WAEC 2025 · Paper 2 · Q6✱✱

(a)
Using mathematical tables, find: (i) $2\sin63.35^\circ$ ; (ii) $\log(\cos44.74^\circ)$ ; (iii) $k$ , given that $\log k - \log(k - 2) = \log 5$ .
Separate values with commas, e.g. 3, −2
(b)
Use logarithm tables to evaluate $\dfrac{3.68^2 \times 6.705}{\sqrt{0.3581}}$ .

Worked solution (try it first)

(a)(i)

From the tables, $\sin 63.35^\circ \approx 0.8938$ , so $2\sin 63.35^\circ \approx 1.788$ .

(ii)

$\cos 44.74^\circ \approx 0.7103$ , and $\log 0.7103 = \bar{1}.8514$ (which is $-0.1486$ ).

(iii)

$\log k - \log(k - 2) = \log\frac{k}{k - 2}$ , so $\frac{k}{k - 2} = 5$ .
Then $k = 5k - 10$ , $4k = 10$ and $k = 2\frac12$ .

(b)

Add and subtract logarithms: $\log(3.68^2) = 2 \times 0.5658 = 1.1316$ .
$\log 6.705 = 0.8264$ .
$\log\sqrt{0.3581} = \frac12(\bar{1}.5540)$
$= \bar{1}.7770$ .
So the log of the answer is $1.1316 + 0.8264 - \bar{1}.7770 = 1.9580 - \bar{1}.7770$
$= 2.1810$ .
The antilog of $2.1810$ is about $151.7$ .

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