2011
(a) Forces \(F_{1} = (3N, 210°)\) and \(F_{2} = (4N, 120°)\) act on a particle of mass 7kg which is at rest. Calculate the :(i) acceleration of the particle ; (ii) velocity of the particle after 3 seconds.(b) \(F_{1} = (…
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2011 WAEC SSCE Further Mathematics Past Questions
2011
(a) \(m \begin{pmatrix} 2 \\ 1 \end{pmatrix} + n \begin{pmatrix} -1 \\ 2 \end{pmatrix} = \begin{pmatrix} 5 \\ -4 \end{pmatrix}\) where m and n are scalars. Find the value of (m + n).(b) A(-1, 3), B(2, -1) and C(5, 3) are…
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2011
(a) An object P of mass 6.5kg is suspended by two light inextensible strings, AP and BP. The strings make angles 50° and 60° respectively with the downward vertical.(i) Express the forces acting on P in component form; (…
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2011
A bag contains 4 red, 6 blue and 8 green identical marbles.(a) If three marbles are drawn at random, without replacement, calculate the probability that :(i) all will be green ; (ii) all will have the same colour.(b) If…
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2011
The table shows the frequency distribution of marks scored by some candidates in an examination.Marks0-910-1920-2930-3940-4950-5960-6970-7980-8990-99Freq2581820155421(a) Draw the cumulative frequency curve of the distrib…
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2011
A survey conducted revealed that four out of every twenty taxi drivers do not have a valid driving license. If 6 drivers are selected at random, calculate, correct to three decimal places, the probability that(a) exactly…
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2011
(a) Find the equation of the tangent to curve \(\frac{x^{2}}{4} + y^{2} = 1\) at point \(1, \frac{\sqrt{3}}{2}\).(b) Express \(\frac{3x + 2}{x^{2} + x - 2}\) in partial fractions.
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2011
The images of points (2, -3) and (4, 5) under a linear transformation A are (3, 4) and (5, 6) respectively. Find the :(a) matrix A ; (b) inverse of A ; (c) point whose image is (-1, 1).
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2011
(a) If \(A = \begin{pmatrix} -2 & 5 \\ 4 & 3 \end{pmatrix}\) and \(B = \begin{pmatrix} 3 & 1 \\ 2 & 3 \end{pmatrix}\), find the values of x and y such that \(BA = 2\begin{pmatrix} 3 & 7 \\ -2 & x…
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2011
(a) Find, from first principles, the derivative of \(f(x) = (2x + 3)^{2}\).(b) Evaluate : \(\int_{1} ^{2} \frac{(x + 1)(x^{2} - 2x + 2)}{x^{2}} \mathrm {d} x\)
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2011
A particle of mass 400g is moving under the action of two forces \(F_{1} = (35N, 210°), F_{2} = (35\sqrt{3} N, 300°)\) and a resistance of 40N. Find the magnitude of the (a) resultant of \(F_{1}\) and \(F_{2}\).(b) resul…
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2011
A tyre manufacturing company researched into the life span of one type of their motorcycle tyres. The results were as follows :Distance(100km)10-1920-2930-3940-4950-5960-69Number of tyres306993573615(a) Draw a histogram…
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2011
(a) Evaluate \(\frac{^{9}P_{3}}{^{15}C_{3}} + \frac{^{5}C_{3}}{^{3}P_{2}}\) correct to two decimal places.(b) A committee of 2 tutors and 5 pupils is to be formed among 6 tutors and 10 pupils. In how many ways can this b…
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2011
(a) Write the following as column vectors: \(r = (10N, 090°) ; q = (8N, 135°)\).(b) Use your answer in (a) to find \((r + q)\).
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2011
Solve \(2^{(2y + 2)} - 9(2^{y}) = -2\).
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2011
(a) Write down the binomial expansion of \((2 - x)^{5}\) in ascending powers of x.(b) Use your expansion in (a) to evaluate \((1.98)^{5}\) correct to four decimal places.
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2011
If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 7x + 4 = 0\), find the equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\).
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2011
If \(f(x) = 6x^{3} + 13x^{2} + 2x - 5\) and \(f(-1) = 0\), find the factors of f(x).
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2011
Find, correct to two decimal places, the acute angle between \(p = \begin{pmatrix} 13 \\ 14 \end{pmatrix}\) and \(q = \begin{pmatrix} 12 \\ 5 \end{pmatrix}\).
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2011
Find the unit vector in the direction of (-5i + 12j).
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