Number worksheet — GCSE Higher

1.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.

2.A three-digit code is made using the digits 1, 2 and 3, and each digit may be used more than once. Work out how many different three-digit codes can be made.

3.Tickets to a theme park cost £38.50 for an adult and £19.75 for a child. A family estimates the total cost for 4 adults and 3 children, by rounding each ticket price to the nearest £5. Work out their estimate for the total cost.

4.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?

5.On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.

6.Work out √25 + 4² − 12 ÷ 3

7.A number is divided by 5, then 6 is subtracted, giving the result −1. Work out the number.

8.A tap fills a 20 litre bucket in 2 minutes 30 seconds. Work out the rate of flow, in litres per minute.

9.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.

10.By considering fourth powers, work out which two consecutive integers ⁴√200 lies between.

11.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.

12.Write these three numbers in order, starting with the smallest: 3/5, 0.55, 58%

13.Work out the value of (√5)⁴

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

15.Work out the exact value of √(2² + 3²)