Further Mathematics questions and answers

Further Mathematics Questions and Answers

Test your knowledge of advanced level mathematics with this aptitude test. This test comprises Further Maths questions and answers from past JAMB and WAEC examinations.

161.

A binary operation * is defined on the set of real number, R, by x*y = x\(^2\) - y\(^2\) + xy, where x, \(\in\)  R. Evaluate (\(\sqrt{3}\))*(\(\sqrt{2}\))

 

\({\color{red}2x} \times 3\)

A.

1 - \(\sqrt{6}\)

B.

\(\sqrt{6}\) - 1

C.

\(\sqrt{6}\)

D.

1 + \(\sqrt{6}\)

Correct answer is D

x*y = x\(^2\) - y\(^2\) + xy

(\(\sqrt{3}\))*(\(\sqrt{2}\)) = (\(\sqrt{3}\))\(^2\) - (\(\sqrt{2}\))\(^2\) + \(\sqrt{3}\) x \(\sqrt{2}\) 

= 3 - 2 + \(\sqrt{6}\)

= 1 + \(\sqrt{6}\) 

162.

Evaluate: \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)

A.

-1

B.

- \(\frac{1}{2}\)

C.

\(\frac{1}{2}\)

D.

1

Correct answer is D

Lim(\(\frac{1 - x}{x^2 - 3x + 2}\))

= \(^{lim}_{x \to 1} \begin{pmatrix} \frac{1 - x}{x^2 - 3x + 2} \end {pmatrix}\)

= \(^{lim}_{x \to 1} \begin{pmatrix} \frac{x - 1}{(x - 2)(x + 1)} \end {pmatrix}\)

= \(\frac{-1}{1 - 2}\)

= \(\frac{-1}{-1}\) 

= 1

164.

Given that X and Y are independent events such that P(X) = 0.5, P(Y) = m and P(X U Y) = 0.75, find the value of m. 

A.

0.6

B.

0.5

C.

0.4

D.

0.3

Correct answer is C

P(X \(\cup\) Y) = P(X)P(Y) 

0.15 = 0.5m

m = \(\frac{0.015}{0.5}\)

= 0.3 

165.