extracted_text:
4-test                                             1.
ARIFMETIK KVADRAT ILDIZ VA UNING XOSSALARI

100 + + 100 ifodada 100 lar soni ham,
ildizlar soni ham n ta. ning qanday eng kichik qiymatida ifodaning butun qismi
1 ga teng bo'ladi?
13)3
1             1              v/lö vrž +
ó — ifodaning qiymatini toping
1
       2                             cp
Agar f (T)                                             bo'lsa,
u holda,
            1                  2                      99
100            100         100 ifodaning
qiymatini toping.
 (0+1)1000 sonni cheksiz o'nli kasr
ko'rinishida yozilganda verguldan keyingi 100-o'rnida turgan raqamni toping. cp
 v/17: -l- v/ý VQÖO tenglama
nechta butun yechirnga ega?
A)2          B)ło            011           D)20
                                           7                               7
2
Hisoblang: r vš + 4 + v/? víš—
13 9
x 4 + va y 2 —    bo'lsa, a;2 — — 2y2 ifodaning
qiymatini toping.
A)12vTá              B)18v/j
C)24                            120
2+0 Hisoblang:
A)                    B)2+x/S
Agar a, +2 + a +2 -F
bo'lsa, a — IO a — ifodaning qiymatini toping.
cvsŤ
lal — a sonining butun qismi
bo'lsin. U holda ifodaning qiymatini toping,
0—15

            1. ARIFMETIK
KVADRAT ILDIZ VA UNING XOSSALARI                                            4-test

131

1-test
2. Ildizli ifodalar

2.

ILDTZLI
  IFODALAR

ifodaning qiymatini
soddalashtiring.
                  A) 11xy3                   B) —II:ry
                                                D)-11TY2                                                                                D)12
kasr maxrajini irratsionallikdan
7             11 bo'lsa, ifodani soddalashtiring.
B)15 018
                                                                                kasr
maxrajini          irratsionallikdan
B)a — D)
y bo'lsa,
                                          B)2y
D)2T
2.' ILDIZLI IFODALAR                                                                                I-test

avfi+l
av/ü- l
D)a+l
2
D)—

2-test                                                                                2.
ILD1zL1 IFODALÃR
b
1 —       -l- 22
ifodañing ifodani
soddalashtiring.
Ko'paytuvchilarga ajrating: mn + rnvTñ -l-

6
ni soddalshtiring.
              C)2vra          D)2v/b
Ifodani soddalashtiring:
— b2
1
v/ã— v/b —ifodani
soddalashtiring.

ILDIZLI IFODALAR

2-test

Ratsional
tenglamalar, Ko'phadlar
1. Kvadrat tenglama
 4
15x2+ a: — 6 = O tenglamani
yeching.
                5 2
tenglamaning ildizini
49 tenglamaning ildizlari
yig'indisini

— 5a;) = 3(x — a) tenglamani yeching.
tenglamani yeching.
O tenglamaning yechimlari
2x2 + 3x — 5 = 0
tenglamaning qaysi ildizi — 9x +8 = O tenglamaning ham ildizi bo'ladi?
92,5
4x2 — 9x -+- 5 = O tenglama katta
ildizining kichik ildiziga nisbatini toping.
                                   5                                  5
B)-          D)4      9
124
ı.

katta
İldİzİnİ toping.
tenglama kichik
ildizining katta
2
D)3
+ 34 — O tenglamaning
kichik ildizini
D)17
tenglamani yeching.

1.

(a: + — 1) — — 8 O tenglama ildizlari yig'indisini toping.
A)-3
— 3c — 5 O tenglama ildizi bo'lsa,
ning qiymatini
toping.
7mo
3
      7                   7                  7
— 7'x 0 va — 8c -h- 7 = O tenglamalarning
umumiy ildizi 10 dan qanchaga kam? D)10
 tenglamaning
haqiqiy ildizlari nechta?
D)Cheksiz ko'p
Ikkita
ketma-ket kelgan natural      sonlar ko'paytmasi 72 ga teng. Bu sonlardan
kichigining ikkilangani kattasidan nechtaga ko'p?
O tenglamaning ildizlari
Son o'qida — 2x — 15 O tenglamaning ildizlari orasidagi
masofani toping.
— 41 = O tenglamaning kichik
                                        C)-7    D)-6
= O tenglamaning
1) —m(c2 +2) +3

1. KVADRAT
TENGLAMA

a ning qanday qiymatlarida — (0-1-3)œ+4a tenglama
teng ildizlarga ega bo'ladi? B){2; 7}
CHI; 9}                        9}
(2x2 — x 15) 2 tenglamaning haqiqiy ildizlari
yig'indiSini toping. 13)-1
11+22 + ...+92
tenglamaning 0 dan farqli ildizini
ko'rsating.
9
      2           B)5                           D)10
mx2 + 3a:+1 ifoda to'la
kvadrat bo'lsa, —1 ning qiymatini toping.
D)16
25x2 — 70c + a = O tenglarna ikki karrali ildizga
ega bo'lsa, a ning qiymatini toping.
A) -49                                  C)49
         D)70
—a: —a — 3 =
0 va a? — 4'X-l-a = O tenglarnalar umumiy ildizga ega bo'ladigan a ning barcha
haqiqiy qiyrnatlari ko'paytrnasini toping.
                    27                  21
                     4                     2
27
2
                             3x2
+ '2a:r                  2
_3,œŽ + 7aa; — 2a2 kasrni
qisqartiring.
B)
                   —
2a              2a —
        C)                 D)
Tenglamani yeching:
1
cp;-4 D)-2
[9] 2 +17) 2 tenglamaning
manfiy butun yechimlari nechta? cp
Noldan farqli a; b sonlari uchun (a -l- b) (a 4- 3b) — (a +
2b)(2a + b) tenglik o'rinli bo'lsa, ning qiymatini toping,
3         3 C)      D)
                    2                            2

2.

2. Ratsional
tenglamalar

 — 17F + 16O
tenglama nechta haqiqiy yechimga ega? B)2
3 — 8 O tenglamani yeching.
D)-l; -2
 9x4
— 82x2 + 9 O tenglamaning rnanfiy ildizlari ko'paytmasini
toping.
1
     3
 3(a3
1) 7(T2 — I) tenglamaning ratsional yechimlari nechta?
D)3
 O tenglama
ildizlari ko'paytmasini toping.
A) -36      B)-12            012
tenglamaning barcha haqiqiy
D)ll
3C — 15 tenglamaning
D)5
O tenglamaning butun
(5c — 4) tenglamaning barcha toping.
              016            D)20
tenglama nechta ildizga

2.

2x — 8:r — 4 tenglamaning
— + 3

2.

(02 — 4x -l- 6) (x4
— 8a2 + 20) 8 tenglama ildizi (to soni bo'lsa, sonining
natural bo'luvchilar sonini toping.
                  B)10          C)12          D)15
4 272 tenglamaning eng katta
va eng kichik ildizlari ayirmasini toping. B)7
— 8x3 + 7m2 + 36m
— 36 O tenglamaning eng katta va eng kichik ildizlari ayirmasini toping. A)5
(x — + (a, — = (a; — b) (a —
tenglamaning yechimlari yig'indisini toping.
                 B)3a            cpa
- b             D)3a - b
             a; —          + (2:c2
2m — 7) 3 tenglamaning
barcha haqiqiy ildizlari ko'paytmasini toping.

A) —42            B)-7
                   1       1       1
tenglamaning irratsional
ildizlari ko'paytmasini toping.
D)12, 5
              1                    1                   1
15 tenglamaning ildizini
toping. B)-4; 3
4- 1

-18

tenglamaning ildizi       bo?lsa, ning qiymatini toping.
3
4
2

19

45 tenglamaning
16 irratsional ildizlarini ko'rsating. 3     5
v'Ãä    13 2        1
— — 3a = O tenglama a ning qanday
rr, 2 -l-
ax
qiymatida yechimga ega
bo'lmaydi?
D)3

3.

3. Viyet teoremasi
— 3c + 1 O tenglamaning
ildizlari Tl va bo'lsa, -4- ifodaning qiymatini
toping.
a? — 7.rr -1- 2 O tenglamaning
ildizlari bo'lsa, ifodaning qiymatini toping.
 2x2 — 5z +
1 O tenglamaning ildizlari bo'lsa, Cl.T2 Tl + ning qiymatini topmg. A)-6 B)-3
b ning qanday qiymatida H- bay 4- 27 tenglarnaning
ildizlaridan biri 9 bo'ladi? A)-12 C)10 D)12
—4v-l-2 O tenglamaning ildizlari bo'lsa,
(T2 —1) —T2 ifodaning qiymatini — 5 O tenglamaning ildizlari Tl va T2 ifodaning
qiymatini toping. D)15
va
2) ifodaning qiymatini
O tenglarna ildizlari qiymatini
toping,
O tenglarnaning
ildizlari va at2 qiymatini toping. D)13
tenglamaning ildizlari va .T2
Tl) ifodaning qiymatini
D)24

3.

14

D)12

2 —
12a — 3) O tenglarna ildizlari 4a2 — ar -1- 9 0 tenglamaning
ildizlari uchun XI -ł-T22 20 tenglikni qanoatlantiradi. Bu
shart — 1 bo'lsa, + 1 ifodaning o'rinli bo'ladigan barcha a lar ko'paytrnasini
qiyrnatini toping. toping.           16 25
19 B)           C)
lżą     3 D)        3
8

12

— 7:r 2 + 14:c — 8
funksiyaning nollari — a,c2 + — 12 O tenglama ildizlaridan a, b va c
bo'lsa, a2 bc + ab2 c+ abc2 ning qiymatini
biri 2 ga teng. Uning qolgan ildizlari yig'indisini toping.
hisoblang,        A)-56     B)-28     C)28       D)56
A)5

18

2
                                                                                —
ax 4- 2             O tenglama ildizi +
— am + ab O tenglama ildizlari a + 1 va
b-ł- I 136 shartni qanoatlantiradi. Bu shart o 'rinli sonlari bo'lsa, q +
b ning qiymatini toping.           bo'ladigan barcha a lar ko'paytrnasini
toping.
a' — 2:c2 — 4a: — 1 O tenglarnaning a, b, c
ildizlari
                                                                                1         1        1
                                                                                uchun                                               1
ning qiymatini
O bo'lsa, —+—-f-— ning
qiymatini c
toping.             toping, A)-2          A)-2
                          3 — 4T2 — a: +
10 O tenglama ildizlari uchun                     a:                  a2 —
4a tenglama ildizlari ayirrnasi 8
x
1 1 ga teng bo'lsa, a ning qiymati quyidagilarning yig'indini toping.
qaysi biriga teng bo'lishi mumkin?
:Ę2.T3

4. Ikkinchi va undan yuqori darajali tenglamalar sistemasi
—
3:cy 10 tenglamalar sistemasidan
 — 3y 5 a: + y ning
qiymat,ini toping.
2
 — 16 t,englamalar
sistemasidan ning
a:
qiymatini toping.
              A)—12                      B)-4D)12

a; + y 10 tenglamalar sistemasinin
+ y2 2xy+
16 yechimlarini ko'rsating.
tenglarnalar sistemasining 28
manfiy yechirnlari (xo; yo) bo'lsa, 2:ro + ning qiymatini toping.
B) -28 C)-20  D)-9
                        tenglamalar sistemasi
nechta haqiqiy yechimga ega?

11

                               + — 2:ry + 4x — 3y — 33 9 0O     tenglarnala,r                       y
2 a? — 6:r -1- 9 tenglamalar sisternasi nechta

sistemasining
butun yechimlari yig'indisini   haqiqiy yechimga ega? toping.         A) B BP
ta 03 ta  ta A) —7               D)7
                                                                                2
                               2

                                                                                5'Ť
+ —1—                                                        — 89

12

a;2 y
+ my'2 48 tenglarnalar sisternasidan yechimlaridan 2'.c2 + 3:ry + y Yning '2
40eng kichik tenglamalar qiyrnatini sistemasitoping. y 14    o
ning eng
katta qiymatini ko'rsating.               A) —11 D)10

18

                       4                                                                                5
sistemasidantenglarnalar
sistemasidan
tenglamalar

19

ifodaning qiyrnatini toping. — nisbatni toping.
     1                               2
D)-

14

       5                                          7
tenglamalar
sisternasini yechib, ac + cb 16 tenglarnalar sistemasidan
(a + b) ning qiymatini toping. a +
21)
              ning
qiyrnatini toping                                                                       B)16          C)64
         D)256
                                                                                —
                36
                                                                                2
+ my Y                bo'lsa,           ning qiymatini
                                                   21                                                        x
                                   x
— 4y —                                                      toping.

a; y sonlari                                               tengliklarni                            7                                                        7
                       9y
—                                                                 13)-2
3 qanoatlantirsa, IT — 3yl ning
qiyrnatini toping.

+
Y2 -I-4X — 23/ — 2 O tenglama nechta natural yechimga ega?
02
tenglamalar
— 28 = sisternasining haqiqiy
ildizlari nechta? A) 3 ta B)2ta ta
                                                                                9             -l-
:v2 y2 + y4 — 189                        tenglamalar
— aty -l- Y sistemasidan ning qiymatini toping. A) 6    13)8        C)12
DPI
b2 + = ab bC CIC
4a + 9b — 3c = 50 ning qiymatini
toping.
                                                                                A)15          B)20          C)30          D)40

2y 3z 18
bo'lsa, a; H- y — z ning
+ 4y2 + 9z2 108
qiymatini toping.
bo'lsa, -1- Y ning qiymatini
— y6 21 toping.
A)123          13)129          0133           D)143
           4                   3
5
312 —
4y + 5 3 2 — + 12
tenglamalar
_ 8z + 17 sistemasi yechimlari ko'paytmasini toping. A) 24              13)18
    C)12       D)36
2
6a; — y 35 tenglamalar sistemasi
yechimlari bo'ladigan lar ichidan eng kichigini toping.
D) —11
       +       25

15

tenglamalar sistemasi uchta

haqiqiy yechimga ega bo'ladigan a ning barcha qiymatlari yig'indsini toping.
A) -5                         05           D) 10
                             1            1
    y; Z sonlari uchun a; -1-                                  I
va
z
         1        19
— tengliklar o'rinli bo'lsa, wyz ning
qiymati quyidagilardan qaysi biri bo'la oladi?
.T2 y2
— 16.T + 4y2 0
F —4x+ 12 — y3 —0     tenglamalar
sistemasining yechimlari yig'indisini toping.
       a? +        15
(x + 2y)2 + 19 tenglamalar sistemasidan la;
+ ning qiymatini toping.
a ning qanday qiymatlarida 2
'2 12 tenglamalar sistemasi yagona
yechimga ega bo'ladi?
tenglamalar sistemasidan b -1- d —
2c — 2a ning qiymatini toping.

