WAEC Mathematics Question 2015 ( Essay Question Seven 7)

QUESTION 7

The table is for the relation 

(a)(i) Use the table to find the values of p and q.

(ii) Copy and complete the table.

(b) Using scales of 2cm to 1 unit on the x- axis and 2 cm to 5 units on the y- axis, draw the graph of the relation for −3≤x≤5$-3\le x\le 5$.

(c) Use the graph to find : 

(i) y when x = 1.8  ; (ii) x when y = -8.

SOLUTION

a(i) To find the value of p and q from the given table of values when x = -3, y= 21

and when x = 4, y = 0.

So considering s = -3 and y = 21 using the givem equation .

Substituting the vale of x and y  into the equation, we have;

21 =9p + 15 +q

21-15 = 9p + q

6 = 9p +q

9p +q = 6...................... (i)

Also, when x = 4 and y = 0

Substituting into the equation 

Substituting the vale of x and y  into the equation, we have;

0 = 16p - 20 + q

0 + 20 = 16p + q

20 = 16p + q

16p + q = 20 .......................(ii)

Solving equation (i) and (ii) simultaneously ,

6 = 9p +q ......................... (i)

20 = 16p + q.....................(ii)

9p +q = 6...................... (i)

16p + q = 20 .................(ii)

Subtracting equation (i) from equation (ii), we have;

(16p-9q) + (q-q) = 20-6

7p + 14

p=2

Substituting p = 2 into equation (i)

9p + q = 6

9(2) + q = 6

18 + q = 6

q = 6 - 18

q = -12

Hence, p = 2 and q = -12

(ii) The equation for the given table of values

  becomes  

ANSWER