WAEC Further Mathematics Past Questions & Answers - Page 51

251.

The equation of a circle is given by \(x^{2} + y^{2} - 4x - 2y - 3\). Find the radius and the coordinates of its centre.

A.

\(3, (-1, 2)\)

B.

\(2\sqrt{2}, (2, -1)\)

C.

\(2\sqrt{2}, (2, 1)\)

D.

\(9, (2, 1)\)

Correct answer is C

Equation of a circle with radius r and centre (a, b).

= \((x - a)^{2} + (y - b)^{2} = r^{2}\)

Expanding, we have

\(x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2}\)

Comparing, with \(x^{2} + y^{2} - 4x - 2y - 3 = 0\)

\(2a = 4 \implies a = 2\)

\(2b = 2 \implies b = 1\)

\(r^{2} - a^{2} - b^{2} = 3 \implies r^{2} = 3 + 2^{2} + 1^{2} = 8\)

\(r = 2\sqrt{2}\)

252.

Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Evaluate \(|Q|P\).

A.

\(\begin{pmatrix} 16 & 36 \end{pmatrix}\)

B.

\(\begin{pmatrix} 8 & 18 \end{pmatrix}\)

C.

\(\begin{pmatrix} 8 & 0 \end{pmatrix}\)

D.

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

Correct answer is A

\(|Q| = \begin{vmatrix} -1 & -2 \\ 3 & 2 \end{vmatrix}\)

= \(-2 - (-6) = 4\)

\(4P = 4\begin{pmatrix} 4 & 9 \end{pmatrix}\)

= \(\begin{pmatrix} 16 & 36 \end{pmatrix}\)

253.

Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Which of the following operations is possible?

A.

\(QP\)

B.

\(P^{2}\)

C.

\(Q^{2}P\)

D.

\(PQ\)

Correct answer is D

A \(1 \times 2\) matrix can be multiplied by \(2 \times 2\) matrix to give a \(1 \times 2\) matrix.

254.

How many ways can 12 people be divided into three groups of 2, 7 and 3 in that order?

A.

7920

B.

792

C.

187

D.

42

Correct answer is A

= \(\frac{12!}{2! 3! 7!} \)

\(\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{2 \times 3 \times 2 \times 7!}\)

= \(7,920\)

255.

Marks 5 - 7 8 - 10 11 - 13 14 -  16 17 - 19 20 - 22
Frequency 4 7 26 41 14 8

The table above shows the marks obtained by 100 pupils in a test. Find the probability that a student picked at random scored at least 14 marks.

A.

0.22

B.

0.41

C.

0.49

D.

0.63

Correct answer is D

No explanation has been provided for this answer.