1999 - WAEC Mathematics Past Questions and Answers - page 1

1

The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?

A
39cm ≤ P ≤41cm
B
38cm ≤ P < 42cm
C
38.5 ≤ P ≤ 41.5cm
D
38.5 ≤ P ≤ 40cm
correct option: b

If the side = 10 cm, correct to the nearest whole number, then

The side ranges from 9.5 cm to 10.5 cm. (9.5 $$\leq$$ s < 10.5)

Perimeter of a rhombus = 4 x side

$$\therefore$$ 4 x 9.5 $$\leq$$ perimeter < 4 x 10.5

= 38 cm $$\leq$$ P < 42 cm

2

Simplify log$$_7$$ 8 - log$$_7$$ 2 + log$$_7$$ 4.

A
0
B
$$2log_7 2$$
C
$$3log_7 2$$
D
$$4log_7 2$$
correct option: d

log$$_7$$ 8 - log$$_7$$ 2 + log$$_7$$ 4

= log$$_7$$ (8/2 x 4)

= log$$_7$$ 16

= 4 log$$_7$$ 2

3

If $$K\sqrt{28}+\sqrt{63}-\sqrt{7}=0$$, find K.

A
-2
B
-1
C
1
D
2
correct option: b

$$K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\ 2K\sqrt{7}+3\sqrt{7}-\sqrt{7}=0\ 2K\sqrt{7}=-2\sqrt{7}\ K=\frac{-2\sqrt{7}}{2\sqrt{7}}\ K=-1$$

4

From a set $$A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]$$, a number is selected at random. Find the probability that is a rational number

A
$$\frac{1}{5}$$
B
$$\frac{2}{5}$$
C
$$\frac{3}{5}$$
D
$$\frac{4}{5}$$
correct option: b

$$A = {3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}}$$

n(A) = 5

Let the rational nos = R

n(R) = 2 (3, $$\sqrt{9}$$)

P(R) = 2/5

5

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below
Find the value of K

A
15o
B
30o
C
60o
D
90o
correct option: b

Total angle in a circle = 360°

$$\therefore$$ 105 + 75 + 2k + k + 3k = 360°

6k = 360 - 180 = 180

k = 180/6 = 30°

6

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below

If he sends $$2\frac{1}{2}$$ hours week on science, find the total number of hours he studies in a week

A
$$3\frac{1}{3}$$ hours
B
5 hours
C
8 hours
D
12 hours
correct option: d

Let x represent the total number of hours spent per week

$$∴ \frac{75}{360} \times x = \frac{5}{2}\ ∴ x = \frac{360 \times 5}{725 \times 2}=12 hours$$

7

A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

A
$$\frac{2}{11}$$
B
$$\frac{4}{11}$$
C
$$\frac{5}{11}$$
D
$$\frac{11}{13}$$
correct option: a

Let the number of people that speak both English and French = x

Then (7 - x) + x + (6 - x) = 11

13 - x = 11 $$\implies$$ x = 2.

$$\therefore$$ P(picking a person that speaks both languages) = 2/11

8

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

A
5
B
6
C
8
D
9
correct option: b

Let the exterior angle = d

Note: Exterior angle + Interior angle = 180°

$$\implies$$ d + 2d = 180°

3d = 180° $$\implies$$ d = 60°

Recall, exterior angle = $$\frac{360}{\text{no of sides}}$$

$$\therefore \text{No of sides} = \frac{360}{60}$$

= 6 sides

9

Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite

A
I and II only
B
II and III only
C
I and III only
D
I, II, and III
correct option: c

Isosceles triangle and Kite shapes have 1 line of symmetry each while the rhombus has 2 lines of symmetry.

10

In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ

A
50o
B
62o
C
112o
D
115o
correct option: d

In triangle RXY, < RXY = < RYX (base angles of an isosceles triangle)

$$\implies$$ 180° - 62° = 2 < RYX

118° = 2 < RYX $$\implies$$ < RYX = 59°

In triangle RYZ, < RZY = 62° (base angles of an isosceles triangle)

$$\therefore$$ < RYZ = 180° - (62° + 62°)

= 180° - 124° = 56°

$$\therefore$$ < XYZ = 56° + 59°

= 115°