Number worksheet — GCSE Higher

1.Work out how many factors 36 has.

2.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.

3.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.

4.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.

5.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.

6.A recipe uses 0.625 kg of flour. Write this mass as a fraction of a kilogram, in its simplest form.

7.Two allotments are combined. Allotment A grows vegetables and flowers in the ratio 3 : 2, and has 20 plots in total. Allotment B grows vegetables and flowers in the ratio 1 : 4, and has 20 plots in total. Work out the fraction of all the plots, in both allotments combined, that grow vegetables.

8.Work out 2 × 3 × 5 + 1 and decide whether the result is a prime number.

9.Work out the reciprocal of (2 + 3)

10.The number 24 can be written as 2³ × 3, and the number 60 can be written as 2² × 3 × 5. Work out the lowest common multiple of 24 and 60.

11.Work out an estimate for 8,900 ÷ 29, by rounding each number to 1 significant figure.

12.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.

13.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

14.A circle has a radius of 3 cm. Which of these is the exact area of the circle?

15.Simplify (5² × 2³)³ ÷ (5³ × 2²)²