2001 - WAEC Mathematics Past Questions and Answers - page 4
What is the range of their age?
How many students are there in the group?
Which of the following is not the the size of an exterior angle of a regular polygon?
The size of an exterior angle = \(\frac{360}{n}\)
From the options, all options can perfectly divide 360°, except 21°.
In the diagram, PQR is a triangle.|PQ| = |PR|, |PS| = |SQ| and PRS = 50°. What is the size of ∠PSQ?
< PQS = 50° (PQ = PR)
< PQS = < SPQ = 50° (QS = PS)
In triangle PSQ, < PQS + < QPS + < PSQ = 180°
50° + 50° + < PSQ = 180°
< PSQ = 180° - 100° = 80°
\(\alpha\) = cos-1(0.625)
= 51.3o
∠PQR = 2\(\alpha\)
= 2(51.3o)
= 102.6
= 103o
In the diagram, PQ is a diameter of the circle and ∠PRS = 58°. Find ∠STQ.
In \(\Delta\) PRQ, < SRQ = 90° - 58°
< SRQ = < QTS = x (angles in the segment)
\(\therefore\) x = 32°
A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle. What is the perimeter of the sector? Take \(\pi =\frac{22}{7}\)
From the diagram
\(r^2 = B^2 + 15^2\
= 64 + 225\
r = \sqrt{289} = 17cm\)
A sector of a circle radius 14 cm subtends an angle 135° at the center of the circle. What is the perimeter of the sector? Take \(\pi = \frac{22}{7}\)
Perimeter of the sector = \(2r + \frac{\theta}{360} \times 2\pi r\)
= \(2(14) + \frac{135}{360} \times 2 \times \frac{22}{7} \times 14\)
= \(28 + 33\)
= 61 cm