MATHEMATICS QUESTIONS AND ANSWERS NOW READY
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^ it means raise to power
/ division
* multiplication
X normal X
SECTION A ANS ALL
==============================
1a)
(y-1)log4^10= ylog16^10
log4^10 (y-1)= log16^y10
4^(y-1)=16y
4^y-1=4^2y
y-1=2y
-1=2y=y
-1=y
y= -y
1b)
let the actual time for 5km/hr be t
for 4km/hr=30mint + t
4km/hr=0.5 + t
distance = 4(0.5+t)
=2*4t
for 5km/hr, time= t
distance =5t
1+4t=5t
t=2hrs
actual distance = 5*2=10km
==============================
2a)
2/3(3x-5)-3/5(2x-3)=3/1
L C M =15
10(3x-5)-9(2x-3)=45
30x-50-18x+27=45
30x-18x=45+50-27
12x-23=45
12x=45+23
12x=68
x=68/12
x=34/6
x=17/3
2b)
U’aS=180-(n+88)
=180-n-88=92-n
also, u’TQ=18m
80degree + 92-n+180-m=180degree
80+92+180-n-m=180degree
352-n-m=180degree
-n-m=180-352
-n-m=-172
+(n+m)= +172
m+n=172dgree
==============================
3a)
Tan 23.6° = h/50
Cross multiply
Tan 23.6° x h/50
h = 50 tan 23.6°
= 21.844m
3b)
Area ofA = 1/2bh
45 = 1/2 x 10 x h
45 = 5h
h = 9cm
Area of < QTUS = 1/2 ( QT + US)h
= 1/2 ( 6 + 16)9
= 99cm^2
==================
4a)
T6=37
T6=a+(6-1)d
T6=a+5d
a+5d=37 —–(eq1)
s6=147
sn=n/2(2a+(n-1)d)
147=3(2a+5d)
49=2a+5d
2a+5d=49 —-(eq2)
a+5d=37 —(eq1)
2a+5d=49 —(eq2)
a=12
4b)
S15=15/2(2(12)+14d)
S15=15/2(24+14d)
from(1)
a+5d=37
12+5d=37
5d=37-12
5d=25
d=5
S15 = 15/2(24+14(15)
S15= 15/2(24+70)
S15=15/2*94
S15=15*42
S15=630
==================
5a)
draw
U=20
B= y-45
S= y-34
B=bag
S=shoe
let n(B)=y
n(S)=y+11
for bag only y-45
for shoe only y-11-45=y-34
5b)
y-45+45+y-34=120
2y-34=120
2y=154
y=154/2
y=77
number of customers who bought shoe = y+11
77+11=88
5c)
n(bag)=77customers
probability =77/120
=0.642
=====================
SECTION B ANS 5 QUESTIONS ONLY
8a )
In Table Form / Tabular form
X = 1, 2, 3, 4, 5
F = m +2, m – 1, 2m- 3, m +5, 3 m- 4 = 8m – 1
Fx = m+2 , 2m – 2, 6 m- 9, 4m +20, 15m – 20 = 28 m – 9
But x̄ ( this symbol ( x̄) means X bar )
= 75 /23
ΣFx / Σf = 75 /23 = 28m – 9/8 m- 1
75/23 = 28m – 9/8m – 1
Cross multiply
75( 8m- 1) = 23 (28 m- 9)
600m – 75 = 644m – 207
– 75 + 207 = 644m – 600 m
132 = 44 m
M = 3
8bi )
In tabular form
X = 1, 2, 3, 4, 5
F = 5, 2, 3, 8, 5
Cum Freq = 5, 7, 10 ,18 , 23
Q 1 = ( N +1 /4) = ( 23+1/4 )
= 6
Q 3 = ( 3N + 1 /4) = ( 3*23+1 /4)
= 18
Inter quarter range = Q 3 – Q 1
=. 18 – 6
= 12
8bii)
Pr . (at least 4 mark )
= 8 +3+2+ 5/23
= 18/23
==============================
10a)
Sin x = 5/13
Using pythagoras rule
M^2 = 13^2 – 5^2 (^ means Raise to power)
M^2 = 169 – 25
M ^2 = 144
M = √144
M = 12
Hence:
Cos x – 2sin x / 2tan x
12/13 – 2(5/13) / 2(5/12)
= 12/13 – 10/23 / 5/6
FIND LCM
= 12 – 10/13 / 5/6
= 12/65
10bi)
Considering < LMB
/MB/^2. = 12^2 – 9.6^2
/MB/^2 = 51.84
/MB/ = √51.84
/MB/ = 7.2m
From < AML
/LA/^2 = 2.8^2 + 9.6^2
/LA/ ^2 = 100
/LA/ = √100
/LA/ = 10m
10bii)
Let the angle be. θ
FromTanθ = 9.6/2.8
Tan θ = 3.4288
θ = Tan^-1 ( 3.4288)
= 73.74°
=============
13ai)
given
x(*)y=x+y/2
i)3(*)2/5=3+2/5/2
=(15+2/5)*1/2
=17/5*1/2
=17/10= 1,7/10
13aii)
8(*)y=8^1/4
=8+y/2 =33/4
32+4y=66
4y=66-32
4y=34
y=34/4
y=17/2
y=8^1/2
13b)
given DABC
AB=(^-4/6) and AC =(3/^-8)
so AP =1/2(^-4/6)
AP=(^-2/3)
hence
CP = CA + AP
CP= -(3/^8)+(^-2/3)
CP = (^-5/11)
100%☑✔✔☑
