MATHS OBJ VERIFIED OBJ
1-10: DCBCABBADA
11-20: CCBDABABBA
21-30: CACCDDDACC
31-40: BCDCDCBADA
41-50: ABACBBDADD
3a)
x+46+180-x+28=180
254-x=180
x=254-180
x=74degrees
(3b)
h=7cm
T=462cm^2
T=pie sqr + 2 pie rH
462= pie( r ^2 +2*7*r)
462/3.142
=r sqr= =14r
r sqr+ 14r=147
r sqr +14r- 147=0
r= 14+-( (sqr(14))-4*1*147)/2*1
r=-(14 +-(196-4))/2
r=(-14+_12)/2
r=(-14+12)/2 or
r=2/2
=1cm
1a)
(0.09*1.21)/(3.3*0.00025)
=(9*10^-2*1.2*10^1)/(3.3*25*10^-5)
=(1089^10^-4)/(82.5*10^-5)
=1.32*10^(-4+6)
=1.32*10^2
1b)
p=5600,T=3,A=1200+5600=6800
A=P(1+R/100)^3
6800=5600(1+R/100)^3
(1+R/100)^3=6800/5600
(1+R/100)^3=1.214
1+R/100=cuberoot(1.214)
1+R/100=1.0667
R/100=1.0667-1
R/100=0.0667
R=0.0667*100
R=66.7%
x+46+180-x+28=180
254-x=180
x=254-180
x=74degrees
(3b)
h=7cm
T=462cm^2
T=pie sqr + 2 pie rH
462= pie( r ^2 +2*7*r)
462/3.142
=r sqr= =14r
r sqr+ 14r=147
r sqr +14r- 147=0
r= 14+-( (sqr(14))-4*1*147)/2*1
r=-(14 +-(196-4))/2
r=(-14+_12)/2
r=(-14+12)/2 or
r=2/2
=1cm
1a)
(0.09*1.21)/(3.3*0.00025)
=(9*10^-2*1.2*10^1)/(3.3*25*10^-5)
=(1089^10^-4)/(82.5*10^-5)
=1.32*10^(-4+6)
=1.32*10^2
1b)
p=5600,T=3,A=1200+5600=6800
A=P(1+R/100)^3
6800=5600(1+R/100)^3
(1+R/100)^3=6800/5600
(1+R/100)^3=1.214
1+R/100=cuberoot(1.214)
1+R/100=1.0667
R/100=1.0667-1
R/100=0.0667
R=0.0667*100
R=66.7%
11a)
Given (3p+4q)/(3p-4q) = 2
3p+4q=2*(3p-4q)
3p+4q=6p-8q
3p-6p=-4q-8q
=-3p=-12q
p/q=-12/-3
p/q=4/1, P=4, q=1
p:q=4;1
(11b)
(i)
perimeter(p)=PQ+PU+QR
PQ=UT+TS+SR
34=PQ+UR+4+4
PQ=UR
34-8=2PQ
PQ=26/2=13cm
(ii)
13=2+TS+2
TS=13-4=9cm
radius®=9/2=4.5cm
Area(A)= pie r sqr+22/7*(4.5)^2
=445.5/7
63.64cm^2
(8a)
diagram
z=110 degree(sum of angles on a straight line)
z=180-110
z=70 dgree
w degree= 70 degree
x+r+w degree= 180 degree(sum of angle in a triangle)
x+2x+70 degree=180 degree
3x=110
x=110/3=36.7 dgeree
(8b)
B=10, G=12
TB=600.00
TB=TG+600
mean of TB=100+ mean of TG
where TB= total collection of boys
TG=total collection by girls
mean of TB= ET/B
mean of TB= (TG+600)/10
100+ mean of TG= (TG+600)/100
mean of TG= mean of TG/12
100+ mean of G/12= (TG+600)/10
(100+TG)/12=(TG+600)/10
10*(1200+TG)=12*(TG+600)
=12000+10TG=12TG+7200
=12TG-10TG=12000-7200
2TG=4800
TG=N2400
TB=TG+600
TB=600+2400
Tb=N3000
(6a)
first term9a)=1.0=1
common diff(d)=3-1=2
last term(L)=101
L=a+(n-1)d
101=1+(n-1)*2
(n-1)*2=100
n-1=100/2
n-1=50
n=501+1
n=51
sum(s)=n/2(2a+(n-1)d)
S=51/2(2*1+(51-1)*2)
s=25.5(2+100)
S=25.5*102=2601
(6b)
UC=95
Bus & Train(B&T)=7
Train & Car( T & C)=3
B&T&C=8
Bus only(x)=B&C only
Bus(b)=47
train(T)=30
