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WAEC Further Mathematics Past Questions & Answers - Page 17

81.

Simplify $\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}$

A.

3

B.

9

C.

27

D.

81

View answer & explanation

Correct answer is B

$\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}$

= $\frac{3^n * 3^n * 3^1 * - 3^2 * 3^2}{3^n * 3^1 - 3^n}$

= $\frac{3^n (3^2 * 3^1)}{3^n (3^1 - 1)}$

= $\frac{27-9}{3-1}$

= $\frac{18}{2}$

= 9

82.

If $log_{10}(3x+1) + log_{10}4 = log_{10}(9x+2)$ , find the value of x

A.

$\frac{1}{3}$

B.

1

C.

2

D.

3

View answer & explanation

Correct answer is C

$log_{10}(3x+1) + log_{10}4 = log_{10}(9x+2)$

$log_{10}4(3x+1) = log_{10}(9x+2)$

4(3x+1) = 9x + 2

12x -4 = 9x + 2

12x - 9x = 2 + 4

3x = 6

x = 2

83.

( $\frac{3√6}{√5} + \frac{√54}{3√5}$ ) $^{-1}$

A.

$\frac{5√3}{6}$

B.

$\frac{3√15}{6}$

C.

$\frac{5√6}{12}$

D.

$\frac{5√3}{12}$

View answer & explanation

Correct answer is C

( $\frac{3√6}{√5} + \frac{√54}{3√5}$ ) $^{-1}$

= $\frac{√5(3√5)}{3√6 + 3√6}$

= $\frac{3*5}{6√6} = \frac{5}{2√6}$

= $\frac{5*2√6}{2√6+2√6} = \frac{10√6}{4*6}$

= $\frac{5√6}{12}$

84.

A binary operation ∆ is defined on the set of real numbers R, by x∆y = $\sqrt{x+y - \frac{xy}{4}}$ , where x, yER. Find the value of 4∆3

A.

16

B.

8

C.

4

D.

2

View answer & explanation

Correct answer is D

x∆y = $\sqrt{x+y - \frac{xy}{4}}$

4∆3 = $\sqrt{4+3 - \frac{4*3}{4}}$

= $\sqrt{4+3-3}$

= $\sqrt{4}$

= 2.

85.

The table shows the distribution of marks obtained by some students in a test

Marks	0-9	10-19	20-29	30-39	40-49
Frequency	4	12	16	6	2

Find the modal class mark.

A.

4.5

B.

14.5

C.

24.5

D.

34.5

View answer & explanation

Correct answer is C

Modal class 20 - 29

Modal class mark = $\frac{20+29}{2}$

= $\frac{49}{2}$

= 24.5

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