WAEC Further Mathematics Past Questions & Answers

301.

The coefficient of the 5th term in the binomial expansion of $(1 + kx)^{8}$ , in ascending powers of x is $\frac{35}{8}$ . Find the value of the constant k.

$\frac{1}{2}$

$-\frac{1}{2}$

-2

View answer & explanation

Correct answer is B

$(1 + kx)^{8} = ^{8}C_{0}(1^{8})(kx)^{0} + ^{8}C_{1}(1^{7})(kx)^{1} + ...$

The 5th term = $^{8}C_{5 - 1}(1^{4})(kx)^{4}$

= $^{8}C_{4} (kx)^{4}$

$\implies 70k^{4} = \frac{35}{8}$

$k^{4} = \frac{\frac{35}{8}}{70}$

$k^{4} = \frac{1}{16}$

$k = \frac{1}{2}$

302.

Find the derivative of $3x^{2} + \frac{1}{x^{2}}$

$6x + 2x^{2}$

$6x + \frac{1}{2x}$

$6x - \frac{2}{x^{3}}$

$6x - \frac{1}{2x}$

View answer & explanation

Correct answer is C

$y = 3x^{2} + \frac{1}{x^{2}} \equiv y = 3x^{2} + x^{-2}$

$\frac{\mathrm d y}{\mathrm d x} = 6x - 2x^{-3}$

= $6x - \frac{2}{x^{3}}$

303.

A binary operation ,*, is defined on the set R, of real numbers by $a * b = a^{2} + b + ab$ . Find the value of x for which $5 * x = 37$

-2

-7

View answer & explanation

Correct answer is B

$a * b = a^{2} + b + ab$

$5 * x = 5^{2} + x + 5x = 37$

$25 + 6x = 37 \implies 6x = 12$

$x = 2$

304.

Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1).

3x - 5y + 13 = 0

3x - 5y - 7 = 0

5x - 3y + 7 = 0

5x + 3y - 1 = 0

View answer & explanation

Correct answer is D

Midpoint between P(4, 5) and Q(-6, -1) = $\frac{4 - 6}{2}, \frac{5 - 1}{2} = (-1, 2)$

Gradient of PQ = $\frac{5 - (-1)}{4 - (-6)} = \frac{3}{5}$

Gradient of line perpendicular to PQ = $\frac{-1}{\frac{3}{5}} = -\frac{5}{3}$

$line = \frac{y - 2}{x + 1} = \frac{-5}{3}$

$3y - 6 = -5x - 5$

$5x + 3y - 6 + 5 = 0 \implies 5x + 3y - 1 = 0$

305.

Two statements are represented by p and q as follows:

p : He is brilliant; q : He is regular in class

Which of the following symbols represent "He is regular in class but dull"?

$q \vee \sim p$

$q \edge \sim p$

$\sim q \edge \sim p$

$\sim q \vee \sim p$

View answer & explanation

Correct answer is B

No explanation has been provided for this answer.

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