Mathematics 0580 · IGCSE · Indices I

Indices I — practice question

Aneel starts with 80 tea bags, $\frac{1}{2}$ kg of sugar and 1 litre of milk. For each cup of tea, he uses: • 1 tea bag • 8 grams of sugar • 40 millilitres of milk.
(a(i)(a))[2]

Work out the fraction of tea bags he uses, written in simplest form.

(a(i)(b))[2]

Work out how many grams of sugar he has left.

(a(ii))[1]

Work out the total number of cups of tea Aneel makes.

(b)[3]

Calculate the amount of money each of them gets.

(c(i))[1]

Write $\frac{3^2 \times 3^4}{3^6}$ as a power of $3$.

(c(ii))[1]

Write $2^{-4}$ as a decimal.

(d(i))[1]

Simplify the expression $(b^5)^3$.

(d(ii))[1]

Simplify fully $\left(\frac{4}{m}\right)^{-2}$.

(e)[2]

Use this information to determine the lowest common multiple (LCM) of 30 and 84.

(f)[1]

Put a ring around the irrational number in the list.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: So, $\frac{15}{80} = \frac{3}{16}$.

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