1994 - WAEC Mathematics Past Questions and Answers - page 3
Which of the following equations can be solved by the points of intersection P and Q of the curve and the line PQ?
The points of intersection of the curve and the line are at x = -2 and x = 2.
\(\therefore\) (x + 2) = 0; (x - 2) = 0.
(x + 2)(x - 2) = 0
\(x^2 - 4 = 0\)
Which of the following is not a factors of 2p\(^2\) - 2?
Find the quadratic equation whose roots are 3 and \(\frac{2}{3}\).
x = 3; x = \(\frac{2}{3}\).
(x - 3)(x - \(\frac{2}{3}\)) = 0
\(x^2 - \frac{2x}{3} - 3x + 2 = 0\)
\(x^2 - \frac{11x}{3} + 2 = 0\)
\(3x^2 - 11x + 6 = 0\)
Which of the following is a root of the equation x\(^2\) +6x = 0?
Factorise: 6x\(^2\) + 7xy - 5y\(^2\)
\(6x^2 + 7xy - 5y^2\)
= \(6x^2 + 10xy - 3xy - 5y^2\)
= \(2x(3x + 5y) - y(3x + 5y)\)
= \((2x - y)(3x + 5y)\)
log8x/x4 = 2
x/x4 = 82 = 1/x3 = 64
x3 = (1/4)3; x = 1/4
The angle subtended at the centre by a chord of a circle radius 6cm is 120°. Find the length of the chord.
\(\frac{r}{6} = \sin 60 \)
\(r = 6 \sin 60\)
= \(6 \times \frac{\sqrt{3}}{2}\)
= \(3\sqrt{3}\)
Chord = 2r = \( 2 \times 3\sqrt{3}\)
= \(6\sqrt{3}\)
A cuboid of base 12.5cm by 20cm holds exactly 1 litre of water. What is the height of the cuboid? (1 litre =1000cm3)
Volume of cuboid = length x breadth x height
12.5 x 20 x h = 1000
250h = 1000
h = 4 cm
= 10057 ≅ 10000km
Calculate, correct to 2 significant figures, the length of the arc of a circle of radius 3.5cm which subtends an angle of 75° at the centre of the circle. [Take π = 22/7].
Length of arc = \(\frac{\theta}{360} \times 2\pi r\)
= \(\frac{75}{360} \times 2 \times \frac{22}{7} \times 3.5\)
= \(4.583 cm\)
\(\approxeq\) 4.6 cm (to 2 sig. figs)