2002 - WAEC Mathematics Past Questions and Answers - page 2
The length, in cm, of the sides of a right angled triangle are x, (x+2) and (x+1) where x > 0. Find , in cm, the length of its hypotenuse
The longest side of a right angle triangle is the hypotenuse.
\((x + 2)^{2} = x^{2} + (x + 1)^{2}\)
\(x^2 + 4x + 4 = x^2 + x^2 + 2x + 1\)
\(2x^{2} - x^{2} + 2x - 4x + 1 - 4 = 0\)
\(x^{2} - 2x - 3 = 0\)
\(x^{2} - 3x + x - 3 = 0 \implies x(x - 3) + 1(x - 3) = 0\)
\((x - 3)(x + 1) = 0 \implies \text{x = 3 or -1}\)
\(x > 0 \implies x = 3\)
The longest side = 3 + 2 = 5.
If log 2 = 0.3010 and log 2\(^y\) = 1.8062, find; correct to the nearest whole number, the value of y.
\(log2 = 0.3010\hspace{1mm}given\
log2^y = 1.8062\
∴ ylog2 = 1.8062\
y=\frac{1.8062}{logy}=\frac{1.8062}{0.3010}=6\)
Points X, Y and Z are located in the same horizontal plane such that Y is 12 km north of X and Z is on a bearing of 270° from X. If |XZ| = 6km, calculate, correct to one decimal place, lYZl
ZY\(^2\) = 12\(^2\) + 6\(^2\)
ZY\(^2\) = 144 + 36 = 180
ZY = \(\sqrt{180}\)
= \(13.416\)
= 13.4 km
The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?
20 members in the ratio 3:1
Number of women = \(\frac{1}{4} \times 20\)
= 5
Let the number of women to be added = x
Total number of members in the committee = 20 + x
\(\frac{5 + x}{20 + x} = \frac{2}{5}\)
\(5(5 + x) = 2(20 + x)\)
\(25 + 5x = 40 + 2x \implies 5x - 2x = 40 - 25\)
\(3x = 15 \implies x = 5\)
∴x + 3 = ky\hspace{1mm}when\hspace{1mm}x = 3, y = 12\
3+3 = 12k\
∴ k = \frac{1}{2}\
\Longrightarrow x + 3 = \frac{1}{2}y\) to find x when y = 8
\(x + 3 = \frac{1}{2}\times 8\
x=4-3\
x = 1\)
Find the nth term of the sequence 4, 10, 16 ,...
\(T_{1} = 4; T_2 = 10; T_3 = 16\)
\(T_{2} - T_1 = T_3 - T_1 = 6\)
\(T_n = a + (n - 1) d\)
= \(4 + (n - 1) \times 6\)
= \(4 + 6n - 6\)
= \(6n - 2\)
= 2(3n - 1)
If (-3, -4) is a point on the line y = mx + 2 find the value of m.
If (-3, -4) is a point on the line then
-4 = -3m + 2
-4 - 2 = -3m
-6 = -3m
m = 2
Which of the following is represented by the above sketch?
From the graph, the zeros of the equation exist at x = -2 and x = 3
\(\therefore\) (x + 2) = 0 and (x - 3) = 0
\(\implies (x + 2)(x - 3) = 0\)
\(x^2 - 3x + 2x - 6 = 0\)
\(x^2 - x - 6 = 0\) is the equation represented on the graph.
In the diagram, SQ is a tangent to the circle at P, XP||YQ, ∠XPY = 56 o and ∠PXY = 80 o.Find angle PQY
< XYQ = 180° - (80° + 56°)
= 44°
< PYQ = 56° (alternate angles, XP||YQ)
< QPY = 90°
< PQY = 180° - (90° + 56°)
= 34°