Waec Further Mathematics 2008 Past Questions and Answers

Question 56:

• WAEC 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 least 2 of them are females.
(b) The table shows the positions awarded to 7 contestants by Judges X and Y in a competition.

Contestant	P	Q	R	S	T	U	V
Judge X	2	7	1	3	6	5	4
Judge Y	4	6	2	3	1	1	5

(i) Calculate, correct to one decimal place, the Spearman's rank correlation coefficient.
(ii) Interpret your answer in b(i) above.

Question 57:

• WAEC 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) $|\overrightarrow{PM}|$ and $|\overrightarrow{PQ}|$ ;
(c) the acute angle between $\overrightarrow{PM}$ and $\overrightarrow{PQ}$, correct to 1 decimal place ;
(d) the area of PQRM.

Question 58:

• WAEC 2008

(a) Forces $F_1=\left(\begin{array}{cc}-5& 4\end{array}\right)N;F_2=\left(\begin{array}{c}2\\ 5\end{array}\right)N;F_3=\left(\begin{array}{cc}2& -1\end{array}\right)N$ and $F_4=\left(\begin{array}{cc}3& -5\end{array}\right)N$ act on a body. Find the :
(i) resultant of these forces ; (ii) fifth force that will keep the body in equilibrium.
(b) A body moving at 20 ms${}^{-1}$ accelerates uniformly at 2.5 ms${}^{-2}$ for 4 seconds. It continues the journey at the speed for 8 seconds, before coming to rest in t seconds with a uniform retardation. If the ratio of the acceleration to the retardation is 3 : 4,
(i) sketch the velocity- time graph of the journey ; (ii) find t ; (iii) find the total distance of the journey.