WAEC Mathematics Past Questions & Answers - Page 196

976.

Which of the following is/are not the interior angle(s) of a regular polygon?

I.108° 
II. 116°
III. 120°

A.

I only

B.

II only

C.

III only

D.

I and III only

Correct answer is B

Using the formula, \((n - 2) \times 180°\) to get the sum of the interior angles. Then we can have

\((n - 2) \times 180° = 108n\) ... (1)

\((n - 2) \times 180° = 116n\) ... (2)

\((n - 2) \times 180° = 120n\) ... (3)

Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon.

(1): \(180n - 360 = 108n \implies 72n = 360\)

 \(n = 5\) (regular pentagon)

(2): \(180n - 360 = 116n \implies 64n = 360\)

 \(n = 5.625\)

(3): \(180n - 360 = 120n \implies 60n = 360\)

 \(n = 6\) (regular hexagon)

Hence, 116° is not an angle of a regular polygon.

977.

If \(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}\) find n

A.

\(-\frac{3}{2}\)

B.

\(\frac{1}{3}\)

C.

-1

D.

-3

Correct answer is C

\(\frac{3^{(1-n)}}{9^{-2n}}=\frac{1}{9}\\
3^{1-n}\times 3^{-2(-2n)} = 3^{-2}\\
1-n-2(-2n)= -2\\
1-n+4n=-2\\
n=-1\)

978.

Given that x ≅ 0.0102 correct to 3 significant figures, which of the following cannot be the actual value of x?

A.

0.01014

B.

0.01021

C.

0.01015

D.

0.01016

Correct answer is A

option A CANNOT BE BECAUSE THE LAST NUMBER BEFORE 1 CAN ONLY BE ROUNDED DOWN TO ZERO.

979.

Evaluate \((111_{two})^2 - (101_{two})^2\)

A.

10two

B.

100two

C.

1100two

D.

11000two

Correct answer is D

\((111_{2})^2 - (101_{2})^2\)

Difference of two squares

\((111 - 101)(111 + 101)\)

= \((10)(1100)\)

= \(11000_{2}\)

980.

In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^o\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm}, find   P\hat{S}Q\)

A.

85o

B.

60o

C.

55o

D.

45o

Correct answer is C

< QPS = < PRS = 65° (angles in the same segment)

< PSR + 40° + 65° = 180°

< PSR + 105° = 180°

< PSR = 75°

< PSR = < PSQ + < QSR

75° = < PSQ + 20° \(\implies\) < PSQ = 75° - 20° = 55°