WAEC Further Mathematics Past Questions & Answers - Page 41

201.

Solve: 8\(^{x - 2}\) = 4\(^{3x}\)

A.

-2

B.

-1

C.

1

D.

2

Correct answer is B

8\(^{x - 2}\) = 4\(^{3x}\)

2\(^{3(x - 2)}\) = 2\(^{2(3x)}\)

2 \(^{3x - 4}\) = 2\(^{6x}\)

2 \(^{x - 4}\)  = 6\(^x\)

\(\frac{-4x}{-4}\) = \(\frac{4}{-4}\)

x = -1

203.

Two forces, each of magnitude 16 N, are inclined to each other at an angle of 60°. Calculate the magnitude of their resultant.

A.

16 N

B.

\(16 \sqrt{3}\) N

C.

18 N

D.

\(18 \sqrt{3}\) N

Correct answer is B

No explanation has been provided for this answer.

205.

Calculate, correct to one decimal place, the angle between 5i + 12j and -2i + 3j.

A.

54.8°

B.

56.3°

C.

66.4°

D.

76.3°

Correct answer is B

\(a . b = |a||b|\cos \theta\)

\((5i + 12j).(2i + 3j) = -10 + 36 = 26\)

\(26 = |5i + 12j||-2i + 3j|\cos \theta\)

\(|5i + 12j| = \sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = 13\)

\(|2i + 3j| = \sqrt{2^{2} + 3^{2}} = \sqrt{4 + 9} = \sqrt{13}\)

\(26 = 13(\sqrt{13})\cos \theta\)

\(\cos \theta = \frac{26}{13\sqrt{13}} = 0.5547\)

\(\theta = 56.3°\)