# 2013 - WAEC Mathematics Past Questions and Answers - page 3

21
If p = (y : 2y $$\geq$$ 6) and Q = (y : y -3 $$\geq$$ 4), where y is an integer, find p$$\cap$$Q
A
{3, 4}
B
{3, 7}
C
{3, 4, 5, 6, 7}
D
{4, 5, 6}
correct option: c
p = (y : 2y $$\geq$$ 6)

2y $$\leq$$ 6

y $$\leq \frac{6}{2}$$

y = $$\leq$$ 3

and Q = (y : y -3 $$\geq$$ 4)

y - 3 $$\geq$$ 4

y $$\geq$$ 4 + 3

y $$\geq$$ 7

therefore p = {3, 4, 5, 6, 7} and Q = {7, 6, 5, 4, 3....}

P$$\cap$$Q = {3, 4, 5, 6, 7}
22
Find the values of k in the equation 6k2 = 5k + 6
A
{$$\frac{-2}{3}, \frac{-3}{2}$$}
B
{$$\frac{-2}{3}, \frac{3}{2}$$}
C
{$$\frac{2}{3}, \frac{-3}{2}$$}
D
{$$\frac{2}{3}, \frac{3}{2}$$}
correct option: b
6k2 = 5k + 6

6k2 - 5k - 6 = 0

6k2 - 0k + 4k - 6 = 0

3k(2k - 3) + 2(2k - 3) = 0

(3k + 2)(2k - 3) = 0

3k + 2 = 0 or 2k - 3 = 0

3k = -2 or 2k = 3

k = $$\frac{-2}{3}$$ or k = $$\frac{3}{2}$$

k = ($$\frac{-2}{3}$$, k = $$\frac{3}{2}$$)
23
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 option: 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
24
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 option: 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
25
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
thebisector 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 option: b
26
When a number is subtracted from 2, the result equals 2 less than one-fifth of the number. Find the number
A
11
B
$$\frac{15}{2}$$
C
5
D
$$\frac{5}{2}$$
correct option: c
Let the number be y, subtract y from 2 i.e 2 - y

2 - y = 4 < $$\frac{1}{5}$$ x y, 2 - y = 4 < $$\frac{y}{5}$$

2 - y - 4 < $$\frac{y}{5}$$

2 - 4 - y $$\frac{x}{5} - 4$$, multiplying through by 5

5(2 - x) = 5($$\frac{x}{5}$$) - 5(4)

10 - 5x = x - 20

-5x - x = -20 - 10

-6x = -30

x = $$\frac{-30}{-6}$$

= 5
27
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 option: a
$$\frac{2}{x + 3} - \frac{1}{x - 2}$$ = $$\frac{2(x - 2) - (x - 3)}{(x + 3) (x - 2)}$$

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

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

= $$\frac{x - 7}{x^2 + x - 6}$$
28
An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
A
15
B
12
C
9
D
6
correct option: b
Let the interior angle = xo

interior angle = 5xo (sum of int. angle ann exterior)

(angles = angle or straight line)

6x = 180

x = $$\frac{180}{6}$$

x = 30o

no. of sides = $$\frac{\text{sum of exterior angles}}{\text{exterior angle}}$$

= $$\frac{360}{30}$$ = 12
29
Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - p = 2, find x
A
-2
B
-1
C
1
D
2
correct option: b
P = x2 + 4x - 2, Q = 2x - 1

Q - p = 2, (2x - 1) - (x2 + 4x - 2) = 2

2x - 1 - x2 - 4x + 2 = 2

-2x - x2 + 1

-x2 - 2x - 1 = 0

x2 + 2x + 1 = 0

x2 + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

x + 1 = 0 or x + 1 = 0

x = -1 or x = -1

x = -1
30
A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume
A
322m3
B
448m3
C
632m2
D
840m2
correct option: b
Volume of pyramid = $$\frac{1}{3}$$ x base area x height

= $$\frac{1}{3} \times 12^4 \times 8 \times 14$$

= 4 x 8 x 14 = 448m3