2008 WAEC SSCE Further Mathematics Past Questions

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2008

(a) An object is thrown up a smooth plane inclined at an angle of 30° to the horizontal. If the plane is 15m long and the object comes to rest at the top, find the :(i) initial speed of the object ; (ii) time taken to re…

2008

(a) Forces \(F_{1} = \begin{pmatrix} -5 & 4 \end{pmatrix} N; F_{2} = \begin{pmatrix} 2 \\ 5 \end{pmatrix} N; F_{3} = \begin{pmatrix} 2 & -1 \end{pmatrix} N\) and \(F_{4} = \begin{pmatrix} 3 & -5 \end{pmatrix}…

2008

The position vectors of points P, Q and R with respect to the origin are \((4i - 5j), (i + 3j)\) and \((-5i + 2j)\) respectively. If PQRM is a parallelogram, find:(a) the position vector of M ;(b) \(|\overrightarrow{PM}|…

2008

(a) Five female and seven male teachers applied for 4 vacancies in a Junior High School. The teachers are equally qualified. Find the number of ways of employing the 4 teachers, if : (i) there is no restriction ; (ii) at…

2008

The following table shows the distribution of marks obtained by some students in an examination.Marks0-910-1920-2930-3940-4950-5960-6970-7980-8990-99Frequency5050406010010050251510(a) Construct a cumulative frequency tab…

2008

A survey indicated that 65% of the families in an area have cars. Find, correct to three decimal places, the probability that among 7 families selected at random in the area(a) exactly 5 ;(b) 3 or 4 ;(c) at most 2 of the…

2008

(a) The point P(3, -5) is rotated through an angle 60° anticlockwise about the origin. (i) Obtain the matrix for the rotation ; (ii) Find the image P' of the point P under the rotation.(b) A linear transformation is give…

2008

(a) Express \(\frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x}\) in partial fractions.(b) If \(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2 \\ 2 & -4 & 6 - x \end{vmatrix} = -24\), find the value of x.

2008

(a) If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x - 6 = 0\), find the equation whose roots are \((\alpha - 2)\) and \((\beta - 2)\).(b) Given that \(\int_{0} ^{k} (x^{2} - 2x) \mathrm {d} x = 4\…

2008

(a) The sum of the first n terms of a sequence is given by \(S_{n} = \frac{5n^{2}}{2} + \frac{5n}{2}\). Write down the first four terms of the sequence and an expression for the nth term.(b) The equation of a circle is g…

2008

The magnitude of a force \(xi + 15j\) is 17N. Find the :(a) possible values of x ; (b) directions of the forces, correct to the nearest degree.

2008

A car travelling at a velocity of 50kmh\(^{-1}\), covers a distance of 20km. If it was accelerating at 6kmh\(^{-2}\), calculate, correct to one decimal place, the time the car took to cover the distance.

2008

The table shows the distribution of marks obtained by some candidates in a test.Marks10-1415-2425-2930-3940-4445-49No of candidates14302218124Draw a histogram for the distribution.

2008

In a hotel, the breakfast is a choice between yam (Y) or plantain (P) or both. The Venn diagram shows the choices made by 25 guests of the hotel.(a) Find the value of x;(b) What is the probability that a guest chosen at…

2008

A straight line passes through the point P(-1, 3). Another line which passes through Q(-4, 4) intersects the first line at the point R(k, 5), where k is a constant. If \(

2008

Differentiate, with respect to x, \(x^{3} + 2x\) from the first principle.

2008

If \(\sin A = \frac{3}{5}\) and \(\cos B = \frac{15}{17}\), where A is an obtuse angle and B is acute, find the value of \(\cos (A + B)\).

2008

A function F is defined on the set R, of real numbers by \(f : x \to px^{2} + qx + 2\), where p and q are constants. If \(f(-2) = 0\) and \(f(1) = 3\), find \(f(-4)\).

2008

In the diagram above, forces P, Q and 50N are acting on a body at M. If the system is in equilibrium, calculate, in terms of \(\theta\), the magnitude of P.

