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WAEC Further Mathematics 2024 Paper

Question : 1

Total: 40

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

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

\sqrt{2}

, find the value of m

Solution:

Concept:

Rationalise the denominator and express both terms with the same denominator to compare coefficients of

\sqrt{2}

Explanation:

Start with

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

Rationalise

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

: multiply numerator and denominator by

\sqrt{2}

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

Also,

\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}}{2} - \frac{\sqrt{2}}{4} = \frac{10\sqrt{2}}{4} - \frac{\sqrt{2}}{4} = \frac{9\sqrt{2}}{4}

Therefore,

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

Comparing both sides gives

m = \frac{9}{4}

Answer:

m = \frac{9}{4}

, which is option B.

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