Number worksheet — GCSE Higher

1.Work out (6 × 10⁷) + (3 × 10⁶). Give your answer in standard form.

2.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.

3.Simplify (5² × 2³)³ ÷ (5³ × 2²)²

4.Last year a company made a profit of £5,200,000. Write this amount in standard form.

5.Work out √144 − 2 × 3 + √25

6.The two shorter sides of a right-angled triangle are √12 cm and √24 cm. Work out the exact length of the hypotenuse.

7.A crowd of 8,400 people is recorded correct to the nearest 100. Work out the smallest possible number of people in the crowd.

8.A courier's van has a weight limit of 850 kg for its parcels. The driver's display shows the total mass of the parcels loaded as 850 kg, correct to the nearest 5 kg. Decide whether the parcels are definitely within the weight limit.

9.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.

10.A number is multiplied by 4, then 8 is added, giving the result 40. Work out the number.

11.In a class, 1/3 of the pupils are girls. There are 12 girls in the class. Work out how many pupils are in the class.

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

13.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.

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

15.Given that 5³ = 125 and 6³ = 216, use a midpoint test to estimate ∛130 to 1 decimal place.