5. KO

5. Ko'phadlar
 P(a) 2x3 —
-1-2T + 1 ko'phadning đarajasini aniqlang.
 P(c)
T3 —5x2 ko'phad ga qoldiqsiz bo'linsa, a + b ning
qiymatini toping.
13)0
2x2 — 3m —
I bo'lsa, P (I) ning qiymatini toping.
— 4x+5 bo'lsa, P (P
(O)) ning qiymatini toping.
                                            C)17              D)25
 P
(a;) 2x3 —T2 + 3T+a va P (—1) 0 bo'lsa, ning qiymatini
toping.
04
ať + bz + c ko'phad uchun
p(O) z: 3 va — Il bo'lsa, a+b—c ning qiymatini toping. D)ll
(m— I) (T—3) ... (x— 10) ko'phadning
ozod hadini toping.
                          B)-55
         C)55          D)10!
ifoda ko'phad bo'ladigan barcha n
natural sonlar yig'indisini toping. D)10
— :c2g5 + :r4y
— 100 ko'phadning darajasini aniqlang.
101 _ + 5m — 2
ko'phad shaklga keltirilganda, uning barcha koeffitsiyentlari yig'indisini
toping.
C)-2

Qandaydir
P(m) butun koeffitsiyentli ko'phad uchun P(l) 8 va P(n) 31 tengliklar o'rinli
bo'lsin. n, ning qabul qilishi murnkin bo'lgan natural qiymatlari
yig'indisini toping. A)26  B)27       C) 30      D)32
a va b ning qanday qiyrnatlarida P
(x) 4 ax4 + bT3 — 3T — 2 ko'phad — I ga qoldiqsiz bo'linadi?

P (a;) ko'pha,dni — — 6 ga bo'lganda 2a; — 5 qoldiq qoladi.
Ushbu ko'phadni — 3 ga bo'lgandagi qc;ldiqni toping.
p(T) uchinchi darajali ko'phad uchun p(O) O; p(l) — 1;p(2) 2
va p(3) z: 6 bo'lsa, p(4) ni toping.
A)40         B)32
         024          D)16

— I) bo'lsin. Agar p ko'phadning koefitsiyentlari
yig'indisi 12 ga teng bo'lsa, ni c — 3 ga bo'lgandagi qoldiqni toping.
A)24         B) 94         032
hadi 5 ga teng
bo'lgan ko'phadning yig'indisi 7 ga teng. Bu ga bo'lgandagi qoldiqni
toping.
— 3) ga
bo'lganda 2T qoldiq qoladi. Pg (T)
ko'phadni T — 3 ga
bo'lgandagi qoldiqni toping.
0216
+ 2a:2 -1- + 3 ko'phadm a;
'2:c4   acc3 + ba; + 100 ko'phadning ildizlaridan biri —1 ga
teng bo'lsa, P(T) ko'phadning koeffitsiyentlari yig'indisini toping. C)202       D)204
:c3 -ł-$-ł-2 va Q(m) x-4-2 bo'lsa, P
(Q(c)) ni a: — 2 ga bo'lganda qoldiqni toping. 070      D) 72

Tengsizlikni
yeching:
D)(—oo; 1] U [4; oo) U {3}
(2x2
— 5x + 4)  — 9)
0
02 + a• — 2 yeching.
C)
(—oo;
—3] u (—2; 1) u [3; 00)
D)
(-oo;
-3] u  2) u [3; 00)

12

1$

> O tengsizlikni yeching.
2) U [3; 00)
4
> $ + I tengsizlikni yeching.
A) (—oo; I]
B) (—oo; —3) IJ    II
Tengsizlikni yeching: a; —
B)a; e (—oo;2) u (3;
4) e (2; 3) u (4; 00)
                            15       4
                                                                           funksiya               < 0 tengsizlikni
yeching.
—
3 .T,2 — — 30 aniqlanish sohasiga tegishli barcha butun sonlar
yig'indisini toping.
A)      16    13)22       024   D)30  C)    2) IJ
(-2;0, 51 U {1}
 2x2 — < x2 — 8x + 8 2x2 qo'sh
tengsizlikning butun yechimlari nechta?
                                                                                (x — I) (æ -Ir  + < O
tengsizlikni yeching.
B)      —2] U [1;
00)
tengsizliklar
sistemasining -10 < x < —4,5 yechimi bo'ladigan eng katta va eng kichik
sonlar yig'indisini toping.

a' — 29x2 -4- 100 < O
tengsizlikning eng katta C) -13    eng kichik butun yechimlari ko'paytmasini
toping.
                                                                                A)-25     C)
—9
Tengsizlikni
yeching:
        1       1
           2œ'2 +
11      3x2 _    + 19
-i- 3x3 — 8x2 — 24 <
O tengsizlikning natural yechimlari nechta?
 C)(—oo; 2]
IJ [4; 00)                                        ta C)2ta         ta
 (x — 2) (2:r2                                                                                2
< O tengsizlikni   tengsizlikni
yeching.   yeching.
A)(—oo; —3]
B) (—oo; —2) IJ [4; 00)
D) (-00;-3) U {2}

14

Tengsizliklar
sisternasini yeching.

 (a•2 + 6x) 2 <
25 tengsizlikning yechimi bo'ladigan oraliqlar uzunliklari yig'indisini
15c — 2x2 — 7 -l- + —
6 funksiya aniqlanish sohasiga tegishli eng katta va eng kichik butun sonlar
ko'paytmasini toping,
— 16x
< 0 tengsizlikni qanoatlantiruvchi
+ + 16
natural sonlar yig'indisini toping. D)10
(x +2) 3 (tr—
3) 4 O tengsizlikning butun yechimlari yig'indisini toping.
B)-l

11

12

tengsizlikning
barcha but,un yechimlari o'rta arifmetigini toping.
 tengsizlikning eng
kichik musbat va -eng kichik manfiy yechimlari ÿig'indisini toping.
           3             3
tengsizlikning
eng  > 3 tengsizlikning yechimi manfiy
yechimlari bo'ladigan oraliqlar uzunliklari yig'indisini toping.

     A)4,25             B)5
1
> 2x tengsizlikning
—;oo
Nechta butun sonlar jufti rn2
+ 23 < 6rn-f- 8n tengsizlikni qanoatlantiradi?
A)6 ta B)8 ta
C) 9 ta D)cheksiz ko'p

cv ning qanday qiymatlarida a:r2
— -l- a -l- 8 > 0 tengsizlik a; ning barcha qiymatlarida o'rinli
bo'ladi?
—9) IJ (1; oo)
B) (0; 00) 1) u
(1; 00) D) (1; 00)
m ning qanday qiymatlarida a;
I > O tenglama 2 ta turli
haqiqiy yechimga ega bo'ladi?
A)(—oo; O) U (4; cx))
B)(—oo; —4) IJ (0; 00) C) (4; OO)
m ning qanday qiymatlarida (m — +
6x + — O tenglamaning ildizlari turli ishorali bo'ladi?
A) (—oo; 2) (4; oo)
C)(—oo; —4) U
(2; co)
m ning qanday qiymatlarida — (rn+5)œ+3m+ 5 O
tenglamaning ikkala ildizi ham 2 dan katta bo'ladi?

A 00)

00)

00)

00)

a < O < b bo'lsa, tengsizlikni
yeching.           a;
B)(—oo; a) IJ (b; oo)

a < O bo'lsa, (ax2 —         -l- 3) O tengsizlikni yeching.
A)(—3; 00)             B)
        00)
              <                   <                             n
< k bo'lsa,
> O
tengsizlikni yeching.
A)(—oo;  IJ            oo)
-k) U t-n; 00)
—m IJ
ax2 — + 2 > 0 tengsizlik ning ixtiyoriy
qiymatida bajariladigan a ning eng kichik natural qiymatini toping.
                         06
    D)7
+ (a -i- I)a: +4 < O tengsizlik yagona yechimga ega
bo'ladigan a ning barcha qiymatlari yig'indisini toping. B)-l
a ning nechta butun qiymatida (a — 2)œ2 + (a
— + 1 < O tengsizlik ning ixtiyoriy qiymatida o'rinli bo'ladi?
D) Cheksiz ko'p

Kvadrat
funksiya
1. Kvadrat funksiya
Koordinata boshidan y 2 10:r 3 parabolaning
simrnetriya o'qigacha bo'lgan masofani toping.
                     B)ło              C)12          D)13
funksiyaning koordinata o'qlari bilan
kesishish nuqtalari koordinatalari yig'indisini toping.
— 5a:r + 9 va y(l) I
bo'lsa, ning qiymatini toping. A)-3
Funksiya nollarini toping.

Quyidagi nutalardan
qaysi biri y 2T2 parabolada yotadi?

166
3 funksiyalarning
D)IV
a; — aa' + 6 funksiya grafigiga tegishli.
Quyidagilardan qaysi biri ushbu funksiya grafigiga tegishli bo'lmaydi?
Quyida
berilgan parabolalardan nechtasining joylashgan?

Kvadrat
  funksiya
1. Kvadrat funksiya

Koordinata boshidan y

3 parabolaning
simrnetriya o'qigacha bo'lgan masofani toping.
A)5          B)10
       C)12
funksiyaning koordinata o'qlari bilan
kesishish nuqtalari koordinatalari yig'indisini toping.
 v(T) aa? — 5a,T + 9
va y(l) ning qiymatini toping.
Funksiya nollarini toping.

Quyidagi nutalardan qaysi biri y parabolada yotadi?
A) (1; —1)      B)(2;5)
15)
2 2x + 3 funksiyalarning
3:rH-b to'g'ri chiziqda yotsa,
(3)-1
+ 4z — 2 funksiya grafigi koordinata tekisligining qaysi
choragidan o'tmaydi? C)lll     D)IV
2
— aa; -1- 6 funksiya Quyidagilardan qaysi
biri ushbu funksiya grafigiga tegishli bo'lmaydi?
Quyida berilgan parabolalardan nechtasining uchi a: 4 to'g'ri
chiziqda joylashgan?
a ning qanday qiymatida y 32 — + a — 3
funksiyaning grafigi koordinatalar boshidan
D)3

166

1.
y        3c — 4.T + 7 kvadrat funksiya OY
o'qini       OY o'qi V                                                           2                          (a

A
nuqtada, y z: —T2 — 7a; — 3 kvadrat funksiya OY o'qini B nuqtada
kesib o'tsa, IABI masofani toping.
                   13)10          C)12
         D)14
y           —
2a'cc + 5 funksiyaning kamayish oralig'i (—oo; 61 ga, eng kichik qiymati b ga
teng bo'lsa, a + b ning qiymatini toping. A)-31   025         D)31
Chizmada y — ax2 + ba:
+ c funksiya grafigi tasvirlangan. Bunga ko'ra, noto 'g'ri tasdiqni ko'rsating.

o

A)c a            B)yo c
m ning qanday qiymatlarida y
—6x-ł-(m-l-3) funksiya grafigi OX o'qini kesmaydi?
12)
C)(6; 00)                         00)
2 to'g'ri chiziq y (a —
parabolaning simmetriya o'qi bo'lsa, parabola OX o'qidan qanday uzunlikdagi
kesma ajratishini aniqlang.
5
A)l
2
parabolaning simmetriya o'qi bo'lsa, parabola uchining
ordinatasini toping.
y           —
4a: + 6 parabola uchidan koordinata boshigacha bö'lgan masofani toping.
A)v/b          B)v/6     C)2vQ
Koordinatalar boshidan o'tuvchi
kvadrat funksiya OX o'qini ikkinchi marła (6;0) nuqtada kesadi. Agar
funksiyaning eng kichik qiymati —9 ga teng bo'lsa, uning tenglamasini tuzing.
A)y            —
B)y      — C)y  — 9m
D)y 9z —
Agar
y (a -1-        (a — + 4 funksiyaning uchi              o'qida yotsa, a ning
qiymatini toping. D)3
f              funksiyaning
grafigiga ko'ra,            ifodaning qiymatini toping,

3

0

a;

A)l

Modulli
tenglama va tengsizliklar
1. Modulli
tenglamalar

7 tenglama ildizlari yig'indisini toping.
                B)3          C)5
        D)7
B)17
Son O'qida pa: — III — 15 tenglama
ildizlarini ifodalovchi nuqtalar orasidagi masofani toping.
15
2

                 — 3)2               — 21       O
tenglamaning haqiqiy

I                          5 bo'lsa,                                 +
a; ni
soddalashtiring.
A)2T — 5                                          D)2T
174

— a ifodani

2-test
cr2
— 2C — 51 — la: — Il tenglamaning barcha haqiqiy ildizlari yig'indisini
toping.
 > O; y < O
bo'lsa,             — 3œ)2 _ ifodani soddalashtiring.
A)5x — 7y
C)-5x + 7y
     14x2 —
91               16x—9 tenglamaning haqiqiy ko'paytmasini toping.
 — 41 + 1x2 — 61 0 tenglama
nechta yechimga ega?
2 a: — 61 -l- 316 — al = 20 tenglamani yeching.
          CP;
10              10
1. MODULLI
TENGLAMALAR
1x — 51 — 8 0 tenglamaning ildizlari yig'indisini
toping.
           B)-7              C)10 D)ll
1x—21 a2 —4a+3 tenglama bitta haqiqiy
ildizgá ega bo'ladigan barcha a Iar yig'indisini toping.
• —1— 31 IO tenglamaning ildizlari ko'paytmasini
toping.
ning qanday qiymatlarida I (a; — 2) (5 —  —
7a; -l- 10 tenglik o'rinli bo'ladi?
B) [0; 2] U [5; 00)
C)(—oo; 2] U
[5; 00)

l—abcl abc, —a-l-cl = a —c, I —al —
—a,bo'lsa, qaysi mulohaza o'rinli?

