WAEC Further Mathematics Past Questions & Answers - Page 21

101.

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

102.

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

103.

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

104.

In △PQR, \(\overline{PQ}\) = 5i - 2j and \(\overline{QR}\) = 4i + 3j. Find \(\overline{RP}\)

A.

-i - 5j

B.

-9 - j

C.

i + 5j

D.

-9i + j

Correct answer is A

\(\overline{PQ}\) = 5i - 2j;  \(\overline{QR}\) = 4i + 3j

 \(\overline{RP}\) = \(\overline{PQ}\) - \(\overline{QR}\)

= 5i - 2j - [4i + 3j] =  5i - 2j - 4i - 3j

= i - 5j

105.

Three forces, F\(_1\) (8N, 030°), F\(_\2) (10N, 150° ) and F\(_\3) ( KN, 240° )are in equilibrium. Find the value of N

A.

5√3

B.

6√2

C.

6√3

D.

9√3

Correct answer is C

No explanation has been provided for this answer.