WAEC Further Mathematics Past Questions & Answers - Page 142

706.

\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\alpha + \beta\).

A.

-2

B.

-\(\frac{3}{2}\)

C.

\(\frac{3}{2}\)

D.

2

Correct answer is C

\(\alpha + \beta = \frac{-b}{a}\)

From the equation, a = 2, b = -3 and c = 4

\(\alpha + \beta = \frac{-(-3)}{2} = \frac{3}{2}\)

707.

A straight line 2x+3y=6, passes through the point (-1,2). Find the equation of the line.

A.

2x-3y=2

B.

2x-3y=-2

C.

2x+3y=-4

D.

2x+3y=4

Correct answer is D

\(2x+3y = 6 \implies 3y = 6-2x\)

\(y = \frac{6}{3} - \frac{2x}{3}\) 

Parallel lines have the same gradient

\(\therefore\) Gradient of the line = \(\frac{-2}{3}\)

Line passes through (-1,2)

Equation: \(\frac{y-2}{x-(-1)} = \frac{y-2}{x+1} = \frac{-2}{3}\)

\(3y-6 = -2x-2 \implies 3y+2x = -2+6 =4\)

708.

Express cos150° in surd form.

A.

\(-\sqrt{3}\)

B.

\(-\frac{\sqrt{3}}{2}\)

C.

\(-\frac{1}{2}\)

D.

\(\frac{\sqrt{2}}{2}\)

Correct answer is B

cos150° = -cos30°

 = \(-\frac{\sqrt{3}}{2}\)

709.

If \(\begin{pmatrix}  2  &  1 \\  4 & 3 \end{pmatrix}\)\(\begin{pmatrix}  5 \\ 4 \end{pmatrix}\)  = k\(\begin{pmatrix}  17.5 \\ 40.0 \end{pmatrix}\), find the value of k.

A.

1.2

B.

3.6

C.

0.8

D.

0.5

Correct answer is C

\(\begin{pmatrix}  2  &  1 \\  4 & 3 \end{pmatrix}\)\(\begin{pmatrix}  5 \\ 4 \end{pmatrix}\)  = k\(\begin{pmatrix}  17.5 \\ 40.0 \end{pmatrix}\)

\(\begin{pmatrix}  10 + 4  \\  20 + 12\end{pmatrix}\) = \(\begin{pmatrix}  14 \\ 32\end{pmatrix}\) = k\(\begin{pmatrix}  17.5 \\ 40.0 \end{pmatrix}\)

k = \(\frac{14}{17.5} = \frac{32}{40} = 0.8\)

710.

How many ways can 6 students be seated around a circular table?

A.

36

B.

48

C.

120

D.

720

Correct answer is C

In a circular seating arrangement, we fix the position of one person and then rotate the others, so we have

\((6-1)! = 5! = 5\times4\times3\times2 = 120\)