2008 WAEC SSCE Further Mathematics Past Questions

(a) An object is thrown up a smooth plane inclined at an angle of 30° to the horizontal. If the plane is 15m long and the object comes to rest at the top, find the :(i) initial speed of the object ; (ii) time taken to re…

(a) Forces \(F_{1} = \begin{pmatrix} -5 &amp; 4 \end{pmatrix} N; F_{2} = \begin{pmatrix} 2 \\ 5 \end{pmatrix} N; F_{3} = \begin{pmatrix} 2 &amp; -1 \end{pmatrix} N\) and \(F_{4} = \begin{pmatrix} 3 &amp; -5 \end{pmatrix}…

The position vectors of points P, Q and R with respect to the origin are \((4i - 5j), (i + 3j)\) and \((-5i + 2j)\) respectively. If PQRM is a parallelogram, find:(a) the position vector of M ;(b) \(|\overrightarrow{PM}|…

(a) Five female and seven male teachers applied for 4 vacancies in a Junior High School. The teachers are equally qualified. Find the number of ways of employing the 4 teachers, if : (i) there is no restriction ; (ii) at…

The following table shows the distribution of marks obtained by some students in an examination.Marks0-910-1920-2930-3940-4950-5960-6970-7980-8990-99Frequency5050406010010050251510(a) Construct a cumulative frequency tab…

A survey indicated that 65% of the families in an area have cars. Find, correct to three decimal places, the probability that among 7 families selected at random in the area(a) exactly 5 ;(b) 3 or 4 ;(c) at most 2 of the…

(a) The point P(3, -5) is rotated through an angle 60° anticlockwise about the origin. (i) Obtain the matrix for the rotation ; (ii) Find the image P' of the point P under the rotation.(b) A linear transformation is give…

(a) Express \(\frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x}\) in partial fractions.(b) If \(\begin{vmatrix} x - 3 &amp; -4 &amp; 3 \\ 5 &amp; 2 &amp; 2 \\ 2 &amp; -4 &amp; 6 - x \end{vmatrix} = -24\), find the value of x.

(a) If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} + 5x - 6 = 0\), find the equation whose roots are \((\alpha - 2)\) and \((\beta - 2)\).(b) Given that \(\int_{0} ^{k} (x^{2} - 2x) \mathrm {d} x = 4\…

(a) The sum of the first n terms of a sequence is given by \(S_{n} = \frac{5n^{2}}{2} + \frac{5n}{2}\). Write down the first four terms of the sequence and an expression for the nth term.(b) The equation of a circle is g…

The magnitude of a force \(xi + 15j\) is 17N. Find the :(a) possible values of x ; (b) directions of the forces, correct to the nearest degree.

A car travelling at a velocity of 50kmh\(^{-1}\), covers a distance of 20km. If it was accelerating at 6kmh\(^{-2}\), calculate, correct to one decimal place, the time the car took to cover the distance.

The table shows the distribution of marks obtained by some candidates in a test.Marks10-1415-2425-2930-3940-4445-49No of candidates14302218124Draw a histogram for the distribution.

In a hotel, the breakfast is a choice between yam (Y) or plantain (P) or both. The Venn diagram shows the choices made by 25 guests of the hotel.(a) Find the value of x;(b) What is the probability that a guest chosen at…

A straight line passes through the point P(-1, 3). Another line which passes through Q(-4, 4) intersects the first line at the point R(k, 5), where k is a constant. If \(

Differentiate, with respect to x, \(x^{3} + 2x\) from the first principle.

If \(\sin A = \frac{3}{5}\) and \(\cos B = \frac{15}{17}\), where A is an obtuse angle and B is acute, find the value of \(\cos (A + B)\).

A function F is defined on the set R, of real numbers by \(f : x \to px^{2} + qx + 2\), where p and q are constants. If \(f(-2) = 0\) and \(f(1) = 3\), find \(f(-4)\).

In the diagram above, forces P, Q and 50N are acting on a body at M. If the system is in equilibrium, calculate, in terms of \(\theta\), the magnitude of P.

The distance between P(x, 7) and Q(6, 19) is 13 units. Find the values of x.

(a) Forces \(F_{1} = \begin{pmatrix} -5 & 4 \end{pmatrix} N; F_{2} = \begin{pmatrix} 2 \\ 5 \end{pmatrix} N; F_{3} = \begin{pmatrix} 2 & -1 \end{pmatrix} N\) and \(F_{4} = \begin{pmatrix} 3 & -5 \end{pmatrix}…

(a) Express \(\frac{2x^{2} - 5x + 1}{x^{3} - 4x^{2} + 3x}\) in partial fractions.(b) If \(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2 \\ 2 & -4 & 6 - x \end{vmatrix} = -24\), find the value of x.