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WAEC Further Mathematics 2010 Paper

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Question : 3

Total: 40

If

\;\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = m\sqrt{2}

, where m is a constant. Find m.

$1\;\frac{1}{2}$
$1\;\frac{1}{4}$
$2\;\frac{1}{4}$
$2\;\frac{1}{2}$

Solution:

Concept:

Express both terms with the common factor

\sqrt{2}

and combine them.

Explanation:

Rationalise

\frac{5}{\sqrt{2}}

:

\frac{5}{\sqrt{2}} = \frac{5\sqrt{2}}{2}

Simplify

\frac{\sqrt{8}}{8}

:

\sqrt{8} = 2\sqrt{2}

, so

\frac{\sqrt{8}}{8} = \frac{2\sqrt{2}}{8} = \frac{\sqrt{2}}{4}

Now subtract:

\frac{5}{\sqrt{2}} - \frac{\sqrt{8}}{8} = \frac{5\sqrt{2}}{2} - \frac{\sqrt{2}}{4}

Combine like terms:

\left(\frac{5}{2} - \frac{1}{4}\right)\sqrt{2} = \left(\frac{10-1}{4}\right)\sqrt{2} = \frac{9}{4}\sqrt{2}

\frac{9}{4}\sqrt{2} = 2\frac{1}{4}\sqrt{2}

Thus,

m = \frac{9}{4} = 2\frac{1}{4}

.

Answer:

m = 2\frac{1}{4}

(Option C).

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