Number worksheet — GCSE Higher

1.A square petri dish has an area of 121 mm². A scientist wants to know its side length. Work out the side length of the dish.

2.Simplify (x⁻²)³, giving your answer as a fraction.

3.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.

4.Work out 3 + 4 × (−2).

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

6.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.

7.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.

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

9.Write 7/12 as a decimal, showing clearly which digit is recurring.

10.A metal cube has a mass of 540 g and a volume of 60 cm³. Work out its density in g/cm³.

11.In a school long jump competition Priya's jump is recorded as 3.8 m and Nadia's jump is recorded as 3.9 m, each correct to the nearest 0.1 m. Priya says she may have jumped further than Nadia. Decide whether Priya is right, and give a reason for your answer.

12.The density of a type of plastic is 0.9 g/cm³. Work out this density in kg/m³.

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

14.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

15.Find the missing number: 17 × ▢ = 391