WAEC 2012 · Paper 2 · Q1

(a)
Without using tables or a calculator, simplify $\dfrac{0.25 \times 3.3 \times 4200}{2.1 \times 1.65 \times 2}$ , leaving your answer in standard form.
(b)
Solve for $x$ if $\log_{10}(3x + 1) + \log_{10}\left(\frac12\right) - \log_{10}(2x - 5) = 0$ .

Worked solution (try it first)

Multiply out the decimals as whole numbers and track the powers of 10: $0.25 \times 3.3 \times 4200 = 3465$ and $2.1 \times 1.65 \times 2 = 6.93$ .
Then $\frac{3465}{6.93} = 500 = 5.0 \times 10^2$ .
(Cancelling first is quicker: $\frac{0.25 \times 3.3 \times 4200}{2.1 \times 1.65 \times 2}$ .
$\frac{3.3}{1.65} = 2$ and $\frac{4200}{2.1} = 2000$ , so it is $\frac{0.25 \times 2 \times 2000}{2} = 500$ .)