Further Mathematics Past Questions

Question 211

waec 2015

If \(\alpha\) and \(\beta\) are the roots of \(x^{2} + x - 2 = 0\), find the value of \(\frac{1}{\alpha^{2}} + \frac{1}{\beta^{2}}\).

A\(\frac{5}{4}\)

B\(\frac{3}{4}\)

C\(\frac{1}{4}\)

D\(\frac{-3}{4}\)

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Question 212

waec 2015

The gradient of a curve at the point (-2, 0) is \(3x^{2} - 4x\). Find the equation of the curve.

A\(y = 6x - 4\)

B\(y = 6x^{2} - 4x + 12\)

C\(y = x^{3} - 2x^{2}\)

D\(y = x^{3} - 2x^{2} + 16\)

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Question 213

waec 2015

If \(x = i - 3j\) and \(y = 6i + j\), calculate the angle between x and y.

A60°

B75°

C81°

D85°

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Question 214

waec 2015

In how many ways can a committee of 5 be selected from 8 students if 2 particular students are to be included?

A20

B28

C54

D58

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Question 215

waec 2015

A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\). Find the y-coordinate of the line when x = 4.

A2

B4

C6

D8

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Question 216

waec 2015

A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\), what is the gradient of the line?

A1

B2

C3

D4

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Question 217

waec 2015

Find the minimum value of \(y = x^{2} + 6x - 12\).

A-21

B-12

C-6

D-3

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Question 218

waec 2015

If \(36, p, \frac{9}{4}, q\) are consecutive terms of an exponential sequence (G.P.). Find the sum of p and q.

A\(\frac{9}{16}\)

B\(\frac{81}{16}\)

C\(9\)

D\(9\frac{9}{16}\)

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Question 219

waec 2015

Given that \(f : x \to \frac{2x - 1}{x + 2}, x \neq -2\), find \(f^{-1}\), the inverse of f.

A\(f^{-1} : x \to \frac{1+2x}{2-x}, x \neq 2\)

B\(f^{-1} : x \to \frac{1-2x}{x+2}, x \neq -2\)

C\(f^{-1} : x \to \frac{1-2x}{x-2}, x \neq 2\)

D\(f^{-1} : x \to \frac{1+2x}{x+2}, x \neq -2\)

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Question 220

waec 2015

Which of the following is a factor of the polynomial \(6x^{4} + 2x^{3} + 15x + 5\)?

A3x + 1

Bx + 1

C2x + 1

Dx + 2

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Question 221

waec 2015

Given that \(P = \begin{pmatrix} -2 & 1 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} 5 & -3 \\ 2 & -1 \end{pmatrix}\), find PQ - QP.

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

B\(\begin{pmatrix} 27 & 12 \\ 16 & -15 \end{pmatrix}\)

C\(\begin{pmatrix} -20 & -6 \\ 12 & -8 \end{pmatrix}\)

D\(\begin{pmatrix} 11 & 12 \\ 30 & -11 \end{pmatrix}\)

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Question 222

waec 2015

Given that \(\frac{2x}{(x + 6)(x + 3)} = \frac{P}{x + 6} + \frac{Q}{x + 3}\), find P and Q.

AP = 4 and Q = 2

BP = 2 and Q = 4

CP = 4 and Q = -2

DP = -2 and Q = 4

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Question 223

waec 2015

Given that \(f : x \to x^{2}\) and \(g : x \to x + 3\), where \(x \in R\), find \(f o g(2)\).

A25

B9

C7

D5

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Question 224

waec 2015

Find the 3rd term of \((\frac{x}{2} - 1)^{8}\) in descending order of x.

A\(\frac{x^{7}}{8}\)

B\(\frac{7x^{6}}{16}\)

C\(\frac{7x^{5}}{4}\)

D\(\frac{35x^{4}}{8}\)

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Question 225

waec 2015

If \(\log_{3} x = \log_{9} 3\), find the value of x.

A\(3^{2}\)

B\(3^{\frac{1}{2}}\)

C\(3^{\frac{1}{3}}\)

D\(2^{13}\)

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Question 226

waec 2015

Solve: \(4(2^{x^2}) = 8^{x}\)

A(1, 2)

B(1, -2)

C(-1, 2)

D(-1, -2)

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Question 227

waec 2015

Solve: \(2\cos x - 1 = 0\).

A\((\frac{2\pi}{3}, \frac{4\pi}{3})\)

B\((\frac{\pi}{6}, \frac{5\pi}{6})\)

C\((\frac{\pi}{5}, \frac{2\pi}{5})\)

D\((\frac{\pi}{3}, \frac{5\pi}{3})\)

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Question 228

waec 2015

Simplify \(\frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}}\).

A\(14(2\sqrt{2} + 6\sqrt{5} - 4\sqrt{10})\)

B\(\frac{1}{14}(2 - 3\sqrt{2} - 4\sqrt{5} - 6\sqrt{10})\)

C\(\frac{1}{14}(3\sqrt{2} + 4\sqrt{5} - 6\sqrt{10} - 2)\)

D\(14(2 + 3\sqrt{2} - 6\sqrt{5} + 4\sqrt{10})\)

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Question 229

waec 2014

Express (14N, 240°) as a column vector.

A\(\begin{pmatrix} -7 \\ -7\sqrt{3} \end{pmatrix}\)

B\(\begin{pmatrix} 7\sqrt{3} \\ 7\sqrt{3} \end{pmatrix}\)

C\(\begin{pmatrix} -7\sqrt{3} \\ -7 \end{pmatrix}\)

D\(\begin{pmatrix} 7 \\ -7\sqrt{3} \end{pmatrix}\)

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Question 230

waec 2014

Evaluate \(\frac{\tan 120° + \tan 30°}{\tan 120° - \tan 60°}\)

A\(\sqrt{3} + \sqrt{2}\)

B\(\frac{2}{3}\)

C\(\frac{1}{3}\)

D\(-2\sqrt{3}\)

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