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= = = *

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= = = "

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0)+,!6" "" ++ : %

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15

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: 1, 4

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. 36-37: : 1, 4, 10, 11

: 1

. 42-43: : 1, 2, 3, 6, 7, 8, 9, 10, 11

: 2

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. 121-122: : 1, 2, 3, 4, 5

. 125: : 1, 2, 3, 7

. 128: : 1, 2, 3, 4, 5, 6

:

: 31, 32, 42, 44,

54, 62, 67

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95,101,105,

122, 134,139

1

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1

2

3

1. : ( ) ( )22x 1 5 10x = :

x = .

( ) ( )22x 1 5 10x = 2 22 x 50x 5 = 2 22 x 50x 5 = ( ) ( )2 22 50 x 5 1 =

: 22 50 0 = ( )22 25 0 = ( )( )2 5 5 0 + = 5 0 5 0 = + =

5 5 = = .

. 5, 5 (1) :

( )( )( ) ( )

2

2

5 5 x

2 50 2 5 5 2 5

= = =

+ +

. 5= (1) 0x 0= , ( ). 5= (1) 0x 50= , .

2. : x x 1 x 31

2 3 6+

=

:

, 6.

x x 1 x 36 6 6 62 3 6+

= ( ) ( ) ( )3 x 2 x 1 6 x 3+ =

3x 3 2x 2 6 x 3+ + = + 3x 2x x 6 3 2 3 + = + ( )3 2 x 3 7 + = + ( ) ( ) 3 x 3 7 1 + = + 3 0 + = 3= .

24. 3

. 3 (1) :3 7

x 3

+=

+

. 3= (1) : 0x 2= , .

3. : ( )( ) 3 x 1 3 2x 4 = :

( )( ) 3 x 1 3 2x 4 = ( )2 2 3 x 2x 3 3 4 + = + ( ) ( )2 2 3 2 x 4 1 + = :

2 3 2 0 + = ( )3 1

2

=

3 1

2

= 2 1= =

. 1, 2 (1) :

( )( )( )( )

2

2 4 2 2 2

x 3 2 1 2 1

+ += = =

+

. 1= (1) : 20x 1 4 0x 3= = .

2= (1) : 20x 2 4 0x 0= = .

4.

36 .

:

xy , : ( ) ( )x10 y y10 x 36+ + = (1) x 3y= (2). (2) :

x10 y 30y y 31y+ = + = y10 x 10y 3y 13y+ = + = (1) : 31y 13y 36 18y 36 y 2 = = = . x 6= , 62.

5. :

i. 2 2x 1 5 = ii. x 1 2 1 x 513 2

=

25. 3

iii. 2 x 1 3x 4 = iv. 2x 1 9 = :

i. 2 2x 1 5 = 2 2x 1 5 = 2 2x 1 5 =

2x 1 3 = 2x 1 7 =

2x 1 3 = 2x 1 7 = 2x 1 7 = .

2x 1 7 = 2x 1 7 = 2x 1 7 = 2x 8= 2x 6= x 4= x 3=

ii. x 1 1 x= = (

), :

2 5 2 51 6 6 6 2( 2) 6 3( 9)3 2 3 2

= = =

2 4 6 3 15 5 5. x 1 5 = = = = x 1 5 x 1 5 = = x 6 x 4= = .

iii. 2 x 1 3x 4 =

: x 1 , x 1

x 1x 1 , x 1

=

+ x 1 :

62( x 1) 3x 4 5x 6 x5

+ = = = , ().

x 1 :

2(x 1) 3x 4 x 2 x 2 = = = ( ).

iv. : 2() 9 ( 3)( 3)= = + -

:

3 3 +

() + +

26. 3

: 1. ( 3,3) 2 9 0 < , () .

2. 3, 3= 2 9 0 = () : x 1 0 x 1 = = .

3. ( , 3) (3, ) + 2 9 0 > , () :

2 2 2

2

x 1 9 x 1 9 x 1 9x 8 10

= = = +

+2

x =

6. : i. x 2 1 x 2 21

2 3

< ii. 2 3x 1 8<

< >

< >

: 7 1

x 1 x 33 3

< < < < .

27. 3

iii. 2 x 1 3 3x 2 x 1 3 5 x 1 15 x 1 1. x 1 5 5 x 1 5 4 x 6

< < < < <

> > < < < < x , 2 2

x x 1 x x 1+ + = + + . :2 2 2x x 1 x 5 x 4 0 x 4 x 2 2 x 2.+ + < + < < < < < .

T

7. < < :

2 = +

:

:

0< < , = +

0> > , =

< < 2 2 0< + < 2 2 = + +

: 2 = + + + = .

8. x,y 2x y 3 x 2y 4 0 + + = .

