2014
(a) A(-1, 2), B(3, 5) and C(4, 8) are the vertices of triangle ABC. Forces whose magnitudes are 5N and \(3\sqrt{10}\)N act along \(\overrightarrow{AB}\) and \(\overrightarrow{CB}\) respectively. Find the direction of the…
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2014 WAEC SSCE Further Mathematics Past Questions
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2014
(a) Given that \(x = 3i - j, y = 2i + kj\) and the cosine of the angle between x and y is \(\frac{\sqrt{5}}{5}\), find the values of the constant k.(b) In the quadrilateral ABCD, \(\overrightarrow{AB} = \begin{pmatrix}…
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2014
The probabilities that Kofi, Kwasi and Ama will pass a certain examination are \(\frac{9}{10}, \frac{4}{5}\) and x respectively. If the probability that only one of them will pass the examination is \(\frac{9}{50}\), fin…
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2014
The histogram above represents the scores of some candidates in an examination. (a) Using the histogram, construct a frequency distribution table indicating clearly the class intervals ;(b) Draw a cumulative frequency cu…
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2014
(a) If \(f(x) = \frac{x - 3}{2x - 1} , x \neq \frac{1}{2}\) and \(g(x) = \frac{x - 1}{x + 1}, x \neq -1\), fing \(g \circ f\).(b)(i) Sketch the curve \(y = 9x - x^{3}\) ; (ii) Calculate the total area bounded by the x- a…
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2014
(a) Express \(\frac{5 + \sqrt{2}}{3 - \sqrt{2}} - \frac{5 - \sqrt{2}}{3 + \sqrt{2}}\) in the form \(a + b\sqrt{2}\).(b) Solve the following equations simultaneously using the determinant method.\(3x - y - z = -2\)\(x + 5…
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2014
(a) Differentiate \((x - 3)(x^{2} + 5)\) with respect to x.(b) If \((x + 1)^{2}\) is a factor of \(f(x) = x^{3} + ax^{2} + bx + 3\), where a and b are constants, find the :(i) values of a and b ; (ii) zeros of f(x).
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2014
Find the direction of the resultant of the forces in the diagram.
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2014
The table shows the distribution of the lengths of 20 iron rods measured in metres :Length (m)1.0 - 1.11.2 - 1.31.4 - 1.51.6 - 1.71.8 - 1.9Frequency23852Using an assumed mean of 1.45, calculate the mean of the distributi…
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2014
A committee of 3 is formed from a panel of 5 men and 3 women. Find the :(a) number of ways of forming the committee ;(b) probability that at least one woman is on the committee.
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2014
The position vectors of P, Q and R are \(11i + j, 5i + \frac{13}{3}j\) and \(2i + 6j\) respectively. (a) Show that P, Q and R lie on a straight line.(b) Find the ratio of \(|\overrightarrow{PQ}| : |\overrightarrow{QR}|\)…
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2014
Find the gradient of \(xy^{2} + x^{2} y = 4xy\) at the point (1, 3).
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2014
If \(\alpha\) and \(\beta\) are the roots of \(3x^{2} + 5x + 1 = 0\), evaluate \(27(\alpha^{3} + \beta^{3})\).
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2014
A binary operation \(\ast\) is defined on the set of rational numbers by \(m \ast n = \frac{m^{2} - n^{2}}{2mn}, m \neq 0 ; n \neq 0\).(a) Find \(-3 \ast 2\).(b) Show whether or not \(\ast\) is associative.
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2014
Solve \((\log_{2} m)^{2} - \log_{2} m^{3} = 10\).
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2014
Express (14N, 240°) as a column vector.
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2014
Evaluate \(\frac{\tan 120° + \tan 30°}{\tan 120° - \tan 60°}\)
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2014
Find \(\lim\limits_{x \to 3} (\frac{x^{3} + x^{2} - 12x}{x^{2} - 9})\)
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2014
Find the distance between the points (2, 5) and (5, 9).
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2014
A ball is thrown vertically upwards with a velocity of 15\(ms^{-1}\). Calculate the maximum height reached. \([g = 10ms^{-2}]\)
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