2010 WAEC SSCE Further Mathematics Past Questions

2010

(a) The position vectors of the points X and Y are \(x = (-2i + 5j)\) and \(y = (i - 7j)\) respectively. Find :(i) (3x + 2y) ; (ii) \(|(y - 2x)|\) ; (iii) the angle between x and y ; (iv) the unit vector in the direction…

2010

A particle moves from point O along a straight line such that its acceleration at any time, t seconds is \(a = (4 - 2t) ms^{-2}\). At t = 0, its distance from O is 18 metres while its velocity is \(5 ms^{-1}\).(a) At wha…

2010

(a) Two ships M and N, moving with constant velocities, have position vectors (3i + 7j) and (4i + 5j) respectively. If the velocities of M and N are (5i + 6j) and (2i + 3j) and the distance covered by the ships after t s…

2010

(a) A manufacturer produces light bulbs which are tested in the following way. A batch is accepted in either of the following cases:(i) a first sample of 5 bulbs contains no faulty bulbs ; (ii) a first sample of 5 bulbs…

2010

(a) Eight coins are tossed at once. Find, correct to three decimal places, the probability of obtaining :(i) exactly 8 heads ; (ii) at least 5 heads ; (iii) at most 1 head.(b) In how many ways can four letters from the w…

2010

The table gives the distribution of marks of 60 candidates in a test.Marks23-2526-2829-3132-3435-3738-40Frequency371521104(a) Draw a cumulative frequency curve of the distribution.(b) From your curve, estimate the : (i)…

2010

The images of (3, 2) and (-1, 4) under a linear transformation T are (-1, 4) and (7, 11) respectively. P is another transformation where \(P : (x, y) \to (x + y, x + 2y)\).(a) Find the matrices T and P of the linear tran…

2010

(a) If \(y = (2x + 3)^{7} + \frac{x + 1}{2x - 1}\), find the value of \(\frac{\mathrm d y}{\mathrm d x}\) at x = -1.(b) Using the substitution, \(u = x + 2\), evaluate \(\int_{1} ^{2} \frac{x - 1}{(x + 2)^{4}} \mathrm d…

2010

(a) Copy and complete the table for the relation: \(y = 2\cos x + 3\sin x\) for \(0° \leq x \leq 360°\).x0°30°60°90°120°150°180°210°y2.003.231.60-3.23(b) Using a scale of 2 cm to 60° on the x- axis and 2 cm to one unit o…

2010

(a) The nth term of a sequence is given by \(T_{n} = 4T_{n - 1} - 3\). If twice the third term is five times the second term, find the first three terms of the sequence.(b) Given that \(\begin{pmatrix} 2 & 0 & 1…

2010

A uniform plank PQ of length 8m and mass 10kg is supported horizontally at the end P and at point R, 3 metres from Q. A boy of mass 20 kg walks along the plank starting from P. If the plank is in equilibrium, calculate t…

2010

The position vector of a particle of mass 3 kg moving along a space curve is given by \(r = (4t^{3} - t^{2})i - (2t^{2} - t)j\) at any time t seconds. Find the force acting on it at t = 2 seconds.

2010

The table shows the marks obtained by a group of students in a class test.Marks40 - 4445 - 4950 - 5455 - 5960 - 6465 - 69No ofstudents491823106(a) Draw a histogram for the distribution ;(b) Use your histogram to estimate…

2010

Five students are to be selected from a large population. If 60% of them are boys and the rest are girls, find the probability that :(a) exactly 3 of them are boys;(b) at least 3 of them are girls.

2010

If \(3x^{2} + 2y^{2} + xy + x - 7 = 0\), find \(\frac{\mathrm d y}{\mathrm d x}\) at the point (-2, 1).

2010

The equation of a curve is \(y = x(3 - x^{2})\). Find the equation of its normal of the point where x = 2.

2010

If the quadratic equation \((2x - 1) - p(x^{2} + 2) = 0\), where p is a constant, has real roots :(a) show that \(2p^{2} + p - 1 < 0\);(b) find the values of p.

2010

(a) Express \(\frac{2\sqrt{2}}{\sqrt{48} - \sqrt{8} - \sqrt{27}}\) in the form \(p + q\sqrt{r}\), where p, q and r are rational numbers. (b) If \(V = A\log_{10} (M + N)\), express N in terms of M, V and A.

2010

Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)

2010

Find the maximum value of \(2 + \sin (\theta + 25)\).