176                                                                     ©lntelligence
Development Center(t.me/idcuz)

Tengla,mani
yeching: — 31 = 0
00)
12a' — 6a. + 61 + a; — 41 tenglamaning barcha haqiqiy
ildizlari ko'paytmasini toping. A)-IO B) 10 D)20

— 5) 2 — 712a — 51 — 2 = O
tenglamaning eng katta va eng kichik ildizlari ayirmasini toping.
Agar va y uchun Ia;2 + 91 + 9 — + y2 = 9 tenglik
o'rinli bo'lsa, a; — y
13a — 91 = 9 - 3a tengliklar
o'rinli bo'lsa, a—
Ib — 81 = 12-8 b ning eng katta
butun qiymatini toping€
178                                                                           (Olntelligence
Development Center(t.me/idcuz)

1.                       TENGLAMALAR

a ning qanday qiymatlarida — 81x1 +
4 — tenglama to'rtta haqiqiy ildizga ega bo'ladi?
        00)
B) (-12;4)                                 00)
— 41 — 41x — 31 = + c tenglama aniq uchta
haqiqiy ildizga ega bo'ladigan c ning haqiqiy qiymatlari nechta?
                 ta
B) I ta C)Ø                    D)cheksiz ko'p

13

+51 + 12X — 31 - 10

O tenglamaning ildizi
bo'lsa, 3:co — I ning qiymatini
toping. A)2

19

[a] — a ning butun qismi bo'lsa, 2 tenglamani yeching.
-1) U (2;3]
-21 IJ [2; 3)
{a} — a ning kasr qismi bo'lsa, =
0,1 tenglama [—3; 3] oraliqda nechta yechimga ega?
                 B)10          C)12
        D)13

1x2 — 41x1 — 131 = a
tenglama eng ko'pi bilan nechta yechimga ega?
D)10
—6x2 + 11x—6 21x— 1 | tenglamaning haqiqiy
ildizlari yig'indisini toping. A)-10      D)IO
— 91 + 1:r2 — — 201 + II
tenglamaning butun yechimlari nechta?
13x — 41 — 5

yechimga ega?

2x2 — — 15

tenglama nechta

— 21

- 201

la• — 41
9

- 20

tenglamaning butun ildizi

bo'lsa,
  2x0 -l- 4

sonining raqamlar yig'indisini
toping.

1-test                                                                                2.
MODULLI TENGSIZLIKLAR
2. Modulli tengsizliklar
                 Tengsizlikni
yeching: 12x — 71 < + Il                                                         —
6 tengsizlikning natural yechimlari
B) (8;oo)
D)(—oo; 2) U (8; 00)
     la;2 —
2x1            IX -l- 41 tengsizlikning barcha butun            tengsizlikni
yeching. yechirnlari yig'indisini toping.
D)9
21x1 > a; -+- 7 tengsizlikni
yeching.yeching.
A)(7; 00)
B) —oo; I)
C)(—oo; O) U (7; 00)
5 tengsizlikning barcha butun
                + 31 < 4x tengsizlikni yeching?                                                                                teng?
A) [1 ; +00)
yeching.
 x2 + >
10 tengsizlikni qanoatlantirmaydigan butun sonlar nechta?
A)5
                C)Cheksiz
ko'p          D) 3
182                                                                     ©lntelligence
Development Center(t.me/idcuz)
    2.                       TENGSIZLIKLAR

31

 < O
tengsizlikning barcha butun yechimlari o'rta arifmetigini toping.
                                                  00,
5           D) 1,25
13:c — 21 < 5 tengsizlikning butun yechimlari nechta?
                   ta B) 3 ta cp ta                ta
1x2
— 91 + 1x2 121 < 0 tengsizlikning butun yechimi  soni
bo'lsa, (L'o (a;o -l- 2) ni toping.
B)15 D) 3
+ 2x < 9 tengsizlikning barcha natural yechimlari yig'indisini toping.
D)10
12x — 51 > —7 tengsizlikni
yeching.
00)
               C)œeR     00)
2-test                                                                                2.
MODULLI TENGSIZLIKLAR
1
Nechta butun son 3 K
2 t,engsizlikning yechimi bo'ladi? A)5ta B)10 ta ta
D)12 ta
     12T2 — -4- 71  + li tengsizlikni  tengsizlik
yechimi qanoatlantiruvchi             barcha butun        sonlar yig'indisini
toping. A)—5
a; +3 O tengsizlikning eng tengsizlikni yeching.        va
eng katta manfiy butun toping.
— — Il 5 tengsizlikning butun yechimlari
yig'indisini toping.
0
tengsizlikning butun yechimlari
              AP                                           D)16
184                                                                     @lntelligence
Development Center(t.me/idcuz)

                                                                                a: 3
                                 ni asosi bo'lgan daraja shaklida
yozing.
                       A)4,
34         B)5, 66                                                                                B)xž
                        C)10
           D)14, 34
Hisoblang: 6 X,/Ą-Š—
ifodani soddalashtiring.
A)2ł/i
c)2VfrV
Hisoblang:
                                                                                B)9v/S
         C)27          D)81
a
25
B)3vrž C)llx/ž          D)12 x K 0 y bo'lsa,           0/7
+ ifodani soddalashtiring.
B)2y
                         C)2y
- 2z              D)2Ť - 2y
Hisoblang
                                                                                C)5
         D)aniqlab bö'lmaydi
Hisoblang:
                      A)O,
75                            C)l, 25
2-test                                                                      1.
RATSIONAL KO'RSATKICHLI DARAJA
ning —
tenglik o'rinli bo'lib, a: va
y o'zaro tub sonlar bo'lsa, y —
ning qiymatini toping.
B)-l
ażbl — albi albž
              ifodani
B)ę/ö                                                                 C)                ifodaning qiymati butun son
bo'lsa, n—natural sonni toping.
                                                                                A)21          B)42          C)63          D)84
       (12 —               + (12 + 6vTá)
3
toping.
                   B)12vrš             C)54                                                                Agar
K 0 bo'lsa,
ifodaning qiymatini toping. A)-3 B)-l               01
2
Hisoblang: A)-2V5
 Hisoblang: 4 |
tartibida joylashtiring. A)a; b; c B)b; c; a       ni
hisoblang.
               C)c;
b; a                                                                              D)
b; a; c
188                                                                   @lntelligence
Development Center(t.me/idcuz)

Irratsional
tenglama va tengsizliklar
1. Irratsional tenglamalar
+ v/ÖZ7r;

140— 5T
190
O tenglamaning ildizlari
I tenglama ildiziga teskari
I tenglama nechta haqiqiy ildizga
03 ta DP
VQ — 2 tenglamani yeching.
tenglamalar sistemasidan b ni

14

TENGLAMALAR

1.
ildizlar
5

                                                                                2.                                TENGSIZLIKLAR

< 4 tengsizlikning tub
sonlardan iborat yechimlari nechta? B)5 ta B)6 ta
        BF ta
            ta
yeching. > —4
tengsizlikni yeching.
A) 00) B) [2;
00) C) [14; 00) D) [18; 00)
< 2 tengsizlikning
< I tengsizlikni yeching.
     A) —00',
7                                                                                C)4ta
            ta
     C) (3; 00)  D)
(—oo; 3)
yechimlari
< 2 tengsizlikni yeching.
A) (—oo; 9)
yeching.
                         >               tengsizlikni
yeching.
       A) [3; 00)                  5; 00)
     C) [4; 00)   D)(—oo;
—4]
< va eng kichik
butun toping,
API B)24
>
A)[2; 11) C) [5; 11)
Tengsizlikni
yeching:
Tengsizlikni
butun sonni toping:
B)3

tengsizlikning yechimi
yig'indisini

Progressiyalar
1. Arifmetik progressiya
Arifmetik progressiyada ał2 bo'lsa, ag ning
qiymatini toping. A)17 B)19 C)21
Arifmetik progressiyada5
va d 3 bo'lsa, ałł ning qiymatini toping.
                A)ll            B)14           C)17           D)20
3 4n — 2 formuła bilan berilgan
ketma-ketlikda ning qiymatini toping.
Agar
arifmetik progressiyada 113-1-05 12 bo'lsa, + 4 ning qiymatini toping.
                A)32         13)36           C)40           D)53
—3; 1; 5; arifrnetik progressiyaning yigirmanchi hadini
toping.
A) 73              B)77       C)
81      D)85
200
Birinchi hacli 5 ga, yettinchi hacli 35 ga teng bo'lgan
arifrnetik progressiyaning uchinchi hadini
B) 10              C)12       D)15
Arifmetik progressiyada aa 30 bo'lsa, arifrnetik
progressiyaning ayirmasini toping. D)10
Arifmetik progressiyada + —35 bo'lsa, 05 -1- (132 ning
qiymatini toping.
                 13)-35       C)35       D)70
Quyidagi ketma-ketliklardan qaysi
biri arifrnetik progressiyaning umumiy hadini ifodalamaydi?
A)3 — 2n       B)4n + 9 D)
2
Birinchi hadi 3 ga, ayirmasi 5 ga teng bo'lgan arifmetik
progressiyaning n-hadi formulasini
3          B)5n— 7 D)8n+3

1.                           PROGRESSIYA

— 6:r2 + (2a — — @ I 0
tenglama ildizlari arifrnetik progressiyani tashkil qilsa, a ning qiymatini
toping.
2 va 30 sonlari orasiga n ta son shunday joylashtirildiki,
natijada, ayirmasi ga teng bo'lgan arifrnetik progressiyani tashkil qiluvchi
qator hosil bo'ldi, n ning qiymatini toping. A)15 B)16 C)17

18

Ixtiyoriy 3 ta ketma-ket kelgan hadlari yig'indisi 40 ga
teng ketma-ketlikning yettinchi va o'n ikkinchi hadlari yig'indisi 23 ga teng.
Ushbu ketma-ketlikni sakkizinclli va o'n yettinchi hadlari yig'indisini toping.
A)17           13)23          C)34           D)40

14

al,
aż' • ,             sonlari arifmetik progressiyaning ketma-ket hadlari
bo'lsa, 1   1             1
(vG1 + v'őJF) ifodani soddalashtiring. A)48  B)96
      C)97       D)98
Arifmetik progressiyada ag • 4- •
a,13 68 va ał8 + aa 17 bo'lsa, ał — d ning qiymatini
toping.
      11        B)fö
7
Arifmetik progressiya hadlari
uchun

(09 —

+ (1,8)                         —

+ 010)

(ał8 —

+ a5) + (028 —

+ 013)

ifodanipg qiymatini toping.
1
soniari tartibda arifmetik
progrešsiyani tashkil qiladigan barcha T lar yig'indisini toping.
(13
—1 bo'lsa, ning qiymatini toping. 30-3            013
—
Arifmetik
progressiyada (13 + + 05               12 va — 02 3         24
tengliklar o'rinli bo'lsa, 012 ning qiymatini toping. A)14, 5 B)16                D)19
— 9x — 28 O
tenglamaning ildizlari qandaydir arifmetik progressiyaning o'n birinchi va o'n
uchinchi hadlari bo'lsa, bu progressiya uchun (ał + 023) • ał2 ning
qiymatini toping.
A)20, 25          B)27         040, 5           D)81

2. Arifrnetik progressiyaning
  yig'indisi

10

ał 1 vad 2
bo'lsa, s20 ning qiymatini A)361         B)399    C)400
10;      12 bo'lsa, S12 toping.
         A)
168          13)174          C)180
Dastlabki
n ta hadining yig'indisi Sn 2n bo'lgan arifinetik progresSiyaning yettinchi
hadini toping. A) 13          B)14       C)15
Ketma-ket kelgan 25 ta butun son yig'indisi 250 ga teng
bo'lsa, sonlardan kichigini toping.
5 3n + 2
formuła bilan berilgan ketma-ketlikning dastlabki 40 ta hadi
yig'indisini toping. A)2500 B)2540 02580 D)2620
Arifmetik
progressiyada ag 11 bo'lsa, S17 ning qiymatini toping. A)176             B)187
0196
4 ga karrali barcha
ikki xonali natural sonlar yig'indisini toping.
A)1188          B)1242
C)1200             D)1250
+ 3; T + 6; arifmetik progressiyaning dastlabki
9 ta hadi yig'indisi 135 ga teng bo'lsa, ning
qiymatini toping.

7
A)2         03D)2
Arifmetik progressiyada S25 — 725 va bo'lsa, d ning
qiymatini toping.
AP
1+3+5+ + 99
ning qiyrnatini toping.
2 '4                                   + 100
100
50
A)
101
51

16

180 bo'lsa, (117 -1- (124 ning
qiymatini toping.
14 K
n K 77 shartni qanoatlantiruvchi 7 ga karrali sonlar yig'indisini toping. A)455              13)462   C)469
+ 0,19    30 bo'lsa, S25 ni qiymatini
toping. A)375     B) 750    0400      D)780
Arifmetik progressiyaning birinchi hadi 3 ga, ayirrnasi
esa 2 ga teng. Uning dastlabki 10 ta hadi yig'indisini toping. A)110 B)120
C)130 D)135

Arifmetik progressiyada ał 5, S4 50 bo'lsa, ayirmasini toping.
D)6
— dn + 2 ko'rinishida berilgan arifmetik
progressiyaning dastlabki 20 ta hadi yig'indisi 355 ga teng bolsa, d ning
qiymatini toping. B) 1,5
Yig'indini
hisoblang: s —12+13,5+15+. . -1-88, 5 90. A)2652                13)2601
02550 D)2703
Arifmetik
progressiyada SĄ             32; SIO — 200 bo'lsa, S20 ni toping. A)632 B)768    C)800
Dastlabki n ta hadining yig'indisi
Sn 2n2 + n bo'lgan arifmetik progressiyaning umumiy hadini toping.
B)2n+ 1
C)4n - 3             D)4n - 1
2772 bo'lsa,       ning
qiymatini toping.
A)20           B)25         C)28          D)56
Arifmetik
progressiyada Sn 450 bo'lsa, n ning qiymatini toping.
A)15           B)29

Arifmetik
progressiyada bo'lsa, progressiyaning yig'indisini toping. A)160         B)320
Sn —arifmetik progressiyaning hadi
yig'indisi bo'lsin. U ifodaning qiymatini toping.
Arifmetik progressiya bo'lsa,           ni
hisoblang..
O'suvchi arifmetik

a1 +  18 al = 192 toping.
A)
110    B)120
Arifmetik progressiyaning dastlabki 10 ta hadi
yig'indisi 100 ga, dastlabki 20 ta hadi yig'indisi esa 300 ga teng. U holda
uning dastlabki 30 ta hadi yig'indisini toping.
B)
500    C)600    D)700
I, d — 2 shartlar bilan berilgan
arifmetik progressiyaning dastlabki n ta hadi va 20 sonining o'rta arifmetigi 8
ga teng bo'lsa, n ning eng katta qiymatini toping.
24, 19, 14, arifmetik
progressiyaning clast,labki
10 ta manfiy hadi yig'indisini
toping.
                         13)-245                 0-235
9 ga karrali barcha 3 xonali sonlar
yig'indisi qanday raqam bilan tugaydi?
13)2
Hisoblang: 2002 — 1962
+1922— 1882 + ...+82—42
B)20000 D)20400

12; d 0,2 bo
'Igan progressiyaning dastlabki 41 ta hacli O'rta arifmetigini toping. A)15, 8
B)16 D)17
Qanday
natural son uchun 2 + 5 H- 8 + (3n — 7) 805 tenglik o'rinli bo'ladi? A)23            13)24     C)25
      D)26
Yig'indini hisoblang:

II

115        43
Arifmetik
progressiyada $6 — S5 12 va SI 1              15 SIO   14 bo'lsa, SIG ning
qiymatini toping. A)195 B)208     C)221    D)234
Yig'indini hisoblang: 1 2 +
22 + 32 -1- ...242
A)2500  13)4850 C)4900  D)9800
Center (t.me/idcuz)

= O, 045 tenglarnadan a; natural sonni
toping.
                  13)10                099            D)100
2;5;8;11.. va  arifmetik
progressiyalarning umumiy hadlaridan yangi arifmetik progressiya tuzildi. Bu
progressiyaning dastlabki 15 ta hadi yig'indisini toping.
         A)1335        B)1350
         C)1425    D)1440
Arifmetik progressiyada SIOO —
S79 = 420 bo'lsin.
U holda
         A)19
       B)20         C)21         D)22
Arifmetik progressiyada ,9200 1000 va 0200 0199 + (1198 —
(1197 + + — a? = 1000 tenglik o'rinli bo'lsin. U holda progressiyaning birinchi
hadi nechaga teng?
C)-90
5 (41, . . .
, arifmetik progressiyani tashkil qiluvchi sonlar uchun

bo'lsa, progressiya ayirmasini
toping.

