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1
D
D
roll
slide D
D
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2
D
D
D
reflection
D
D
D
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3
grouping,array's, at the rate
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4
grouping sharing
Arre'y prod-uct, - Rate porduct andGrouping - Cartesian prod-uct
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5
Groupingsharing
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6
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7
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8
conservations
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9
AM PM
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10
Box chart
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11
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12
i
=, <,>
i i i
, ,
i
2, 3
logaa =1; loga1 = 0
log xy = log x + log y;
log xy
= log x - log y ;
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13
ii
iii
ii
Of
1.01011011101111—1.12112111211112—
2 , 3 , 5
2 , 3
a b
log xn = n log x, Nlogaa = N
ii
ii
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14
iviii
(100a + 10b + c)(a, b, c
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15
v
¼, ¾.....
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16
2n, 2n+1
ax x a z
,m n z(i) am . an = am+n (ii) (am)n = amn
(iii) am/an =am-n (m-n) N (iv)am.bm = (ab)m (v)
x2y
(i)
a, b, c ax2 +
bx + c, a 0
.:
(x + y + z)2
x2 + y2 + x2+ 2xy + 2yz + 2zx
i
ii
i
ii
iii
2+x 2x, 7x+y 7xy
(a b)2 = a2 2ab + b2,a2 – b2 = (a – b) (a + b)
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17
(x ± y)3 x3 ± y3 ± 3xy (x ± y)x3 + y3 + z3 3xyz (x + y + z) (x2 + y2 + z2 – xyyz zx)x3 +y3
(x + y)(x2 xy + y2)x3 y3
(x y)(x2 + xy + y2)
(ii)
x- y-
x- y-
iii
ax2+bx+c=0, (a 0).
iv
n n
n .
iv
x + a x + b
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18
(i)
i sin2A + cos2A = 1,
(ii) 1 + tan2A = sec2A,(iii) cot2A + 1 = cosec2A.
i
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19
(ii)
P (x1, y1) Q (x2, y2)
m : n
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20
i (i)
(ii)
1800
ii
(i)
(ii
(iii
(iv
(v
ii
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21
ii
iii
1800
(iii)
().
Riders
iii
2D 3D
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22
iv
v
().
( ).
ii
iii
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23
(iv)
iv
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24
(v)
(vi)
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25
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26
(vii)
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27
(i) ii
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28
(Pie dia-grams)
(i)
(ii)
i
ii
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29
(i)