2012
(a) Find the angle between the vectors \(a = \begin{pmatrix} -3 \\ 4 \end{pmatrix}\) and \(b = \begin{pmatrix} -8 \\ -15 \end{pmatrix}\).(b) Given that \(a = (4N, 060°)\) and \(b = (3N, 120°)\), find, in component form,…
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2012 WAEC SSCE Further Mathematics Past Questions
2012
(a) Given that \(p = (4i - 3j)\) and \(q = (-i + 5j)\), find r such that \(|r| = 15\) and is in the direction \((2p + 3q)\).(b) Forces of magnitude 8N, 6N and 4N act at the point P, as shown in the above diagram. Find th…
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2012
(a) A body P of mass 5kg is suspended by two light inextensible strings AP and BP attached to a ceiling. If the strings are inclined at angles 40° and 30° respectively to the downward vertical, find the tension in each o…
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2012
(a) Two items are selected at random from four items labelled (p, q, r, s).(i) List the sample space if sampling is done (1) with replacement ; (2) without replacement.(ii) Find the probability that r is at least one of…
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2012
The table gives the distribution of heights in metres of 100 students.Height1.40-1.421.43-1.451.46-1.481.49-1.511.52-1.541.55-1.571.58-1.601.61-1.63Freq241930241461(a) Calculate the : (i) mean height ; (ii) mean deviatio…
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2012
(a) A fair die with six faces is thrown six times. Calculate, correct to three decimal places, the probability of obtaining :(i) exactly three sixes ; (ii) at most three sixes.(b) Eight percent of screws produced by a ma…
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2012
(a)(i) Find the sum of the series \(A(1 + r) + A(1 + r)^{2} + ... + A(1 + r)^{n}\).(ii) Given that r = 8% and A = GH 40.00, find the sum of the 6th to 10th terms of the series in (i).(b) Find the equation of the tangent…
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2012
(a) Evaluate : \(\int_{1} ^{4} \frac{x(3x - 2)}{2\sqrt{x}} \mathrm {d} x\)(b) The equation of a circle is given by \(2x^{2} + 2y^{2} - 8x + 5y - 10 = 0\). Find the :(i) coordinates of the centre ; (ii) radius of the circ…
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2012
(a) Write down the matrix A of the linear transformation \(A(x, y) \to (2x -y, -5x + 3y)\).(b) If \(B = \begin{pmatrix} 3 & 1 \\ 5 & 2 \end{pmatrix}\), find :(i) \(A^{2} - B^{2}\) ; (ii) matrix \(C = B^{2} A\) ;…
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2012
(a) The polynomial \(f(x) = x^{3} + px^{2} - 10x + q\) is exactly divisible by \(x^{2} + x - 6\). Find the :(i) values of p and q ; (ii) third factor.(b) The volume of a cube is increasing at the rate of \(2\frac{1}{2} c…
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2012
The marks scored by 35 students in a test are given in the table below.Marks1-56-1011-1516-2021-2526-30Frequency2712851Draw a histogram for the distribution.
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2012
Simplify \(^{n + 1}C_{4} - ^{n - 1}C_{4}\)
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2012
Three forces \(-63j , 32.14i + 38.3j\) and \(14i - 24.25j\) act on a body of mass 5kg. Find, correct to one decimal place, the :(a) magnitude of the resultant force ;(b) acceleration of the body.
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2012
The gradient function of \(y = ax^{2} + bx + c\) is \(8x + 4\). If the function has a minimum value of 1, find the values of a, b and c.
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2012
Write down the first three terms of the binomial expansion \((1 + ax)^{n}\) in ascending powers of x. If the coefficients of x and x\(^{2}\) are 2 and \(\frac{3}{2}\) respectively, find the values of a and n.
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2012
The twenty-first term of an Arithmetic Progression is \(5\frac{1}{2}\) and the sum of the first twenty-one terms is \(94\frac{1}{2}\). Find the :(a) first term ; (b) common difference ; (c) sum of the first thirty terms.…
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2012
Express \(3x^{2} - 6x + 10\) in the form \(a(x - b)^{2} + c\), where a, b and c are integers. Hence state the minimum value of \(3x^{2} - 6x + 10\) and the value of x for which it occurs.
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2012
Two functions g and h are defined on the set R of real numbers by \(g : x \to x^{2} - 2\) and \(h : x \to \frac{1}{x + 2}\). Find : (a) \(h^{-1}\), the inverse of h ;(b) \(g \circ h\), when \(x = -\frac{1}{2}\).
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2012
Simplify \(\frac{x^{3n + 1}}{x^{2n + \frac{5}{2}}(x^{2n - 3})^{\frac{1}{2}}}\)
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2012
The diagram above is a velocity-time graph of a moving object. Calculate the distance traveled when the acceleration is zero.
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