2006 WAEC SSCE Further Mathematics Past Questions

2006

(a) A body of mass 5 kg is placed on a smooth plane inclined at an angle 30° to the horizontal. Find the magnitude of the force: (i) acting parallel to the plane (ii) required to keep the body in equilibrium. [Take g = \…

2006

(a) A ball P moving with velocity \(2u ms^{-1}\), collides with a similar ball Q, of different mass, which is at rest. After collision, Q moves with \(u ms^{-1}\) and P with velocity \(\frac{1}{2} u ms^{-2}\), in the opp…

2006

(a) A body of mass 15 kg is suspended at a point P by two light inextensible strings \(\overrightarrow{XP}\) and \(\overrightarrow{YP}\). The strings are inclined at 60° and 40° respectively to the downward vertical. Fin…

2006

(a) Two pupils are chosen at random from a group of 4 boys and 5 girls. Find the probability that the two pupils chosen would be boys.(b) Twenty percent of the total production of transistors produced by a machine are be…

2006

The table shows the distribution of hours spent at work by the employees of a factory in a week.Time (in hours)20 - 2930 - 3940 - 4950 - 5960 - 6970 - 79No of persons811232585(a) Draw an ogive for the distribution.(b) Us…

2006

(a) A man P has 5 red, 3 blue and 2 white buses. Another man Q has 3 red, 2 blue and 4 white buses. A bus owned by P is involved in an accident with a bus belonging to Q. Calculate the probability that the two buses are…

2006

(a) Using the substitution \(u = 5 - x^{2}\), evaluate \(\int_{1}^{2} \frac{x}{\sqrt{5 - x^{2}}} \mathrm {d} x\).(b) If \(y = px^{2} + qx; \frac{\mathrm d y}{\mathrm d x} = 6x + 7\) and \(\frac{\mathrm d^{2} y}{\mathrm d…

2006

(a) The gradient of the tangent to the curve \(y = 4x^{3}\) at points P and Q is 108. Find the coordinates of P and Q.(b) Given that \(A = 45°, B = 30°, \sin (A + B) = \sin A \cos B + \sin B \cos A\) and \(\cos (A + B) =…

2006

(a) Simplify \(\frac{\sqrt{75} - 3}{\sqrt{3} + 1}\), leaving your answer in the form \(a + b\sqrt{c}\); where a, b and c are rational numbers.(b) The points (7, 3), (2, 8) and (-3, 3) lie on a circle. Find the (i) equati…

2006

An object is projected vertically upwards with a velocity of 80 m/s. Find the :(a) Maximum height reached(b) Time taken to return to the point of projection. [Take g = \(10 ms^{-2}\)].

2006

A body of mass 5 kg resting on a smooth horizontal plane, is acted upon by force 6i + 2j, 5i + 4j and 4i - j. Calculate the:(a) velocity of the body(b) Magnitude of its velocity after 4s.

2006

The table shows the distribution of the ages of a group of people in a village.Ages (in years)15 - 1819 - 2223 - 2627 - 3031 - 3435 - 38Frequency4033251084Using an assumed mean of 24.5, calculate the mean of the distribu…

2006

(a) There are 6 points in a plane. How many triangles can be formed with the points?(b) A family of 6 is to be seated in a row . In how many ways can this be done if the father and mother are not to be seated together?

2006

Find the equation of the tangent to the curve \(y = \frac{x - 1}{2x + 1}, x \neq -\frac{1}{2}\) at the point (1, 0).

2006

If (x + 2) and (x - 1) are factors of \(f(x) = 6x^{4} + mx^{3} - 13x^{2} + nx + 14\), find the (a) values of m and n.(b) remainder when f(x) is divided be (x + 1).

2006

If \(2^{2x - 3y} = 32\) and \(\log_{y} x = 2\), find the values of x and y.

2006

The sum of the 2nd and 5th terms of an arithmetic progression (AP) is 42. If the difference between the 6th and 3rd term is 12, find the (i) Common difference(ii) first term(iii) 20th term.

2006

Two functions f and g are defined by \(f : x \to 3x - 1\) and \(g : x \to 2x^{3}\), evaluate \(fg(-2)\).

2006

If \((x - 3)\) is a factor of \(2x^{3} + 3x^{2} - 17x - 30\), find the remaining factors.

2006

A binary operation â™¦ is defined on the set R, of real numbers by \(aÂ â™¦ b = \frac{ab}{4}\). Find the value of \(\sqrt{2}Â â™¦ \sqrt{6}\).

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