Oку Жоспары Математика 8 Сынып Нұсқа 3 Тамыз 2014

8-

2 4 68.1 : 68.1 : 108.2 : 148.2 : 198.2 : 258.3 . 318.3 : 378.3 : 438.3 : 478.4A : 508.4 : 548.4 : 58 65 65

13 2014 : : 8 1 33+2 2 38+2 3 48+2 4 35+10

8.1A (18 ) ; .8.2A (13) , , . ; ( , - , ); .

8.3A I (15 ) 30 II (11 ) , ; ; 8.4A (10 ) ; ; ; ; , .

8.1B (15 ) ; ; ; .8.2B (17 ) ; , (a+b>c); , , ; .

8.3 (18 ) ; , ; ; .8.4B (10 ) ; .

8.2C (8 ) ; ; ; , () ; ; .

8.3C (4 ) , ; .

8.4C (15 )

, , . (, 2)

Issue 1Date: 28/03/2012253 2014

. , . . . . , . . . -, , . , , . : (, ); (, , , ); , ; (, -, -, -,- ..) ; , (, ; , - ); (, , , , , ); (, , , ); , . . , . : (1) , (2) / . , . : , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . , , . , , / . , .4

, . Issue 1Date: 28/03/2012

8

8.1 :

: 18

,

.

.

/

: .

: .

, , , , , , , , ;, , , . , . - . , - . . . . . . : ; ; .

.

.

-

AA 8.20

AA 8.21

AA 8.22

AA 8.23

AA 8.24

AA 8.25 ( (), (), () , ();

, , ;

;

;

, , ;

(, 8 ). . . . . .:y x : ; . , - . . : . :a2 - 2ab + b2 :

. , . .:- - . : ; , ; ; , . ; . , .

: , , , : " , , " .

/

/ , .

:http://library.wolfram.com/webMathematica/Mathematics/Expand.jsp

http://igcsemaths.pbworks.com/w/page/6366117/Algebra

http://nrich.maths.org/377

:http://nrich.maths.org/370

http://nrich.maths.org/337


. . .

W = G = I = f =

8

8.1 :

: 15

; .

.

.

/

: .

: . , , , , , , , , ., , ,

, . - . . - . - . - . . . / . : ; ; , .

.

, .

-

AA 8.16

AA 8.17

AA 8.18

: ;

;

i i i i i i ;

.:

2ab .2ab(a+5b-7ab) . . : , . . : :ax2 + bx + c , a = 1 . a > 1 x2 a .

W

, 2 -12 = 0, 2 4 + 3 -12 = 0, ( + 3) 4( + 3) = 0, (x+3)(x-4)=0,, x + 3=0 x 4=0., x = -3 +4.

W

G / I F

G / I , . :http://library.wolfram.com/webMathematica/Mathematics/Expand.jsp

:http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/factorisinghirev1.shtml

: http://igcsemaths.pbworks.com/w/page/6366117/Algebra

: http://nrich.maths.org/377



: :http://nrich.maths.org/273

. . .

W = G = I = f =

8

8.2 :

: 13

. .

, , . .

.

/

: .

: , , , ., , 2D- , 3D- , , ., ., , , 5/6/7- ., , . :, , . / / / . : , , , ./ ././ . 2 . y . . y ./ . . .- y . ? ? / . . ? ? / ? 2 , . 2 , . , . x y , p q .

.

6 7 ; .

-

8.1

8.2

8.3

8.3

8.1

8.2

8.4

8.2

8.3

8.10

8.4

8.1

: (, , );

, , ;

() .

;

( , );

( , );

;

, ;

;

(, , );

, , , ,

, , , 6-7 . : () , ? ? ? - , . (6-) . . , : ? ? ? / / / /// . . . ? ? / / / D , ? ? ? ? ? X () . ? ? ? . ? . ( , - ). 7 .10 . . . , ( ) . GeoGebra . , . . .

W

( )

G .

I

I /G ?

W

I

W

I

I / G

.


, 2 / / .

3D

:http://regentsprep.org/regents/math/geometry/GPB/theorems.htm

. . .

W = G = I = f =

8

8.2 :

: 17

; .

, , .

.

/

: , .

: .

: , , , , . :, , , , . , , , , . ., -, . ? / / / / . ?... ? . 3 . 2 2 . . 90 - . ? . ?a2 + b2 = c2 / / ? . / ? - . / ? . /.

.

;

-

8.5

8.5

8.14

8.15

8.16

8.10

8.4

8.7

8.8

8.9

8.6

8.6

8.2

8.4

, ;

;

;

;

,

.

( ,-

, ;

, ;

;

( , );

, , , , ;

, , -

. , , .. , .. / a+b > c . ; a+b = c . a= 7 c, b= 16 c c = 8 c . ?

. . . . . . 6 , 2:1 - .

.

2 .

W

show me ( ) , .

F

W

I

W

, .

I

I

I

I

52 ( ):http://users.erols.com/bram/geometry.html

:http://www.basic-mathematics.com/triangle-inequality-theorem-proof.html

, , Meccano .

