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WAEC Further Mathematics Past Questions & Answers - Page 29

141.

If the binomial expansion of (1 + 3x) $^6$ is used to evaluate (0.97) $^6$ , find the value of x.

0.03

0.01

-0.01

-0.03

View answer & explanation

Correct answer is C

(1 + 3x ) $^6$ = (0.97) $^6$

1 + 3x = 0.97

3x = 0.97.1

$\frac{3x}{3} = \frac{0.03}{3}$

x = -0.01

142.

In which of the following series can be the formula S = $\frac{a}{1 - r}$ where a is the first term and r is the common ratio, be used to find the sum of all the terms?

4 + 8 + 16 + 32 + ...

$\frac{1}{2}$ + 2 $\frac{1}{2}$ + 12 $\frac{1}{2}$ + 62 $\frac{1}{2}$ + ..

$\frac{4}{81}$ + $\frac{2}{27}$ + $\frac{1}{9}$ + $\frac{1}{6}$ + ...

128 + 64 + 32 + 16 + ...

View answer & explanation

Correct answer is D

No explanation has been provided for this answer.

143.

A stone was dropped from the top of a building 40m high. Find, correct to one decimal place, the time it took the stone to reach the ground. [Take g = 9.8ms $^{-2}$ ]

2.9.seconds

2.8 seconds

2.6 seconds

1.4 seconds

View answer & explanation

Correct answer is A

s = $\frac{1}{2}gt^2$

40 = $\frac{1}{2} \times 9.8 \times t^2$

$\frac{80}{9.8} = t^2$

t = $\sqrt{8.16326}$

t ≈ 2.9 secs

144.

Given that F = 3i - 12j, R = 7i + 5j and N = pi + qj are forces acting on a body, if the body is in equilibrium. find the values of p and q.

p=-10, q=7

p=-10, q=-7

p=10, q=- 7

p-10, q=7

View answer & explanation

Correct answer is C

If the body is in equilibrium then

F + R = N

3i - 12j + 7i + 5j = pi + qj

10i - 7j = pi + qj

p = 10, q = -7

145.

Find the angle between i + 5j and 5i - J

0 $^o$

45 $^o$

60 $^o$

90 $^o$

View answer & explanation

Correct answer is D

a = i + 5j and b = 5i - j

cos $\theta$ = $\frac{a.b}{|a|.|b|}$

= $\frac{(1 \times 5) + (5x - 1)}{(\sqrt{1^2 + 5^2}) (5^2 + (-1))^2}$

= $\frac{5 - 5}{\sqrt{26}\times \sqrt{26}}$ = 0

x = cos $^{-1}$ (0), x = 90 $^o$

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