2009
(a) The position vectors of points A, B and C are \(i + 5j , 3i + 9j\) and \(-i + j\) respectively. (i) Show that points A, B and C are collinear; (ii) Determine the ratio \(|AB| : |BC|\).(b) A uniform beam XY of mass 10…
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2009 WAEC SSCE Further Mathematics Past Questions
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2009
Coplanar force 4N, 8N, 6N, 4N and 5N act at a point as shown in the diagram. If the 6N force acts in the direction 090°, calculate the :(a) magnitude of the resultant force;(b) direction of the resultant force.
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2009
(a) The position vectors of points L and M are (5i + 6j) and (13i + 4j) respectively. If point K lies on LM such that LK : KM is 2 : 3, find the position vector of K.(b) Three poles are situated at points A, B and C on t…
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2009
The table below shows the corresponding values of two variables X and Y.X33312825232219171614Y46410121014151822(a) Plot a scatter diagram to represent the data.(b) Calculate \(\bar{x}\), the mean of X and \(\bar{y}\), th…
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2009
(a) The distribution of the lives (in days) of 40 transitor batteries is shown in the table:Battery life(in days)26-3031-3536-4041-4546-5051-55Frequency4713862(a) Draw a histogram for the distribution.(b) Use your graph…
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2009
(a) Simplify \(^{n + 1}C_{3} - ^{n - 1}C_{3}\)(b) A fair die is thrown five times. Calculate, correct to three decimal places, the probability of obtaining (i) at most two sixes ; (ii) exactly three sixes.
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2009
(a) Use the trapezium rule with five ordinates to evaluate \(\int_{0} ^{1} \frac{3}{1 + x^{2}} \mathrm {d} x\), correct to four significant figures.(b) If \(A = \begin{pmatrix} 2 & 1 \\ 3 & 2 \end{pmatrix}\), fin…
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2009
(a) Evaluate \(\int_{1} ^{2} \frac{x}{\sqrt{5 - x^{2}}} \mathrm {d} x\)(b)(i) Evaluate: \(\begin{vmatrix} 2 & -3 & 1 \\ 0 & 1 & -2 \\ 1 & 2 & -3 \end{vmatrix}\)(ii) Using your answer in b(i), solv…
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2009
(a) Using the same axes, sketch the curves \(y = 6 - x - x^{2}\) and \(y = 3x^{2} - 2x + 3\).(b) Find the x- coordinates of the points of intersection of the two curves in (a).(c) Calculatethe area of the finite region b…
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2009
(a) The 3rd and 6th terms of a Geometric Progression (G.P) are 2 and 54 respectively. Find the : (i) common ratio ; (ii) first term ; (iii) sum of the first 10 terms, correct to the nearest whole number. (b) The ratio of…
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2009
The position vector of a body, with respect to the origin, is given by \(r = 4ti + (12 - 3t)j\) at any time t seconds. (a) Find the velocity of the body ;(b) Calculate the magnitude of the displacement between t = 0 and…
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2009
The coordinates of the vertices of triangle ABC are A(-2, 1), B(4, -2) and C(1, 8) respectively. If D(x, y) is the foot perpendicular from A to BC, find (a) an equation connecting x and y ; (b) the unit vector in the dir…
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2009
A student representative council consists of 8 girls and 6 boys. If an editorial board consisting of 5 persons is to be formed, what is the probability that the board consists of(a) 3 girls and 2 boys ;(b) either all gir…
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2009
The probabilities of Rotey obtaining the highest mark in Mathematics, Physics and Biology tests are 0.9, 0.75 and 0.8 respectively. Calculate the probability of getting the highest marks in at least two of the subjects.
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2009
Given that \(\tan 2A = \frac{2 \tan A}{1 - \tan^{2} A}\), evaluate \(\tan 15°\), leaving your answer in surd form.
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2009
If the quadratic equation \((x + 1)(x + 2) = k(3x + 7)\) has equal roots, find the possible values of the constant k.
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2009
Solve the simultaneous equations : \(\log_{2} x - \log_{2} y = 2 ; \log_{2} (x - 2y) = 3\)
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2009
(a) Solve : \(2x^{2} + x - 6 < 0\)(b) Express \(\frac{5 - 2\sqrt{10}}{3\sqrt{5} + \sqrt{2}}\) in the form \(m\sqrt{2} + n\sqrt{5}\) where m and n are rational numbers.
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2009
In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find an expression for tan y.
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2009
In the diagram, a ladder PS leaning against a vertical wall PR makes angle x° with the horizontal floor. The ladder slides down to a point QT such that angle QTR = 30° and SNT = y°. Find the relation between x and y.
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