Number worksheet — GCSE Higher

1.Nadia has £84. She spends 3/7 of it on a jacket and the rest on a bag. Work out the ratio of the amount spent on the jacket to the amount spent on the bag, in its simplest form.

2.A restaurant adds a service charge of 15% to a bill of £120. Work out the service charge.

3.Light travels at 3 × 10⁸ metres per second. Work out how far light travels in 2 × 10⁻⁶ seconds. Give your answer in standard form.

4.A photograph uses 4 × 10⁶ bytes of storage. A memory card holds 3.2 × 10¹⁰ bytes. Work out how many of these photographs the card can hold. Give your answer in standard form.

5.A set of kitchen scales displays the mass of a bag of sugar as 0.63 recurring kilograms, meaning 0.636363... kg with the block '63' repeating forever. Convert this mass to a fraction of a kilogram, then work out the mass in grams, giving your answer to the nearest gram.

6.Expand and simplify √3(2 + √12).

7.Work out how many factors 36 has.

8.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

9.Work out 3/4 − 5/12 exactly, giving your answer in its simplest form.

10.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

11.Work out ⁴√16

12.Work out 100 − 4 × 5²

13.Insert one pair of brackets into 2 + 3 × 5 − 1 so that the calculation is equal to 24. Which calculation is correct?

14.Write ∛(x²) as a single power of x.

15.Write these numbers in order, starting with the largest: −0.6, 0.45, −0.15, 0.5, −0.09