Dastlabki n, na natural son yig'indisini Sn bilan belgilaylik. Masalan S3 1 3 =
6. U holda
-l- s3ó yig'indini hisoblang.
13)4980
D)5050
sonlarning har biri I ga yoki -1 ga  O
quyidagilarning qaysi biriga
                                         C)101
         D)102
Arifmetik progressiyaning
dastlabki 50 ta toq o'rinda turgan hadlari yig'indisi uning dastlabki 50 ta
juft o'rinda turgan hadlari yig'indisidan 100 taga karn. Agar progressiyaning
birinchi hadi 2 ga teng bo'lsa, uning dastlabki 100 ta hadi yig'indisini toping.
B)IOIOO
Dastlabki 101 ta natural son
ichidan 100 tasi olinib, ularning yig'indisi hisoblandi. Agar
yig'indi 5100 ga teng bo'lsa,
yig'indida qaysi son qatnashmagan?
D)101
progressiyada
Sn —dastlabki n ta bo'lsin, Agar Sn+2 + Sn_2 — 2Sn = 12 va al 2; an = 101
bo'lsa, n—?
                                   C)35         D)36

                                                                                3-ůcst

1, 5, 12, 22, 35,...
sonlar ketma-ketligidagi hadlar farqi 4,7, 10,13 ošhib borrnoqda, Bu
ketrna-ketlikning 100-hadi nechaga teng?
                         A) 14950       B) 15000
                         C)
15050       D)15100
Ian) ketma-ketlikda al 102 va an+1 — an munosabat
o'rinli bo'ladi. Agar bu ketma-ketlikning dastlabki 100 ta hadi yigřindisi
100 ga teng bo'lsa, uning 101 ta hadi nechaga teng?
                          A)-2
       B)-1              0100
Hisoblang: I • 19 -F 2 • 18 -F- 3
• 17 + +
                          A)1260           B)1330

01400
190 bo'lsa, ning qiymatini toping.
                         oo, 9    D)0,
95
Arifrnetik
progressiyada S3 6 va SG 3. Agar sŮ —9 bo'lsa, n ning qiymatini toping. B)9               010
                                                       Center(t.me/idcuz)
                                                                                3.            PROGRESIYA

3, Geometrik progresiya

1
Birinchi
hadi — ga, maxraji 3 ga teng bo 'Igan
18 geometrik progressiyaning oltinchi hadini
toping. 243     27
        2              2
1
Geometrik
progressiyada bl — va q 2 3 b3
-1- ba ning qiymatini toping. A)l
     27 Geometrik progressiyada bl — va
bo'lsa, progressiya maxrajini toping.
2
    3
O'suvchi geometrik progressiyani ko'rsating.
1
A)       12; 18; 24;
...     13)9; 3; 1; - ...
3 C)2; 4; 8; 16...   D)5; 10; 15;
z: 216 bo'lsa, b3 • bil ning qiymatini
toping.
c)24vQ
3,
a, b, c, 48 sonlari musbat hadli geometrik progressiyaning ketma-ket hadlari
bo'lsa, a+b-l-c
ning
qiyrnatini toping.
B)       36     C)42   D)48
Geometrik progressiyaning umumiy hadi bn — 1—2n

bo 'Isa, uning
maxrajini toping.
2
                  3
Maxraji
2 ga teng bo'lgan geometrik
progressiyaning
uchinchi va oltinchi hadlari yig'indisi 108 ga teng bo'lsa, uning ikkinchi
hadini toping.
                      C)12       D)18
Geometrik
progressiyada b7 — 56 va bl bo'lsa,
b5 ning qiymatini toping.
                  B)
140   C)28   D)42
Geometrik
progressiyada bl •b2•b3 27 va b5 24 bo'lsa, bl ning qiymatini toping.

Center(t.me/idcuz)

3.                             PROGRESIYA

Geometrik progressiyaning  hadlari
ayirmasi 48 ga teng. Agar va b3 sonlari arifmetik progressiyaning hadlari
bo'lsa, b4 — b2 ning qiymatini toping. A)108 B)144
0156       D)114
Laboratoriya
xonasidagi ikkita idishning birinchisida 192 ta, ikkinchisida 1458 ta virus
bor, Har soat so'ngida birinchi idishdagi har bir virus teng uchga, ikkinchi
idishdagi har bir virus teng ikkiga bo'linadi. Necha soatdan so'ng idishlardagi
viruslar soni tenglashadi?
-1-2; 3vTý + I va 23 —
X„'TJ sonlari ko'rsatilgan
tartibda geometrik progressiyaning ketma-ket hadlari
bo'ladigan barcha y lar yig'indisini yoki y (agar u yagona bo'lsa)ni toping.
AP, 25     B)ll,
25
Geometrik progressiyani tashkil qiluvchi
uchta musbat son yig'indisi 21 ga, bu sonlarga teskari 7 miqdorlar
yig'indisi — ga teng.
12 toping.
A)3                              012 D)9
łan) ketma-ketlikda an • (n -1- I) va ał O,
5 bo'lsa, (199 ni toping. A) 99      B)lš
1
Center
(t.me/idcuz)
progressiyani tashkil
bo'Isa, b2 ning
102 va
                              C)512
         D)102
progressiyada bl + b2 -1- b3 13 va z: 54
bo'lsa, uning maxrajini toping.
a; 15; b
arifmetik progressiyaning, a; 9; b esa geometrik progressiyaning ketma-ket
qiymatini toping.
27
D)—10
qonuniyat bilan berilgan qanday

                                                                4.
                                 PROGRESSIYANING YIG'INDISI
4. Geometrik progressiyaning yig'indisi

Maxraji 3 ga teng
bo'lgan geometrik
progressiyaning dastlabki 5 ta hadi yig'indisi 484 ga teng.
Progressiyaning birinchi hadini toping.
bl 3, b2 0,75 bo'lgan cheksiz kamayuvchi geometrik
progressiya hadlari yig'indisini toping.
Cheksiz kamayuvchi geometrik
progressiyaning yig'indisi 6 ga, birinchi hadi 4 ga teng. Progressiyaning
dastlabki 4 ta hadi yig'indisini toping.
                          100                                      320
                        27                                          81
                                        6
Hisoblang: — + — + —•
                        7
49          43
                 7                          7
Hisoblang: 2 + 6+ 18 + +2 . 319 A)320 _ 1 B)3 19 —
1
1)
ning oxirgi raqamini
Cheksiz karnayuvchi geometrik progressiyada S 4b1
bo'lsa, progressiya mahrajini toping.
3
formuła bilan berilgan geometrik
progressiyaning dastlabki 5 ta hadi yig'indisini
                   13)93                C)189
27 3'20 — 321 ni
hisoblang.
1 321 B)
4
1 — 321
D)
2

4.  PROGRESSIYANING YIG'INDISI

b2 Geometrik progressiyada
bl b4
—
-1- + ning qiymatini toping. b3 1     1
      9        3
Cheksiz karnayuvchi geometrik birinchi hadi
ikkinchi hadidan 12 yig'indisi esa 27 ga teng, uchinchi hadini toping. A)l BP
2
Umurniy hadi bn kamąyuvchi
geometrik toping.
BP
Agara
b va 5a 3b bo'lsa, I+g-łifodaning qiymatini toping.
    5      3
Agar O K a; K I

a; ning qiymatini
toping.
Center(t.me/idcuz)
Bifinchi hadi I
ga va maxraji 2 ga teng bo'lgan geometrik progressiyaning dastlabki 10 ta hadi
yig'indisi nechaga teng?
A)513   B)511
C)1023    D)1025
Hisoblang:
Geometrik
progressiyada Sc 9S3 bo'lsa, progressiyaning maxrajini toping,
Cheksiz
kamayuvchi geometrik progressiyada 2b1 +2b3 5b2 va ba I tengliklar o'rinli
bo'lsa, progressiya yig'indisini toping.
                   BP            D)16
Geometrik
progressiyada S7 — 56 192 va 12 bo'lsa, b5 ning qiyrnatini toping.
                  B)36   C)48   D)
108

2-test                                                           4.
GEOMETRIR PROGRESSIYANING YIG'1Nb1S1

13      35

16         64

.yig'indini
210 10

2
cheksiz SI geometrik
Agar
02 uning
esa marka.zidan Barcha

 +
hisoblang.
                                      7
2
22 2
Ushbu
                   2              2               2
yig'indini hisoblang. A)1047 B)1048 01049 D)1050
Hisoblang:
3 3 '3 3
Maxraji q ga teng bo'lgan bl, . ,
.
kamayuvchi geometrik progressiya yig'indisi ga teng.
bl, . . . sonlardan tuzilgan progressiya hadlari yig'indisi S2 ga teng. S? 7S2
bo'lsa, q z?
Ol markazli aylana radiusi 8 ga teng. markazli aylana
Ol markazli aylana urinib, markazidan o'tadi. 03 markazli aylana  3 ta, son
ayirmasi gą teng bo'lgan arifmetik progressiyani tashkil etadi. Agar
birinchi sondan I ayirib, uchinchi songa 5 qo'shsak, geometrik progressiya
hosil bo'ladi. Hosil bo'lgan geometrik progressiyaning dastlabki 7 ta hadi
yig'indisini toping.
         A)405                13)456
0508                D)512
7 20—1 + I
formuła bilan berilgan ketma-ketlikning dastlabki 10 ta hadi yig'indisini
toping.
A)1023 B)1033 C)521
1
Agar 1 m K 2 bo'lsa,
+ . . . — —— 3 tenglama ildizini toping.
C)
Chizmadagi katta kvadratning tomoni 12 ga teng. Har
bir kwadrat o'zidan oldingi kvadrat bilan umurniy uchga ega va uning
markazidan o'tadi. Barcha kvadratlar yuzlari yig'indisini toping.

02 markazli
  aylanaga urinib, uning o'tadi va hokazo (aylanalar cheksiz).
aylanalar uzunliklari yig'indisini toping.
                                                                                A)108         13)192          C)216          D)288
                                                                                2T—5
2m —5
2     4              3 9 +
  tenglarnani yeching.
A)247          B)32łr         C)48łr         D)64Ťr

12cm

Cheksiz kamayuvchi geometrik progressiya hadlari
yig'indisi 100 ga teng, Bu geometrik progressiyaning barcha hadlari kvadratlari
yig'indisi esa 1000 ga teng.   Geometrik progressiya maxraji       qisqarmas
kasrga teng bo'lsa, m + n ni toping.
                      C)10              D)20
 (Ysuvchi geometrik progressiyani tashkil
etuvchi uchta son yig'indisi 26 ga teng. Agar ikkinchi son 4 ga
oshirilsa, bu sonlar arifmetik progressiyani tashkil qiladi. Bu arifmetik
progressiyaning dastlabki 10 ta hadi yig'indisini toping.
A)270          13)380         C)390    D)420
Hisobang: —  1
Ibn) geometrik progressiyada a
bl + b2 + 53 +
 bo'lsa, bl
•b2'b3'... • b100 ifoda quyidagilardan qaysi biriga teng.

50                      99                   100                49
a B)                      blOO
ketma-ketlikdagi sonlar farqi geometrik
progressiyani tashkil qiladi. Bu ketma-ketlikning to'qqizinchi hadini
toping.
38 - 1    38 1 B)
    2                         2
    39 — 1                       39
-1- I
C)          +1       D)

      2                                   2
Center(t.me/idcuz)
Cheksiz kamayuvchi geometrik progressiyada
                            +         + . . .  12
+ X/Ő—.T3
+
                13)9
       C)12         D)18
Uchta son maxraji 3
ga teng bo'lgan geometrik progressiyani tashkil etadi. Agar birinchi va
ikkinchi songa 8 qo'shilsa, arifmetik progressiya hosil bo'ladi.
Geometrik progressiyaning dastlabki 6 ta hadi yig'indisini toping.
                      B)652         C) 712         D)728
cheksiz
kamayuvchi geometrik progressiyalar uchun bl
4 bo'lsa, blT1 + bez:ť2 + b3X3... ifodaning
                   13)36         C)42          D)45
Cheksiz
karnayuvchi geometrik progressiyaning barcha hadlarining yig'indisi uning
dastlabki 10 ta hadi yig'indisidan 2 marła katta.
Agar progressiyaning dastlabki 21 ta hadi ko'paytmasi 10240 bo'lsa, uning
birinchi hadini toping. B)"        D)żvrž
250 ning qiymatini
3
— tr; ning butun qismi)
251 — 2
B) 251 32 D)
                              3
3

Matnli
  masalalar
1. O'rta arifmetik va o'rta
  geometrik qiymatga oid masalalar

6; —2; 7 va 5 sonlarining o'rta
arifmetigini toping.
B)4
18;12 va 64 sonlarining o'rta
geometrigini toping.
A)12x3/á
 13)18 C)24
a, b, c sonlarining O'rta
geometrigi 12 ga teng bo'lsa, 4a; 6b va — sonlarining o'rta geometrigini
toping.
13)12                    C)18           D)24
12;
18; 21 va sonlarining o'rta arifmetigi ga teng bo'lsa, T ni toping. A)15          B)16
      C)17       D)18
4,3; 2,1; 3,5 va sonlarining o'rta arifmetigi 4,1 ga teng
bo'lsa, a: ning qiymatini toping.
220
8;18 va T sonlarining
o'rta geometrigi a; ga teng bo'lsa, T ning qiymatini toping.
                  B)12            C)16           D)18
Ayirmasi 28 ga teng ikki sonning o'rta arifmetigi 18
ga teng. Bu sonlardan kichigini toping. D)10
Beshta sonning O'rta arifmetigi 16 ga, boshqa 3 ta
sonning o'rta arifmetigi esa 40 ga teng. Shu 8 ta sonning o'rta arifmetigini
toping.
                   B)25           C)28           D)32
O'rta arifmetigi 12 ga teng beshta sonning kattasi
qolganlarining yig'indisiga teng. Bu sonlardan kattasini toping.
                  B)20
         025          D) 30
Ikki sonning o'rta arifmetigi ularning O'rta
geometrigidan 1,(6) marła ortiq. Bu sonlar nisbatini toping.
B)25 : 9
D)9 : 4

