Number worksheet — GCSE Higher

1.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.

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

3.Write 0.005 in standard form.

4.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.

5.√700 lies between which two consecutive integers?

6.Write 12 as a product of its prime factors.

7.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.

9.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.

10.Work out (−2/5) × (−10/3). Give your answer as a fraction in its simplest form.

11.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

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

13.A supermarket sells apples at £1.85 per kg. Anna buys 3.6 kg of apples. Estimate the cost by rounding each number to 1 significant figure before multiplying. Work out Anna's estimate.

14.A driving instructor is working out how many current-style UK number plates are possible. The format is 2 letters, then 2 digits, then a space, then 3 letters (for example AB12 CDE). The letters I, O and Q are never used in any letter position, leaving 23 allowed letters, but every letter and every digit may repeat anywhere on the plate. Work out how many different number plates are possible, giving your answer in standard form to 2 significant figures.

15.A bag holds 5 different sweets. Noah takes 2 of the sweets out of the bag together, so the order in which he takes them does not matter. Work out how many different pairs of sweets he could take.