Number worksheet — GCSE Higher

1.A circle has a circumference of 8π cm. Work out the exact area of the circle in terms of π.

2.The thickness of a sheet of card is 0.02384 cm. Write this thickness correct to 2 significant figures.

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

4.Work out 1 1/2 ÷ 3/4 exactly, giving your answer in its simplest form.

5.Without using a calculator, estimate the value of √70 × ∛65, giving your answer to 1 significant figure.

6.Simplify ⁴√(16a⁸b¹²)

7.Expand and simplify (2 + √3)², giving your answer in the form a + b√3.

8.A length, L cm, has the error interval 24.5 ≤ L < 25.5. Write down the degree of accuracy to which the length was measured.

9.The number 36 can be written as 2² × 3², and the number 84 can be written as 2² × 3 × 7. Work out the highest common factor of 36 and 84.

10.Simplify x⁶ ÷ x²

11.Estimate the value of √45, giving your answer to the nearest whole number.

12.A number, n, is a multiple of both 6 and 9. Work out the smallest possible value of n that is greater than 20.

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

14.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

15.A school orders 187 packed lunches for a trip. Each packed lunch costs £4.85. The school has £900 to spend. By rounding each number to 1 significant figure, work out an estimate for the total cost and decide whether £900 is enough.