(draw the venn diagram)
Bus only= 47-(7+8+x)
x=47-15+x
47=x+x+7+8
47=2x+15
2x=47-15
2x=32
x=32/2
=16
Train only= 30-(7+8+2)
=30-18=12
(6bi)=x=16
(6bii)
number who travelled by at leasttwo means
=7+1+3+8
=19
(7a)
given;
(x-2)/4=(x+2)/2x
2x*(x-2)=4*(x+2)
2x^2 -4x= 4x+8
2x^2-4x-4x-8=0
2x^2-8x-8=0
x^2-4x-4=0
x^2-4x=4
x^2-(4* 1/2)=4+(2)^2
(x-2)^2=4+4
(x-2)^2=8
(x-2)= sqr root
x-2=+-2.83
x=+-2.83
x=+_2.83+2
x=-2.83+2
x=4.83 or x=-0.83
(7b)
P+Q+S=180 degree(sum of angles in a triangle)
52 degree+ 90 degree+ S= 180 degree
142+ S=180
S=180-142
S=38 degree
(i)52+38+SQT
=180 degree
SQT=180-90
SQT=90 degree
(ii)PQT= 52 degree
(3b)
h=7cm
T=462cm^2
T=pie sqr + 2 pie rH
462= pie( r ^2 +2*7*r)
462/3.142
=r sqr= =14r
r sqr+ 14r=147
r sqr +14r- 147=0
r= 14+-( (sqr(14))-4*1*147)/2*1
r=-(14 +-(196-4))/2
r=(-14+_12)/2
r=(-14+12)/2 or
r=2/2
=1cm
(4a)
Pr(3)=x/total
total=25+30+x+28+40+32
=155+x
0.225=x/155+ x
=34.875+0.225x=x
x-0.225x=34.875
=0.775x=34.875 degree
x=34.875/0.775
=45
(4b)
Pr(even)=30+28+40+32
=90
Pr(even)=90/200=9/20
Pr(prime no)=25=30+45+40
=140
Pr(prime no)=140/200=14/20
Pr(even or prime)=9/20 + 14/20
(5a)
Area PSR=1/2*PR*SM
PR=8+6=14cm
36=1/2 * 14* 6
36=1/2 * 14* 6 *QR
QR=8.6cm
(5b)
diagram
sin45 degree= 10.65/h
h=10.65/sin 45 degree
=10.65/0.7071
h=15.06cm
Given (3p+4q)/(3p-4q) = 2
3p+4q=2*(3p-4q)
3p+4q=6p-8q
3p-6p=-4q-8q
=-3p=-12q
p/q=-12/-3
p/q=4/1, P=4, q=1
p:q=4;1
(11b)
(i)
perimeter(p)=PQ+PU+QR
PQ=UT+TS+SR
34=PQ+UR+4+4
PQ=UR
34-8=2PQ
PQ=26/2=13cm
(ii)
13=2+TS+2
TS=13-4=9cm
radius®=9/2=4.5cm
Area(A)= pie r sqr+22/7*(4.5)^2
=445.5/7
63.64cm^2
(8a)
diagram
z=110 degree(sum of angles on a straight line)
z=180-110
z=70 dgree
w degree= 70 degree
x+r+w degree= 180 degree(sum of angle in a triangle)
x+2x+70 degree=180 degree
3x=110
x=110/3=36.7 dgeree
(8b)
B=10, G=12
TB=600.00
TB=TG+600
mean of TB=100+ mean of TG
where TB= total collection of boys
TG=total collection by girls
mean of TB= ET/B
mean of TB= (TG+600)/10
100+ mean of TG= (TG+600)/100
mean of TG= mean of TG/12
100+ mean of G/12= (TG+600)/10
(100+TG)/12=(TG+600)/10
10*(1200+TG)=12*(TG+600)
=12000+10TG=12TG+7200
=12TG-10TG=12000-7200
2TG=4800
TG=N2400
TB=TG+600
TB=600+2400
Tb=N3000
(6a)
first term9a)=1.0=1
common diff(d)=3-1=2
last term(L)=101
L=a+(n-1)d
101=1+(n-1)*2
(n-1)*2=100
n-1=100/2
n-1=50
n=501+1
n=51
sum(s)=n/2(2a+(n-1)d)
S=51/2(2*1+(51-1)*2)
s=25.5(2+100)
S=25.5*102=2601
(6b)
UC=95
Bus & Train(B&T)=7
Train & Car( T & C)=3
B&T&C=8
Bus only(x)=B&C only
Bus(b)=47
train(T)=30
(draw the venn diagram)
