2004 - WAEC Mathematics Past Questions and Answers - page 5
41
The values of x when y = 3 are approximately
A
-4.7 and 1.4
B
-4.6 and 1.5
C
-3.6 and 0.4
D
-3.6 and 1.5
correct option: b
Users' Answers & Comments42
Which of the following quadratic equations has \(-\frac{1}{2}\) and \(\frac{3}{4}\) as its roots?
A
8x2 + 11x - 3 = 0
B
8x2 -11x – 3 = 0
C
8x2 + 2x -3 = 0
D
8x2 - 2x – 3 = 0
correct option: d
X2 - (sum of the roots)x + (product of the roots) = 0
Sum of the roots \(= -\frac{1}{2}+\frac{3}{4} = \frac{-2+3}{2}=\frac{1}{4}\)
Product of the roots = \(-\frac{1}{2}\times \frac{3}{4}=\frac{-3}{8}\
X^2-\left(\frac{1}{4}\right)x-\frac{3}{8} = 0. Taking \hspace{1mm}the\hspace{1mm} common\)
\(8x^2-2x-3=0\);
Users' Answers & CommentsSum of the roots \(= -\frac{1}{2}+\frac{3}{4} = \frac{-2+3}{2}=\frac{1}{4}\)
Product of the roots = \(-\frac{1}{2}\times \frac{3}{4}=\frac{-3}{8}\
X^2-\left(\frac{1}{4}\right)x-\frac{3}{8} = 0. Taking \hspace{1mm}the\hspace{1mm} common\)
\(8x^2-2x-3=0\);
43
The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is
A
the perpendicular bisector of the line segment X Y
B
a line parallel to the line segment XY
C
a circle with XY as diameter
D
the line perpendicular to the line segment XY
correct option: a
Users' Answers & Comments44
Given that \(P\propto \frac{1}{\sqrt{r}}\) and p = 3 when r = 16, find the value of r when p =-5
A
48
B
64
C
72
D
324
correct option: b
\(P \propto \frac{1}{\sqrt{r}} P=3\hspace{1mm}r=16\
P = \frac{k}{\sqrt{r}}\Rightarrow 3 = \frac{k}{\sqrt{16}}\Rightarrow \frac{3}{1} = \frac{k}{4} \ \Rightarrow K = 12 \Rightarrow K = 12; P\sqrt{r} = k \Rightarrow \sqrt{r} = \frac{k}{p}\
r = \frac{(k)^2}{P}=12^2 \div \frac{3}{2}=\left(\frac{12}{1}\times \frac{2}{3}\right)=8^2\
r = 64\)
Users' Answers & CommentsP = \frac{k}{\sqrt{r}}\Rightarrow 3 = \frac{k}{\sqrt{16}}\Rightarrow \frac{3}{1} = \frac{k}{4} \ \Rightarrow K = 12 \Rightarrow K = 12; P\sqrt{r} = k \Rightarrow \sqrt{r} = \frac{k}{p}\
r = \frac{(k)^2}{P}=12^2 \div \frac{3}{2}=\left(\frac{12}{1}\times \frac{2}{3}\right)=8^2\
r = 64\)
45
Which of the following is/are true? In a plane, the locus of points I. Equidistant from a straight line is a circle radius d where d is the distance between the point and the straight line.
II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.
II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.
A
I only
B
II only
C
III only
D
I, II and III
correct option: c
Users' Answers & Comments46
The sides of two cubes are in the ratio 2:5. What is the ratio of their volumes?
A
4:5
B
8: 15
C
6:125
D
8:125
correct option: d
The ratio of the two cubes = 2:5
Volume of the two cubes = 2\(^3\) : 5\(^3\) = 8 : 125
47
Given that p = 2, q = -5 and r = - 4, evaluate 3p2 - q2 - r3
A
101
B
77
C
51
D
-27
correct option: c
3(2)2 - (-5)2 - (-4)3
3(4) – (25) – (-64); 12 – 25 + 64 = 51
Users' Answers & Comments3(4) – (25) – (-64); 12 – 25 + 64 = 51
48
A Cooperative Society, charges an interest of 51/2% per annum on any amount borrowed by its members. If a member borrows N125,000, how much does he pay back after one year?
A
N136875
B
N131,875
C
N126750
D
N126250
correct option: b
The rate of interest charge = 51/2% p.a
The amount borrowed = N125, 000:00
Interest charge \(=\frac{11}{200} of N125,000\
= 11 \times N625.00 = N6,875.00\)
The amount refunded by the member with interest charge by the cooperative society
N125,000+N6,875.00 = N131,875.00
Users' Answers & CommentsThe amount borrowed = N125, 000:00
Interest charge \(=\frac{11}{200} of N125,000\
= 11 \times N625.00 = N6,875.00\)
The amount refunded by the member with interest charge by the cooperative society
N125,000+N6,875.00 = N131,875.00
49
A bag contains 3 red and 2 white identical balls. lf 2 balls are picked at random from the bag, one after the other and with replacement, find the probability that they are of different colours
A
\(\frac{36}{625}\)
B
\(\frac{16}{625}\)
C
\(\frac{12}{25}\)
D
\(\frac{13}{25}\)
correct option: c
Prob(RW or WR) = Prob(RW) + Prob(WR)
\(Prob(R) = \frac{3}{5}:Prob(W) = \frac{2}{5}\
Prob(RW\hspace{1mm}or\hspace{1mm}WR)=\frac{3}{5}\times\frac{2}{5}+\frac{2}{5}\times \frac{3}{5}\
\frac{6}{25}+\frac{6}{25}=\frac{12}{25}\)
Users' Answers & Comments\(Prob(R) = \frac{3}{5}:Prob(W) = \frac{2}{5}\
Prob(RW\hspace{1mm}or\hspace{1mm}WR)=\frac{3}{5}\times\frac{2}{5}+\frac{2}{5}\times \frac{3}{5}\
\frac{6}{25}+\frac{6}{25}=\frac{12}{25}\)
50
A point on the ground is 5m away from the foot of a vertical wall 7 m high, Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall
A
36o
B
44o
C
46o
D
54o
correct option: d
θ= angle of depression of the point from the top of the wall
\(tan\theta = \frac{7}{5}=1.4; \theta = tan^{-1}(1.400)\
\theta = 54.4^{\circ}; \theta = 54^{\circ}\) to the nearest degree
Users' Answers & Comments\(tan\theta = \frac{7}{5}=1.4; \theta = tan^{-1}(1.400)\
\theta = 54.4^{\circ}; \theta = 54^{\circ}\) to the nearest degree