2000 - WAEC Mathematics Past Questions and Answers - page 5
A tap leaks at the rate of 2cm\(^3\) per seconds. How long will it take the tap to fill a container of 45 liters capacity? (1 liters = 1000cm\(^3\))
Total capacity of the container = 45 liters = 45 x 1000
= 45000 cm\(^3\)
Time to fill the container = \(\frac{45000}{2}\)
= 22500 seconds
= \(\frac{22500}{3600}\)
= 6 hr 15 mins
The length of the parallel sides of a trapezium are 5cm and 7cm. If its area is 120cm\(^2\), find the perpendicular distance between the parallel sides
Area of trapezium = \(\frac{1}{2} (a + b)h\)
\(120 = \frac{1}{2} (5 + 7) \times h\)
\(120 = 6h\)
\(h = 20 cm\)
The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\pi = \frac{22}{7}\)
Length of arc = \(\frac{\theta}{360} \times 2\pi r\)
\(50 = \frac{75}{360} \times 2 \times \frac{22}{7} \times r\)
\(r = \frac{50 \times 360 \times 7}{75 \times 2 \times 22}\)
\(r = \frac{420}{11}\)
= 38.18 cm \(\approxeq\) 38.2 cm (3 sig. figs)
\frac{}{} = r^2 = 38.5\
r^2 = \frac{38.5 \times 7}{22}\
r = \sqrt{12.25} = 3.5\
diameter = 2r = 2 \times 3.5 = 7cm\)
Find the volume (in cm\(^3\)) of the solid shown above
Total volume = (5 x 5) x 5 + (5 x 5) x 2
= 125 + 50
= 175 cm\(^3\)
3 + 6x - x - 2x^2 = 0\
3(1 + 2x) - x(1 + 2x) = 0\
(3-x)(1+2x)=0\
3-x = 0 \hspace{1mm}or \hspace{1mm}1+2x = 0\
x = 3\hspace{1mm} x = -\frac{1}{2}\
x = 3 \hspace{1mm}or\hspace{1mm} x =-\frac{1}{2}\)
If the simple interest on N2000 after 9 months is N60, at what rate per annum is the interest charged?
\(I = \frac{PRT}{100}\)
\(R = \frac{100I}{PT}\)
\(R = \frac{100 \times 60}{2000 \times \frac{3}{4}}\)
\(R = \frac{6000}{1500}\)
= 4%