:

2x y 3 x 2y 4 0 2x y 3 0 + + = = x 2y 4 0+ =

2x y 3 = x 2y 4+ = , :

2x y 3 4x 2y 6 5x 10 x 2x 2y 4 x 2y 4 y 2x 3 y 1

= = = =

+ = + = = =

9. 2 5 5 2 + = + =

:

28. 3

2 5 5 2 2 5 5 2 2 5 5 23 3 7 7

+ = + + = + + =

= = = =

10. 2 5 5 2 + < +

+

14. 2f (x) x 4x 4 x 3= + + x :i. f .

ii. f.

:

i) x 2f (x) (x 2) x 3 x 2 x 3= + = + .

:

x 2 , x 2 0 x 2x 2

x 2 , x 2 0 x 2

= + <

30. 3

: 2x 5 , x 2

f (x)1 , x 2

+ =

31. 3

: 8 4 2 4 2 2 250 25 2 25 2 5 298 49 2 49 2 7 2200 100 2 100 2 10 2

= = =

= = =

= = =

= = =

: ( )( ) ( )( )( ) 2

8 50 98 200 2 2 5 2 7 2 10 2

3 2 3 2 9 2 9 2 18

= =

= = =

:

18. : 3 3 3 3 43 3 3 3

+ + =

+

:

( )( )( )

( )( )( )

2 2

2 2

3 3 3 3 9 3 6 3 12 6 3 2 39 3 63 3 3 3 3 3

3 3 3 3 9 3 6 3 12 6 3 2 39 3 63 3 3 3 3 3

+ + + + += = = = +

+

+ = = = =

+ +

: 3 3 3 3 2 3 2 3 43 3 3 3+

+ = + + = +

19. : 3 4 1

5 2 6 2 6 5+ =

+

:

:

( )( )( )

( ) ( )2 2

3 3 5 2 3 5 2 3 5 2 5 2

35 2 5 2 5 2 5 2+ + +

= = = = +

+

( )( )( )

( ) ( )2 2

4 4 6 2 4 6 2 4 6 2 6 2

46 2 6 2 6 2 6 2

= = = =

+ +

32. 3

( )( ) 2 21 6 5 6 5

6 56 5 6 5 6 5 6 5

+ += = = +

+

: 3 4 15 2 6 2 6 5

5 2 6 2 6 5+ = + + = + =

+

:

20. : i. 42x - 162 = 0 ii. 33x + 81 = 0

iii. 64x + 8 = 0 iv. 62x = 64x

:

i.

4

4

4

2x 162x 81x 81x 3

=

=

= =

42x -162 = 0 ii. 3

3

3

3x 81x 27

x 27x 3

=

=

=

=

33x + 81 = 0

iii.

6

6

4x 8x 2

=

=

64x + 8 = 0 iv.

( )6

5

5

5

5

2x 64x 02x x 32 0x 0 x 32 0x 0 x 32x 0 x 32x 0 x 2

=

=

= =

= =

= =

= =

62x = 64x

21. : i. 32(3x - 2) + 16 = 0

ii.

4 42x -1 3 - x-1 =

3 2 iii. 6 3x - 9x + 8 = 0

:

33. 3

i.

3

3

3

2(3x 2) 16(3x 2) 83x 2 83x 2 23x 0x 0

=

=

=

=

=

=

32(3x - 2) + 16 = 0 ii.

( ) ( )

4 4

4 4

4 4

4

4

4

2x 1 3 x6 6 63 2

2 2x 1 6 3 3 x4x 2 6 9 3x7x 17

17x

717

x7

=

=

=

=

=

=

4 42x - 1 3 - x- 1 =

3 2iii.

3

2

3 3

W x

:

W 9W 8 0( 9) 49W

29 7W

2W 1 W 8x 1 x 8x 1 x 2

=

+ =

=

=

= =

= =

= =

6 3x - 9x + 8 = 0

f (x) f (x) 0f (x) f (x) 0 0

0

= = >= = = > < >

f (x) g(x) f (x) g(x) f (x) g(x)= = = f (x) g(x)

1

2 .

f (x) g(x)=

.

f (x) g(x)

-

.

, -

.

, -

.

34. 4

1

2

3

4

1. 2x

1x =+ , :

4

4

3

3

2

2

x

1x

x

1x

x

1x +=+=+

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

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............................................................................................................................

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............................................................................................................................

............................................................................................................................

2. : 03x)(12)(x1)(2x 333 =+++

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

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............................................................................................................................

35. 4

3. :

) ( ) ( ) ( ) ( )2222 2x312x2x1x +=++ ) 6

15x

3

12x

2

2x +=

++

+

) ( ) ( )3x1,21x0,50,3x +=++............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

4. :

) ( ) 1-x1 2= ) ( ) 2x2 2 += ) 4x2x 2 +=............................................................................................................................

