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Monday, 4th May, 2015
Further Mathematics 2(Essay) ---------- 8.30am –11.00am
Further Mathematics 1(Obj) ----------- 2.30pm – 4.00pm
2a)
(2,1) (6,7)
The centre of the circle rs the midpoint of the circle
(2+6/2,1+7/2) = (4,4)
Hence the equation of the centre (4,4) passingthrough
(2,1) and (6,7) is
(x-4)^2 + (y-4)^2 =r^2
r^2=(2-4)^2 + (1-4)^2
r^2=(-2)^2 +(-3)^2
r^2=4+9
r^2=13
r= root13
(2,1) (6,7)
The centre of the circle rs the midpoint of the circle
(2+6/2,1+7/2) = (4,4)
Hence the equation of the centre (4,4) passingthrough
(2,1) and (6,7) is
(x-4)^2 + (y-4)^2 =r^2
r^2=(2-4)^2 + (1-4)^2
r^2=(-2)^2 +(-3)^2
r^2=4+9
r^2=13
r= root13
2b)
Thus the equation of the circle is
(x-4)^2 + (y-4)^2 =13
x^2-8x+16+y^2+8x+16=13
x^2+y^2-16x+32-13=0
therefore x^2+y^2-16x+19=0
Thus the equation of the circle is
(x-4)^2 + (y-4)^2 =13
x^2-8x+16+y^2+8x+16=13
x^2+y^2-16x+32-13=0
therefore x^2+y^2-16x+19=0
5)
Initial velocity,u
Acceleration, a=3ms^-2
final velocity, v=33ms^2
time t=6 seconds
distance interval
v=u+at
u=V-at
u=33-3 6
u=33-18
u=15m/s
Area of triangle =1/2bh
therefore 1/3 6*33
=99m
Initial velocity,u
Acceleration, a=3ms^-2
final velocity, v=33ms^2
time t=6 seconds
distance interval
v=u+at
u=V-at
u=33-3 6
u=33-18
u=15m/s
Area of triangle =1/2bh
therefore 1/3 6*33
=99m
7)
no of boys=8
no of girls=6
total no of students=14
Pr(B)=8/14=4/7
Pr(G)=6/14=3/7
Pr(B1nB2)=8/14 7/13=4/13
Pr(G1nG2)=6/14 5/13=15/91
a)B1B2UG1G2 is the event that both students selected
are the same
Pr(B1B2UG1G2)=Pr(B1B2)+Pr(G1G2)
=4/13+15/91=60/1183
b)different sex
Pr(B1G2UG1B2)
=4/7 5/13+6/14 7/13
20/91+3/13=60/1183
no of boys=8
no of girls=6
total no of students=14
Pr(B)=8/14=4/7
Pr(G)=6/14=3/7
Pr(B1nB2)=8/14 7/13=4/13
Pr(G1nG2)=6/14 5/13=15/91
a)B1B2UG1G2 is the event that both students selected
are the same
Pr(B1B2UG1G2)=Pr(B1B2)+Pr(G1G2)
=4/13+15/91=60/1183
b)different sex
Pr(B1G2UG1B2)
=4/7 5/13+6/14 7/13
20/91+3/13=60/1183
(8)
total force xi+yj=3(j)+4(-i+j)+2(i+j)
=3j-4i+4j+2i+2j
=-4i+2i+3j+4j+2j
=-2i+9j
resultant force R=sqr roor(x^2 + y^2)
=sqr roor( (-2)^2 + (9)^2
=sqr root (4 +810
=sqr root(85)
=9.22N
=9.2N
tita^-1(y/x)=
=tan^-1(9/2)
=tan^-1(9/-2)
=tan^-1(-4.50)
=102.53 degree(put 0 up)
=103.5
the rsultant is 92N in the direction 103.5 degree to the
horizontal
total force xi+yj=3(j)+4(-i+j)+2(i+j)
=3j-4i+4j+2i+2j
=-4i+2i+3j+4j+2j
=-2i+9j
resultant force R=sqr roor(x^2 + y^2)
=sqr roor( (-2)^2 + (9)^2
=sqr root (4 +810
=sqr root(85)
=9.22N
=9.2N
tita^-1(y/x)=
=tan^-1(9/2)
=tan^-1(9/-2)
=tan^-1(-4.50)
=102.53 degree(put 0 up)
=103.5
the rsultant is 92N in the direction 103.5 degree to the
horizontal
(12a)
tabulate(make a table ); do not write this
Class interval:0.4-0.5, 0.6-0.9, 1.0-1.2, 1.3-1.4,
1.5-1.7
Class boundrary: 0.35-0.55, 0.55-0.95, 1.25-1.45,
1.45-1.75
Class(x): 0.45, 0.75, 1.10, 1.35, 1.60
freq(f): 2, 8, 12,6,6,
Ef=34. put this under F column
draw the diagram
tabulate(make a table ); do not write this
Class interval:0.4-0.5, 0.6-0.9, 1.0-1.2, 1.3-1.4,
1.5-1.7
Class boundrary: 0.35-0.55, 0.55-0.95, 1.25-1.45,
1.45-1.75
Class(x): 0.45, 0.75, 1.10, 1.35, 1.60
freq(f): 2, 8, 12,6,6,
Ef=34. put this under F column
draw the diagram
(12b)
tabulate(make a table); do not write this
Class(x): 0.45, 0.75, 1.10, 1.35, 1.60
f: 2,8,12,6,6
(x-A): -0.65, 0.35, 0, 0.25, 0.50
f(x-A): -1.3, 2.8, 0, 1.5, 3.0
Ef(x-A)=6.
Mean height(x)= A +(Ef(x-A))/Ef
=1.1+ 6/34
=1.1 + 0.1765
=1.2765
=1.3m
tabulate(make a table); do not write this
Class(x): 0.45, 0.75, 1.10, 1.35, 1.60
f: 2,8,12,6,6
(x-A): -0.65, 0.35, 0, 0.25, 0.50
f(x-A): -1.3, 2.8, 0, 1.5, 3.0
Ef(x-A)=6.
Mean height(x)= A +(Ef(x-A))/Ef
=1.1+ 6/34
=1.1 + 0.1765
=1.2765
=1.3m
(13a)
Edem and his wife can be seated next to each other in 2
ways once this accomplished, the remaining members of
the family can be seated 5!(factorial) ways. Hence the
total nu,ber of ways of seating Edem and his wife are
next to each 0other is
2 5!=240 ways
Edem and his wife can be seated next to each other in 2
ways once this accomplished, the remaining members of
the family can be seated 5!(factorial) ways. Hence the
total nu,ber of ways of seating Edem and his wife are
next to each 0other is
2 5!=240 ways
(13b)
real ball=4
Black balls= 5
total no of balls =9
Pr(R)=4/9
Pr(B)=5/9
(i)A red ball was picked 3times:
Pr(R1) Pr(R2) Pr(R3)
=4/9 4/9* 4/9
=64/729
real ball=4
Black balls= 5
total no of balls =9
Pr(R)=4/9
Pr(B)=5/9
(i)A red ball was picked 3times:
Pr(R1) Pr(R2) Pr(R3)
=4/9 4/9* 4/9
=64/729
(ii)
A black ball was picked at most 2 times
Pr(B1) Pr(B2)
=5/9 5/9* =25/81
KEEP REFRESHING..A black ball was picked at most 2 times
Pr(B1) Pr(B2)
=5/9 5/9* =25/81
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