Further Mathematics 2012 Waec Past Questions and Answers

Question 46 :

• WAEC 2012

The gradient function of \(y = ax^{2} + bx + c\) is \(8x + 4\). If the function has a minimum value of 1, find the values of a, b and c.

Question 47 :

• WAEC 2012

Three forces \(-63j , 32.14i + 38.3j\) and \(14i - 24.25j\) act on a body of mass 5kg. Find, correct to one decimal place, the :
(a) magnitude of the resultant force ;
(b) acceleration of the body.

Question 48 :

• WAEC 2012

Simplify \(^{n + 1}C_{4} - ^{n - 1}C_{4}\)
= \(\frac{(n + 1)!}{4! (n - 3)!} - \frac{(n - 1)!}{4! (n - 5)!}\)
= \(\frac{(n + 1)(n)(n - 1)(n - 2)(n - 3)!}{4! (n - 3)!} - \frac{(n - 1)(n - 2)(n - 3)(n - 4)(n - 5)!}{4! (n - 5)!}\)
= \(\frac{(n + 1)(n)(n - 1)(n - 2)}{4!} - \frac{(n - 1)(n - 2)(n - 3)(n - 4)}{4!}\)
= \(\frac{(n - 1)(n - 2) [n(n + 1) - (n - 3)(n - 4)]}{4!}\)
= \(\frac{(n - 1)(n - 2) [n^{2} + n - n^{2} + 7n - 12]}{24}\)
= \(\frac{(n - 1)(n - 2)[8n - 12]}{24}\)
= \(\frac{(n - 1)(n - 2)(2n - 3)}{6}\)

Question 49 :

• WAEC 2012

The marks scored by 35 students in a test are given in the table below.

Marks	1-5	6-10	11-15	16-20	21-25	26-30
Frequency	2	7	12	8	5	1

Draw a histogram for the distribution.

Question 50 :

• WAEC 2012

(a) The polynomial \(f(x) = x^{3} + px^{2} - 10x + q\) is exactly divisible by \(x^{2} + x - 6\). Find the :
(i) values of p and q ; (ii) third factor.
(b) The volume of a cube is increasing at the rate of \(2\frac{1}{2} cm^{3} s^{-1}\). Find the rate of change of the side of the base when its length is 2cm.