Number worksheet — GCSE Higher

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

2.Which of these numbers rounds to 0.048 when rounded to 2 significant figures?

3.A netball team has 8 players. Two of them are chosen to be captains, and the two captains have equal standing. Work out how many different pairs of captains could be chosen.

4.Two-digit numbers are formed using the digits 2, 5, 7 and 8, and each digit may be used only once in a number. Work out how many of these two-digit numbers are even.

5.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.

6.A cyclist rides at a steady speed of 8 metres per second. Work out this speed in kilometres per hour.

7.Write down the exact decimal value of the fraction 1/6.

8.The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

9.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.

10.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

11.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.

12.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.

13.A cycle route is 350 m long. A footpath runs alongside it for 3/7 of that length. Work out the length of the footpath.

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

15.Work out an estimate for 588 ÷ 31, by rounding each number to 1 significant figure.