From www.042portal.blogspot.com
^ it means raise to power
/ division
* multiplication
X normal X
SECTION A ANS ALL
==============================
1a)
(y-1)log4^10= ylog16^10
log4^10 (y-1)= log16^y10
4^(y-1)=16y
4^y-1=4^2y
y-1=2y
-1=2y=y
-1=y
y= -y
1b)
let the actual time for 5km/hr be t
for 4km/hr=30mint + t
4km/hr=0.5 + t
distance = 4(0.5+t)
=2*4t
for 5km/hr, time= t
distance =5t
1+4t=5t
t=2hrs
actual distance = 5*2=10km
==============================
2a)
2/3(3x-5)-3/5(2x-3)=3/1
L C M =15
10(3x-5)-9(2x-3)=45
30x-50-18x+27=45
30x-18x=45+50-27
12x-23=45
12x=45+23
12x=68
x=68/12
x=34/6
x=17/3
2b)
U’aS=180-(n+88)
=180-n-88=92-n
also, u’TQ=18m
80degree + 92-n+180-m=180degree
80+92+180-n-m=180degree
352-n-m=180degree
-n-m=180-352
-n-m=-172
+(n+m)= +172
m+n=172dgree
==============================
3a)
Tan 23.6° = h/50
Cross multiply
Tan 23.6° x h/50
h = 50 tan 23.6°
= 21.844m
3b)
Area of
45 = 1/2 x 10 x h
45 = 5h
h = 9cm
Area of < QTUS = 1/2 ( QT + US)h
= 1/2 ( 6 + 16)9
= 99cm^2
==================
4a)
T6=37
T6=a+(6-1)d
T6=a+5d
a+5d=37 —–(eq1)
s6=147
sn=n/2(2a+(n-1)d)
147=3(2a+5d)
49=2a+5d
2a+5d=49 —-(eq2)
a+5d=37 —(eq1)
2a+5d=49 —(eq2)
a=12
4b)
S15=15/2(2(12)+14d)
S15=15/2(24+14d)
from(1)
a+5d=37
12+5d=37
5d=37-12
5d=25
d=5
S15 = 15/2(24+14(15)
S15= 15/2(24+70)
S15=15/2*94
S15=15*42
S15=630
==================
5a)
draw
U=20
B= y-45
S= y-34
B=bag
S=shoe
let n(B)=y
n(S)=y+11
for bag only y-45
for shoe only y-11-45=y-34
5b)
y-45+45+y-34=120
2y-34=120
2y=154
y=154/2
y=77
number of customers who bought shoe = y+11
77+11=88
5c)
n(bag)=77customers
probability =77/120
=0.642
=====================
SECTION B ANS 5 QUESTIONS ONLY
8a )
In Table Form / Tabular form
X = 1, 2, 3, 4, 5
F = m +2, m – 1, 2m- 3, m +5, 3 m- 4 = 8m – 1
Fx = m+2 , 2m – 2, 6 m- 9, 4m +20, 15m – 20 = 28 m – 9
But x̄ ( this symbol ( x̄) means X bar )
= 75 /23
ΣFx / Σf = 75 /23 = 28m – 9/8 m- 1
75/23 = 28m – 9/8m – 1
Cross multiply
75( 8m- 1) = 23 (28 m- 9)
600m – 75 = 644m – 207
– 75 + 207 = 644m – 600 m
132 = 44 m
M = 3
8bi )
In tabular form
X = 1, 2, 3, 4, 5
F = 5, 2, 3, 8, 5
Cum Freq = 5, 7, 10 ,18 , 23
Q 1 = ( N +1 /4) = ( 23+1/4 )
= 6
Q 3 = ( 3N + 1 /4) = ( 3*23+1 /4)
= 18
Inter quarter range = Q 3 – Q 1
=. 18 – 6
= 12
8bii)
Pr . (at least 4 mark )
= 8 +3+2+ 5/23
= 18/23
==============================
10a)
Sin x = 5/13
Using pythagoras rule
M^2 = 13^2 – 5^2 (^ means Raise to power)
M^2 = 169 – 25
M ^2 = 144
M = √144
M = 12
Hence:
Cos x – 2sin x / 2tan x
12/13 – 2(5/13) / 2(5/12)
= 12/13 – 10/23 / 5/6
FIND LCM
= 12 – 10/13 / 5/6
= 12/65
10bi)
Considering < LMB
/MB/^2. = 12^2 – 9.6^2
/MB/^2 = 51.84
/MB/ = √51.84
/MB/ = 7.2m
From < AML
/LA/^2 = 2.8^2 + 9.6^2
/LA/ ^2 = 100
/LA/ = √100
/LA/ = 10m
10bii)
Let the angle be. θ
From
Tan θ = 3.4288
θ = Tan^-1 ( 3.4288)
= 73.74°
=============
13ai)
given
x(*)y=x+y/2
i)3(*)2/5=3+2/5/2
=(15+2/5)*1/2
=17/5*1/2
=17/10= 1,7/10
13aii)
8(*)y=8^1/4
=8+y/2 =33/4
32+4y=66
4y=66-32
4y=34
y=34/4
y=17/2
y=8^1/2
13b)
given DABC
AB=(^-4/6) and AC =(3/^-8)
so AP =1/2(^-4/6)
AP=(^-2/3)
hence
CP = CA + AP
CP= -(3/^8)+(^-2/3)
CP = (^-5/11)
100%☑✔✔☑
From www.042portal.blogspot.com
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