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2010 WAEC SSCE Further Mathematics Past Questions

(a) The position vectors of the points X and Y are \(x = (-2i + 5j)\) and \(y = (i - 7j)\) respectively. Find :(i) (3x + 2y) ; (ii) \(|(y - 2x)|\) ; (iii) the angle between x and y ; (iv) the unit vector in the direction…

A particle moves from point O along a straight line such that its acceleration at any time, t seconds is \(a = (4 - 2t) ms^{-2}\). At t = 0, its distance from O is 18 metres while its velocity is \(5 ms^{-1}\).(a) At wha…

(a) Two ships M and N, moving with constant velocities, have position vectors (3i + 7j) and (4i + 5j) respectively. If the velocities of M and N are (5i + 6j) and (2i + 3j) and the distance covered by the ships after t s…

(a) A manufacturer produces light bulbs which are tested in the following way. A batch is accepted in either of the following cases:(i) a first sample of 5 bulbs contains no faulty bulbs ; (ii) a first sample of 5 bulbs…

(a) Eight coins are tossed at once. Find, correct to three decimal places, the probability of obtaining :(i) exactly 8 heads ; (ii) at least 5 heads ; (iii) at most 1 head.(b) In how many ways can four letters from the w…

The table gives the distribution of marks of 60 candidates in a test.Marks23-2526-2829-3132-3435-3738-40Frequency371521104(a) Draw a cumulative frequency curve of the distribution.(b) From your curve, estimate the : (i)…

The images of (3, 2) and (-1, 4) under a linear transformation T are (-1, 4) and (7, 11) respectively. P is another transformation where \(P : (x, y) \to (x + y, x + 2y)\).(a) Find the matrices T and P of the linear tran…

(a) If \(y = (2x + 3)^{7} + \frac{x + 1}{2x - 1}\), find the value of \(\frac{\mathrm d y}{\mathrm d x}\) at x = -1.(b) Using the substitution, \(u = x + 2\), evaluate \(\int_{1} ^{2} \frac{x - 1}{(x + 2)^{4}} \mathrm d…

(a) Copy and complete the table for the relation: \(y = 2\cos x + 3\sin x\) for \(0° \leq x \leq 360°\).x0°30°60°90°120°150°180°210°y2.003.231.60-3.23(b) Using a scale of 2 cm to 60° on the x- axis and 2 cm to one unit o…

(a) The nth term of a sequence is given by \(T_{n} = 4T_{n - 1} - 3\). If twice the third term is five times the second term, find the first three terms of the sequence.(b) Given that \(\begin{pmatrix} 2 &amp; 0 &amp; 1…

A uniform plank PQ of length 8m and mass 10kg is supported horizontally at the end P and at point R, 3 metres from Q. A boy of mass 20 kg walks along the plank starting from P. If the plank is in equilibrium, calculate t…

The position vector of a particle of mass 3 kg moving along a space curve is given by \(r = (4t^{3} - t^{2})i - (2t^{2} - t)j\) at any time t seconds. Find the force acting on it at t = 2 seconds.

The table shows the marks obtained by a group of students in a class test.Marks40 - 4445 - 4950 - 5455 - 5960 - 6465 - 69No ofstudents491823106(a) Draw a histogram for the distribution ;(b) Use your histogram to estimate…

Five students are to be selected from a large population. If 60% of them are boys and the rest are girls, find the probability that :(a) exactly 3 of them are boys;(b) at least 3 of them are girls.

If \(3x^{2} + 2y^{2} + xy + x - 7 = 0\), find \(\frac{\mathrm d y}{\mathrm d x}\) at the point (-2, 1).

The equation of a curve is \(y = x(3 - x^{2})\). Find the equation of its normal of the point where x = 2.

If the quadratic equation \((2x - 1) - p(x^{2} + 2) = 0\), where p is a constant, has real roots :(a) show that \(2p^{2} + p - 1 &lt; 0\);(b) find the values of p.

(a) Express \(\frac{2\sqrt{2}}{\sqrt{48} - \sqrt{8} - \sqrt{27}}\) in the form \(p + q\sqrt{r}\), where p, q and r are rational numbers. (b) If \(V = A\log_{10} (M + N)\), express N in terms of M, V and A.

Simplify \((1 + 2\sqrt{3})^{2} - (1 - 2\sqrt{3})^{2}\)

Find the maximum value of \(2 + \sin (\theta + 25)\).

(a) The nth term of a sequence is given by \(T_{n} = 4T_{n - 1} - 3\). If twice the third term is five times the second term, find the first three terms of the sequence.(b) Given that \(\begin{pmatrix} 2 & 0 & 1…

If the quadratic equation \((2x - 1) - p(x^{2} + 2) = 0\), where p is a constant, has real roots :(a) show that \(2p^{2} + p - 1 < 0\);(b) find the values of p.