1993 - JAMB Mathematics Past Questions and Answers - page 5

The two equations are y = x(2 - x) and y = (x - 1)(x - 3)
The root of these equations are points where the graph of the equations cuts the x axis; but at these points = 0
put y = 0; 0 = x(2 - x)
0 = (x - 1)(x - 3)
x = 0 or x = 2; x = 1 or x = 3
The values of x at P, Q, R are increasing towards the positive direction of x-axis
at P, x = 1 at Q, x = 2 at R, x = 3
P, Q, R are respectively (1, 2, 3)
Users' Answers & Comments

< PSO = (\frac{1}{2}) < SOQ = (\frac{1}{2})(180) = 90o
< RTS = < PQS = 32o (Alternative angle)
< PSQ = 90 - < PSQ = 90o - 32o
= 58o
Users' Answers & Comments
OQ = OR = radii
< ROQ = 180 - 86 = 84o
(\bigtriangleup)OQR = Isosceles
R = Q
R + Q + 84 = 180(angle in a (\bigtriangleup))
2R = 96 since R = Q
R = 48o
ORQ = 48o
Users' Answers & Comments
Construction joins R to P such that SRP = straight line
R = 180o - 107o
< p = 180o - (107o - 34o)
108 - 141o = 39o
Angle < S = 39o (corr. Ang.) But in (\bigtriangleup)SRT
< S = < T = 39o
SRT = 180 - (39o + 39o)
= 180o - 78o
= 102o
Users' Answers & Comments
Since QRU= Xo
RSU = Xo, But RSU = 180o - (50o + 35o)
= 180o - 85o
= 95o
x = 95o
Users' Answers & Comments
Using angle bisector theorem: line PS bisects angle QPR
QS/QP = SR/PR
3/4 = SR/g
4SR = 27
SR = (\frac{27}{4})
= 6(\frac{3}{4})cm
Users' Answers & Comments
SQ2 + OS2 = OQ2 + 52 = 142
SQ2 = 142 - 52
196 - 25 = 171
ST2 + TQ2 = SQ2
ST2 + 22 = 171
ST2 = 171 - 4
= 167
ST = (\sqrt{167})
= 12.92 = 12.9cm
Users' Answers & Comments
Since area of square PQRS = 100cm2
each lenght = 10cm
Also TUYS : XQVU = 1 : 16
lengths are in ratio 1 : 4, hence TU : UV = 1: 4
Let TU = x
UV = 1: 4
hence TV = x + 4x = 5x = 10cm
x = 2cm
TU = 2cm
UV = 8cm
But TU = SY and UV = YR
YR = 8cm
Users' Answers & Comments
TH = tan 45o, TH = QH
(\frac{TH}{5 + QH}) = tan 30o
TH = (b + QH) tan 30o
QH = 56 (5 + QH) (\frac{1}{\sqrt{3}})
QH(1 - (\frac{1}{\sqrt{3}})) = (\frac{5}{\sqrt{3}})
QH = (\frac{5\sqrt{3}}{\sqrt{3}} - \frac{1}{\sqrt{3}})
= (\frac{5}{\sqrt{3} - 1})
Users' Answers & Comments