1

D

D

roll

slide D

D

2

D

D

D

reflection

D

D

D

3

grouping,array's, at the rate

4

grouping sharing

Arre'y prod-uct, - Rate porduct andGrouping - Cartesian prod-uct

5

Groupingsharing

6

7

8

conservations

9

AM PM

10

Box chart

11

12

i

=, <,>

i i i

, ,

i

2, 3

logaa =1; loga1 = 0

log xy = log x + log y;

log xy

= log x - log y ;

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

14

iviii

(100a + 10b + c)(a, b, c

15

v

¼, ¾.....

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)

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

18

(i)

i sin2A + cos2A = 1,

(ii) 1 + tan2A = sec2A,(iii) cot2A + 1 = cosec2A.

i

19

(ii)

P (x1, y1) Q (x2, y2)

m : n

20

i (i)

(ii)

1800

ii

(i)

(ii

(iii

(iv

(v

ii

21

ii

iii

1800

(iii)

().

Riders

iii

2D 3D

22

iv

v

().

( ).

ii

iii

23

(iv)

iv

24

(v)

(vi)

25

26

(vii)

27

(i) ii

28

(Pie dia-grams)

(i)

(ii)

i

ii

29

(i)