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Further Mathematics Past Questions

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Question 251

waec 2013

Forces 50N and 80N act on a body as shown in the diagram. Find, correct to the nearest whole number, the horizontal component of the resultant force.

A13N

B43N

C57N

D95N

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Question 252

waec 2013

A committee consists of 5 boys namely: Kofi, John, Ojo, Ozo and James and 3 girls namely: Rose, Ugo and Ama. In how many ways can a sub-committee consisting of 3 boys and 2 girls be chosen, if Ozo must be on the sub-committee?

A35

B30

C18

D12

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Question 253

waec 2013

The function \(f : F \to R\)

= \(f(x) = \begin{cases} 3x + 2 : x > 4 \\ 3x - 2 : x = 4 \\ 5x - 3 : x < 4 \end{cases}\). Find f(4) - f(-3).

A28

B26

C-26

D-28

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Question 254

waec 2013

The angle subtended by an arc of a circle at the centre is \(\frac{\pi}{3} radians\). If the radius of the circle is 12cm, calculate the perimeter of the major arc.

A\(4(6 + 5\pi)\)

B\(4(6 + 2\pi)\)

C\(4(3 + 3\pi)\)

D\(4(3 + 5\pi)\)

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Question 255

waec 2013

Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 9) internally in the ratio 2 : 3.

A\((5\frac{2}{3}, \frac{2}{5})\)

B\((\frac{2}{5}, 5\frac{2}{5})\)

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

D\((\frac{-2}{5}, 5\frac{2}{5})\)

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Question 256

waec 2013

Evaluate \(\int_{0}^{2} (8x - 4x^{2}) \mathrm {d} x\).

A\(-16\)

B\(\frac{-16}{3}\)

C\(\frac{16}{3}\)

D\(16\)

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Question 257

waec 2013

An object is thrown vertically upwards from the top of a cliff with a velocity of \(25ms^{-1}\). Find the time, in seconds, when it is 20 metres above the cliff. \([g = 10ms^{-2}]\).

A0 and 1

B0 and 4

C0 and 5

D1 and 4

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Question 258

waec 2013

Given that \(P = \begin{pmatrix} y - 2 & y - 1 \\ y - 4 & y + 2 \end{pmatrix}\) and |P| = -23, find the value of y.

A-4

B-3

C-1

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Question 259

waec 2013

Given that \(\frac{\mathrm d y}{\mathrm d x} = \sqrt{x}\), find y.

A\(2x^{\frac{3}{2}} + c\)

B\(\frac{2}{3}x^{\frac{3}{2}} + c\)

C\(\frac{3}{2}x^{\frac{3}{2}} + c\)

D\(\frac{2}{3}x^{2} + c\)

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Question 260

waec 2013

Find the range of values of x for which \(x^{2} + 4x + 5\) is less than \(3x^{2} - x + 2\)

A\(x > \frac{-1}{2}, x > 3\)

B\(x < \frac{-1}{2}, x > 3\)

C\(\frac{-1}{2} \leq x \leq 3\)

D\(\frac{-1}{2} < x < 3\)

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Question 261

waec 2013

The fourth term of an exponential sequence is 192 and its ninth term is 6. Find the common ratio of the sequence.

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

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

C\(2\)

D\(3\)

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Question 262

waec 2013

Differentiate \(x^{2} + xy - 5 = 0\).

A\(\frac{-(2x + y)}{x}\)

B\(\frac{(2x - y)}{x}\)

C\(\frac{-x}{2x + y}\)

D\(\frac{(2x + y)}{x}\)

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Question 263

waec 2013

Find the equation of the line that is perpendicular to \(2y + 5x - 6 = 0\) and bisects the line joining the points P(4, 3) and Q(-6, 1).

Ay + 5x + 3 = 0

B2y - 5x - 9 = 0

C5y + 2x - 8 = 0

D5y - 2x - 12 = 0

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Question 264

waec 2013

Given that \(f(x) = 2x^{3} - 3x^{2} - 11x + 6\) and \(f(3) = 0\), factorize f(x).

A(x - 3)(x - 2)(2x + 2)

B(x + 3)(x - 2)(x - 1)

C(x - 3)(x + 2)(2x -1)

D(x + 3)(x - 2)(2x - 1)

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Question 265

waec 2013

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 6x + 5 = 0\), evaluate \(\frac{\beta}{\alpha} + \frac{\alpha}{\beta}\).

A\(\frac{24}{5}\)

B\(\frac{8}{5}\)

C\(\frac{5}{8}\)

D\(\frac{5}{24}\)

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Question 266

waec 2013

If \(\sqrt{x} + \sqrt{x + 1} = \sqrt{2x + 1}\), find the possible values of x.

A1 and -1

B-1 and 2

C1 and 2

D0 and -1

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Question 267

waec 2013

Find the third term in the expansion of \((a - b)^{6}\) in ascending powers of b.

A\(-15a^{4}b^{2}\)

B\(15a^{4}b^{2}\)

C\(-15a^{3}b^{3}\)

D\(15a^{3}b^{3}\)

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Question 268

waec 2013

If \(f(x) = x^{2}\) and \(g(x) = \sin x\), find g o f.

A\(\sin^{2} x\)

B\(\sin x^{2}\)

C\((\sin x)x^{2}\)

D\(x \sin x\)

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Question 269

waec 2013

Express \(\log \frac{1}{8} + \log \frac{1}{2}\) in terms of \(\log 2\).

A3 log 2

B4 log 2

C-3 log 2

D-4 log 2

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Question 270

waec 2013

Given that \(a^{\frac{5}{6}} \times a^{\frac{-1}{n}} = 1\), solve for n.

A-6.00

B-1.20

C0.83

D1.20

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