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.

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 \(\Delta\) 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 \(\Delta\) PO'Q, 

\(12^2 = 8^2 + 8^2 - 2(8)(8) \cos <PO'Q\)

\(144 - 128 = -128 \cos < PO'Q\)

\(\cos < PO'Q = - 0.125\)

\(< PO'Q = 97.2°\)

In \(\Delta\) POQ,

\(\cos 23.6 = \frac{x}{15}\)

\(x = 15 \times \cos 23.6\)

= 13.75 cm

In \(\Delta\) 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