2017 - WAEC Mathematics Past Questions and Answers - page 2
Solve: - \(\frac{1}{4}\) < \(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\)
\(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\); \(\frac{3}{4}\) (3x - 2) > - \(\frac{1}{4}\)
3(3x - 2) < 2; 3(3x - 2) > -1
9x - 6 < 2; 9x - 6 > -1
9x < 8; 9x > 5
x < \(\frac{5}{9}\); x > \(\frac{8}{9}\)
Simplify; 3x - (p - x) - (r - p)
An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)]
lac = \(\frac{\theta}{360}\) x 2\(\pi\)r
7.5 = \(\frac{\theta}{360}\) x 2 x \(\frac{22}{7}\) x 7.5
7.5 = \(\frac{330\theta}{2520}\)
\(\theta\) = \(\frac{7.5}{0.1309}\)
\(\theta\) = 57.29
\(\theta\) = 57 \(^o\)
Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.
Volume of a cylinder = \(\pi r^2h\)
40\(\pi cm^3\) = \(\pi. 4^2h\)
40\(cm^3\) = 16h
h = 2.5cm/sec
In 4 seconds, 2.5cm x 4
= 10cm
The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres
Vol of a cubiod = L x b x h
v = 13cm x 10cm x 70cm
= 9100cm
Since it is half-filled = \(\frac{9100}{2}\)cm
= 4550cm
4550cm \(\to\) 4.55 litres
If the total surface area of a solid hemisphere is equal to its volume, find the radius
T.S.A of hemisphere = 3\(\pi r^2\)
vol of hemisphere = \(\frac{2}{3} \pi r^2\)
3\(\pi r^2\) = \(\frac{2}{3} \pi r^2\)
3 = \(\frac{2}{3} \pi r\)
9 = 2r
r = \(\frac{9}{2}\)
r = 4.5cm
Which of the following is true about parallelogram?
Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)
Gradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)
= \(\frac{-2 -1}{2 + 1}\)
= \(\frac{-3}{3}\)
= -1
If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ
\(\sqrt{(x_2 - x_1)^2 + (y_2 - Y_1)^2}\)
= \(\sqrt{(2 - 2)^2 + (5 - 3)^2}\)
= \(\sqrt{0^2 + 2^2}\)
= \(\sqrt{4}\)
= 2 units
A bearing of 320\(^o\) expressed as a compass bearing is