GCSE / IGCSE Maths – Number

Work out, giving each answer as a fraction in its simplest form:(a) $\dfrac{2}{3} + \dfrac{3}{4}$(b) $\dfrac{2}{3} \times \dfrac{9}{10}$(c) $3\dfrac{1}{2} \div \dfrac{7}{8}$(d) $\dfrac{2}{5} + \dfrac{3}{8} \times \dfrac{4}{9}$

(a) Write $84$ and $126$ as products of their prime factors.(b) Hence find the highest common factor (HCF) and lowest common multiple (LCM) of $84$ and $126$.

(a) Write $0.\dot{4}\dot{5}$ as a fraction in its simplest form.(b) Show that $0.2\dot{7} = \dfrac{5}{18}$.

Simplify fully:(a) $\sqrt{50} + \sqrt{18}$(b) $(3 + \sqrt{5})(2 – \sqrt{5})$(c) $\dfrac{6}{\sqrt{3}}$(d) $\dfrac{4}{3 – \sqrt{5}}$

Work out, giving your answers in standard form:(a) $(3.2 \times 10^5) \times (4 \times 10^{-3})$(b) $(8.4 \times 10^7) \div (2.1 \times 10^{-2})$(c) $7.5 \times 10^{-4} + 2.4 \times 10^{-5}$

(a) Decrease $340$ by $15$ percent.(b) A jacket costs $65$ pounds before VAT. VAT is charged at $24$ percent. Find the price including VAT.(c) In a sale, all prices are reduced by $20$ percent. A coat costs $96$ pounds in the sale. Find its original price.

(a) Amira invests $4500$ pounds at $3$ percent per year compound interest. Find the value of the investment after $3$ years, to the nearest penny.(b) A car bought for $12\,000$ pounds loses $15$ percent of its value each year. Find its value after $4$ years, to the nearest pound.

A length is measured as $4.7$ cm, correct to 1 decimal place.(a) Write down the error interval for the length $l$.(b) A mass $m$ is given as $12.30$ kg correct to 2 decimal places. Write down the upper bound of $m$.

A rectangle has length $8.4$ cm and width $3.6$ cm, each measured correct to 1 decimal place. Calculate the upper and lower bounds of the area of the rectangle.

A sprinter runs $120$ m, measured to the nearest metre, in $15.4$ s, measured to the nearest $0.1$ s.(a) Calculate the upper bound and the lower bound of the sprinter’s average speed.(b) By considering your answers to (a), write down the average speed to a suitable degree of accuracy, and explain your reasoning.

The population of a town is $2.4 \times 10^4$. Each year it increases by $8$ percent.(a) Show that after $n$ years the population is $2.4 \times 10^4 \times 1.08^n$.(b) After how many complete years will the population first exceed $4 \times 10^4$?

Show that $\dfrac{(\sqrt{8} + 2)^2}{\sqrt{2}}$ can be written in the form $a\sqrt{2} + b$ where $a$ and $b$ are integers.