(a) If \(f(x) = \frac{x - 3}{2x - 1} , x \neq \frac{1}{2}\) and \(g(x) = \frac{x - 1}{x + 1}, x \neq -1\), fing \(g \circ f\).

(b)(i) Sketch the curve \(y = 9x - x^{3}\) ; (ii) Calculate the total area bounded by the x- axis and the curve \(y = 9x - x^{3}\).

The histogram above represents the scores of some candidates in an examination. 

(a) Using the histogram, construct a frequency distribution table indicating clearly the class intervals ;

(b) Draw a cumulative frequency curve of the distribution and use it to estimate the :

(i) median ; (ii) quartile deviation.

The probabilities that Kofi, Kwasi and Ama will pass a certain examination are \(\frac{9}{10}, \frac{4}{5}\) and x respectively. If the probability that only one of them will pass the examination is \(\frac{9}{50}\), find the :

(a) value of x ; 

(b) probability that at least one of them will pass the examination.

(a) Given that \(x = 3i - j, y = 2i + kj\) and the cosine of the angle between x and y is \(\frac{\sqrt{5}}{5}\), find the values of the constant k.

(b) In the quadrilateral ABCD, 

 \(\overrightarrow{AB} = \begin{pmatrix} -5 \\ -1 \end{pmatrix}, \overrightarrow{AC} = \begin{pmatrix} -6 \\ -9 \end{pmatrix}\)

and \(\overrightarrow{BD} = \begin{pmatrix} 4 \\ -7 \end{pmatrix}\). Show whether or not ABCD is a parallelogram.

(a) A(-1, 2), B(3, 5) and C(4, 8) are the vertices of triangle ABC. Forces whose magnitudes are 5N and \(3\sqrt{10}\)N act along \(\overrightarrow{AB}\) and \(\overrightarrow{CB}\) respectively. Find the direction of the resultant of the forces.

(b) A particle starts from rest and moves in a straight line. It attains a velocity of 20 m/s after covering a distance of 8 metres. Calculate : 

(i) its acceleration ; (ii) the time it will take to cover a distance of 40 metres.