Toshloq tumani

mas hs‘ulot

Dars mavzusi. Algebraik ifodalar.
Dars maqsadlari: o‘quvchilarga algebraik
ulaming fanga qiziqishlarini oshirish.


Sana:


ifodalami o‘rgatish,


Darsning borishi:

1. 
   Tashkiliy qism.
   
2. 
   Algebraik ifodalar.
   

Algebraik ifodalar.


Harflar yoki raqamlar va harflar bilan ifodalangan bir necha hadlami amallar yordamida birlashtirishdan iborat boMgan yozuv algebraik ifoda deyiladi.


Masalan:


ae x 2 ’ 100


+ У:


jc + 5 3 cd


Algebraik ifodaning qiymati deb, undagi harflar o‘rniga berilgan son qiymatlarini qo‘yib, shu sonlar ustida tegishli amallami bajargandan keyin kelib chiqqan songa aytiladi.
X
Misol: — + у ifodaning qiymatini toping, bu yerda jc=24, y=2
~гт 1 • 1 24 6 _ 6
Yechish: — + 2 = — + 2 = 2—.
100 25 25


Harflar yordamida juft va toq sonlar formulasini yozish mumkin. Agar a juft son bo‘Isa:


agar b toq son bo‘Isa:


a=2n


b=2n+\


bu yerda: n -natural son yoki nol.
Arifmetik amallaming xossalari:
I. Qo‘shish va ko‘paytirish.

1. 
   o‘rin almashtirish qonuni
   

a+b=b+a, a-b=b-a

2. 
   guruxlash qonuni ³
   

3) taqsimot qonuni


(a+b)+c=a+(b+c), (a-b)c=a(b-c)


a{b+c)=a-b+a-c

2. 
   Ayirish.
   

Ayirishni qarama - qarshi songa qo‘shish bilan almashtirish mumkin:
a-b=a+(-b)

2. 
   Bo‘lish.
   

Bo‘lish bo‘luvchiga teskari bo‘lgan songa ko‘paytirish bilan almashtirish mumkin:


a 1
- = a- — b b


Nol sonining xossalari:
a+0=a, a - 0=a,


a-0=0,


^ - mavjud emas.

3. Mustahkamlash. Test yechiladi.

TESTLAR.
d

1. 
   a=4b va c+3b=0 (Ьф0) boTsa, - ni toping.
   

c
12 112 A) -1- B)l- C)l- D)-- E) -- ⁷ 3 ⁷ 3 ⁷ 3 ⁷ 3 ' 3

2. 
   Agar ab=9 va 3b=8c boTsa, ac ni hisoblang.
   

A) 3- B) 3- C) 3- D) 3- E) 3-

^J 1 j ₉ /₃

2 1

3. 
   a sonning b songa nisbati - ga teng, c sonning b songa nisbati - ga teng, c sonning a songa nisbatini toping.
   

2 5 5 3 4
А)- В)- C)- D)- E) -

^}Ъ ^}6 ^} 4 ^J 5

4. 
   26-25-25-24+24-23-23-22-12-8 ning qiymatini toping.
   

A) 106 В) 1 C) 54 D) 8 E) 0

5. 
   2M8-19-18+18-17-17-16+16-15-15-14 ning qiymatini toping.
   

A) 50 B)100 C) 98 D) 24 E) 110

6. 
   18-36-16-36+24-27-25-24-2Е5 ning qiymatini toping.
   

A) 45 B)1 C)0 D) 15 E) 115

7. 
   21-13+24-13+45-12+25-44-89-24 ning qiymatini toping.
   

A) 79 B) 126 C) 89 D) 0 E) 1

8. 
   36-24-33-24+17-11-14-11+18-16-15-16 ni hisoblang.
   

A) 166 B) 155 C) 180 D) 2354 E) 153

9. 
   27-23-24-23+21-19-18-19+17-11-14-11 ni hisoblang.
   

A) 165 B) 159 C) 143 D) 203 E) 189

10. 
    2M7-18-17+17-15-15-14+18-13-15-13 ni hisoblang.
    

A) 125 B) 135 C) 205 D) 180 E) 165

11. 
    139-15+18-139+15-261+18-261 ni hisoblang.
    

A) 13200 B) 16200 C) 14500 D) 17500 E) 15100

12. 
    Agar jc=4,5 va y=3,5 boTsa, x³-x²y-xy²+y³ ni hisoblang.
    

A) 10 B) 9,5 C) 8 D) 7,2 E) 11

13. 
    Agar jc=71,8 va y=70,8 boTsa, x³-y³-2y²-3y-l+x²-2xy ni hisoblang.
    

A) 1 B) 21 C) 79 D) 87,5 E)92,l

14. 
    Agar a = boTsa, a²b²-ab + \ ifodaning qiymatini toping.
    

A) 4 B)+ C)1 D)+ E)2

4. 
   Darsni yakunlash.
   
5. 
   Uyga vazifa: test yechish tematik axborotnomalardan
   

Tayyorladi:
Tekshirdi: 0’TIBDO‘ :


“ ” 20 y.

Xossalari.
1) a^n-a^m =a^M;	2) a^n:a^m =a";	3) (a")"
4) {a-b)^n =a^nb^n;	5)Г|Т4а>°,,>о;	6)a°=l.

Ikki xonali son xona qo‘shiluvchilari yig‘indisi shaklida quyidagicha yozilishi mumkin: аЛО+b, bu yerda a - o‘nliklar soni, b - birliklar soni; uch xonali sonni a- \()^2+b- \()+c ko‘rinishda yozish mumkin, bu yerda a - yuzliklar soni, Z>-o‘nliklar soni, c-birliklar soni. To‘rt xonali, besh xonali va h.k. sonlar ham xuddi shu tartibda xona qo‘shiluvchilari yig‘indisi shaklida yoziladi. Misol: Quyidagi sonlami xona qo‘shiluvchilari yig‘indisi shaklida yozing. Yechish: 1) 235121=2-10^5+3-10^4+5-10^3+M0^2+2-10+l; 3 532037=3-10^6+5-10^5+3-10^4+2-10^3+3-10+7; 70 1 508=7-10^5+l-10^3+5-10^2+8; 10101=1-10^4+M0^2+1. 3. Mustahkamlash. Test yechiladi. TESTLAR. Quyidagilardan qaysi biri -1 ga teng? A) (-(-l)^2)^3 B)(-(-l)^2)^4 C)(-(-l)^3)^6 D)((-l)^3)^2 E) ((-1)^2)^4 Quyidagi ifodalardan qaysi biri 1 gateng? A) (-(-l)^3)^3 В) -((-I)^5)^4 C)((-l)^3)^5 D)(-(-l)^2)^3 E) -((-I)^2)^3 Quyidagi ifodalardan qaysi biri 1 gateng? A) ((-l)^5)^2	B)(-(-l)^4)^5	C)((-l)^3)^3	D)(-(-l)^2)^3	E)((-l)^3)^5
r\in—1 Л ^z '^z 2 4n+\	ni soddalashtiring.
A) 2^4n+2	B) 2^2n'^2	C) 2^n'^2 D) 2^4n'^2 E) 2^4n+1
2^и+1	ni soddalashtiring.
A) 2^4n+1	B) 2^2n‘^2	C) 2^n‘^2 D) 2^4n_1 E) 2^4n‘^2
2^w—3 23w+3 6. :	• 2 ^1+” ni soddalashtiring.
A) 2^5n	B) 2^4n+2	C) 2^4n+1	D) 2^3n	E) 2^4n

7.