:http://en.wikipedia.org/wiki/Angle_bisector_theorem

. : 15 . 12 . .F

. . .

W = G = I = f =

8

8.2 :

: 8

: ). . .

.

.

/

: .

: . // / . / / / / / (). , , , . . . , . / . . . y . . . . - / .

.

, . .

-

8.3

8.15

8.1 :

.

. :) ?) ?) ?) .) ) . , , ?

. .2 . ? ? .P(X=2) . P(X=12) P(X=2) . . (: , )

G

W . . , P[X = x]. , . , ( ) . I / G F

( , ,):http://nrich.maths.org/6963


8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.1 , , ;

;

; ;

;

;

;

, , ;

;

, . . . . . . , . . . . , , . , . , . , .. . . . , , , . . . , . . W

I / G , .

I /G

I

W

W

G

I

:http://www.bbc.co.uk/schools/gcsebitesize/maths/data/representingdata2rev5.shtml

http://www.bbc.co.uk/schools/gcsebitesize/maths/data/representingdata3hirev3.shtml

:http://www.eng.stat.kz/Pages/default.aspx

:http://www.census.gov/aboutus/stat_int.html

1954 : , (1991) ; ,ISBN 0140136290

8.9

, , , .

, . , Excel- . , . Excel- :http://support.microsoft.com/kb/304421

. .

W = G = I = f =

8

8.3 .

: 15

, , . 8.3B : .

.

.

/

: .: .

, ., , , , ./ . , , . /., . / . 90 . / . / . /. /. . . . . / .

.

.

-

8.11

8.7

8.12

8.8

8.13

8.10

8.11

8.3

8.4

: , ;

, ;

;

;

, ;

30 ;

30 ;

, , ;

, , - .

: : : . , . .5 , .

.. :

aabc

a+b+c=180 ( )

. , , .. , .: . . . . . . ? . . ( ). , , .

.

. , . - ?

. , . , . : ( ). , . -- . . , . W

F

G/ I

G

W

I ( , ?)

--;- -;- -;-- --.

, . : , , , , ..I / G .

:http://www.geom.uiuc.edu/docs/doyle/mpls/handouts/node20.html

http://labspace.open.ac.uk/mod/resource/view.php?id=365220

, , : , , , .

( ):http://www.mathopenref.com/congruenttriangles.html

. .

W = G = I = f =

8

8.3 :

: 11

, . . .

, - .

.

/

: .

: .

, , , / - / . / , . , ./ // l/. / / // . 2 . . . / 2 . ? ? ? ? ?/ ? ?2 ? ? ? ? / ?

.

, .

-

8.17

: , , , ;

: : : . , . . , 2000 . , , , . : ; ; ; . . . : , , :

W

I, G , .

.

:http://www.mathsisfun.com/geometry/constructions.html

:http://www.mathopenref.com/constructions.html

4 - , 2 - , .

8.18 . . . ? , . ? ? , , . / . , .: :8 c, 4 c, 8 c9 c , 9 c, 9 c6 c, 8 c, 10 cFW

G

I F

W

I F

, 3D- ? http://nrich.maths.org/6307

3D :; / : , .I/G

2D .: :

:

M.. :

. . , . .

I

I / M . :http://www.mcescher.com/Gallery/gallery.htm.. :http://nrich.maths.org/2578 :http://www.maths2art.co.uk/islamicart.htmhttp://www.vam.ac.uk/content/articles/t/teachers-resource-maths-and-islamic-art-and-design/

. .W

W = G = I = f =

8

8.3 :

: 18

, .

, .

.

/

: , .: . /, , , , , , . , , , . . /? , . x , y . - - , .

.

.

-

8.2

8.5

8.6

8.7

8.8

8.9

8.10

:

( );

; , , ; ;

;

;

( , , );

y= 3x -2 . ? .:, , . (, ) . , :3x-2=0 3x + 3y +5 =0. / . . ( ).: 20 , . 22 , . ? : (1) x-20 = y+20(2) x+22 = 2 x (y-22) , . ( ). , . . : : y=2x y=2x+2 , . , : y= 2x-2 2y = 4x-4. : : . . . . : ; ; ; ; . . , . . . . , ( ).W

:ax+b=0

G/I

F

I

W

I F

G

I

W

I F

W

W / G

I / G F :http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/simultaneoushirev1.shtml

:http://www.transum.org/software/sw/starter_of_the_day/Similar.asp?ID_Topic=42

.


:http://www.youtube.com/watch?v=XM7Q4Oj5OTc

PowerPoint- :www.btinternet.com/~mathsanswers/Simultaneous_Equations.ppt

8.2 . . , , - .G

I

. . .

W = G = I = f =

8

8.3 :

: 4

, , . .

, .

.

/

: .:- ., (), , , ., , . x- , y- , ? . 5- , 18 , .

.

, .