1, O'RTA ARIFMETIK VA O'RTA GEOMETRIK QIYMATGA
OID MASALALAR 1-test

Qatorga o'sish tartibida 7 ta gon Ulardan dastlabki 4
tasinilłg o•rta ariflť'. ga, oxirgi 4 tasining o'rta arifmetigi 22 ga
tcng. Agar qatordagi barcha sonlar O'rta arifmetigi 14 bo'lsa, qatorda yozilgan
to'rtinchi sonni toping.
         B)16                C)17          D)18
Sońlardan biri ikkinchisidan 5 marta katta. Agar
ularning o'rta geometrigi IO ga teng bo'lsa, kichik sonni toping.
13)2vG                                       D)5vQ
3, a: — y, 2x + sonlarining 15 ga teng bo'lsa, -F q;
va a sonlarining arifmetigini toping. A)12 B)14 C)15

IO ta har xil natural sonlarning O'rta
arifmetigi IO ga teng. Bu sonlardan eng kattasi eng ko'pi bilan nechaga tong
bo'lishi mumkin? A)45    B)50       055         D)65
a -l- I va b -l- I sonlarining
o'rta arifmetigi 6 ga, o'rta geometrigi esa 4 ga teng. a2 va
sonlarining o'rta arifmetigini toping. A)5      B)40       045
        D)50
Center
(t.rne/idcuz)
1
1 1 • c sonlm•; orometrigi 3 ga, sonlaring o'rta
arnmetigi esa 1 ga teng. ab; bc; ca sonlari o'rta arifmetigi nechaga teng?
                 13)9         C)27
72 ta natural son o'rta arifmetigi quyidagilardan qaysi
biriga teng bo'la olmaydi? (Sonlar har xil bo'lishi shart emas)
C)12, 675              D)13,
375
Uchta son o 'rta arifmetigi a ga teng. Agar ikkinchi va
uchinchi sonlar o'rta arifmetigi a -F I ga, birinchi va uchinchi sonlar O'rta
arifmetigi esa a + 2 ga teng bo'lsa, bu uchta sonlardan eng katt,asi va eng
kichigining ayirmasini toping.
Sinfdagi 26 ta o'quvchining o'rtacha o'zlashtirish
ko'rsatkichi 72% ga teng edi. Bitta o'quvchi boshqa sinfga o'tgandan keyin,
qolgan o'quvchilarning o'zlashtirish ko'rsatkichi 71,6% ga teng bo'ldiv Sinfdan
ketgan o'quvchining o'zlashtirish ko'rsatkichini toping.
                   B)78          C)80          D)82
Birinchi hadi I ga, maxraji 2 ga
teng bo'lgan geometrik progressiyaning dastlabki 15 ta hadining o;rta
geometrigini toping.
A)32         13)128         C)256          D)512

I-test                                                                                2.
FOIZGA OID MASALALAR
2. Foizga oid masalalar
1 a sonining
45 foizi b sonining 75 foiziga teng.aż soni y ning 40%iga teng bo'lsa, y
soni 'V ning sonining a soniga nisbatini toping.necha foiziga teng bo'ladi?
                                                         B)O,
7A)60                                                 B)140                0150
Ishchining
oylik maoshi dastlab 12% ga, keyin yana 10% ga oshdi, Uning maoshi jami necha 2
a sonining 40%i b ga, b sonining 45%i c ga teng.foizga oshgan?
c soni a sonining necha foizini
tashkil qiladi?A)22      D)24 A)12            B)16       C)18       D)24
Kutubxonadagi
kitoblarning 60 % i ingliz tilida, qolganlari Uzbek tilida. Agar ingliz
tilidagi kitoblar o'zbek tilidagi kitoblardan 250 ta ko'p Idishning 60%i suv
bilan to'ldirilgan. Idishga bo'lsa, kutubxonada jami nechta kitob bor? yana
30 litr suv quyilsa, uning 75%i to'ladi. IdishA) 1000 B) 1200 sig'imi necha
litr?
                                                                                C)1250
         D)1300
             A)IOO           B)150                 0200
Mahsulot narxi avval 20% ga,
keyin yana 10% ga oshib 363 so'rn bo'ldi. Mahsulotning dastlabki narxi necha
so'm edi? Kubning qirrasi 20% ga kamaytirilsa, uning A)250 13)265 C) 270 hajmi
necha foizga karnayadi?
             A)
40          B)48, 8           C)51, 2           D)60
Agar ko'paytuvchilardan biri 40% ga oshirilib, ikkinchisi
30 % ga kamaytirilsa, ko'paytma qanday o'zgaradi? A)IO % ga oshadi
Musbat .vr songa teskari
son a; ning 49%ini tashkilB) 10 % ga kamayadi qiladi. ni toping.C)2 % ga oshadi
                   49                                     100
                  100                10                                           49D)2
% ga kamayadi

Ikkita son yig'indisi 50 ga teng. Birinchi sonning
 1
 qismiga ikkinchi
sonning 20%i qo'shilsa, yig'indi 14 ga teng bo'ladi. Sonłałdan
kattasini toping.
A)27           B)30
         C)33          D)35
Ish
haqi ikki marta bir xil foizga oshirildi. Natijada, ish haqi dastlabkisiga
nisbatan 156%ga oshdi. Ish haqi har safar necha foizga oshirilgan? A)45    B)50       C)60
      D)78
40 soni 32 sonidan necha foizga ko'p? A)15 B)20       C)25
      D)30
Mahsulotning bozordagi bahosi
uning tannarxidan 30% ga qimmat. Talab kamligi tufayli mahsulot narxi 10% ga
arzonlashtirildi. Agar mahsulotning yangi narxi 14040 so'rn bo'lgan bo'lsa,
uning tannarxini toping. A)11500 B) 12000
012500          D)13000
Bir son ikkinchisidan 60% ga ko'p. Bu sonlarning o'rta
arifmetigi katta sondan necha foizga kam?
018, 75%
Narxi 40000 so'm bo'lgan mahsulot
avval
qandaydir foizga, keyin undan uch marta katta bo'lgan foizgm
OShib 57200 so'rn bo'ldi. Narx birinchi marta oshganidąn keyin mahsulot
necha so'rn bo'lgan? A)44000 B)44800
045600        D)46000
Farangizdagi
pulning 80%i Solihadagi pulning 30%iga teng. Soliha necha % pulini Farangizga
bersa, ularning pullari miqdori tenglashadi? B)25               C)31, 25 D)62,
5
a
sonining 30%i b sonining 25%iga teng bo'lsa, b soni a sonidan necha foizga
ko'p? B)20              C)25
Sotuvchi do'kondagi mahsulotning
80%ini foyda bilan, qolganini 10% foyda bilan
sotdi.
Bunga ko'ra sot,uvchi necha %
foyda qildi? B)lő C)18             D)19
a soni b sonidan c% ga ko'p. U
holda b soni a sonidan necha foizga kam?
100c
100 - c
        100c                  100c
I-test
3. Harakatga oid masalalar
G'ildirak aylanasining uzunligi 2,5 metr. G'ildirak 72
marła aylanganda qancha masofani bosib o'tadi? A)160     B)180    C)200          D)220
Yengil avtomobil ikki shahar orasidagi masofani 6 soatda
bosib o'tadi. Agar shaharlar orasidagi masofa 480 krn bo 'Isa, mashinaning yo'l
davomidagi o'rtacha teziligini (km/soat) toping. A)60 13)70 C)75 D)80
A shahardan bir vaqtda, bir xil yo'nalishda ikkita
avtomobil yo'lga chiqdi, Ularning tezliklari mos ravishda 78km/soat va
72krn/soat. Ikki soatdan keyin ular orasidagi masofa necha km bo'ladi? A)9 B)12
C)15
Oralaridagi masofa 720 km bo'lgan ikki shahardan bir-biriga
qarab ikki poyezd yo'lga chiqdi. Poyezdlarning tezliklari mos ravishda 90
km/sooat va 7()km/soat bo'lsa, ular necha soatdan keyin uchrashishadi?
Mashina dastlabki 4 soat davomida 72 km/soat tezlik bilan,
keyin 5 soat davomida esa 63 krn/soat tezlik bilan yurgan bo'lsa, uning bu
vaqtdagi o'rtacha tezligini toping. (km/soat)
            A)66       13)67         068          D)69
3. HARAKATGA OID
MASALALAR
Oralaridagi masofa 240 km bo'lgan ikki shahardan bir-biriga
qarab kelayotgan ikki avtomobil harakat boshlanganidan 2 soat O'tib
uchrashishdi. Agar bir avtomobilning tezligi ikkinchisining tezligidan 6
km/soat ga kam bo'lsas katta a,vtomobilning tezligi (km/soat) qancha?
A) 54           B)61          C)63
         D)66
Katerning daryo oqimi bo'ylab tezligi 40km/soat, oqimga
qarslli tezligi esa 24krn/soat bo'lsa, daryo oqimining tezligini (km/soat)
toping.
Oralaridagi masofa 800 krn bo'lgan A va B shaharlardan
ikki avtomobil bir-biriga qarab, bir vaqtda yo'lga chiqdi. A shahardan chiqqan avtomobilning
tezligi 90km/soat, B shahardan chiqqan avtomobil teżligi esa 70km/soat
bo'lsa, avtomobillar B shahardan qanday masofada uchrashishadi?
A)280           B)350          C)450          D)540
Mashina 3,5 minutda 6 km yo'l yursa, u 42 sekundda
necha metr yo'l bosadi? A) 1000 B)lłoo C)1200
Bir shahardan 60 km/soat tezlikda avtobuš va
oradan 3 soat o'tgach, shu shahardan avtobus yo'nalishida 90km/soat tezlik
bilan yengil avtomobil yo'lga chiqdi. Necha soatdan keyin yengil avtomobil
avtobusga yetib oladi?
3. HARAKATGA
om MASALALAR
Uzunligi 600 metr bo'lgan poyezd
ustun yonidan

25 sekundda o'tib ketdi. Bu poyezd uzunligi 960 metr
bo'lgan tuneldan necha sekundda o'tadi? A)40 B)60 C)65 D)70
1
Avtomobil yoSlning 5
qismini 90 km/soat,

tezlik bilanł qolgan qismini esa 60 km/soat tezlik
bilan bosib o'tdi. Avtomobilning butun yo'l davomidagi o'rta.cha tezligini
(km/soat) da topinig.
              A)67,
5          B)70                                 D)75
Motorli qayiq daryo oqimi
bo'ylab 60 km va

oqimga qarshi 56 km masofani bosib o'tishi
uchun 3,5 soat, vaqt tala,b etiladi. Agar dar,yo
oqimining tezligi 6
km/soat bo'Isa, motorli qayiqning daryo oqimi bo'.ylab tezligini toping,
(krn/soat)
              A)28        B)34         C)40        D)46
 Kerna dengizda 4 soat
davornida A nuqtadan B nuqtaga suzib keldi. Keyingi 3 soatda AB ga
perpendikulyar ravishda suzib C nuqtaga suzib bordi. Kema butun yo'l davomida
o'zgarrnas tezlik bilan harakatlangan va dastlabki manzildan 180 km uzoqlikda
bo'lsa, uning
tezligini (km/soat) toping. A)30 13)36 C)45 D)60
Kater daryo oqimi bo'ylab 5 soatda qancha masofani O'tsa,
oqimga qarshi 6 soatda harn shuncha masofani o 'tadi. Uning turg'un suvdagi
tezligi daryo oqimi tezligidan
necha marła katta?
                     A)5                 13)6
                C)10                    D)ll
Ikki avtomobil uzunligi 18 krn bo
'Igan a,ylana
halqa bo'ylab, bir nuqtadan bir xil yo'nalishda harakat
boshladi. Birinchi avtornobilning tezligi 94 km/soat, ikkinchisiniki esa 100
km/soat bo'lsa, necha soatdan keyin ikkinchi avtomobil birinchisini bir aylana
halqaga ortda qoldiradi? cp,5
Oralaridagi masofa 180 krn bo'lgan ikki shaharlardan
biridan ikkinchisiga qarab avtobus, oradan 30 minut o'tgach esa ikkinchisidan
birinchisiga qarab yengil avtomobil yo'lga chiqdi. Agar
avtomobilning tezligi avtobusning tezligidan 15 km/soatga ko'p, harnda ular yo'lning
o'rtasida uchrashgan bo'lsa, avtobus tezligi necha krn/soat? A)40 B) 45 C)50
Poyezdning tezligi 25m/s bo 'Isa, u 3 soat,da qancha masofani
(km) bosib o'tadi? APIO B)240 C)270 D)300
Mashina o'rtacha tezligini 25% ga oshirib, ma'lum masofani
rejadagidan 1 soat 12 minut tezroq bosib o'tdi. Agar u tezligini 50% ga
oshirganida, bu masofani qąncha vaqtda (soat) bosib o'tar edi?
Uydan maktabgacha botlgan masofani aka 24 minut,da, uka esa
30 minutda bosib o'tadi. Agar uydan aka ukasidan 3 minut kechroq chiqsa,
qancha vaqtda ukasiga yetib oladi? A)12 13)15 C)18 D)24

1-test                                                               4.
  ISH VA ARALASHMAGA 011) MASALALAR
4. Ish va aralashmaga oid masalalar

