# 1999 - WAEC Mathematics Past Questions and Answers - page 1

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

**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

Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.

**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

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

**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\)

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

**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

*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

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**correct option:**b

Total angle in a circle = 360°

\(\therefore\) 105 + 75 + 2k + k + 3k = 360°

6k = 360 - 180 = 180

k = 180/6 = 30°

*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

**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\)

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?

**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

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

**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

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

**correct option:**c

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

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

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**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°