Waec Further Mathematics 2012 Past Questions and Answers

Question 46:

• WAEC 2012

The gradient function of $y=a{x}^2+bx+c$ 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 $f(x)=x^3+p{x}^2-10x+q$ 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 $2\frac{1}{2}c{m}^3{s}^{-1}$. Find the rate of change of the side of the base when its length is 2cm.