Ishni birinchi
ishchining yolg'iz o'zi 18 kunda, ikkinchisi esa 36 kunda bajaradi. Agar ular
birgalikda ishlasa, ishni necha kunda bajara olishadi?
B)10                           C)12
Birinchi
ishchi ishni 0,8 soatda, ikkinchisi soatda tugatadi. Ikkala ishchi birgalikda
ishlasa, ishni necha minutda tugatadi? A)30             B)36       C)40       D)45
Usta
ishni 30 kunda tugata oladi. Agar usta 18 kun ishlasa, ishning qanday qismi
tugallanmay qoladi?
5
Birinchi quvur hovuzni 12 soatda,
ikkinchi esa• 18 soatda to'ldiradi. Agar ikkala quvur bir paytda ochib
qo'yilsa, 3 soatda hovuzning qancha qismi to'l di?
C)
Beshta usta kuniga 6 soatdan
ishlab ma'lurn ishni
8 kunda bajaradi. Xuddi shunday ishni 12 ta usta
kuniga 5 soatdan ishlab, necha kunda bajara oladi?
A)3                                        D)6
Ishni 16 kishi 6 kunda tugata oladi. Shu ishni 4 kunda
tugatish uchun yana nechta ishchi kerak bo'ladi?
D)24
Birinchi va ikkinchi ishchi ishni 18 soatda, ikkinchi
va uchinchi ishchi 12 soatda, uchala ishchi birgalikda 9 soatda bajaradi. U
holda ikkinchi ishchining yolg'iz o'zi bu ishni necha soatda bajaradi? A)24
B)27 C)36 D)48
Bir ishni birinchi ishchi 10 soatda, ikkinchi ishchi
15 soatda, uchinchisi 30 soatda bajaradi. Uchala ishchi 3 soat ishlaganidan
so'ng, uchinchi ishchi ketib qoldi. Qolgan ishni birinchi va ikkinchi ishchi
necha soatda bajaradi?
Usta va shogird bir soatda birgalikda 60 ta detal
tayyorlay oladi. Bunda usta 2 soatda qancha detal tayyorlasa, shogird 3 soatda
shuncha detal tayyorlaydi. Shogirdning o'zi 5 soatda nechta detal tayyorlay
oladi?
A)90 ta      B)115
ta      C)120 ta                 ta
Birinchi ishchining yolg'iz o'zi ishni II kunda,
ikkinchi ishchining yolg'iz o'zi esa 17 kunda bajaradi. Agar ishning
uchdan birini birinchi ishchi, qolganini ikkinchi jshchi baja,rsa, ish necha
kunda bajariladi?
A)12        B)13         C)14         D)15

4. ISH VA
ARALASHMAGA 011) MASALALAR

Funksiyalar
1. Funksiya (1-qism)

 bo'lsa, f3) ning qiymatini
toping.
A)-18                               C)12          D)18
f         532 — 43 3 bo'lsa, f
(—1) -1- f(2) ning qiymatini toping. A)20               B)24       027         D)28
Juft funksiyani ko'rsating:

                _           — 8) funksiya nollarini toping.
0); (0; 64)
0); (o; 72)
0); (0; 64)
Toq funksiyani ko'rsating:

228
-4- m 6 funksiya uchun f (x) f (1)
ko'paytmasini toping.
uchun f (2) 12
C)1,5
— C2 +3.T—1 bo'lsa, f(3) ning qiymatini
D)13
bo'lsa, f(f(3))ni toping.
D)25
bo'lsa, f(2) ning qiymatini
D)35

1.

emas?
B)
14)
C)
(3;
7,5)  D)     1,5)
— 5m bo'lsa, k k ning qanday qiymatida
y grafigi (—5; I) nuqtadan o'tadi? A) -16 B) -6 C) 6
f(-2)
toping.
Grafikka ko'ra, f (—4) ning qiymati f(—l) ning
qiymatidan qanchaga kichik ekanligini
• f(5)
 f(a) -ł- 3ax2
+ 3 funksiya uchun bo'lsa, f (2) ning qiymatini toping.
(3)-11
1.

f(a;) + 6:r2 + 12:r+8 bo'lsa, f(C/Ť— 2) ning
qiyrnatini toping. A)—7
Quyidagi berilgan funksiyalardan
nechtasi juft funksiya?
4x8 3:r2
          —    + 21 + IvG—2
3
Ix —2 • (5x2
— 4:c)
A)l        BP
If(x)                                                   bo
'Isa,
— 7x -1-5 m K 2 f (4) ning
qiymatini toping.
A)17           B)65
        C)72          D)82
f (x) •              O
tenglama nechta yechimga ega?
                              T2
—5m+1 bo'lsa, f ( 2)1                         (3)
ning qiymatini toping.
B)-7
f (a) juft funksiya va 5f (a)
16T2 + 40 bo'lsa, f (x)
funksiyani toping.
A)
f(x)          +
2:r2 -1-5
B)
f (x) 4T6 +
H- 20 — 2:r2 — 5 x6 — 2T2 — 5
+ -1- I) bo'lsa, f f (2 — v”S) ni
hisoblang.
A) 12           B)
14                       C) 80 D) -8v/S —2
f (m) funksiyaning grafigi Oy ö'qiga nisbatan simmetrik.
f (2) 5; f (—3) 9 bo'lsa, 4f(—2) + 3/(3) ning qiymat,ini toping.
                        13)-7         C)27          D)47
— I tenglamaning musbat ildizlari nechta?
f(T)                  bo'lsą,
           + 4)
tenglamadan — 25 ning qiymat,ini toping,
1
     5           B)5          025          D) 125

1.

Agar
f (x -l- 3) = 2f(œ) -1- 5 va f(2) = 4 bo'lsa, 3 bo'lsa, f(8) ni f (8) ning
qiymatini toping. A)25 13)26 C)28
f(x) = f (10)   36 bo'lsa, f(30) ning qiymatini toping.
funksiya
berilgan B) -84                C)36       D)126
0 tenglamaning ildizlari
Agar f@—y) = f(m) —f (y) va f
(12) = 18 bo'lsa,
f (24) ning qiymatini toping.
                       B)12
        C)36          D)72
— 1) = — I bo'lsa,
 funksiya juft
funksiya bo'lsa, a + b ning qiymatini toping.
bo'lsa, f (5m) = O tenglama
C)
O, 84         D) -o, 84
2f (a) -l- 4
va f(3) — 5 bo'lsa, f(192)
D)
192

1,

Berilgan funksiya grafigiga ko'ra f (f

va f(4)

5 bo'lsa, f
  (16) ning

tenglamaning yechimlari sonini toping.

3f(y)

2

2

3

4 SC

qiyrnatini
toping.
                                                                                A)5          13)15          C)25         D)75
Agar l) _
2f(x) + I va f (I) I bo'lsa, f (105) ning qiymatini toping.
A) 2 104 1 BPI04 + 1 1 D)2 105
+ 1
                                                                                f (x) juft va                  toq
funksiya berilgan. Agar
D)9                                                  f
(2)                 4, g(3) —2 va h(a;) — bo'lsa, h(3) ni hisoblang.
                           Agar
f (m)                                                         bo 'Isa,
1

1
                                                         ning qiyrnatini toping.                                     Agar
f                                 funksiya berilgan bo'lsa,
• f(100)
                                    60
ta                                                                                u
hołda M                                                             ning
f(-l) . •
f(-100) qiymatini toping.
A) e4950  —4950 C) e5050               D)
c—5050
1
                           Agar
f (x)                                  bo' sa, f(l) -ł- f(2) +
J'(3) + +
f(97) ning qiyrnatini toping.
                                97            B)
33           C) 197           D) 97                                  f (x) •
g(a) O tengsizlikni yeching.

5

2

—6

7

                               300                100              300                100
                                                   1           6
                          Agar
f (T)                       bo'lsa, f
7
                   1           8
ning qiymatini
toping.
9
                                                                                97                             6;
-51 U 1—4; 11 u 15; 71
0; 21 u 15; 71
bo'lsa, f (6) ni toping. 6; -51 U Ij U (2; 31 U (5; 71
                                           B)
o          C) 97          D) 98
2.

2. Funksiya (2-qism)

3x2 — 6x

4
3

3

3 —        funksiyaning
aniqlanish sohasini toping.
             y
= 8x — 4 funksiyaga teskari funksiya y         + b
bo'lsa, ab
                                           1                  1                                                                                qiymatini
A)32
                                          16               16
D)24
= 5c — 7 funksiyaning
qiymatlar sohasini toping.
              A)          00)           B)(—oo;
—7]                                                                                sohasini
C) [7; 00)00)
+ 19 funksiyaning
qiymatlar  sohasini toping.
A) (4; 00) C) [4; 00)
funksiyani Chizmada quyidagi
funk$iyalardan qaysi birining grafigi tasvirlangan?
                                                                                aniqlanish
sohasiga

(—9) ning qiymatini
funksiyaning qiymatlar
101 C) (1*; 00)
grafigi tasvirlangan. ning qiymatini
toping.
5
D)12
funksiya T € (4; 00) oraliqda
funksiyaning qiymatlar
sohasini

3.

3. Funksiya (3-qism)
y — 7
funksiyani OX o'qiga nisbatan simrnetrik ko'chirishdan hosil bo'lgan funksiyani
hosil bo'lgan aniqlang.
4

funksiyani OX o'qiga nisbatan simmetrik
ko'chirishdan hosil bo'lgan funksiyani aniqlang.
y — — 3x + 5 funksiyani (.)X O'qiga nisbatan simmetrik
ko'chirishdan hosil bo'lgan funksiyani aniqlang,   tó'g'ri chiziqqa              hosil
bo'lgan
funksiyani
     o'qiga nisbatan simmetrik ko'chirishdan hosil bo'lgan
funksiyani aniqlang.         (2; 7) nuqtaga nisbatan hosil bo'lgan
funksiyani
 y
—2a;2 — + 3 funksiya o'qiga nisbatan sirnmetrik ko'chirishdan hosil
bo'lgan funksiyani aniqlang.

3.
                         (3-QISM)

2x—3y+2 O to'g'ri chiziq grafigini y
z: to'g'ri chiziqqa nisbatan simmetrik ko'chirganda, qaysi chiziq grafigiga
o'tadi?
C) 3T— 2y+2— o
vektor
funksiya
—
2 parabola grafigini a(—2; 3) vektor bo'yicha parallel ko'chirganda, parabola
uchi qaysi nuqtaga O'tadi?
OX
o'qi bo'yicha siljitishdall qaysi funksiya grafigi
y x
— 2 tos g'ri chiziqni x 3 to'g'ri chiziqqa nisbatan simmetrik
ko'chiring.
(Dy
o'qi bo'yicha funksiya grafigi
Y 4
to'g'ri chiziqni y —1 to'g'ri chiziqqa nisbatan simmetrik ko'chiring.
1
birlik yuqoriga bo'ladi?  y
7 — 3.v to'g'ri chiziqning 'Y 3 ga nisbatan simmetrigi y k.r-l-b bo'lsa, k4-b
ning qiymat,ini toping.
                     13)3                                 D)10

f(a)
+ x — 2 bo'lsa, f(2i) ni toping. A)2x2 + m 2
— 3z — 7 bo'lsa, f(a: + 2) — f(3c) ni toping.
B)-6z• - 8 C)12T-8
f (x + 2) + f(6 — x)bo'lsa, f(4) ning qiymatini
toping„
            AP                     D)16
va f (4) 4 bo'lsa,
a; ning qiymatini toping.
           A)16          B)24
         C)32          D)48
                              —4 bo'lsa,                 ni
soddalashtiring.
— 8a2 -1- 16
— 8x2 + 20
— 8a;ż + 12
2
3.                           (3-QISM)

                 f(2œ)          8x2
— 6:r+ I bo'lsa, f ning qiymatini                        f          O
tenglama 4 ta ildizga ega bo'lib, ildizlari

toping.                                                                                yig'indisi
12 ga teng. f ('2m — 6)       O tenglama
A)32x                                                                                ildizlari
yig'indisini toping.

B)4T2 —
C)2x
fC;3)                               bo'lsa, f(a;) ni
toping.
B)
C)
C)                 D)
'2x +11
f(T) — 6 va 2 — bo'lsa, g(x) funksiyani toping.         a: —
2 — 2œ        A) a; C)
f (a;) va  funksiyalar quyidagi shartlarni qanoatlantiradi:
f (x) 2:r2
—   1 f (920;) ) 292 (x) — +4 U holda f(2)
9(-1)    toping.
A) -9 B)-6       a;
f (x) 0 tengsizlikning yechimlar to'plami e [3; 6]
bo'lsa, f ( — 1 < O tengsizlikni yeching,
3
B)12           C)15
          D)18
4c2 -l- 4 a:             bo'lsa, f
(x) ni toping. 2 1
a: D)
bo'lsa, f (x) ni toping.
B)
D)
a:
bo'lsa, f (a;) ni
a;
1 B)
a; bo'lsa, f (I)
2

ning qiymatini toping.
18]         D) [12; 21]

Ko'rsatkichli
tenglama va tengsizliklar
1. Ko'rsatkichli tenglamalar
                          =
81 tenglamani yeching.
                                    C)16     D)'25
                                =                 tenglamadan
noma'lum a; ni
toping.

D)5
ildizlari tenglamani yeching.
0  tenglamaning ildizlari yig'indisini
toping.
yechimlari soni = O tenglama nechta  —
m ildizga ega?
ildizining
kichik ildiziga nisbatini toping, B)— 6 6
4x2 —2

tenglamaning ko'paytmasini toping.
tenglamani yeching. cp,8
Tenglamani yeching. (O, OI)3x • (0, A)-3
B)-2 cp
tenglamaning

2m—3 — 51 3 —x
tenglarnaning yechimlari yig'indisini toping.
B)12                        C)13          D)17
33T +                         + 27 + 32—0 1000 tenglama
ildizlari ayirmasining modulini
toping.
AP
 tenglamalar sistemasini qanoatlantiruvchi
barcha .ż; lar yig'indisini toping.

• 2xe
— — 2 O tenglamaning haqiqiy ildizlari sonini toping. A) a        ta CP
ta

13

4 c+ 2 -l- — 2x+6 - 2 6 T +
15 — — 0 tenglarna ildizlari ko'paytmasini toping.
A)-4 B)-l
 — 3 . 64T —O
8 tenglamaning
tenglamaning nechta
tenglama nechta
tenglamani yeching.

