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WAEC Further Mathematics 2010 Paper

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Question : 15

Total: 40

\begin{vmatrix} 3 & x \\ 2 & x-2 \end{vmatrix} = -2

find the value of x.

-8
4
-4
8

Solution:

Concept:

For a

2 \times 2

determinant,

\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc

.

Explanation:

Expand the determinant using the formula

ad - bc

.

Here,

a = 3

,

b = x

,

c = 2

, and

d = x - 2

.

So,

\begin{vmatrix} 3 & x \\ 2 & x-2 \end{vmatrix} = 3(x-2) - (x)(2)

.

Simplify:

3(x-2) - 2x = 3x - 6 - 2x = x - 6

.

Given that this equals

-2

, write:

x - 6 = -2

.

Add

6

to both sides:

x = -2 + 6 = 4

.

Answer:

x = 4

, which is option B.

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