Number worksheet — GCSE Higher

1.Work out 2 3/4 − 1 5/6. Give your answer as a fraction in its simplest form.

2.A machine fills bags of sugar and shows the mass of each bag to the nearest 10 g. A checker rejects any bag whose actual mass is less than 996 g. One bag shows a mass of 1,000 g on the machine. Decide whether this bag could be rejected, and give a reason for your answer.

3.Write 5/6 as a decimal, showing clearly which digit recurs.

4.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.

5.A digital timer truncates every time to 1 decimal place. It shows a swimmer's time for one length as 12.3 seconds. Using t for the swimmer's actual time in seconds, write down the error interval for t.

6.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.

7.Work out the value of 6² − 4³.

8.A pair of trainers is priced at £80 online. The shop takes 25% off the price and then adds £10 for next-day delivery. Work out the total cost.

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

10.A fabric is dyed blue and yellow in the ratio 3 : 5. A tailor uses 1.5 m of blue fabric and the matching amount of yellow fabric needed for the ratio. Work out the total length of fabric used.

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.Write 60 as a product of its prime factors, using index notation.

13.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

14.Simplify 3² ÷ 3⁵, giving your answer as a single power of 3.

15.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.