Bus only= 47-(7+8+x)
x=47-15+x
47=x+x+7+8
47=2x+15
2x=47-15
2x=32
x=32/2
=16
Train only= 30-(7+8+2)
=30-18=12
(6bi)=x=16
(6bii)
number who travelled by at leasttwo means
=7+1+3+8
=19
(7a)
given;
(x-2)/4=(x+2)/2x
2x*(x-2)=4*(x+2)
2x^2 -4x= 4x+8
2x^2-4x-4x-8=0
2x^2-8x-8=0
x^2-4x-4=0
x^2-4x=4
x^2-(4* 1/2)=4+(2)^2
(x-2)^2=4+4
(x-2)^2=8
(x-2)= sqr root
x-2=+-2.83
x=+-2.83
x=+_2.83+2
x=-2.83+2
x=4.83 or x=-0.83
(7b)
P+Q+S=180 degree(sum of angles in a triangle)
52 degree+ 90 degree+ S= 180 degree
142+ S=180
S=180-142
S=38 degree
(i)52+38+SQT
=180 degree
SQT=180-90
SQT=90 degree
(ii)PQT= 52 degree
(3b)
h=7cm
T=462cm^2
T=pie sqr + 2 pie rH
462= pie( r ^2 +2*7*r)
462/3.142
=r sqr= =14r
r sqr+ 14r=147
r sqr +14r- 147=0
r= 14+-( (sqr(14))-4*1*147)/2*1
r=-(14 +-(196-4))/2
r=(-14+_12)/2
r=(-14+12)/2 or
r=2/2
=1cm
(4a)
Pr(3)=x/total
total=25+30+x+28+40+32
=155+x
0.225=x/155+ x
=34.875+0.225x=x
x-0.225x=34.875
=0.775x=34.875 degree
x=34.875/0.775
=45
(4b)
Pr(even)=30+28+40+32
=90
Pr(even)=90/200=9/20
Pr(prime no)=25=30+45+40
=140
Pr(prime no)=140/200=14/20
Pr(even or prime)=9/20 + 14/20
(5a)
Area PSR=1/2*PR*SM
PR=8+6=14cm
36=1/2 * 14* 6
36=1/2 * 14* 6 *QR
QR=8.6cm
(5b)
diagram
sin45 degree= 10.65/h
h=10.65/sin 45 degree
=10.65/0.7071
h=15.06cm
MATHS SYMBOLS TO BE USE
__________________
/ means DIVISION
* means multiplication
tita u should know dat.
rais means raise to power
^ means raise to power
sqr rut/ squar rut means square root
----(1) means equation 1
yr means year
f(x-xbar) means x MINUS x BAR as in statistics
which means that MINUS WILL BE ON TOP OF x.
, (Comma) means NEXT LINE, THIS MEANS THAT THE FOLLOWING NUMBER IS UNDER THE
NUMBER IT IS FOLLOWING i.e UNDER.
It is
usually used during STATISTICS when drawing a
table.
X:1,2,3,4,
FX: 4,6,8,10
FX-Xbar: 10,8,6,4,
DRAW A TABLE WITH X|FX|(FX-Xbar)
The above statement means that:
~For X, it has 1 2 3 4 5 6 under it. which means 1
is under 2, 2 is under 1, 3 is under 2, 4 is under 3
and so on...
~Under FX you have 4, then 6 under 4, then 8g
under 6, then 10 under 8, then 12 under 10.....
~Under FX-Xbar you have 10, then 8 under 10,
then 6 under 8, then 4 under 6, then 2 under 4,
then 1 under 2....
IN A CLEARER WAY:
→ comma means NEXT LINE(e.g)
x : 1,2,3
fx : 4,5,6
fx-xbar : 10,8,6,4
x|fx |fx-x¯¯|
1| 4 | 10 |
2| 6 | 8 |
3| 8 | 6 |
4| 10| 4 |
Class interval:
60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99.
X: 62,67,72,77,82,87,92,97.
F: 2,3,6,11,8,7,2,1.
FX: 124,201,432,847,656,609,184,97.
