weighed is modelled by M = 200 × (1/2)ⁿ. Work out the mass the model gives after 3 years.

2.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

3.Simplify ⁴√(16a⁸b¹²)

4.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.

5.Work out (2/3)² + (1/2)². Give your answer as a fraction.

6.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

7.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

8.Priya adds 3.6 and 0.45 on paper and writes down 3.65 as her answer. Work out the correct value of 3.6 + 0.45.

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

10.A recipe for one cake needs 2/3 of a cup of sugar. Priya has 3 1/2 cups of sugar. Work out how many complete cakes she can make.

11.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.

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

13.A gym increases its membership price by 1/5. The original price is £60. Work out the new price.

14.In a box of chocolates 5/8 are milk chocolates and the rest are dark chocolates. Work out the number of dark chocolates as a fraction of the number of milk chocolates.

15.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.