How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.
Multiply (x2 - 3x + 1) by (x - a)
x3 - (3 + a) x2 + (1 + 3a)x - a
x3 - (3 - a)x2 + 3ax - a
x3 - (3 - a)x2 - (1 = 3a) - a
x3 + (3 - a)x2 + (1 + 3a) - a
Correct answer is A
(x2 - 3x + 1)(x - a) = x3 - 3x2 + x - ax2 + 3ax - a
= x3 - (3 + a) x2 + (1 + 3a)x - a
Rationalize \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)
5 - 2\(\sqrt{6}\)
5 + 2\(\sqrt{6}\)
5\(\sqrt{6}\)
5
Correct answer is B
\(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\)
= \(\frac{2\sqrt{3} + 3 \sqrt{2}}{3\sqrt{2} - 2 \sqrt{3}}\) x \(\frac{3\sqrt{2} + 2 \sqrt{3}}{3\sqrt{2} - 2 \sqrt{3}}\)
\(\frac{4(3) + 9(2) + 2(6) \sqrt{6}}{9(2) - 4(3)}\)
\(\frac{12 + 18 + 12\sqrt{6}}{1`8 - 12}\)
= \(\frac{30 + 12\sqrt{6}}{6}\)
= 5 + 2\(\sqrt{6}\)
Simplify \(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
- \(\frac{1}{2}\sqrt{5}\)
\(\frac{1}{2}\sqrt{5}\)
-- \(\frac{1}{4}\sqrt{5}\)
5
Correct answer is B
\(\frac{1}{1 + \sqrt{5}}\) - \(\frac{1}{1 - \sqrt{5}}\)
= \(\frac{1 - \sqrt{5} - 1 - \sqrt{5}}{(1 + \sqrt{5}) (1 - \sqrt{5}}\)
= \(\frac{-2\sqrt{5}}{1 - 5}\)
= \(\frac{-2\sqrt{5}}{- 4}\)
= \(\frac{1}{2}\sqrt{5}\)
Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
1 - 4 log3
-1 + 2 log 3
-1 + 5 log2
1 - 2log 2
Correct answer is D
2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\)
= log \(\frac{72}{125}\)
= log \(\frac{5}{2}\)
= log \(\frac{10}{4}\)
= log 10 - log 4
= log10 10 - log10 22
= 1 - 2 log2
What is the product of \(\frac{27}{5^1}\)(3)-3 and \(\frac{(1)^{-1}}{5}\)?
5
3
1
\(\frac{1}{25}\)
Correct answer is D
\(\frac{27}{5^1}\)(3)-3 x \(\frac{(1)^{-1}}{5}\) = \(\frac{27}{5}\) x \(\frac{1}{3^3}\) x \(\frac{1}{\frac{1}{5}}\)
= \(\frac{27}{5}\) x \(\frac{1}{27}\) x \(\frac{1}{5}\)
= \(\frac{1}{25}\)