2002 - WAEC Mathematics Past Questions and Answers - page 3
For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?
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+x+2-2x}{(1-x)(1+x)} = \(\frac{3-x}{1-x^2}\)\)
\frac{1}{2}(9+12)\times h = 105\
h = \frac{105 \times 2}{21} = 10cm\)
462 = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times h \
h = \frac{3 \times 462}{22 \times 7}\ h = 9\)
A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime.
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 the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|.
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