Sh. A. Alimov, O. R. Xolmuhamedov, M. A. Mirzaahmedov

0‘zingizni tekshirib ko‘ring!
1. Hisoblang:
1) (17,2-4,01+4,01-32,8):l|;
?

•2

V²/

25 0,03-4.

67. 
    Tenglamani yeching:
    

1. 
   (2jc + 1) + 3jc = 16; 3) (x-5) -(5 -3x) = 2;
   
2. 
   (*-4) + (x + 6) = 4; 4) 23-(* + 5) = 13.
   

67. 
    Ifodani awal soddalashtirib, keyin uning son qiymatini toping:
    

1. 
   (2c + 5d)-(c + 4d), bunda с = 0,4, d = 0,&,
   
2. 
   (3a - 4b) - (2a-3b), bunda a = 0,12, 6 = 1,28;
   
3. 
   (7х + 8_-у)-(5л:-2_-у), bunda x = -—, >> = 0,025;
   
4. 
   (5c-6b)-(3c-5b), bunda с = -0,25, b = 2^X~.
   

1. 
   bobga doir mashqlar
   

Algebraik ifodaning son qiymatini hisoblang (69—75):

67. 
    1) a + bc, bunda a = -1, b = 3, c = 0;
    

2. 
   a-be, bunda a = 2, b = -l, c = -3;
   
3. 
   (a + b)c, bunda a = 1, b = -3, с = 2;
   
4. 
   (a-b)c, bunda a = 3, b-1,2, с = 5;
   
5. 
   (a-b) + (c-d), bunda a = 4, b = 2, c- 3, d = -1;
   
6. 
   (a-b)-(c-d), bunda a = 0, b = -4, c = -2, d = 3;
   
7. 
   a-(b-c), bunda a = 0,5, b = ~, с = -1,2;
   

2

8. 
   a-(b-c)-d, bunda a = 5,2, Z> = 1,3, c = 2,8, d = 2,S.
   

⁷⁰* 1) 5(x-.y)²; 2) 3(x + .y)²; 3) (5x-.y)²; 4) (3x + j>)², bunda x = 2,5, >> = 4,5.
⁷¹-1) 2((a-b)² + l)- 3) ((a-b)a-8):2;

2. 
   4(3-(a-b)²); 4) (5a-(a + b)):3, bunda a = 5, b = -l.
   

⁷^• 1) 3(a + b)-2ab', 3) 3(a-b) + 2ab\

2. 
   3a + b-2ab\ 4) 3a-b + 2ab, bunda a = 1,2, b = 1,8.
   

73. 
    n -tf-3c², bunda b = -2,c =
    

2 3

2. 
   -0,75о⁵+1-^6², bunda a = -2, 6 = 3;
   
3. 
   ((a¹ +26)⁶, bunda cr = -3.
   

73. 
    1) 7x²-2ax, bunda x <3 = 1,5;
    

2. 
   Зсгх-5л'², bunda ^{= a} = ^_~5
   
3. 
   2m'(3m²-k)², bunda /w = --, A: = 0,75;
   

2

2. 
   3m²(2m²-n)², bunda ” = “> /и = -0,5.
   

73. 
    Hisoblang:
    

1. 
   _ У bunda / = -2;
   

3/' + 4/ -1

S /iu rasmda nechta uchburchak, kvadrat va to‘g‘ri to'rtburchak bor?

73. 
    Bir gektar ko‘kalamzor bir yil davomida havoni 70 t changdan tozalashga qodir. 10 ga; 100 ga; m gektar ko‘kalamzor bir yilda havoni necha tonna changdan tozalaydi? Umumiy maydoni 16 000 ga bo‘lgan ko‘kalamzor havoni necha tonna changdan tozalaydi?
    
74. 
    Avtomobilning harakat tezligi ikki marta ortishi bilan uning tormozlanish yo‘li to‘rt marta ortishi ma’lum. Jadvallardan foydalanib, harakat tezligi 30 km/soatdan 60 km/soatga ortganda tormozlanish yo‘lining uzunligini toping:
    

Yengil mashina uchun:
v (km/soat)	t (m)
30	7,25

Yuk mashinasi uchun:
v (km/soat)	t (m)
30	9,5

73. 
    (Abu Rayhon Beruniy masalasi.) Agar 10 dirham pul Jdo oyda 5 dirham foyda keltirgan bo‘lsa, 8 dirham puldan uch oyda qancha foyda olish mumkin?
    

Torrnoz
y
m
o'li

1. 
   
   rzxs *— вст casr -аса :
   
   

bobga doir sinov mashqlari—testlari ” ,# C3B ЙЗТ iLXT Ш'-l !
Quyida siiiuv (test) mashqlari keltirilgan bo‘lib, ularning har biriga 5 tadan ,javob“ berilgan. 5 ta ,javob“ning faqat bittasi to‘g‘ri, qolganlari esa noto‘g‘ri. Sizdan sinov mashqlarini bajarish yoki boshqa mulohazalar yordamida ana shu to‘g‘ri javobni topish (uni belgilash) talab qilinadi.

