JOSHIYEMZY

 joshiyemzy Maths Type D
1 - 10 : ABADCEBAED
11 - 20 : BBBAEBABEE
21 - 30 : AEBCDAEDDB
31 - 40 : DCDEBCBCDB
41 - 50 : BEBDBEDEDA
51 - 60 : CABBEEBABC
MTH TYPE A
1 - 10 : DEDEDADBDA
11 - 20 : BBDADCDACC
21 - 30 : BBCCAEBABA
31 - 40 : AADEDDBABC
41 - 50 : CCADEDECCA
51 - 60 : DBEBDABAAD
See maths Symbols we are using
1 a )
x :y :z * 6: 5: 8
M =x /6 = y /5 =5 / 8
x :y :z * 6m :5 m :8 m
1 . 8x = 6m
y = 3 m
z = 8 m
12 x - 48 / 4 y + 2 =12 (6 m )- 8( 8 m )/ 4( 5m ) + 8m
= 72 m - 72 m /20 m +8 m
= 0 m /28 m
= 0
1 b )
un = ar^ 1
us =ar 46
2 / 81 = 2r ^ 4
81 × 2r ^ 4 / 81 × 2= 2 /81 × 2
r ^ 4= 1 /81
r = 4rot 1 /81 , r =1 /3 .
ii )sum = a( 1- r ^ n )/1 - r
= 2 (1 - ( 1/ 3 )5 )/ 1- 1/ 3
= 2 (1 - 1 / 243)/2 / 3
= ( 242/243)/ 2 /3
484/ 243- 2 / 3
484/ 243× 3/ 2
= 242/ 81
2 a )
number of sides = 12
radius of circle= 10 cm
area =?
n ש 2= 360
12 © 2 =360
© 2 = 360/12 =30 °
© 1 + © 2 =180- 30
© 1 = 150
When © 1 and © 2 are interior and exterior
angle of a polygon A sector has are .
Area of sector =© /360× rot8 ^ 2
= 150/ 360× 22 /7 × 100/1
A = 130- 95 cm^ 2
2 b )
1 / 2( 2x + 1 )- 2 / 5( x - 2)= 3
2 x + 1/ 3- 2 x - 4/ 3 =3
10 x +5 - 6 x +12 /15 =3 / 1
Cross multiple
4 x + 17 = 45
4 x /4 = 28 / 4
x = 7 .
No 4 )
Total Fruit = 80 + 60 = 140
( ai )
( i) Pr one of each fruit is picked
( 79 / 140 * 60 / 139) + ( 59 / 140 * 80 / 139)
= 4740 /19 , 460 + 4720 / 19 , 460
= 9460 /19 , 460 = 0 . 486
4 aii )
Pr one type of fruit is picked
( 79 / 140 * 78 / 139) + (39 / 140 * 5 p/ 139)
= 6162 /19 , 460 + 3422 / 19 , 460
= 9584 / 19 , 460 = 0. 492
4 b )
5 X /8 - 1 /6 ≤ X / 3 + 7/ 24
Multiply through by 24 i:e
15 X - 4≤ 8 X + 7
15 X - 8X ≤ 7 + 4
7 X = 11
X ≤ 11 /7 ===> X ≤ 1 4/ 7
5 a )
3 / X + 2 - 6 / 3X - 1
3 ( 3X - 1 ) - 6 ( X + 2) / (X + 2 ) ( 3 X - 1)
9 X - 3 - 6X - 12 /(X + 2) (3 X - 1)
3 X - 15 / (X + 2) (3 X - 1)
5 b )
C . I = P [ 1 +r /100]^
= 25000 [ 1 +12 /100]^ 3
= 25000 [ 1 +0 . 12 ]^ 3
= 25000 * 1. 4049
= 35122 . 50
= N 35 , 122. 50
6 a )
X + - 3 / 2
X = 2 /3 or X= 2
( X + 3 /2 )^ 2 or ( X - 2 )
( X + 3 /2 ) (X - 2)
X (X - 2) + 3 /2 ( X - 2)
X ^ 2 - 2X + 3 X / 2 - 3
2 X ^ 2 - 4 X + 3 X - 6
2 X ^ 2 - X - 6
6 b )
h / h+ 8 = 6 /10
10 h = 6 h + 48
h = 12
H = h + 8
H = 12 + 8
H = 20
Volume = 1 /3 A . h
= 1 / 3 (10 * 10 ) * 20 - 432/ 3
= 2000 / 3 - 432/ 3
= 1568 /3
= 522. 67 cm 3
7 a )
titan /360× 2 pie r cos t
d = 55 / 360× 2 × 22 / 7× 640 cos 4
d = 55 × 44 × 6400 cos 4 / 2520
d = 55 × 44 × 6400 × 0496 / 2520
d = 15 , 449. 28 / 2520
d = 6130 . 67
d ~ 6130 km.
ii )distance along gent circle
D = tita /360× 2 pie r
D = 55 / 360× 2/ 7 × 22 /7 × 6400/ 1
D = 55 × 44 × 6400 /2520
D = 15 , 488× 6400 / 2520
D = 6144 . 03
D =~ 6146 km.
