2017 - WAEC Mathematics Past Questions and Answers - page 3
Given that cos 30\(^o\) = sin 60\(^o\) = \(\frac{3}{2}\) and sin 30\(^o\) = cos 60\(^o\) = \(\frac{1}{2}\), evaluate \(\frac{tan 60^o - q}{1 - tan 30^o}\)
Tan 60 = 3; Tan 30 = 1
\(\frac{\tan 60^o - 1}{1 - tan 30^o}\) = \(\frac{\sqrt{3 - 1}}{1 - \frac{1}{\sqrt{3}}}\) = \(\frac{\sqrt{3 - 1}}{\frac{3 - 1}{\sqrt{3}}}\)
= \(\frac{\sqrt{3 - 1}}{1} \times \frac{\sqrt{3 - 1}}{\sqrt{3}}\)
= \(\frac{\sqrt{3 - 1}}{1} \times \frac{\sqrt{3}}{\sqrt{3}}\)
= \(\sqrt{3}\)
In what number base was the addition 1 + nn = 100, where n > 0, done?
Simplify; \(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)
\(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)
\(\sqrt{12}\) + 2 x 2 - 2\(\sqrt{3}\)
2 \(\sqrt{3}\) - 2 \(\sqrt{3}\) + 4
= 4
Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.
Sum of all exterior angles is 360\(^o\)
360\(^o\) (30\(^o\) - 40\(^o\))
360 - (130\(^o\))
230\(^o\)
remaining is 46\(^o\) = \(\frac{230}{46}\) = 5
5 + 3 = 8 sides; Octagon
Find the 6th term of the sequence \(\frac{2}{3} \frac{7}{15} \frac{4}{15}\),...
a = \(\frac{2}{3}\), d = \(\frac{7}{15}\) - \(\frac{2}{3}\)
= 7 - 10
= \(\frac{-3}{15}\)
d = - \(\frac{-1}{5}\)
T6 = a + 5d
= \(\frac{2}{3}\) + 5(\(\frac{-1}{5}\)
= \(\frac{2}{3}\) - 1
= \(\frac{2 - 3}{3}\)
= \(\frac{-1}{3}\)
The roots of a quadratic equation are \(\frac{-1}{2}\) and \(\frac{2}{3}\). Find the equation.
(x + \(\frac{1}{2}\)) (n - \(\frac{2}{3}\))
\(x^2 - \frac{2}{3^x} + \frac{x}{2} - \frac{1}{3}\)
\(6x^2 - 4n + 3n - 2 = 0\)
\(6x^2 - x - 2 = 0\)
Make x the subject of the relation d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)
d = \(\sqrt{\frac{6}{x} - \frac{y}{2}}\)
\(d^2 = \frac{6}{x} - \frac{y}{2}\)
\(2xd^2 = 12 - xy\)
\(2xd^2 + xy = 12\)
x = \(\frac{6 + 12}{d^2 + y}\)
Consider the statements: p it is hot, q: it is raining
Which of the following symbols correctly represents the statement "It is raining if and only if it it is cold"?
Given that t = \(2 ^{-x}\), find \(2 ^{x + 1}\) in terms of t.
t = \(2^{-x} = \frac{1}{2^{x}}\)
\(\implies 2^{x} =\frac{1}{t}\)
\(2^{x+1} = 2^{x} \times 2^{1}\)
= \(\frac{1}{t} \times 2 = \frac{2}{t}\)
Two bottles are drawn with replacement from a crate containing 8 coke, 12 and 4 sprite bottles. What is the probability that the first is coke and the second is not coke?
Total = 8 + 12 + 4
= 24
\(\frac{8}{24} \times (\frac{12}{24} + \frac{4}{24}\))
= \(\frac{1}{3} \times (\frac{1}{2} + \frac{1}{6}\))
= \(\frac{1}{3} \times \frac{3 + 1}{6}\)
\(\frac{1}{3} \times \frac{4}{6} = \frac{2}{9}\)