1. 
   о = 2,4, £ = 3,6, Л = 1,6 bo‘lsa, s = ^(a + b) ifodaning son qiymatini
   

toping. A) 48;

B) 3,18;

E) 4,8.

C) 6,36; D) 0,48,

A
S
— +a a

D) -+a-
a
) + В) -+2a; C) 2
2a a

3. 
   Teng yonli uchburchakning perimetri P ga, asosining uzunligi a ga teng. Uchburchakning yon tomoni uzunligini topish uchun ifoda tuzing.
   

A) 2a-P\ B) 2P-а- C) P-a\ D) kP-a); E) P-2a.
31

3. 
   а = 2,5, b = 2,4 va с = 3,5 bo‘lsa, К = обе ifodaning son qiymatini toping.
   

A) 18,3; B) 21; C) 2,1; D) 12,1; E) 121.

3. 
   o = 5, 6 = 6,4, c = 4,5 bo'lsa, S = 2(ab + ac+be) ifodaning son qiymatini toping:
   

A) 50,45; B) 83,3; C) 166,6; D) 109; E) 54,5.

3. 
   Ona farzandlari uchun a so‘mdan 8 ta rasm daftar, b so'mdan 5 ta
   

ruchka, с so‘mdan 20 ta daftar sotib oldi. Jami xaridni hisoblash uchun ifoda tuzing.
A) 33(a+b+c)\ В) 8о+25(6+с); С) ШаЬс,
D) 8cr+1006cr; E) 8cr+56+20c.

3. 
   Qavslarni oching va soddalashtiring: 5д+(3я-(4я + 3)).
   

А) 8я + 3; В) 4o-3; C) -4cr-3; D) 3-4cr; E) 4cr + 3.

3. 
   Ifodani soddalashtiring va uning a = 2,4; b = l,5 bo‘lgandagi qiymatini toping: 0,5 (2a-3b)-(4b + 2,5a).
   

A) 17,4; B)-17,4; C)-1,4; D)-11,85; E) 0,6.
Ifodaning son qiymatini toping (11—14):

3. 
   (64,2-7,02 + 17,9 14,04):4—.
   

13
A) 169; B) 16,9; C) 159; D) 15,9; E) 149.

3. 
   3— 0,87-2,34 1,8 + 3i-li.
   

29 3 2
A) 67; B) 3,788; C) -6,2; D) -3,788; E) 9,3.

3. 
   (35,7-12,24-21,4-6,12):l|.
   

A) 578; B) 306; C) 162; D) 16,2; E) -16,2.

3. 
   (-1,5)-(2,7: (—0,9) — (—7,2): 3,6) + 2,4 (-2,5).
   

A) -6; B) -7,5; C) 7,5; D) -4,5; E) 4,5.

32. 
    
    

3. 
   To‘g‘ri to‘rtburchakning perimetri p ga, asosi a ga teng. Uning balandligini hisoblash uchun ifoda tuzing.
   

A) 0,5 -(p-а); В) p-2a\ C)
p-2a
D) p-2a; ^E) 2 '

3. 
   Uchburchak bir tomonining uzunligi a ga teng bo‘lib, u ikkinchi tomonidan 2 sm qisqa, uchinchi tomonidan esa 3 sm uzun. Shu uchburchakning perimetrini hisoblash uchun ifoda tuzing.
   

А) За- 1; В) 3a-5; С) 3a + 5;
D) 1-3a; E) 3a+ 2.

3. 
   Ifodani soddalashtiring va uning a — 2,7, b = 42 bo‘lgandagi son qiymatini toping: 3(2a -b)- 2(a - 2b).
   

A) 24,36; B) 27,6; C) 8,7; D) 15; E) 14.

3. 
   Uchburchak bir tomonining uzunligi a ga teng. Ikkinchi tomoni uzunligi bu tomonning 80 % ini tashkil qiladi. Uchinchi tomoni esa birinch va ikkinchi tomonlar yig‘indisining yarmiga teng bo‘lsa, shu uchburchakning perimetrini toping.
   

A) 1,8a; B) 2,7a; C) 3a;

4. 
   3a+ 0,8; E) 2a+0,8.
   

§ Tarixiy masalalar

1. 
   Al-Xorazmiy masalasi. Sondan uning uchdan biri va to‘rtdan biri ayirilsa, 8 qoladi. Sonning o‘zini toping.
   
2. 
   Al-Xorazmiy masalasi. Sen o‘nni ikki qismga ajratding, keyin ulardan birini boshqasiga bo‘lding, bo‘linmada to‘rt chiqdi. Sen o‘nni qanday qismlarga ajratding?
   

(D Geron masalasi (eramizning I asri). Hovuzga ikkita quvurdan suv keladi. Birinchi quvurdan 1 soatda 1 m³, ikkinchi quvurdan 1 soatda 4m³ suv tushadi. Hovuzning hajmi 12 m³. Ikkala quvur baravar ochib qo‘yilsa, bo‘sh hovuz qancha vaqtda to‘ladi?