WAEC Mathematics Past Questions & Answers - Page 99

491.

Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction

A.

\(\frac{x - 7}{x^2 + x - 6}\)

B.

\(\frac{x - 1}{x^2 + x - 6}\)

C.

\(\frac{x - 2}{x^2 + x - 6}\)

D.

\(\frac{x - 27}{x^2 + x - 6}\)

Correct answer is A

\(\frac{2}{x + 3} - \frac{1}{x - 2}\) = \(\frac{2(x - 2) - (x - 3)}{(x + 3) (x - 2)}\)

= \(\frac{2x - 4 - x - 3}{x^2 - 2x + 3x - 6}\)

= \(\frac{x -7}{x^2 + x - 6}\)

= \(\frac{x - 7}{x^2 + x - 6}\)

492.

When a number is subtracted from 2, the result equals 4 less than one-fifth of the number. Find the number

A.

11

B.

\(\frac{15}{2}\)

C.

5

D.

\(\frac{5}{2}\)

Correct answer is C

Let the number be y, subtract y from 2 i.e 2 - y

2 - y = 4 < \(\frac{1}{5}\) y,

2 - y = \(\frac{y}{5}\) - 4

2 - y + 4 = \(\frac{y}{5}\)

6 =  \(\frac{y}{5}\) + y

6 =  \(\frac{y + 5y}{5}\)

6 =  \(\frac{6y}{5}\) 

multiplying through by 5
6 * 5 = 6y

\(\frac{30}{6}\) = y

= 5

493.

What is the locus of the point X which moves relative to two fixed points P and M on a plane such that < PXM = 30o

A.

the bisector of the straight line joining P and M

B.

an arc of a circle with PM as a chord

C.

the bisector of angle PXM

D.

a circle centre X and radius PM

Correct answer is B

No explanation has been provided for this answer.

494.

The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k

A.

zero

B.

-2

C.

-4

D.

-8

Correct answer is D

y = x2 + 2x + k at point(2,0) x = 2, y = 0

0 = (2)2 + 2(20 + k)

0 = 4 + 4 + k

0 = 8 + k

k = -8

495.

If y varies directly s the square root of (x + 1) and y = 6 when x = 3, find x when y = 9

A.

8

B.

7

C.

6

D.

5

Correct answer is A

y \(\alpha\) \sqrt{x + 1}\), y = k\sqrt{x + 1}\)

6 = k\(\sqrt{3 + 1}\)

6 = k\(\sqrt{4}\)

6 = 2k

k = \(\frac{6}{2}\) = 3

y = \(\sqrt{(x + 1)}\)

9 = 3\(\sqrt{(x + 1)}\)(divide both side by 3)

\(\frac{9}{3}\) = \(\frac{3\sqrt{x + 1}}{3}\)

3 = \(\sqrt{x + 1}\)(square both sides)

9 = x + 1

x = 9 - 1

x = 8