-

8.5

8.6

:

, ;

;

. , : 5, 20, -3, 2x, ., 5, 18. +13, 4 -2, 2-7, .. ? .: ( ) ( ). . . , . PowerPoint ; , . , : y ....- . . . . , , . . , . . . . , , ( ). . . . W , .

G

W

I / G .

W

I , .

I , .

G , , (). .

: :http://mrlsmath.com/wp-content/uploads/2008/01/Silent-Function-Factory-PPt/Silent-Function-Factory-PPt.html

307, 409 :http://functions.wolfram.com/

: :http://www.youtube.com/watch?v=DAGUNSLNa4s

. 8.4C: : , , .

W = G = I = f =

8

8.4A :

:10

, ; .

; .

.

/

: , . : . (), . /, / , () .X / Y Z X Z - Y / . () ? .

.

.

-

8.15

8.16

8.17

:

(, );

;

.

W . : . 2000 . .W : : ; ; ; . : ; ; .I / G , : : , , . .F .: 12 . 1000. ? .: x -3 x < 2 - : .: 6x , .

I F

, .

: ; ; .

. I / G /W

I F

. , I F

W

I F

W

I/G

I F

W

W

I / G

I / G F :http://www.purplemath.com/modules/ineqsolv.htm

:http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bkc16.pdf

:http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/inequalitiesrev4.shtml

:http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/inequalitiesrev3.shtml

:http://academic.cuesta.edu/smanor/math23dl/Additional/inequal.htm :http://nrich.maths.org/626

. . . .

W = G = I = f =

8

8.4 :

: 10

, , ; , .

.

.

/

: .: , . , , , ., , . /// (), . / / ? .

.

.

-

8.16

8.17

8.15

8.18

8.19

8.20

8.21

8.22

: ;

y = , k- ;

;

;

;

;

;

. y=kx+b (y=mx+c) ax + by = (7.3B) , .: y=2x, y=x+3, y=2x 2, y= - x. . . . , .W , . ; ; ; ; ; . . . .: . , , . . . . . , . . . , . . . y=x2 y=x3 . . W PowerPoint- .

. F

W

F

I

I

I / G

W, I

W

I F

W

W . . , : ; ; ; . . . . , , , . :http://www.printfreegraphpaper.com/

http://www.mathsphere.co.uk/resources/MathSphereFreeGraphPaper.htm

:http://www.math.unt.edu/mathlab/emathlab/recognizing%20graphs%20of%20polynomial%20functions.htm

():http://www.algebrahelp.com/calculators/function/graphing/

():http://rechneronline.de/function-graphs/

:http://www.s-cool.co.uk/a-level/m/coordinate-geometry/revise-it/curvesaths

. . .

W = G = I = f =

8

8.4 :

: 15

; ;

.

.

/

:

:

, , , , , , , , , , ,

,

,

, ,

, ,

.

.

X/Y ?

X , Y ,

.

, , ,

-

9.1

9.2

9.3

9.4

9.5

9.6.

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.1:

;

;

;

;

;

;

, ;

;

:

2 , / (). , .

3 () , .

. .

, : 1 , ?

, 2 . .

2 .

pi . , .

.

A4 . (210 mm) . (297 mm ) . .

. . .

. 1:2

. , .

.

, .

, : , .

, 2 , 5, 100 3 , 36, 7

.

.

: 1- 20- ?

, .

:) ) ) ) 2 ) , )

- ?

. . .

.

(radical) .

:

ab = ab (a b >0 )

a/b = a / b

a = a2 =aa

(e.g. 2

,.

, f(x)= (x) ( ). .

, / .

. , . . . , .W

W

W / G ; .

2 . 2 , a/b , , . 2 , .

I

.

I / G

W

I / G

:e ( )i ( ),

f"" : - ( "" ) "'" ; surdus ( "" "") , , , , underst

, .

f

I f

W

I / G

W

I f

W

I

I / G

G :http://www.math.com/school/subject1/lessons/S1U1L9GL.html

i :http://mathworld.wolfram.com/SquareRoot.html

:http://www.bbc.co.uk/schools/gcsebitesize/maths/number/surdsrev1.shtml

:http://www.pballew.net/oldsqrt.htm

:http://en.wikibooks.org/wiki/A-level_Mathematics/OCR/C1/Indices_and_Surds

. .W

W = G = I = f =

83 2014

. , .:8.3C : 3 :

: -:

: : :

8.6 , .

/ . .

. : , , , , , , / :

1-2 ; .

-

10 : , 235 35 . , , . ? ? . ? 0,5 , 5 , 100 , ?TP:

20 , . . :x + y = 3 ? 0- .x+0 =3 (x=3, y=0) 0 + y =3 (x=0, y=3) . . , , x=1 . . x y =1 ,

10 . . . , .: x , , 1 , , , .

? ? ? - ( )

, . . -

.

.

: , .

.

.

/ ? ? ? ? ? ? . .

( ).1:

2: ( )? 1:

2: ?

Documents

Oку Жоспары Математика 8 Сынып Нұсқа 3 Тамыз 2014