2018 - WAEC Mathematics Past Questions and Answers - page 2
The volume of a cylindrical tank, 10m high is 385 m\(^2\). Find the diameter of the tank. [Take \(\pi = \frac{22}{7}\)]
Volume of a cylinder = \( \pi r^2\)h
385 = \(\frac{22}{7}\) x \(r^2\) x 10
385 x 7 = 22 x \(r^2\) x 10
\(r^2\) = \(\frac{385 \times 7}{22 \times 10}\)
= 12.25
r = \(\sqrt{12.25}\)
= 3.5m
Hence, diameter of tank = 2r
= 2 x 3.5 = 7m
The surface area of a sphere is \(\frac{792}{7} cm^2\). Find, correct to the nearest whole number, its volume. [Take \(\pi = \frac{22}{7}\)]
Surface area of a sphere = \(4 \pi r^2\)
\(4 \pi r^2\) = \(\frac{792}{7}cm^2\)
4 x \(\frac{22}{7}\) x \(r^2\) = \(\frac{792}{7}\)
\(r^2\) = \(\frac{792}{7}\) x \(\frac{7}{4 \times 22}\)
= 9
r = \(\sqrt{9}\)
= 3cm
Hence, volume of sphere
= \(\frac{4}{3} \pi r^3\)
= \(\frac{4}{3} \times \frac{22}{7} \times 3 \times 3 \times 3 \)
= \(\frac{4 \times 22 \times 9}{7}\)
\(\approx\) = 113.143
= 113\(cm^3\) (to the nearest whole number)
The angles of a polygon are x, 2x, 2x, (x + \(30^o\)), (x + \(20^o\)) and (x - \(10^o\)). Find the value of x
x + 2x + 2x + (x + \(30^o\)) + (x + \(20^o\)) + (x - \(10^o\)) = (2n - 4) x \(90^o\)
8x + 50 \(^o\) - 10\(^o\) = (2 x 6 -4) x 90\(^o\)
8x + 40\(^o\) = 8 x 90\(^o\) = 720\(^o\)
8x = 720\(^o\) - 40\(^o\) = 680\(^o\)
x = \(\frac{680^o}{8}\)
= 85\(^o\)
If M and N are the points (-3, 8) and (5, -7) respectively, find |MN|
|MN| = \(\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)
= \(\sqrt{(-3 -5)^2 + (8 - 7)^2}\)
= \(\sqrt{(-8)^2 + (8 + 7)^2}\)
= \(\sqrt{64 + (15)^2}\)
= \(\sqrt{64 + 225}\)
= \(\sqrt{289}\)
= 17 units
The equation of the line through the points (4,2) and (-8, -2) is 3y = px + q, where p and q are constants. Find the value of p.
Using the two - point from
\(\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}\)
\(\frac{y - 2}{-2 - 2} = \frac{x - 4}{-8 - 4}\)
\(\frac{y - 2}{-4} = \frac{x - 4}{-12}\)
\(\frac{-12(y -2)}{-4}\) = x - 4
3(y -2) = x -4
3y - 6 = x - 4
3y = x - 4 + 6
3y = x + 2...
By comparing the equations;
3y = px + , p = 1
The mean of 1, 3, 5, 7 and x is 4. Find the value of x
Mean = \(\frac{\sum x}{n}\)
4 = \(\frac{1 + 3 + 5 + 7 + x}{5}\)
4 x 5 = 16 + x
20 - 16 = x
4 = x
x = 4
The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at randon scored either 4 or 7 goals.
Prob. (team scored 4 goals) = Prob. (team scored 7 goals) = \(\frac{3}{25}\)
Hence, probability that a team selected at random scored either 4 or 7 goals;
= \(\frac{6}{25} + \frac{3}{25}\)
= \(\frac{9}{25}\)
The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at random scored at most 3 goals.
No. of teams that scored at most 3 goals = 3 + 1 + 6 = 10
Hence, probability that a team selected at random scored at most 3 goals
= \(\frac{10}{25}\) = \(\frac{2}{5}\)
The total surface area of a hemispher is 75\(\pi cm^2\). Find the radius.
Total surface area of hemisphere is
3\(\pi r^2\) = 75\(\pi cm^2\)
\(r^2\) = \(\frac{75 \pi}{3 \pi}\)
\(r^2\) = 25
r = \(\sqrt{25}\)
r = 5cm
Find the value of x for which \(\frac{x - 5}{x(x - 1)}\) is defined
The expression \(\frac{x - 5}{x(x - 1)}\) is defined whten
x(x - 5) = 0.38
either x = 0 or x - 5 = 0
Hence, x = 0 or x = 5