                                                                                2.                                           TENGSIZLIKLAR
2. Ko'rsatkichli
tengsizliklar
(2œ — 8) + 7) > 0
tengsizlikning eng kichik natural yechimini toping.
(T + e)7m
4tengsizlikni yeching. A)(—oo; 4) tengsizlikning
eng kichik butun

       5x2 —4$+4 < 1 tengsizlikni
yeching.
               c)
[2; oo)                                                                                qanoatlantiruvchi
eng
1
funksiyaning
aniqlanish
             sohasini
toping.                                                                                -tenglama
nechta natural
              A)[4; 00)                     5) U (5; 00)
C)    (5; 00)      D) (—oo;41 CJ (5; 00)D)3
tengsizliklar sistemasining barcha
natural sonlar
D)    20

2.
KO'RŞ4TKICHL1 TENGSIZLIKLAR                                                                           2-test

Logarifmlar
1.
Logarifmik hisoblashlar va shakl almashtirishlar

Hisoblang: log2 16 -V- log3 81 — log5 25
Hisoblang: log4 8 + log8 4  13)2
Hisoblang: 510gr, 3 _ 310g3 5 A)—2 13)-1
1 Hisoblang: + log21 s 81
A)2            C)16    D)18
           loga a + loga a2 — loga (13
ni hisoblang. cp
Hisoblang: In 2e — In 2 + In e2 cp
Hisoblang:
log3 16 + log3 30 — log3 160 A)l
log5
16 Hisoblang:
log5 8
log5 3 = a bo'lsa,
log5 75 ni a orqali ifodalang.
               C)2a+1  D)2a
loga
b = 2 bo'lsa, logb 02 ning qiymatini toping.
1
254

Hisoblang:
1 Hisoblang:
logą 180
log3 180
1
2
         1 Hisoblang:
1 log15 15!
Hisoblang: 64
og7 B)vfr
Ig 2 a va Ig 3 qaysi biriga teng?
+
          C) 6a + 21)          D)2a+ 61)
8T 49Y
bo'lsa, log7 2 ni 'X va y orqali ifodalang.
23
3y
Agar loga 2 a va log3 5 b bo'lsa, ava b orqali
ifodalang.
A)
C)
log@ b + logb a 4 bo'lsa, logi qiymatini toping
A)12          B)14
       C)16
log3 2
— log3 6 ni hisoblang,
Agar
loga 5 a va va b orqali ifodalang. ab B) ab ab C)              D) ab
   • o, 25 ÁG% ifodaning
toping,
13)4
a; b; c musbat
sonlar uchun a4b o'rinli
bo'lsa, 4 log2 a2 +4 log4 b ifodaning qiymatini toping.

13

14

log?2
24 — log2 3 • log2 48 ifodaning
hisoblang.
 13
cp D)
2
410g7
3+2    31087 4+1 ni hisoblang. C)13     D)16

Ig 7 a va Ig5
orqali ifodalang. B)
D)
b bo'lsa, log175
20 ni a va b
2— 1)

toping.                                                                                b
orqali ifodalang.
3
A)vQ                            cp
Agar log12 6 = a
va log12 5 = b bo'lsa, log360 120 ni a va b orqali ifodalang.  4x+1 .31—2x va a             102    bo'lsa,
f(a)
194 — 199
B)
D)
— log3 4; b = log4 5 va c = log5 7
bo'lsa, log2 3 log2 18 log3 147 ni a; b; c lar orqali ifodalang. log2 6
log2 3(1 + log2 3) A)abc + 2 B) abc + I
               1)
     D)2abc+ 1
+ Igb+ Ig3 bo'lsa, b ni a orqali
a
I
— log: 3                                                                 ni
hisoblang.    B)3(a — I
9
(log2 3 + log3 2 + I) log2                                                                                D)
a C) 1093           D)— 109 3
a bo'lsa, log18 36 ni a orqali
B)
(log? 3 • log12 4 — log4 3) •log12 4. (log4 3 + log3 4
+ 2) ning qiymatini toping.            D)4a — I

va Ig(a -1- b)
sonlari ko'rsatilgan tartibda arifmetik progressiyaning ketma-kct hadlari a —
logi, 25 ifodaning qiymatini
01
bo'lsa,
1000
999 + Ig 2     D)2+1g5
uchun logx 4096 soni ham
                                                                                C)7ta
            ta
loga ab + ab ifodaning eng
O božlsa,
u hołda
D)3
                                                                                2.                              FUNKSIYALAR

2. Logarifmik funksiyalar
y
Iog2 funksiyaning [8; 128] oraliqdagi eng katta va eng kichik qiymatlari
yig'indisini toping. A)7      D)10
a = log2 b = log4 va c log 1 5 sonlarini o'sish
tartibida joylashtiring.
Quyidagi funksiyalardan nechtasi juft funksiya?
+ 3)
 y = logr_x (a;2 —
3a + 2) + funksiyaning aniqlanish sohasini toping. A) (—co; 1) U (2; 6) U (6;
00)
sohasi
log5 a; = 5x tenglama
nechta ildizga ega? cp

3.

3. Logarifmik tenglamalar
12) O tenglamaning yechimlari yig'indisini
toping.
1092 (:r2 — 2T) 3 tenglamani
yeching. B)-4
1 1 tenglamani yeching.
soni log 95-a ( — 3) 3
tenglamaning yechimi bo 'Isa — 2mo ning qiymatini toping. C)15  D)24
(log2
a: — 3) • log2(m — 3) O tenglama ildizlari yig'indisini toping.
                       C)12       D)16

logi A)3

log2 log2 log2 T O tenglama yechimining
raqamlari yig'indisini toping.
A)3                D)12
log2T
+ log2 a,' O tenglama ildizlari ko'paytmasini toping.
2
logx_3 (9z — 20) tenglamaning ildizlari yig'indisini toping.
D)13
log2 (I — log3 (2 —
log2 T)) z: O tenglamani yeching.
—
98 tenglamani yeching.

4
Center (t.me/idcuz)

(T -1- y) 1
ning qiymatini toping.
A)20               B)14
016               D)25
        log3                                         10gr,
(a:2—2)
(a. -1- kichik ildizi
bo'lsa, • (co -1-3) ning toping. A)-2
ko'paytmasini toping.
•
log2 (a — 5) O tenglama yagona ega bo'ladigan a ning barcha yig'indisini
toping. A)—14  B)-8
log3 ($2 — 4z + 7) + log3 (x2 tenglama
nechta ildizga ega?

4. LOGARIFMIK TENGSIZLIKLAR

4. Logarifmik tengsizliklar
             Tengsizlikni
yeching: log5 (æ -l- 2) < [1]                                   loga
(4x-1- I) > 4 tengsizlikning eng kichik natural
                                                                                B)20          C)21          D)22
log4 (5 + m) < tengsizlikning eng katta va eng
kichik butun yechimlari yig'indisini toping.             tengsizlikni yeching.
Tengsizlikni yeching: 5x < 7
               7; 00)                     log5 7)
            C)
(—oo; log5 7)      D) (0; 00)                                                         log
1 (2x — 4) > logI — I) tengsizlikni yeching.
Tengsizlikni yeching: 2 < log3(7 — x) < 4
                                                                                22
105 -l- log4 a,' + logsæ > — tengsizlikning eng
kichik natural yechimini toping.
                                                                                C)15
         D)17

frigonometriya
1. Asosiy tushunchalar
                2160
ning radian o'lchovini toping.                                                                                —6769
ga burganda qaysi
              47r            5łr           67t           9łr                                                     o'tadi?
                               B)                C)                 D)
                  3              4              5              8
       2      Qaysi javobda manfiy son ko'rsatilgan?
               A)
sin 3410 • sin 4       B) tg2 • ctg6
               C) sin 4 • cos 4      D) sin 7 • cos 3                                                                                słn3
sonlarining nechtasi ctg2
 tg2430 ;
n cos 3120 ; c sin 3470 sonlarining ishoralarini
aniqlang.
Qaysi chorakdan olingan barcha a burchaklar
— sin Q ifodaning qiymati musbat
B) faqat II
D) faqat IV
P(I; O) nuqtani 2700 ga burishdan hosil
bo'lgan nuqtaning koordinatalarini toping.
ifodaning qiymatini toping.
I IT
                                radian burchakning gradus
o'lchovini
12
                toping.                                                                                ifodaning
eng katta va eng kichik
                 A)1500                                                                     B)
1550
C) 1650
274

2-test
a sin 1820 • cos 290 0
; b = sin 2340 • tg103 0 , c cos 470 0 •
ctg1660 , d = tg202 0 • ctg1470 sonlarining
nechtasi manfiy son?
n butun soni uchun 18700 +
2rrn bo'lsa, a ning eng kichik musbat qiymatini toping.  B) 70 0 C)1300

237t
               n,
butun soni uchun 5               '27cn bo'lsa, a ning
eng kichik musbat qiymatini
toping.
27C
5
Qaysi javobda manfiy son
ko'rsatilgan?
                          167r        87r
A) sin — • tg—
                            t                   3
                          23T
       257r
B)
cos — • tg— 7 4
147r
C)   tg         • cos
3
7              197r D) cos (—5n) • sin
4
nuqtani 600 ga
burganda qaysi nuqtaga o'tadi?
1. ASOSIY
TUSHUNCHALAR
Agar a II chorakda bo'lsa, 12 sin
actgal — I cos al ni soddalashtiring.
A)—3 cos             B)
— cos C)coso  D)3 cos Q
ifodalarning nechtasi ma'noga ega? A)hech
biri
Hisoblang: sin 30 0 + sin2 300 +
sin3 300 + ... D)2
y = 2 — 6 sin a: funksiyaning
qiymatlar sohasini toping.

3 -l- 2 cos2 a;
funksiyaning qiymatlar sohasini
toping.

14

cosa
quyidagi qiymatlarning nechtasini qabul qila oladi?
2
v6—2
 4) USS
ifodaning
eng katta qiymatini toping. D);
1  cos a; + cos2 a;
+ cos c -l- ... = — bo'lsa, cosa; ning 4 qiymatini toping.
 ning eng katta
qiymatini toping.
             A)613                            D)ll
 tga + ctga = 2
bo'lsa, tg200 a -l- ctg2 a ning qiymatini toping.
02100
1-test                     2. ASOSIY TRIGONOMETRIK AYNIYATLAR
2a Asosiy
trigonometrik ayniyatlar

1 Agar sina —
qiymatini toping,
Ifodani
soddalashtiring;
A) —ctgx    B)
ctgc C) —tgc   D)tgæ
Agar tgcv 3
bo'lsa, qiymatini toping. A) 2 B) 1,5 C) 3
3 cos
a — sin a = 2 munosabat cos a + 2 sin a ning qiymatini toping. 1 1
5
Quyida
berilgan ifodalarning
Q
uchun o' inli?
1
A)sina — —
—;cos — 4 4
                     2         1
B)sin
=— ; COS =
C)tga = 5; ctga O, 4
2
1
— ctga —
3
3
Ifodani
soddalashtiring:
—1 + cos2
a I — sin2 a
        sin a      cos
a
A)cosa
+ sin a B)ÇOS a — sin a
C)— cos a — sin a D)—
cos a + sin ce
37r
'Ir < < —
bo'lsa, cos2 + tga) -l- sin ifódani soddalashtiring.
A)— sina — cos a
B)cosa + sin a
D)sin — cos a
Ifodani
soddalashtiring:
(tga -l- ctga) 3 —
(tga — ctga) 3
C)6tga + 2ctg3 a
D)6ctga -l- 2ctg3
a
Ifodani
soddalashtiring: (sina + sin [3) (sina — sin [3) + (cos + cos (3) (cos a — cos
(3)
Agar
tga — — va — < a < T bo'lsa, sino +
                           4

cos a ni toping.

        7       1

1     7
        D)-

      5      5

        5      5

+ ctga)

2.        TRIGONOMETRIK AYNIYATLAR

3
           Agar sm  a va a € — ; r bo'lsa, 10 cosa -1- Soddalashtiring:
                                        5                          cos — sin4 a:
cos4 a; — siną a;
6ctga ning
qiymatini toping.
              A)—16    B)—2         D)16            cos cos
— sin a; B)—2 cos sin-1- sin a;
                                                                                C)2 sin a;  D)2 cos a:
3 sin -1-5
             Agar ctga  3
bo 'Isa       cos
2 sin a — cosa
          hisoblang.                              cos:r
— sin:c bo'lsa, cos sin ifodaning
A)—27
B)-20 qiymatini toping.2 D)-16      1
                                                                                4      8           4
Agar
4 sin a + 3 cos 3 bo'lsa, ctga ning Soddalashtiring: cos a; + 2 cos2 x
sin 2 sin a — cos cy S
qiymatini
toping. (cos x + sin 9 7 7 A)— cos B) — sin T D)!
                       7              9     7              C)sin  D)
cos a;
I — cos2 a,'

3 sin2 a + 6 cos2 a

(cos a.' — sin x — (cos c -1- sin
  .T) ctg:v

cos2 a + 2 sin a cos Q ni hisoblang.

        4        4

50

    tg:c     ctg:c

9

D)
     4       4

         Agar łga 4 bo'lsa,                    19                  2
ni soddalashtiring,

          sin a: O, 6 bo'lsa 1 -1-tg2a• ning
qiymatini toping. ifodaning (cosa — qiymatini + toping.3) + (sina —
                                                                                A)—14    B)-12

2. ASOSIY
TRIGONOMETRIK AYNIYATLAR
bo'lsa, Itga ctgal ning
                                                                                C)
4         D) 2vfG
4- 7) I bo'lsa, c qaysi biriga
D)10
                                                                                ctga;
-l- I                        ifodani
1
                                                                                sin6
CY       cos6         ifodani
bo'lsa, cos a; sin x ni orqali
B)
2
2
2.                    TRIGONOMETRIK
AYNIYATLAR

                Agar łga — ctga        4 bo 'Isa, tg4
a 4- ctg4 0 ning                    t gr               8 va n;
3łr               bo'lsa, sin T + cos x
                                                                                15              2
 qiymatini toping.
ifodaning qiymatini toping,
A)184     13)226 C)322    D)326     23
                                                                                17                  17
Agar sin a O, 6 bo'lsa, sina+sin2 a-l-sin
ifodaning qiymatini toping.
                                                                        2                                                     sina
I va 4cosa + sina                 | bo'lsa, łg:r ning

qiymatini toping.
15
15
                                                                                15                 8
                                    2 a         tg2a          ctg
Q             ifodani
tg2 Q — ctg sin 2 Q cos 2
a soddalashtiring.
                                B)sin2 Q           C)tg2a
5 sin Q -1- coscv    bo'lsa, sin3 a -4- cos3 ning
4
qiymatini toping.
95 75 115
128 64 128 64
sin:r m va log27 cos T n bo'lsa, ctga: ni
m va n orqali ifodalang.
C)33n — 3 2m y
5sin2 ;Ę• — 2 cos2 x funksiyaning eng kichik
qiymatini toping.
0-2

15

sina cos
T           A va sina -1- cosa:              B bo'lsa, quyidagi munosabatlardan
qaysi biri to'g'ri? A)A2 + B2 1 łga)2 8
B)
A 2 + B — 1      bo'lsa, I cos al ning qiymatini
toping.
C)
B 2 - 214 — 1   1
               D)B2                     1                                                                                B)-
2
3. KELTIRISH

3. Keltirish formulalari
Soddalashtiring:
37r
CO$(T — a) • ctg
2
A) — cos  B) — sin C)cos a D)sin a
4
ifodani
Ifodani soddalashtiring:
sin 1600 — sin 20 0
Soddalashtiring:
cos 200 0
— cos 20 0
A)tg700 B)ctg700        D)-tg700
tg4200 + tg5700 ning
qiymatini toping.
B)-— 3
                3                3
Quyidagilardan qaysi biri sin 200 ga teng
ernas?
             A)cos
700              B)sin 1600
             C)cos 2900             D)sin 340 0

                             sin(180
0 + Q) cos(270 0 — Q)                             37r,

016

Soddalashtiringsin (Tr — a) -l- cos (27r — a)
+ sin
          A)—ctga   B)-l                          D)tga3rr
                                                                            sin — a) +
cos2 (î a)

ifodani
  soddalashtiring.

