WAEC Further Mathematics Past Questions & Answers - Page 19

91.

Find the equation of the normal to the curve y= 2x\(^2\) - 5x + 10 at P(1, 7)

A.

y+x-3 =0

B.

y-x+6=0

C.

y - x - 6=0

D.

y -x+ 3 =0

Correct answer is C

From y= 2x- 5x 10 ; dy/dx= 4x-5

But at (1, 7); m\(_1\) = (dy/dx)\(_{1,7}\)

= 4(1) - 5 = -1

Using m\(_1\)m\(_2\),= -1; m\(_2\) = 1.

Gradient m\(_2\), of normal at (1,7) is 1.

Using y - y\(_1\) = m(x - x\(_1\))

y - 7 = 1(x - 1) ;

y - 7 = x - 1

y - x - 6 = 0

92.

The gradient ofy= 3x\(^2\) + 11x + 7 at P(x.y) is -1. Find the coordinates of P. 

A.

(-3, -2)

B.

(-2,-3)

C.

(-2,3)

D.

(2,2)

Correct answer is B

y= 3x\(^2\) + 11x +7;

dy/dx = 6x + 11= -1;

6x = -12;

x=-2

y=  3x\(^2\) + 11x + 7

At x-2,

y= 3(-2)\(^2\) +11(-2) + 7

= 12 - 22 + 7= -3

p(x, y) = (-2,-3)

93.

A bag contains 8 red, 4 blue and 2 green identical balls. Two balls are drawn randomly from the bag without replacement. Find the probability that the balls drawn are red and blue.

A. 12/91 B. C. D.

A.

12/91

B.

16/91

C.

30/91

D.

32/91

Correct answer is D

Total balls = 8+4+2= 14

n(R) = 8, n (B) =4, n(G) = 2

Without replacement, it is p(RB) or p(BR)

= (8/14 x 4/13) + (4/14 + 8/13) = 16/91 + 16/91

= 32/91

95.

If 2i +pj and 4i -2j are perpendicular, find the value of p.

A.

2

B.

3

C.

4

D.

5

Correct answer is C

(2i + pi) (4i - 2j) =0

2 x 4 - p x 2=0 ;

8-2p = 0;   2p-8;

p=4