Nabteb 2015 Mathematics Obj And Theory Answers.
Note :- PLEASE Make sure You Translate some word back to Mathematics equations E.g degree, approximate,cheta and Square E.T.C
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Theory
SECTION A
Q1
(a)
Log 8/Log12-Log3
(a)
Log 8/Log12-Log3
Solution :-
Log2^3/Log12/Log3
=Log2^3/Log2^2+Log3-Log3
= 3 Log2/2 Log2
= 3/2.
Log2^3/Log12/Log3
=Log2^3/Log2^2+Log3-Log3
= 3 Log2/2 Log2
= 3/2.
(1b)
81^0.25/32^0.2
81^0.25/32^0.2
Solution :-
3^4(0.25)/2^5(0.2)
= 3^1/2^1
= 3/2.
3^4(0.25)/2^5(0.2)
= 3^1/2^1
= 3/2.
Q2
(a)
5th term = a+4d=9
8th term=a+7d=27
Now
a+4d=9.......(1)
a+7d=27.....(2)
---------------------------
-3d=-18
d=-18/-3
d=6
(a)
5th term = a+4d=9
8th term=a+7d=27
Now
a+4d=9.......(1)
a+7d=27.....(2)
---------------------------
-3d=-18
d=-18/-3
d=6
From (1) above
a+4d=9
a+4(6)=9
a+24=9
a=9-24
a=-15.
a+4d=9
a+4(6)=9
a+24=9
a=9-24
a=-15.
2b.
First term a=x
Third term ar^2=y
(i) a/ar^2=x/y
1/r^2=x/y
r^2=y/x
r=y/x square
First term a=x
Third term ar^2=y
(i) a/ar^2=x/y
1/r^2=x/y
r^2=y/x
r=y/x square
(ii)
a=8 ar^2=18
a/ar^2=8/18
1/r^2=4/9
r^2=9/4
r=9/4 square
=r =3/2.
a=8 ar^2=18
a/ar^2=8/18
1/r^2=4/9
r^2=9/4
r=9/4 square
=r =3/2.
Q3.
a.
4x-3/3-4x+2/5=1
a.
4x-3/3-4x+2/5=1
Solution :-
5(4x-3)-3(4x+2)=15
20x-15-12x-6=15
8x-21=15
8x=15+21
8x=36
X=36/8
=9/4.
X=9/4 or 4.5.
5(4x-3)-3(4x+2)=15
20x-15-12x-6=15
8x-21=15
8x=15+21
8x=36
X=36/8
=9/4.
X=9/4 or 4.5.
(bi) X=[2,3,5,7]
(ii) y=[1,2,3,4,5,6,7]
(iii) z=[2,4,6,8,10]
(ii) y=[1,2,3,4,5,6,7]
(iii) z=[2,4,6,8,10]
(c)i.
Draw your set
Draw your set
(3Cii) x^1n z^1n y
No=[1,2,3,4,5,6,7,8,9,10]
x^1=[1,4,6,8,9,10]
Z^1=[1,3,5,7,9]
X^1 n Z^1=[1,9]
Therefore X^1 n Z^1 n Y=[1].
No=[1,2,3,4,5,6,7,8,9,10]
x^1=[1,4,6,8,9,10]
Z^1=[1,3,5,7,9]
X^1 n Z^1=[1,9]
Therefore X^1 n Z^1 n Y=[1].
Q4
pr(musa will pass)=2/3.
pr(isa will pass)=5/8.
pr(umaru will pass)=3/4.
(a)pr(the three will pass)=7/3+5/8+3/4=5/16.
pr(musa will pass)=2/3.
pr(isa will pass)=5/8.
pr(umaru will pass)=3/4.
(a)pr(the three will pass)=7/3+5/8+3/4=5/16.
(4b).
Pr(none of them will pass)
=(1-2/3)*(1-5/8)*(1-3/4)
1/3*3/8*1/4=1/32.
(4c)
Pr(musa and isa only will pass)
=2/3*5/8*1/4
=5/48.
Pr(none of them will pass)
=(1-2/3)*(1-5/8)*(1-3/4)
1/3*3/8*1/4=1/32.
(4c)
Pr(musa and isa only will pass)
=2/3*5/8*1/4
=5/48.
Q5
Draw the diagram
Tan 68 degree=8/BC
BC=3.23m
Therefore
BD=3.23/2
=1.62m.
Draw the diagram
Tan 68 degree=8/BC
BC=3.23m
Therefore
BD=3.23/2
=1.62m.
(ii)
Draw diagram again put 1.62m between B and D
Tan cheta=8/1.62=4.9383
Cheta=tan-1 (4.9383)
Cheta=78.6degree approximate to 79degree
Therefore<ADB=78.6degree.
tan cheta=3.23/8=0.4038
cheta=tan-1 (0.4038)
Therefore <DAC=21.99degree approximate to 22degree.