F(x-x bar)2:
561.12,414.18,273.36,33.66,84.48,476.42,351.12,333.06
MEANING OF THE ABOVE EXPRESSION:
Bar means Minus on top of d number or Variable
and comma means next line which means each of
them are unda. Eg 60-64 is unda Class interval,
then 65-69 is unda 60-64,etc .So comma means
unda.
NOTE THAT WHEN U SEE SOMETHING LIKE THE
ABOVE TWO EXAMPLES, U WILL NEED TO DRAW A
TABLE..
YOU NEED TO KNOW THESE ALSO:
MATHS CODES:
1) ,(comma) means next line.
(e.g)
x : 1,2,3
fx : 4,5,6
fx-xbar : 7,8,9
x|fx |x¯¯|
1| 4 | 7 |
2| 5 | 8 |
3| 6 | 9 |
2)*=multiplication sign. y
3)^ = Riase to pwer
4)P also means raised to power eg 10P6 means 10 raised to power six.
5)log3(base 4) ..Note:the base must be SUBSCRIPT .
6)x bar = mean symbol(x¯¯)
7)Pie = pie symbol eg Area of a circle is (Pie r2).
8)Tita = θ eg Sinθ.
10)Root or Rut or Sqrt or sqr root = √ ; eg Root2 means √2
11)/ means ÷
12)----(1) means equation 1
__________________
/ means DIVISION
* means multiplication
tita u should know dat.
rais means raise to power
^ means raise to power
sqr rut/ squar rut means square root
----(1) means equation 1
yr means year
f(x-xbar) means x MINUS x BAR as in statistics
which means that MINUS WILL BE ON TOP OF x.
, (Comma) means NEXT LINE, THIS MEANS THAT THE FOLLOWING NUMBER IS UNDER THE
NUMBER IT IS FOLLOWING i.e UNDER.
It is
usually used during STATISTICS when drawing a
table.
X:1,2,3,4,
FX: 4,6,8,10
FX-Xbar: 10,8,6,4,
DRAW A TABLE WITH X|FX|(FX-Xbar)
The above statement means that:
~For X, it has 1 2 3 4 5 6 under it. which means 1
is under 2, 2 is under 1, 3 is under 2, 4 is under 3
and so on...
~Under FX you have 4, then 6 under 4, then 8g
under 6, then 10 under 8, then 12 under 10.....
~Under FX-Xbar you have 10, then 8 under 10,
then 6 under 8, then 4 under 6, then 2 under 4,
then 1 under 2....
IN A CLEARER WAY:
→ comma means NEXT LINE(e.g)
x : 1,2,3
fx : 4,5,6
fx-xbar : 10,8,6,4
x|fx |fx-x¯¯|
1| 4 | 10 |
2| 6 | 8 |
3| 8 | 6 |
4| 10| 4 |
Class interval:
60-64,65-69,70-74,75-79,80-84,85-89,90-94,95-99.
X: 62,67,72,77,82,87,92,97.
F: 2,3,6,11,8,7,2,1.
FX: 124,201,432,847,656,609,184,97.
F(x-x bar)2:
561.12,414.18,273.36,33.66,84.48,476.42,351.12,333.06
MEANING OF THE ABOVE EXPRESSION:
Bar means Minus on top of d number or Variable
and comma means next line which means each of
them are unda. Eg 60-64 is unda Class interval,
then 65-69 is unda 60-64,etc .So comma means
unda.
NOTE THAT WHEN U SEE SOMETHING LIKE THE
ABOVE TWO EXAMPLES, U WILL NEED TO DRAW A
TABLE..
YOU NEED TO KNOW THESE ALSO:
MATHS CODES:
1) ,(comma) means next line.
(e.g)
x : 1,2,3
fx : 4,5,6
fx-xbar : 7,8,9
x|fx |x¯¯|
1| 4 | 7 |
2| 5 | 8 |
3| 6 | 9 |
2)*=multiplication sign. y
3)^ = Riase to pwer
4)P also means raised to power eg 10P6 means 10 raised to power six.
5)log3(base 4) ..Note:the base must be SUBSCRIPT .
6)x bar = mean symbol(x¯¯)
7)Pie = pie symbol eg Area of a circle is (Pie r2).
8)Tita = θ eg Sinθ.
10)Root or Rut or Sqrt or sqr root = √ ; eg Root2 means √2
11)/ means ÷
12)----(1) means equation 1
GOODLUCK
=================================
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