.MATHEMATICS-Answers
VERIFIED MATHEMATICS OBJ
1-10 CCAADDEECE
11-20 EEBABAADCC
21-30 CBEEDABDDD
31-40 BCCCDDCADE
41-50 BDCDDCDECD
51-60 BCDCAEDCDD
Use This No1 pls is more acurate
====================
8ai)
y=(4x+9)^3
Let u=4x+9
y=u^3
du/dx=4,dy/du=3u^2
dy/dx=dy/du*dy/dx
=4*3u^2
=12u^2
Recall u=4x+9
therefore dy/dx=12(4x+9)^2
8aii)
y=(3x-2)^3(x^2+4)^2
u=(3x-2)^3, v=(x^2+4)^2
du/dx=3.3(3x-2)^3-1
dv/dx=2x.2(x^2+4)^2-1
du/dx=9(3x-2)^2
dv/dx=4x(x^2+4)
dy/dx=Vdu/dx +Udv/dx
=(x^2+4)^2[9(3x-2)^2+(3x-2)^3][4x(x^2+4)]
=(x^2+4)(3x-2)^2(9x^2+36+12x^2-8x)
=(x^2+4)(3x-2)^2(21x-8x+36)
8b)
y-y1=m(x-x1)
y-6=2(x-2)
y-6=2x-4
y=2x-4+6
y=2x+2
6i)
7+8+x = 47
15+ 2x =47
2x = 47- 15
2x/2 = 32/2
divide both side by 2
x=16
6ii)
tran only;:
7+8 + 3 + y=30
18 +y =30
y=30 -18 =12
:. Tran only =12
iii) at least two: 7+ 16+ 3 +8 =34
iv)16 + 7 +12 +16 +8 + 3 + Q=95
62+ Q =95
Q= 95 -62
Q=33 :. Car only = 33
=========================
3a)
NO (3a)
I=#30,000
R=3%
T= 4YRS
P=100 X 1/RT =100 X 30,000/3 X 4
=25,000#
(3B)
#7000 T0 FRANCS
8FRANS= #1
?FRANCS =7000
CROSS MULTIPLY
=#56,000 FRANCS
SPENDING 49,400 FRANCS
56,000-49,400 = 6600
CONVERTING 6,600 FRANCS TO # AT 10 FRANCS TO 1#
10 FRANCS—– 1#
6600 FRANCS—?#
=6,600/10 X1
5)
tabulate
Mark- 21-25,26-30,31-35,36-40,41-45,46-50
F- 6,8,12,4,6,4=40
X- 23,28,33,38,43,48
FX- 138,224,396,152,258,192=1360
Class Boundaries- 20.5-20.5, 25.5-30.5,35.5-40.50,40.5-45.5
5i)
MEAN
(X)=EFX/EF=1360/40=34
MODE
L1+[Fm-Fa/2fm-fa-fb]c
=30.5+[12-8/2(12)-8-4]5
=30.5+[4/12]5
=30.5+1.67
=32.17
7a)
a+2d=11---eq1
-(a+8d)=29
-6d/-6=-18/-6
d=3
Sub for d=3 in eq1
a+2(3)=11
a+6=11
a=11-6
a=5
7b)
L = ar^n-1
729/3 = 3/3 x 3^n-1
243 = 3^n-1
3^5 = 3^-1
5 = n-1
N = 5+1
= 6
Sn = a(r^-1)/r-1 = 3(3^6 - 1)/3-1
Sn = 3( 729 -1)/2
S6 = 3 x 728/2
S6 = 1092
7c)
3x^3/3 + x | 2,1
(2^3 + 2) - (1^3+1)
(8+2) - (1+1)
= 8
3a)
NO (3a)
I=#30,000
R=3%
T= 4YRS
P=100 X 1/RT =100 X 30,000/3 X 4
=25,000#
(3B)
#7000 T0 FRANCS
8FRANS= #1
?FRANCS =7000
CROSS MULTIPLY
=#56,000 FRANCS
SPENDING 49,400 FRANCS
56,000-49,400 = 6600
CONVERTING 6,600 FRANCS TO # AT 10 FRANCS TO 1#
10 FRANCS—– 1#
6600 FRANCS—?#
=6,600/10 X1
5)
tabulate
Mark- 21-25,26-30,31-35,36-40,41-45,46-50
F- 6,8,12,4,6,4=40
X- 23,28,33,38,43,48
FX- 138,224,396,152,258,192=1360
Class Boundaries- 20.5-20.5, 25.5-30.5,35.5-40.50,40.5-45.5
5i)
MEAN
(X)=EFX/EF=1360/40=34
MODE
L1+[Fm-Fa/2fm-fa-fb]c
=30.5+[12-8/2(12)-8-4]5
=30.5+[4/12]5
=30.5+1.67
=32.17
1)
tabulate
Number-
5932
*6141
num
3679
*3113
den
Log
3.7732
3.7882
7.5612
3.5657
3.4931
7.0588
anti log
7.5612
7.0588/0.5024/3=0.1675
anti log
=1471*10
================================
3a)
P=100I/RT=100*30,000/4*3
P=N250,000
================================
5)
tabulate
Mark- 21-25,26-30,31-35,36-40,41-45,46-50
F- 6,8,12,4,6,4=40
X- 23,28,33,38,43,48
FX- 138,224,396,152,258,192=1360
Class Boundaries- 20.5-20.5, 25.5-30.5,35.5-40.50,40.5-45.5
5i)
MEAN
(X)=EFX/EF=1360/40=34
MODE
L1+[Fm-Fa/2fm-fa-fb]c
=30.5+[12-8/2(12)-8-4]5
=30.5+[4/12]5
=30.5+1.67
=32.17
7b)
L = ar^n-1
729/3 = 3/3 x 3^n-1
243 = 3^n-1
3^5 = 3^-1
5 = n-1
N = 5+1
= 6
Sn = a(r^-1)/r-1 = 3(3^6 - 1)/3-1
Sn = 3( 729 -1)/2
S6 = 3 x 728/2
S6 = 1092
7c)
3x^3/3 + x | 2,1
(2^3 + 2) - (1^3+1)
(8+2) - (1+1)
= 8
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