WAEC Past Questions and Answers - Page 1035

5,171.
5,172.

Find the inverse of  \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)

A.

\(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)

B.

\(\begin{pmatrix} 1 & -1 \\ 1.5 & -2 \end{pmatrix}\)

C.

\(\begin{pmatrix} -2 & 1 \\ 1.5 & 1 \end{pmatrix}\)

D.

\(\begin{pmatrix} -2 & -1 \\ 1.5 & 1 \end{pmatrix}\)

Correct answer is A

Let A =  \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\);

|A| = -8 - (-6) = -8 + 6

|A| = -2

A\(^{-1}\) = \(\frac{1}{-2}\) =  \(\begin{pmatrix} -2 & 2- \\ 3 & 4 \end{pmatrix}\)

= \(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)

5,173.

A binary operation * is defined on the set of real numbers, R, by

P * q = \(\frac{q^2 - p^2}{2pq}\). Find 3 * 2

A.

\(\frac{13}{12}\)

B.

\(\frac{5}{12}\)

C.

-\(\frac{5}{12}\)

D.

\(\frac{-1}{2}\)

Correct answer is C

P * q = \(\frac{q^2 - p^2}{2pq}\).

3 * 2 (where p = 3, q = 2)

i.e 3 *2 =  \(\frac{3^2 - 2^2}{2 *3 * 2}\)

=  \(\frac{4 - 9}{12}\)

= \(\frac{-5}{12}\)

5,174.

For what value of k is 4x\(^2\) - 12x + k, a perfect square?

A.

-9

B.

\(\frac{-9}{4}\)

C.

\(\frac{9}{4}\)

D.

9

Correct answer is D

4x\(^2\) - 12x + k;

a = 4, b = -12, c = k.

For perfect square  b\(^2\) = 4ac

(-12)\(^2\) = 4 * 4 * k;

144 = 16k

k = 144\16

k = 9

5,175.

If f(x) = 4x\(^3\) + px\(^2\) + 7x - 23 is divided by (2x -5), the remainder is 7. find the value of p

A.

-7.0

B.

-8.0

C.

-9.6

D.

9

Correct answer is B

f(x) = 4x\(^3\) + px\(^2\) + 7x - 23

If f(x) is divided by (2x -5), the remainder is f(\(\frac{5}{2}\))

f\(\frac{5}{2}\) = 4\(\frac{5}{2}\)\(^3\) + p\(\frac{5}{2}\)\(^2\) + 7\(\frac{5}{2}\) - 23

Hence;

 = \(\frac{125}{8}\) + \(\frac{25}{4}\) p + \(\frac{35}{2}\) - 23

28 = 250 + 250p + 70 - 92

25p = -200;  p = -8.0