AQA GCSE Maths: Number

A rectangular sheet of metal has length $7.4$7.4 cm and width $3.5$3.5 cm, each measured to the nearest $0.1$0.1 cm.

(a) Write down the upper bound and the lower bound of the length. (2 marks)

(b) Calculate the upper bound for the area of the sheet. (2 marks)

(c) By considering bounds, write down the area of the sheet to a suitable degree of accuracy, justifying your answer. (1 mark)

(a) In a sale, the price of a coat is reduced by $15\%$15%. The sale price is £127.50. Work out the original price of the coat. (3 marks)

(b) £4000 is invested in an account paying $2.5\%$2.5% compound interest per year. Work out the value of the investment at the end of $3$3 years, giving your answer to the nearest penny. (1 mark)

(a) Write $360$360 as a product of its prime factors, giving your answer in index form. (2 marks)

(b) Find the highest common factor (HCF) and the lowest common multiple (LCM) of $360$360 and $84$84. (2 marks)

Show that $\frac{2}{3} + \frac{3}{4} \div \frac{9}{8}$32​+43​÷89​ can be written as a single fraction in its simplest form. (3 marks)

Write $\dfrac{12}{\sqrt{3}}$3​12​ in the form $a\sqrt{3}$a3​, where $a$a is an integer. (2 marks)

Write $0.0042$0.0042 in standard form. (1 mark)