WAEC Mathematics Past Questions & Answers - Page 293

1,461.

The sum of an interior angles of a regular polygon is 30 right angles. How many sides has the polygon?

A.

34 sides

B.

30 sides

C.

26 sides

D.

17 sides

E.

15 sides

Correct answer is D

Sum of interior angles in a polygon = \((2n - 4) \times 90°\)

\(\therefore (2n - 4) \times 90° = 30 \times 90°\)

\(\implies 2n - 4 = 30 \)

\(2n = 34 \implies n = 17\)

The polygon has 17 sides.

1,462.

In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ∠SQR = 68°, find ∠PQT.

A.

34o

B.

48o

C.

56o

D.

68o

E.

73o

Correct answer is C

< STQ = < SQR = 68° (alternate segment)

\(\therefore\) < STQ = 68° 

< TQS = \(\frac{180° - 68°}{2}\)

= \(\frac{112}{2} = 56°\)

\(\therefore\) < PQT = 180° - (68° + 56°)

= 180° - 124°

= 56°

1,463.

The angle of a sector of a circle radius 10.5cm is 120°. Find the perimeter of the sector [Take π = 22/7]

A.

22cm

B.

33.5cm

C.

43cm

D.

66cm

E.

115.5cm

Correct answer is C

Perimeter of a sector = \(2r + \frac{\theta}{360} \times 2\pi r\)

= \(2(10.5) + \frac{120}{360} \times 2 \times \frac{22}{7} \times 10.5\)

= \(21 + 22\)

= 43 cm

1,464.

The area and a diagonal of a rhombus are 60 cm\(^2\) and 12 cm respectively. Calculate the length of the other diagonal.

A.

5cm

B.

6cm

C.

10cm

D.

12cm

E.

15cm

Correct answer is C

Area of rhombus = \(\frac{pq}{2}\)

where p and q are the two diagonals of the rhombus.

\(\therefore 60 = \frac{12 \times q}{2}\)

6q = 60 \(\implies\) q = 10 cm

1,465.

A cone is 14cm deep and the base radius is 41/2cm. Calculate the volume of water that is exactly half the volume of the cone.[Take π = 22/7]

A.

49.5cm3

B.

99cm3

C.

148.5cm3

D.

297cm3

E.

445.5cm3

Correct answer is C

Volume of a cone = \(\frac{1}{3} \pi r^2 h\)

r = 4\(\frac{1}{2}\) cm; h = 14 cm

Volume of cone = \(\frac{1}{3} \times \frac{22}{7} \times \frac{9}{2} \times \frac{9}{2} \times 14\)

= 297 cm\(^3\)

When half- filled, the volume of the water = \(\frac{297}{2} = 148.5 cm^3\)