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WAEC Mathematics 2013 Paper

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Question : 23

Total: 48

If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9

8
7
6
5

Solution:

Concept:

Direct variation means

y = k\sqrt{x+1}

, where

k

is the constant of proportionality.

Explanation:

Given

y = 6

when

x = 3

.

Substitute into

y = k\sqrt{x+1}

:

6 = k\sqrt{3+1}

.

6 = k\sqrt{4}

.

6 = 2k

.

So

k = \frac{6}{2} = 3

.

Therefore, the relation is

y = 3\sqrt{x+1}

.

Find

x

when

y = 9

:

9 = 3\sqrt{x+1}

.

Divide both sides by

3

:

3 = \sqrt{x+1}

.

Square both sides:

9 = x + 1

.

Hence,

x = 9 - 1 = 8

.

Answer:

x = 8

Option A.

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