math-algebra short techniques and formulas by tanbircox
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MATHTRANSCRIPT
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( )( ) ( )
( ) (x)
( )
.
/ .
/
( ) (y)
( )
.
/ .
/
( ) ( ) ( ) [ (x) +(y)]
( ) ( )
( ) ( ) [ (x) (y)]
( ) ( )
( ) ( ) ( ) ( )
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( )
( ) ( )
( ) ( ) ( ) ( )
( )( )( ) ( ) ( )
( )
( ) ( )
( )
( ) ( )
( )( )
( ) *( ) ( ) ( ) +
( ) ( ) ( ) ( )( )( )
( )( )
( )( )
( )( )
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, q (a b ) x q (q= a+b) r (r=ab) ( ) ( )( )
1) q>0, r>0 ( )( )
2) q0 ( )( )
3) q>0, r
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a (n a )
( )
( )
( ) ( )
. /
( )
x =y
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a n
10
x =
x =
( )
.
/
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, MCQ , MCQ Answer Choice x y x y ( )
,
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1(First Term) n(Last Term) (Common Difference) =Second term first Term = 1
(Number of Terms) =
+ 1
(Sum of the Series) =
=
( )
(Avarage of the Series) =
=
a + (a+d) + (a+2d) ( d) n ,
= a
d =
= n
n ( ) (n )d
n =
n =
* (n )d+
, = a
r =
= n n =
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r >0 1 r ,
n
r < 0 1 r (.1 -.9 ) ,
n
-1
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1, 4, 9, 16. 5, 5 ]
1 , 9 , 25, 49, 81 , 5 7 9 ]
9 36 81 144 .. 5, ( ) ( ) ]
81, 27, . 3, 1 9 , ]
1, 2, 3, 5, 8 , 13 , 21 , 34. 55[ = ]
8, 11, 17, 29, 53,.. 101 [8, 8+(11-8),11+(17-11), ]
1, 3, 6, 10, 15, 21,. 28 [ 1,(1+2),(3+3),(6+4), (10+5)]
2, 8, 18, 32, 50 [ 2,(2+6),(8+6+4),(18+6+4+4), (32+6+4+4+4)]
2, 4, 8, 14, 22, 32. 44 [ 2,(2+2),(4+2+2),(8+2+2+2), (14+2+2+2+2)]
0, 5, 12, 21, 32.. 45 [ 0,(0+5),(5+5+2),(12+5+2+2), (21+5+2+2+2)]
13, 17, 25, 41,.. 73 [ 13,(13+22),(17+23),(25+24), (41+25)]
5, 7, 11, 19,.. 5 [ 5,(5+21)(7+22),(11+23),(19+24)]
8 [ 4,(4+21)(6+22),(10+23),(18+24)]
3, 6, 4, 9, 5, 12, 6,. 5 , t1:t3:t5:t7 5 | t2:t4:t6:t8 9 5-
8 9 7 , (t1 +4),(t2+8)(t3+4)(t4+8)]
7 5 5 8 9
, t3:t5:t7 ( 7-2),(27-4),(27-6),(27-8)| t4:t6:t8 (5 ) (5 ) (5 9)-
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0, 9, 17, 2435, 39, 42 .
5 8
1, 3, 6 9 5 8
7
7 5
7 9 5
9
7 8 5 5 9 7
7 5 9 7 5
15, 13, 12, 11, 9, 9..
7 8 8 7
8 5 8 9
9 7 5 8
9 5 7 99
5 7
5 7 7
5 8 7 8
9 7 5 5 8
21, 18, 9 7
8 5 5 9
5 9
7 7 5 5
5 9 5 5
5 7
7 8 8 8 8
3, 7, 28, 32, 8, 12, 48, 5
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