Number worksheet — GCSE Higher

1.Work out √144 − 2 × 3 + √25

2.Light travels at 2.998 × 10⁸ metres per second. A distant object in space is 3.1 × 10¹⁵ metres from Earth. Work out an estimate for the number of seconds light takes to travel from the object to Earth, by rounding each number to 1 significant figure.

3.A student works out the exact area of a circle with radius 4 cm by squaring the radius but forgetting to multiply by π. Work out the correct exact area of the circle, in terms of π.

4.Simplify √8 + √18, giving your answer in the form k√2.

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

6.The population of a planet is 8 × 10⁹. Write this population as an ordinary number.

7.A minibus can carry 16 passengers. A school is taking 179 pupils on a trip. By rounding 179 to the nearest 10, work out an estimate for the number of minibuses needed, given that the school cannot hire part of a minibus.

8.A number, x, is truncated (not rounded) to 1 decimal place and the result is 6.2. Write down the error interval for x.

9.An allotment is divided into two plots in the ratio 2:3. The larger plot has an area of 18 m². Work out the fraction of the total area taken up by the smaller plot.

10.Work out the value of 2⁻⁴

11.Work out the value of 6² − 4³.

12.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.

13.Work out (−2)³ + (−3)² − (−4)

14.In a youth club the number of girls is 2/3 of the number of boys. What fraction of the members of the club are girls?

15.A charity shop buys a coat for £24 and sells it for a profit that is 3/8 of the buying price. Work out the selling price.