WAEC Further Mathematics Past Questions & Answers - Page 32

156.

Given that X  : R \(\to\) R is defined by x = \(\frac{y + 1}{5 - y}\) , y \(\in\) R, find the domain of x

A.

{y : y \(\in\) R, y \(\neq\) 0}

B.

{y : y \(\in\) R, y \(\neq\) 1}

C.

{y : y \(\in\) R, y \(\neq\) 5}

D.

{y : y \(\in\) R, y \(\neq\) 7}

Correct answer is C

No explanation has been provided for this answer.

157.

If  \(\begin{pmatrix} p+q & 1\\ 0 & p-q \end {pmatrix}\) = \(\begin{pmatrix} 2 & 1 \\ 0 & 8 \end{pmatrix}\)

Find the values of p and q

A.

p = 5, q = 3

B.

p = 5, q = -3

C.

p = -5, q = -3

D.

p = -5, q = 3

Correct answer is B

p + q = 2

p - q = 8

\(\overline{\frac{2p}{2} = \frac{10}{2}}\)

p = 5

from p + q = 2

5 + q = 2

q = 2 - 5 

= -3

158.

If \(\int^3_0(px^2 + 16)dx\) = 129. Find the value of p

A.

9

B.

8

C.

7

D.

6

Correct answer is A

\(\int^3_0(px^2 + 16)\) = 129

\(\frac{px^2 + 1}{0 + 1} + 16x|^3_0 = 129\)

\(\frac{px^3}{3} + 16x|^3_0 = 129\)

(\(\frac{p(3)^3}{3} + 16(3)\)) - 0 = 129

9p + 48 = 129

9p = 129 - 48 

\(\frac{9p}{9} = \frac{81}{9}\) 

p = 9

159.

If cos x = -0.7133, find the values of x between 0\(^o\) and 360\(^o\) 

A.

44.5\(^o\) , 224.5\(^o\)

B.

123.5\(^o\) , 190.5\(^o\)

C.

135.5\(^o\) , 213.5\(^o\)

D.

135.5\(^o\) , 224.5\(^o\)

Correct answer is D

cos x = -0.7133

x = cos \(^{-1}\)(0.7133) 

= 44.496\(^o\) 

x = 180 - 44.495\(^o\) 

x = 135.5\(^o\)

and x = 180\(^o\)  + 44.495\(^o\) 

= 224.5\(^o\)

160.

Find the inverse of \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)

A.

\(\begin{pmatrix} 5 & 1 \\ -3 & 2 \end{pmatrix}\)

B.

\(\begin{pmatrix} 2 & -5 \\ -1 & 3 \end{pmatrix}\)

C.

\(\begin{pmatrix} -5 & 2 \\ -1 & 3 \end{pmatrix}\)

D.

\(\begin{pmatrix} 5 & 1 \\ 2 & 3 \end{pmatrix}\)

Correct answer is B

Let A = \(\begin{pmatrix} 3 & 5 \\ 1 & 2 \end{pmatrix}\)

|A| = (3 x 2 - 5 x 1) 

= 6 - 5

= 1

A\(^{-1}\) = \(\begin{pmatrix} 2 & -5 \\ -1 & 3 \end{pmatrix}\)