WAEC Past Questions and Answers - Page 1033

5,161.

If sin x = \(\frac{12}{13}\) and sin y = \(\frac{4}{5}\), where x and y are acute angles, find  cos (x + y)

A.

\(\frac{48}{65}\)

B.

\(\frac{13}{15}\)

C.

\(\frac{-33}{65}\)

D.

\(\frac{-48}{65}\)

Correct answer is C

From Pythagoras' theorem

when sin x = \(\frac{12}{13}\), cos x = \(\frac{5}{13}\)

Using cos (x + y) = cosx cosy - sinxsiny

\(\frac{5}{13}\) * \(\frac{3}{5}\) - \(\frac{12}{13}\) * \(\frac{4}{5}\)

= \(\frac{-33}{65}\)

5,162.

If ( 1- 2x)\(^4\) = 1 + px + qx\(^2\) - 32x\(^3\) + 16\(^4\), find the value of (q - p)

A.

-32

B.

-16

C.

16

D.

32

Correct answer is D

( 1- 2x)\(^4\) = 1 + px + qx\(^2\) - 32x\(^3\) + 16\(^4\) 

compared with:  1 - 8x + 24x\(^2\) - 32x\(^3\) + 16\(^4\)

q = 24 and p = -8

(q - p) = 24 - [-8] = 32

5,163.

Given that F\(^1\)(x) = x\(^3\)√x, find f(x)

A.

\( \frac{2x^{9/2}}{9} + c \)

B.

\( 2x^{9/2} + c \)

C.

\( \frac{2x^{5/2}}{5} + c \)

D.

\( x^4 + c \)

Correct answer is A

F1 (x) = x\(^3\) √x = x\(^{7/2}\)

F(x) = \(\frac{x^{7/2 +1}}{7/2 + 1}\) + c

= \(\frac{x^{9/2}}{9/2}\)

= \(\frac{2x^{9/2}}{9}\) + c

5,164.

A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) - t\(^3\).

Calculate the distance travelled in the third second.

A.

5.5m

B.

14.5m

C.

26.0m

D.

30.0m

Correct answer is A

From  S = 12t + \(\frac{5}{2t^2}\) - t\(^3\);

Distance traveled in 2 seconds

 S = 12[2] + \(\frac{5}{2[2]^2}\) - 2\(^3\).

= 24 + 10 - 8 = 26m

Distance traveled in 3 seconds

 S = 12[3] + \(\frac{5}{2[3]^2}\) - 3\(^3\)

= 36 + 22.5 - 27 = 31.5m

Distance traveled in the 3rd second

= 31.5m - 26m

: S = 5.5m

5,165.

A stone is thrown vertically upward and distance, S metres after t seconds is given by S = 12t + \(\frac{5}{2t^2}\) - t\(^3\).

Calculate the maximum height reached.

A.

418.5m

B.

56.0m

C.

31.5m

D.

30.0m

Correct answer is C

S = 12t + \(\frac{5}{2t^2}\) - t\(^3\);

ds/dt =  12 + 5t - 3t\(^2\)

At max height ds/dt = 0

i.e 12 + 5t - 3t\(^2\)

(3t + 4)(t -3) = 0;

t = -4/3 or 3

Hmax = 12[3] + \(\frac{5}{2[3]^2}\) - 3\(^3\)

= 36 + 45/2 - 27

= 31.5m