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WAEC Mathematics Past Questions & Answers - Page 223

1,111.

Given that (2x + 7) is a factor of $2x^2 + 3x - 14$ , find the other factor

x + 2

2 - x

x - 2

x + 1

View answer & explanation

Correct answer is C

$2x^2 + 3x - 14$

$2x^2 + 7x - 4x - 14$

$x(2x + 7) - 2(2x + 7)$

= $(x - 2)(2x + 7)$

The other factor = (x - 2).

1,112.

If x varies inversely as y and $x = \frac{2}{3}$ when y = 9, find the value of y when $x=\frac{3}{4}$

$\frac{1}{18}$

$\frac{8}{81}$

$\frac{9}{2}$

View answer & explanation

Correct answer is D

$x \propto \frac{1}{y}$

$x = \frac{k}{y}$

$\frac{2}{3} = \frac{k}{9}$

$3k = 18 \implies k = 6$

$x = \frac{6}{y}$

When y = $\frac{3}{4}$ ,

x = $\frac{6}{\frac{3}{4}}$

= $\frac{6 \times 4}{3}$

= 8

1,113.

Given that $27^{(1+x)}=9$ find x

-3

$\frac{-1}{3}$

$\frac{5}{3}$

View answer & explanation

Correct answer is B

$27^{(1+x)}=9\\ 3^{3(1+x)}=3^2\\ 3(1+x)=2\\ 3+3x = 2\\ 3x = -1 x = \frac{-1}{3}$

1,114.

Given that $x = -\frac{1}{2}and \hspace{1mm} y = 4 \hspace{1mm} evaluate \hspace{1mm} 3x^2y+xy^2$

-5

-1

View answer & explanation

Correct answer is A

$x = -\frac{1}{2}, y = 4\\ 3x^2y + xy^2\\ 3\left[-\frac{1}{2}\right]^2 \times 4 \times + \left(\frac{-1}{2}\right)(4)^2\\ 3\times \frac{1}{4} \times 4 -\frac{1}{2} \times 16\\ 3-8 = -5$

1,115.

In the diagram, POS and ROT are straight lines, OPQR is a parallelogram. |OS| = |OT| and ∠OST = 50°. Calculate ∠OPQ.

160^o

140^o

120^o

100^o

View answer & explanation

Correct answer is D

< T = < S = 50° (OS = OT)

< SOT = 180° - 2(50°) = 80°

< ROP = 80° (vertically opposite angle)

$\therefore$ < OPQ = 180° - 80° = 100° (adjacent angles)

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