2002 - WAEC Mathematics Past Questions and Answers - page 1
In the diagram O is the center of the circle. Reflex angle XOY = 210° and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.
Given, Length of minor arc = 5.5m
Angle subtended by minor arc = 360° - 210° = 150°
\(\therefore 5.5 = \frac{150}{360} \times 2 \times \frac{22}{7} \times r \)
\(\frac{55r}{21} = 5.5\)
\(r = \frac{5.5 \times 21}{55}\)
r = 2.1m
Length of major arc = \(\frac{210}{360} \times 2 \times \frac{22}{7} \times 2.1\)
= \(7.7m \approxeq 8m\) (to the nearest metre)
A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is \(2\sqrt{3}\) cm. Calculate the volume of the pyramid
\(BD^2 = 4^2 + 4^2\)
\(BD = \sqrt{16 + 16} = \sqrt{32}\)
\(BD = 4\sqrt{2} cm\)
\((2\sqrt{3})^2 = (2\sqrt{2})^2 + h^2\)
\(h^2 = 12 - 8 = 4\)
\(h = \sqrt{4} = 2 cm\)
Volume of pyramid = \(\frac{a^2 h}{3}\)
= \(\frac{4^2 \times 2}{3}\)
= \(\frac{32}{3} = 10\frac{2}{3} cm^3\)
The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area
Curved surface area or a cone \(=\pi rl\)
from the information \(l^2 = 4^2 + 3^2 = 16+9\
l = \sqrt{25} = 5; ∴ C.S.A\hspace{1mm} = \frac{22}{7}\times 3 \times 5\
Since \frac{22}{7}=\pi ∴ C.S.A\hspace{1mm} =\hspace{1mm}15\pi\)
In the diagram above, ∠PQU=36°, ∠QRT = 29°, PQ||RT. Find ∠PQR
< UQR = 29° (alternate angles)
< PQR = < PQU + < UQR
= 36° + 29°
= 65°
Simplify \(5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)\)
\(5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)\
\frac{21}{4}\div \left(1\frac{4-3}{6}\right)\
\frac{21}{4}\div \left(1\frac{1}{6}\right)\
\frac{21}{4} \times \frac{6}{7}= 4\frac{1}{2}\)
0.5x - 5x = 0.35-2.6\
-4.5x = -2.25\
x = \frac{-2.25}{-4.5}\
0.5\)
(2x+5)o + 2xo + (x-20)o + xo + (3x+10)o + (x + 15)o = 360o; 10x = 350
x = 35
=1 \times 2^6 + 0\times 2^5 + 0\times 2^4 + 1\times 2^3 + 0\times 2^2 + 1\times 2^1 \
=64+8+2+1=75_{ten}\
∴ m = 7 \)
The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x- axis at P and R and the y- axis at Q.
What is the value of y at Q?
The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x- axis at P and R and the y- axis at Q.
When \(y = 3\frac{1}{3}\), what is the positive value of x?