2013
The displacement S metres of a particle from a fixed point O at time t seconds is given by \(S = t^{2} - 6t + 5\).(a) On a graph sheet, draw a displacement- time graph for the interval \(0 \leq x \leq 6\).(b) From the gr…
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2013 WAEC SSCE Further Mathematics Past Questions
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2013
A particle is under the action of forces \(P = (4N, 030°)\) and \(R = (10N, 300°)\). Find the force that will keep the particle in equilibrium.
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2013
(a) Three vectors a, b and c are \(\begin{pmatrix} 8 \\ 3 \end{pmatrix}, \begin{pmatrix} 6 \\ -5 \end{pmatrix}\) and \(\begin{pmatrix} 2 \\ -3 \end{pmatrix}\) respectively. Find the vector d such that \(|d| = \sqrt{41}\)…
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2013
(a) The probability that a man wins a race is 0.8. In four different races, what is the probability that he wins : (i) all races ; (ii) no race ; (iii) at most 3 races ?(b) A class consists of 5 girls and 10 boys. If a c…
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2013
(a) A bag contains 5 blue, 4 green and 3 yellow balls. All the balls are identical except for colour. Three balls are drawn at random without replacement. Find the probability that : (i) all three balls have the same col…
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2013
The table gives the relationship between the height, in metres, of a plant and the number of days it is left to grow.Number of days(x)1020304050607080Height (y)1.01.11.21.41.61.82.02.3(a) Using a scale of 2 cm to represe…
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2013
(a) Find the maximum and minimum points of the curve \(y = 2x^{3} - 3x^{2} - 12x + 4\).(b) Sketch the curve in (a) above.
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2013
(a) The sum of the first three terms of a decreasing exponential sequence (G.P) is equal to 7 and the product of these three is equal to 8. Find the :(i) common ratio ; (ii) first three terms of the sequence.(b) Using th…
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2013
(a) Using a scale of 2 cm to 30° on the x- axis, 2 cm to 0.2 units on the y- axis, on the same graph sheet, draw the graphs of \(y = \sin 2x\) and \(y = \cos x\) for \(0° \leq x \leq 210°\) at intervals of 30°.(b) Using…
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2013
(a) Differentiate \(\frac{x^{2} + 1}{(x + 1)^{2}}\) with respect to x.(b)(i) Evaluate \(\begin{vmatrix} 1 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \end{vmatrix}\).(ii) Using the answer in (b)(i), solv…
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2013
A stone is dropped vertically downwards from the top of a tower of height 45m with a speed of 20 ms\(^{-1}\). Find the :(a) time it takes to reach the ground ;(b) speed with which it hits the ground. [Take \(g = 10 ms^{-…
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2013
The initial velocity of a particle of mass 0.1kg is 40 m/s in the direction of the unit vector j. The velocity of the particle changed to 30 m/s in the direction of the unit vector i. Find the change in momentum.
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2013
The table shows the distribution of ages of 22 students in a school.Age (years)12-1415-1718-2021-2324-26Frequency610321Using an assumed mean of 19, calculate, correct to three significant figures, the :(a) mean age ; (b)…
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2013
Three school prefects are to be chosen from four girls and five boys. What is the probability that :(a) only boys will be chosen ;(b) more girls than boys will be chosen ?
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2013
The line \(2y = x + 3\) meets the circle \(x^{2} + y^{2} - 2x + 6y - 15 = 0\) at points M and N, where N is in the first quadrant. Find the coordinates of M and N.
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2013
A side of a rectangle is three times the other. If the perimeter increases by 2%, find the percentage increase in the area of the rectangle.
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2013
Calculate the gradient of the curve \(x^{3} + y^{3} - 2xy = 11\) at (2, -1).
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2013
(a) If the coefficient of \(x^{2}\) and \(x^{3}\) in the expansion of \((p + qx)^{7}\) are equal, express q in terms of p.(b) A man makes a weekly contribution into a fund. In the first week, he paid N180.00, second week…
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2013
A body is kept at rest by three forces \(F_{1} = (10N, 030°), F_{2} = (10N, 150°)\) and \(F_{3}\). Find \(F_{3}\).
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2013
If \(\frac{^{n}C_{3}}{^{n}P_{2}} = 1\), find the value of n.
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