Number worksheet — GCSE Higher

1.4ˣ = 64. Work out the value of x.

2.√700 lies between which two consecutive integers?

3.A plumber charges a call-out fee of £45 and then £28 for each hour she works. She is at a house from 09:15 until 12:45. Work out the total charge.

4.Simplify ⁴√(16a⁸b¹²)

5.A plank of wood is 5 1/4 m long. Pieces of length 3/4 m are cut from it. Work out how many complete pieces of 3/4 m can be cut from the plank.

6.A florist has 60 red roses and 84 white roses. She wants to make identical bunches using all the flowers, with the greatest possible number of bunches. Work out how many red roses will be in each bunch.

7.Sam rounds 0.070268 to 3 significant figures and writes 0.0703. Which of these statements is correct?

8.A lift has a safe working load of 500 kg. Four people get in the lift and the lift's display records their total mass as 493 kg, correct to the nearest kg. Decide whether the four people are definitely within the safe working load.

9.Work out (2 × 10³) × (3 × 10⁴). Give your answer in standard form.

10.c = 50, correct to the nearest 10. d = 18, correct to the nearest whole number. Work out the upper bound of c − d.

11.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.

12.The radius of a circular pond is given as 3.2 m, correct to 1 decimal place. Calculate the upper bound for the area of the pond, giving your answer correct to 3 significant figures.

13.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.

14.A market trader buys 8 melons at £1.35 each. He sells all of them for a total of £15.60. Work out his profit.

15.Write 5,000,000 in standard form.