2002 - WAEC Mathematics Past Questions and Answers - page 3

The equation $\frac{3x-2}{4x^2+9x-9}$ is undefined when the denominator = 0.

$4x^2+9x-9=0$

$4x^2+12x-3x-9=0$

$4x(x+3)-3(x+3)=0$

$(4x-3)(x+3)=0$

x = $\frac{3}{4}$ or x = -3.

(\frac{1}{1-x} + \frac{2}{1+x}<br /> \frac{1+x+2-2x}{(1-x)(1+x)} = (\frac{3-x}{1-x^2}))

(\frac{1}{2}(a+b)\times h = 105cm^2<br /> \frac{1}{2}(9+12)\times h = 105<br /> h = \frac{105 \times 2}{21} = 10cm)

From (V = \frac{1}{3}\pi r^2 h. \hspace{1mm} r =\frac{14}{2}<br /> 462 = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times h <br /> h = \frac{3 \times 462}{22 \times 7}\ h = 9)

Y = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

Number of prime numbers = 3

Prob(picking  a prime number) = $\frac{3}{12}$

= $\frac{1}{4}$

 In $\mathrm{\Delta }$ POQ, 

${12}^2={15}^2+{15}^2-2(15)(15)\cos <POQ$

$144=450-450\cos <POQ$

$450\cos <POQ=450-144=306$

$\cos <POQ=\frac{306}{450}=0.68$

$<POQ=47.2°$

In $\mathrm{\Delta }$ PO'Q, 

${12}^2=8^2+8^2-2(8)(8)\cos <P{O}^{\prime }Q$

$144-128=-128\cos <P{O}^{\prime }Q$

$\cos <P{O}^{\prime }Q=-0.125$

$<P{O}^{\prime }Q=97.2°$

In $\mathrm{\Delta }$ POQ,

$\cos 23.6=\frac{x}{15}$

$x=15\times \cos 23.6$

= 13.75 cm

In $\mathrm{\Delta }$ PO'Q, 

$\cos 48.6=\frac{y}{8}$

$y=8\times \cos 48.6$

= 5.29 cm

$\therefore$ OO' = x + y = 13.75 + 5.29

= 19.04 cm