7 b )
Length of sector tita / 360× 2pie r
L = 120/360× 2 /1 × 22 / 7× 42 / 1
L = 120× 44 × 42 / 2520
L = 221760/2520
L = 88 cm
L = 2 pie r
Where r is the radius of circumference
88 = 2× 22 / 7 × r
88 × 7= 44 r
R = 88 × 7 /44
R = 616/44
R = 14 cm .
Curved surface area
= pie rc
A = 22 / 7 × 14 × 42 /1
A = 22 × 14 × 4 ^ 2 / 7
A = 12936 / 7
A = 1848 cm^ 2 .
8 a )
X = 60 / t - - - - - - - - - - > ( i)
Y = 180/t - - - - - - - - - - > (ii )
T 1 = 60 / X
T 2 = 100/Y
T 1 + T 2 = 5
60 /X + 180/Y = 300 - - - - - - - - - - > ( i)
180/ X + 60 / Y = 260 - - - - - - - - - - > (ii )
Let P =1 /X
2 = 1 / Y
60 p + 180 Q = 300
180p + 6 Q = 200
P + 3Q = 5
9 P + 3 Q = 13
Substract (i )from (ii )
8 p = 8
P = 8/ 8 ÷ P = 1
Subtract P into (i)
P + 3Q = 5
1 + 3 Q = 5
3 Q = 5 - 1
3 Q = 4
Q = 4/ 3
P = 1 ÷ 1 = 1/ X ÷ X = 1
4 / 3 = 1/ Y ÷ Y = 3 /4
8 b )
2001 - - - - - - - - - 25 , 700
2002 - - - - - - - - - 15 /100 X 25 , 700 + 25 , 700 =
29 , 555
Amount of tax in 2002
= 29 , 555 * 12 . 5 /100
= N 3694 . 375
= N 3690
8 c )
Log25
Log16 25 /100
Log16 2 /4
Log4 6 - 1
- 1 /2 Log4 ^ 4
- 1 /2
9 ai )
W =K + C /2
24 = k + C /16
384 = 16 K + C - - - - - - - ( i)
18 = K + C / 4
72 + 4 K + C - - - - - - - - - (ii )
16 K + C = 384
4 K + C = 72
Substact (ii ) from ( i)
12 k /12 = 312/12
K = 26
Substract K into ( i)
16 k + C = 384
C = 384 - 416
C = - 32
W =k + C/ t2
W =26 - 32 / t2
( ii)
When W = - 46 , t=?
- 46 = 26 - 32 / t2
t 2 = - 32 /- 72
t = Sqrt 16 / 36 = 4 /6
= 2 /3
9 b )
V = Pie r 2 . d = 14 , r = 7 cm
1232 = 22 /7 * 7 ^ 2 * h
h = 7 * 1232/ 22 * 49
h = 8624 / 1074
h = 8 cm
11 a )
y ^ 1= x ^ 2 ( 3x + 1)^ 2
v = (2 x +1 )^ 2
v = m ^ 2
dm / dx= 2
dv /dm = 2m
dy /dx =dv /dm × dm / dx
= 2 m × 2
= 4 m
dy /dx =4 (2 x +1 )
dy /dx =udv / dx+ v whole no . dy /dx
= x ^ 2 4 ( xx + 1)^ 2 , × 3 x
= 4 x ^ 2 (2 x +1 )+ 2 x (2 x + 1 )^ 2.
11 b )
[ 3 3 - 1 ]
[ 1 0 2 ]
[ 3 - 2 3]
+ 2 [ 0 - ( - 4 )- 3[ 63 ]
+ - 1( - 2 )
8 + 9 +2
= 19 .
11 c )
m =y 2 - y 1/ x 2- x 1
y - y 1 = m (x - x 2 )
m =4 - 3 / - 1 - 2
m =- 1/ 3
y 1 - y 2 =- 1/ 3 (x - x 2 )
y - 3= 1 /3 (x - 2 )
y - 3= - 4 / 3+ 2 /3
3 y = - x +11
y = - 1 /3 x + 11 /3 .