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WAEC Further Mathematics Past Questions & Answers - Page 5

21.

An exponential sequence (G.P.) is given by 8√2, 16√2, 32√2, ... . Find the nth term of the sequence

A.

82n

B.

2(n+2)2

C.

2(n+3)

D.

8n2

Correct answer is B

8√2, 16√2, 32√2, ..

a=82;r=T2T1=16282=2

Tn=arn1

Tn=82×2n1

Tn=23×2n1×2

Tn=23+n1×2

22.

Solve 6 sin 2θ tan θ = 4, where 0º < θ < 90º

A.

18.43º

B.

30.00º

C.

35.26º

D.

19.47º

Correct answer is C

6 sin 2θ tan θ = 4, where 0º < θ < 90º

sin 2θ = 2sin θ cos θ and tanθ = \frac{sinθ}{cosθ}

= 6 x 2sin θ cos θ x \frac{sin θ}{cos θ} = 4

= sin^2 θ = 4

= sin^2 θ = \frac{4}{12}=\frac{1}{3}

=sin θ = \frac{\sqrt1}{3}=\frac{1}{\sqrt3}

= θ = sin^{-1}(\frac{1}{\sqrt3})

∴ θ = 35.26º

23.

Given that r = (10 N , 200º) and n = (16 N , 020º), find (3r - 2n).

A.

(62 N , 240º)

B.

(62 N , 200º)

C.

(62 N , 280º)

D.

(62 N , 020º)

Correct answer is D

r = (10 N, 200º) and n = (16 N, 020º)

In rectangular form:

r = 10cos 200ºi + 10sin 200ºj = -9.397i - 3.420j

n = 16cos 20ºi + 16sin 20ºj = 15.035i + 5.472j

3r = -28.191i - 10.260j

2n = 30.070i + 10.945j

3r - 2n = (-28.191i - 10.260j) - (30.070i + 10.945j)

3r - 2n = -58.261i - 21.205j

|3r - 2n| = √((-58.261)^2 + (-21.205)^2) = 62 N

tan θ =\frac{-21.205}{-58.261} = 0.3640

θ = tan^{-1} (0.3640) = 20^o

∴ (62 N , 020º)

24.

Simplify: \frac{log √27 - log √8}{log 3 - log 2}

A.

\frac{3}{2}

B.

-\frac{1}{4}

C.

-\frac{3}{2}

D.

\frac{1}{4}

Correct answer is A

\frac{log √27 - log √8}{log 3 - log 2}

= \frac{log √3^3 - log √2^3}{log 3 - log 2}

= \frac{log3^{3/2} - log2^{3/2}}{log3}

=\frac{^3/_2(log 3 - log 2)}{log 3 - log 2}

\therefore\frac{3}{2}

25.

The table shows the mark obtained by students in a test.

Marks 1 2 3 4 5
Frequency 2 k 1 1 2

A.

4

B.

1

C.

2

D.

3

Correct answer is B

 x̄ =\frac{∑fx}{∑f}= 3

=\frac{(1 \times 2)+(2 \times k)+(3 \times 1)+(4 \times 1)+(5 \times 2)}{2 + k + 1 + 1 + 2}= 3

=\frac{2 + 2k + 3 + 4 + 10}{6 + k} = 3

=\frac{19 + 2k}{6 + k} = 3

=\frac{19 + 2k}{6 + k} = \frac{3}{1}

=19+2k=3(6+k)

=19+2k=18+3k

=2k-3k=18-19

=-k=-1

∴k=1