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WAEC Mathematics 2013 Paper

Question : 11

Total: 48

\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}

Solution:

Concept:

Evaluate fractional exponents by converting them to roots, then substitute given values.

Explanation:

Given

x = 64

and

y = 27

Substitute into

\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}

First, simplify each term:

x^{\frac{1}{2}} = 64^{\frac{1}{2}} = \sqrt{64} = 8

y^{\frac{1}{3}} = 27^{\frac{1}{3}} = \sqrt[3]{27} = 3

x^{\frac{2}{3}} = 64^{\frac{2}{3}} = (\sqrt[3]{64})^2 = 4^2 = 16

Now substitute these values into the expression:

\frac{8 - 3}{27 - 16} = \frac{5}{11}

Answer:

\frac{5}{11}

So the correct option is C.

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