1989 - WAEC Mathematics Past Questions and Answers - page 2
An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle?
[Take π = 22/7]
L = 14cm, r = 7cm; \(\theta\)= ?
L = \(\frac{\theta}{360}\) x 2πr
14= \(\frac{\theta\}{360}\) x 2π(7)
\(\theta = \frac{360 \times 14}{44}\)
=114.55°
If twice a certain integer is subtracted from 5 times the integer, the result is 63. Find the integer.
Let the integer = y
\(\therefore\) 5y - 2y = 63
3y = 63 \(\implies\) y = 21
If 3\(^y\) = 243, find the value of y.
Points X and Y are respectively 20km North and 9km East of a point O. What is the bearing of Y from X? Correct to the nearest degree
tan\(\theta\) = 9/20 = 0.45
\(\theta\) = tan\(^{-1}\) 0.45 = 24.2°
the bearing of y from x = 180 0 - 0 = 180° - 24.2°
the bearing = 155.8°
\(\approxeq\) 156°
In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ∠AOD = ∠BOD
In \(\Delta DOB\), let < DOB = \(\alpha\)
In \(\Delta DOB\), \(5^2 = 3^2 + s^2\)
\(s^2 = 25 - 9 = 16\)
\(s = 4cm\)
\(\sin \alpha = \frac{4}{5}\)
\(\alpha = \frac{< AOB}{2}\)
Length of chord = \(2r \sin (\frac{\theta}{2})\)
|OB| = r = 5cm
L = \(2(5)(\frac{4}{5})\)
= 8 cm