............................................................................................................................

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............................................................................................................................

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............................................................................................................................

5. 60%. -

50ml -

70%. ml .

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36. 4

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6. 250 ..

. -

, .

-

.

.

.

, ,

( ) . ! ,

,

. ,

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7. . : 4

5x

4

23x

2

1x ++

. : ( ) 2x11x + - .

............................................................................................................................

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37. 4

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8. ,

14 24,

1.

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9. . x 2 + x + 1

A =x

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............................................................................................................................

............................................................................................................................

10. :

. 2 2x 1 3 x 4x 3 = + . x 2 3 x 1 2x 3+ =

38. 4

. 2x 5 5 2x = . 2 2x 2x 2x x = =

. 12x2x +=+ . 6x1x3 +=+

042x1x =+++

............................................................................................................................

............................................................................................................................

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11. . 32,

39. 4

............................................................................................................................

............................................................................................................................

12. : . x 3 2x 5+ < . 2x 1 x 5 < +

. 2x 3 x 2x 5 < + . 22 x 2x 1 10< + +

............................................................................................................................

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............................................................................................................................

23. 0> > 2 2 2

+ + = +

+

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45. 4

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24. , , :

+ ++ + =

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............................................................................................................................

46. 5

1

2

3

4 5

1

. N :

i) 2x i) 13x + iii) 12x

47. 5

i) 4 16 ii) 3 5 4 222 iii) 3 2 43 3 3

iv) 5 35 5

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3

) -

4070 m2

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258m . -

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,

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( -

) 40m. -

. ;

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48. 5

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4

. : 2x - 4 x + 4 = 0

. 027x

1x28

x

1x

36

=+

+

+

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2

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Venn.

-

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Venn.

y = x, y = x + .

.

f(x).

f -

x.

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(x, y)

,

1 3 .

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, -

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y = x, y = x + .

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50. 1

!"# !"#

$% & '(

!## !

!"! #$#%& '

()

*+)&*+''

,-#,(.-

/*+01!/*2013/+201

1

$111 4540/0/ ==

1

$111 656/780/9:0 == -

; +=1

$1

1

$11 664540/

-

( ) ( )1$11$1 66440/ += .

1

1

51. 1

*' 1$ 5- 4646 1$ ==

52. 2

1

"" 2

:

. 62: : 1, 5, 7

. 67-68: : 5, 6, 7, 8

. 72-73: : 2, 4, 5, 9, 10, 11

. 77-78: : 3, 6

: 1, 5

:

:

177,180,182,192,196

53. 3

1

2

3

1. ( )f x 2x = + x .i. f x = 1 f x = 2 -

7, .

ii. ( y) : f ( 3) 2y f (1) 15 0 + > .iii. f.

:

i. : f (1) 2f (2) 7= 2 2(4 ) 7+ = + 2 8 2 7+ = + 1 =: f (x) 2x 1, x= +

ii. f ( 3) 2y f (1) 15 0 + > 5 2y 3 15 0 + > 5 2y 3 15 > 2y 3 3 < 3 2y 3 3 < < 0 2y 6< < 0 y 3< 2 x 1 6 >

x 1 3 -

(2,4) .

64. 4

1

2

3

4

1. 2 2f (x) x 2x 1 x 4x 4= + + + + xi. f

ii. .

:

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65. 4

2. 3

22x x 6f (x)x x 1

+ =

+ + () : y 2x 3=

i. f

ii. () f fCiii. () ()

fC .:

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3. A(1,3), B(2,3) (1, 5)

i. , , .

ii. xx , .

:

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66. 4

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4. f(x) = |x + 1| + |x|

:

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67. 4

5. 1 (-2,-1)

2

(-1,-2) .

) 1,

2 -

.

) 1,

2

) -

1,

2;

:

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68. 4

6. : 2x2)(f(x) =

:

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69. 5

1

2

3

4 5

1

.1. :

1x

1f(x) i)

2 +=

1x

x-4f(x) ii)

2

=

1xx

xf(x) iii)

=

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2

.1. (1, 3)

i) xx

ii) yy

............................................................................................................................

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70. 5

3

R :

i) 32xy : 1x1-y:21

+=+=

ii) ( ) 7x2y : 3xy:43

+=+=

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

............................................................................................................................

4

:y = (2 + 2)x + - 1. R

:

i)

ii) xx.

iii) 1: y - x = 2002.

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3

:

x+= 0 0 .

.

-

.

.

.

.

.

72. 1

1

!

"# $#%$&'(% %!

% $ %)$%*%+

,&-'$(

% $ %)$%*%+

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