Draw diagram again put 1.62m between B and D
Tan cheta=8/1.62=4.9383
Cheta=tan-1 (4.9383)
Cheta=78.6degree approximate to 79degree
Therefore<ADB=78.6degree.
tan cheta=3.23/8=0.4038
cheta=tan-1 (0.4038)
Therefore <DAC=21.99degree approximate to 22degree.
SECTION B
Q6.
a. 3^x+1:-9^1=1
Solution:-
3^x+1 divide by 3^-2= 3 cheta
3^x+1/3^-2= 3 cheta
3^x+1+2 = 3 cheta
3^x+3= 3 cheta
a. 3^x+1:-9^1=1
Solution:-
3^x+1 divide by 3^-2= 3 cheta
3^x+1/3^-2= 3 cheta
3^x+1+2 = 3 cheta
3^x+3= 3 cheta
Therefore
X+3=0
X=-3
X+3=0
X=-3
(b)
3x+2y=7.......(1)
7x-3y=1........(2)
(1)*3=9x+6y=21.....(3)
(2)*2=14x-6y=2.......(4)
----------------------------
23X=23
X=23/23=1
X=1.
3x+2y=7.......(1)
7x-3y=1........(2)
(1)*3=9x+6y=21.....(3)
(2)*2=14x-6y=2.......(4)
----------------------------
23X=23
X=23/23=1
X=1.
from (1)
3x+2y=7
3(1)+2y=7
3+2y=7
2y=7-3
2y=4
Y=4/2
Y=2.
3x+2y=7
3(1)+2y=7
3+2y=7
2y=7-3
2y=4
Y=4/2
Y=2.
6c.
18x^2-8/6x^2-11x-10
Solution:-
18x^2-8/6x^2+4x-15x-10
18x^2-8/2x(3x+2)-5(3x+2)
18x^2-8/(3x+2) (2x-5)
2(9x^2-4)/(3x+2)(2x-5)
18x^2-8/6x^2-11x-10
Solution:-
18x^2-8/6x^2+4x-15x-10
18x^2-8/2x(3x+2)-5(3x+2)
18x^2-8/(3x+2) (2x-5)
2(9x^2-4)/(3x+2)(2x-5)
=2(3x-2)/2x-5.
Q7.
Square 3(2 square 2 + square) + square 2(square 2 (square 3 - square 2)
Solution:-
2 square 6+ square 9 + square 6- square 4
3 square +3-2
=3 square 6+1.
Square 3(2 square 2 + square) + square 2(square 2 (square 3 - square 2)
Solution:-
2 square 6+ square 9 + square 6- square 4
3 square +3-2
=3 square 6+1.
b.
11,a,b,21^1/2
a=11, d=a-11, n=4
Ln=21^1/2
Ln= a+(n-1)d
Ln= 11+(3)(a-11)
43/2=11+(3)(a-11)
43=2[11+3a-33]
43=2[39-22]
43=69-44
69=87
a=87/6=14.5.
11,a,b,21^1/2
a=11, d=a-11, n=4
Ln=21^1/2
Ln= a+(n-1)d
Ln= 11+(3)(a-11)
43/2=11+(3)(a-11)
43=2[11+3a-33]
43=2[39-22]
43=69-44
69=87
a=87/6=14.5.
Q8
a.
Perimeter =2per r
=2*22/7*56
2*22*8=352m.
P=100+352=452m.
a.
Perimeter =2per r
=2*22/7*56
2*22*8=352m.
P=100+352=452m.
b.
Draw the diagram
(i) sin 37degree =AD/15
AD= 15+Sin 37degree
AD =15*0.6018
AD =9.03cm
Draw the diagram
(i) sin 37degree =AD/15
AD= 15+Sin 37degree
AD =15*0.6018
AD =9.03cm
(ii) cos 37degree=DE/15
DE=15*Cos 37degree
DE=15*0.79786
DE=11.98cm.
DE=15*Cos 37degree
DE=15*0.79786
DE=11.98cm.
(ii)
Total Area=L*b
Area =(11.98)*2*9.03
Area =216.36cm^2.
Area of Traingle=1/2 b*h sin cheta
=1/2*11.94*9.03*sin 37 cheta
=54.09*0.6018
=32.55cm^2.
Area of shaded portion
=216.36-32.55
=183.81cm^2.
Total Area=L*b
Area =(11.98)*2*9.03
Area =216.36cm^2.
Area of Traingle=1/2 b*h sin cheta
=1/2*11.94*9.03*sin 37 cheta
=54.09*0.6018
=32.55cm^2.
Area of shaded portion
=216.36-32.55
=183.81cm^2.
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