A) cos a + sin a
B) 2cosa + sina

cos(37r -l- a) • cos(4rr — a)

C) sina

Soddalashtiring
577
  ctg(5T -l- a) sin
2
A)— sin a    B)— cosa
C)sin a      D) cos

D) cos Q + 2 sina
cos 12 0
Hisoblang:

sin2 (a — 3T) -l- cos2    — —

sin 102 0

tg1330

2
2
13                           tg
cos(a
27ö) ifodani sodda,lashtiring. 5
A) —2 sin B) — 2 Agar tga 12 va 0 <
bo'lsa, 2 sin CE

2        sin — + a ni hisoblang. sin cy  2
sin a

                                                                                13             1313
3
       Agar cos a     va
0 <       bo'lsa,

37r 5rr  sin sin     ni
hisoblang.     19      2     ctg (3T — C) ni soddalashtiring.
cos(n
        4      3                                   a)       +
x)
S                                    B)—5   B)
— sin a; C)sin
             sin 320 0         0
sin2
10 0 + sin2 80 0 ni hisoblang.
                                                                                A)2sin2100    cos2 10 0
C)ctg2100

           tg2500         cos 170

t9700

sin
  40

cos 10 0

1715           0    ifodaning
qiymatini
toping

Ifodaning eng kat,ta qiymatini
toping:
57T
a) + Sin — Q'                       3
3 -F 1
— a: — ctg(7r — a:) -l- tg(; + x)
2 bo'lsa, f(—) ifodaning
qiymatini toping
D)v/S
Agar cosŽ
a + cos2 13 I va O < < — ; O < /3 < — 2 bo'lsa, 0 2
+/3 2 +2 sin(Q -+-ß)aß ning qiymatini toping.
2
ctg(700  t
bo'lsa, ctg2 (70 0 — 20) -l- ctg2 (20C +
20) ni t orqali ifodalang.
A)t2
— 2                            C)t2           D)t2 + 2
a = ctg2 (3T — a;) bo'lsa, ab
ning qiymatini toping.
A)l                                            D)27

ctg10 0 = m bo'lsžt,             190 0 • sin 280 0
ni m orqali ifòdalang.
2             1
A)rn2 + 1             rn 2 1
1  2 C)     D)
cos 0 0 + cos 1 0 -I-COS 2 0 +
... + cos 1790 + cos 180 0 + cos 181 0 ning
qiymati quyidagilardan qaysi biriga teng?
A)— cos 1 0                    B)—
        1 0 D)cos 1 0
3 sin 1120 -I- 5 cos 158 0
Hisoblang:
cos 202 0
cp
41 0 +
490 + cos2 50 0
D)16
2
               03T                cos(2T — x)
— bo'lsa,
2                                           sin(7r
-l- Y) ctg
2 ni soddalashtiring.
B)-l

4. QO'SHISH

4. QC) 'shish formulalari
Hisoblang:
sin 62? cos 280
-l- cos 62 0 sin 28 00
                          A)sin
340                       B)sin 440
                          C)sin
880
tg53 0 — tg8 0
Hisoblang:
              A)
—tg610             B)ctg610
                       D)tg610                                                                                —
[3)
                                      2                     3
              Agar tgct —       va tgß             bo'lsa,
tg(a + /3) ni                                                                   ni
                                      5                     4
toping.
                   14                                   31
                   23                             C)18
Ifodani
soddalashtiring:       8T sin 4x bo'lsa, f ({6) cos(a — (3) —
B)cos a cos [3
         C)cos
Q cos (3 -l- 2 sin a sin 13
-F y) = 20 va tgx= l bo'lsa, ctgy ning
qiymatini toping,         qiymatini toping.
02
21
19
sin(a
+ (3) — cos Q sin [3 ni sin(a — P) — sin a cosp soddalashtiring. tga
A)—l    C)
                                  tgß            tgß
tga + tgß + tgatgßtg(a +
P) tg(a -f- P) ning toping.
cos 72 0 + sin 72 0 tg36 0 ning
qiymatini
(cos39 0 + cos21 0 ) 2 +
(sin 39 0 — sin 21 0 ) qiymatini toping.
< 2m burchaklari
4
13             5— bo'lsa,
qiymatini toping.
16
           C)
                     65                   65
4. QO'SHISH

cos
p — łga sin '34 cos 540
                                               ni
soddalashtiring.
sin
p -1- łga cos p$ cos 240 — sin 240 A)tg(a (3)D)2v/á — 13)
burchaklar uchun łga + tgp 3 va
ctgcž Hctg" 4 tenglik o'rinli bo'lsa, tg(a + F) ning sin(a + 60 0
) 4- sin(a — 60 0 ) qiyrnatini toping.    cos(a + 60 0
) -1- cos(a — 60 0 )
               A) 12        B) —12                                                                                C)
3+ COS Q ning qiymatini toping.
7
5
tg(a; + y) 6 va tg(at — y) 3 tengliklar o'rinli
bo'lsa, tg2T ning qiymatini toping.
9
B)
179
                   9               17
                                                                                3                tg:r
                        17                    9                                                                                —
bo'lsa,         ning qiymatini
tgy
sina: + siny a va cos T + cos y b bo'lsa, cos(a: —
y) ni a va b orqali ifodalang.
2
2 — a2 —
b2
B)
2 + + tg35 0
) ning ab — 2 C)
2
D)16
D)
2
1
              sin cos a                va a 13                                                   bo'lsa,
sin(a +1
6        va tgł' — — bo'lsa, tg(o + + ning qiyrnatini
toping.    5 3          3              7             toping.
                2             4            5                                               8D)3

Ifodani soddalashtiring:
sin(ß — a) (1 tgactgß) -l- sin(a -l- [3) : (I + tgactgß)
A)
2 sin a cos B)2 sin(a -l-
[3) C)2 sin(cx — 13) D)2 cos a sin (3
Hisoblang: A/S sin 750
— sin 15 0
B)       C)vQ
2
Q—/3 bO'lsa,
(sin a-I-sin ning qiymatini toping. A)2
1 tga
ning qiymatini
toping.
A)1 - vQ    -3

17

ifodaning
    qiymatini toping.

1

C)A/S

sin(300
    + a)

1

bo'lsa, tga ning qiymatini

sin(30 0 — a) toping.

4

9
D)

5

tgŽ — tg2
9

ad-cos (3)
bo'lsa,
3
tg (a + t) bo'lsa,
ctga ning qiymatini
toping,
3   2
        2        3
    1     3
     5      5
Hisóblang:
sin2 240 + sin 840 sin 360
1
3
2
4
4 cos(600 + a) cos(600 — Q) tga O, 4
bo'lsa,
COS2
Q ifodaning
qiymatini toping. A)0, 52
coo, 84     48
2
1
                       ; cos cos y — va sin a: sin y —
3
4
bo'lsa,
sin(a; + y) ning qiymatini toping.
B)
12
        119     12
C)
       12       23

5.

5. Ikkilangan burchak formulalari
                      3
        1 cos            5 bo'lsa, cos2U ning
qiymatini toping.                         Agar sin 20 = — bo'lsa, tga+ctga ning
qiymatini
24
25
24
25
— bo'lsa, 12ctg2c—5 cos ifodaning tg:r = 3 bo'lsa, sin 2m
ning qiymatini toping.
D)-4, 9
Agar 3 sin a; — 2cos.c O bo'lsa, cos ning qiymatini
toping.
1
                                                                               13)îës12
3
1
sin IOC (sin 5m + cos 5x) 2 tg2xctg2c ni
soddalashtiring.220 b bo'lsa, cos 460 ni B)tg4x  ifodalang.

C)sin IOC
1 + cos 20

sin 20 A)tga C) 2tga
D)cos 10m
                                                                                D)b2
— a2
ni soddalashtibing. ni hisoblang.
B)ctga
D)2ctga

sin2 38
 ifodalang.                             orqali
ifodalang.
                       1     2
   A)2a2    B)—           D)a2
3
Ifodani soddalashtiring: sina,' + cosa; — 5
bo'lsa, sin ning qiymatini ctga(l — cos 20)    toping.
 A)— sin Ża      cosa                         16
 C)sin '20 1))2 sin a                         25
sin 10 0 cos 10 0 bo 'Isa, tg2a
1     — ning qiymatini 0 ni
soddalashtiring. sin 40
toping.                                        0             1
3
B)
                                                             D)á4                             2
sin 10 0
4
1
D)cos 20 0 4 cos 200
ctg;r 5 bo'lsa, cos ning qiymatini toping.
ifodaning qiymatini
toping.
           13                   13
D)3
4 sin 20 2 cos a sin a S bo'lsa, sin 20 — 2 cos a ning qiymatini ctga — 47 bo'lsa, 2 2 cossin2
2 a a — — sin sin 2a20 ning qiyrnatini toping.
A)-9    4 9
7
2
cos2 150 -1 cos
75 0 cos 150
2
— cos
•
16Sin a: I toping.
sin 3z COS 3Q,•
sina COS T
toping.
2
Agar sina — cosa qiymatini toping.
B)O, 84
D)0, 96

5.
2

Agar cos 20 bo'lsa, cos4 sin4
cv ning 3 qiymatini toping.
11
        18              3
1
Agar cos
20                         munosabat o'rinli bo'lsa,

cos6 Q — sinG a ifodaning son qiymatini toping.
         7                 7                  5                 5
         9         B)
27          C) 18                9
ifodani

soddalashtiring. 4                4 sin2 '2(Y             cos2
2a 8 8
C) sin2
20                               D) cos2 20
0
D)4x/S
tg258o
cos
24                                     ifodani soddalashtiring.
A)   2 (1
2tga — sina +3 cosa 6 bo'lsa, cos 20 ni toping.
B)   0,6
D) 0,8
Ifodani soddalashtiring:
tg2 370
+ 2tg370 tg16 0 B)tg530
cos 90 cos 18 0 cos 366 cos
720 sm 90 ning qiyrnatini toping.
1             1              1
B)—D)
                        8             4
a bo'lsa,
                     0                                                     sin
330 ni a orqali
0 cos
120 sin 12 0 z: a bo'lsa, sin 720 cos
720 ni a
B)
I 02 D)
a

Ifodani soddalashtiring:                                                                                2tg2
Q — 5tga-F2 0 bo'lsa,
                             27T
cos — COS — cos — cos —
17          17   17           17           ning
qiymatini toping. B)              01
        32                 16
tg1 0 +
2tg20 + 4tg40 + 8tg8 0 + 16   • cos 10240
ifodani tg16 0 4-32tg580 ifodani soddalashtiring. sin
20480 A)tgIP B)32ctg1Ö               B)1024 sin cv
C)tg320          D)ctg10                                                                                sin
20480
D)
2048 sin
a, bo'lsa, cos 1300 ni a orqali ifodalang.
B) sin 30
ning qiyrnatini toping. a2 + I
11               13 D)          16
2 — O bo'lsa, cos2m ning
ning qiymatini hisoblang. tg— -1-
ctg—
     12           12
ifodaning qiymatini toping.
8 cos 24— — 8 cos2 — 24 + I ning qiymatini toping.                                                                          D)v/S

6.

6. Geometrik masalalar
D)l, 65
: ED— 2 bo'lsa, łga ning
katak birlik kvadrat bo'lsa,

ko'ra, CD
ning
0
4

BOA burchak
tangensini toping. 3 bo'lsa,

ACB burchak
kosinusini toping.tga ning

tga ning Chizmadagi har bir katak birlik kvadrat
bo'lsa, ABC burchak kotangensini toping.

17
6.

birlik kvadrat bo'lsa,

7. KO'PAYTMA
VA YIG'INDI UCHUN

7. Ko'paytma va yig'indi uchun formulalar

10

         cos 239 + cos 830 ifodani
soddalashtiring.                                Hisoblang: cos 42 0 -l-
cos 18 0
                A)-VSsin530                                              B)cos
53 0sin 142 0 + sin 180
               C)sin
53 0                 530                                                                                D)v/j
sin 64 0 + sin 26 0 ifodani
soddalashtiring:
                A)Usin190                                                            13)0
sin 190sin 40 0 -Hsin 200 — cos 10 0 ifodani
soddalashtiring.
C)ucos19 0100             13)0
                                                                                C)cos
100
sin a cos 3a ko'paytmani yig'indiga
o'tkazing.
             A)sin
4a — sin 2a                                                                           Hisoblang:  sin
46 0 — sin 740
B)sin 4a -l- sin 2a
D)
2
C)sin 2a — sin 4a
D)cos 4a + cos '2a
1
Hisoblang: cos
34 0 cos 26 0 — — sin 820 2
             2 cos 2a cos 3a ko'paytmani yig'indiga o'tkazing.                            1                        C)
— cos 8 0                    1
A)cos 5a + cos2
B)cos 50 — cos Q
C)cos — cos 5a D)sin 5a — sin a
          37T sin — + sin —
Tr IO ifodaning qiymatini
toping.
cos — 20 Šin(a -l- 13) —
Šin(a1 cos(a -l- ,13) + cos(a ifodani soddalashtiring. 2 2
         A)tga        B)tgß
         C)ctga       D)ctgB
7. KO'PAYTMA
VA YIG'INDI UCHUN
8 sin 660 + 4 cos 204
30  ning        cos 840 + cos 360 ning qiymatini
toping. qiymatini toping.       D)12

13

1
cVS
cos 550 + sin 85 0

Ifodani soddalashtiring:

C)

4(sin 5 0 + sin 15 0 )                            0
• (I cos 20)
cos 5 0 + cos 15 0
AP sin 200 B)2tg200 sin 200 D)4cos 20 0

8

                4                   2

         łga         3 bo'lsa,

COS 31' -1- COS 2:1' + COS

ning

qiymatini toping.

sin 3a; -1- sin 2z + sin
3 C)-

sin '2a — sin 8cy ifodani soddalashtiring. cos 80 + cos 20
A) —tg3a             B)
  —ctg3cť
C)—tg3a        D) —tg5a

4

4

Agar

va cos a
2

3

17

                                                                                4
cos 25 0             ning qiymatini toping.

toping.

Hisoblang: (tg420 + tg180 )
  sin 480 sin 720

B)—

A)v/5                 B) — 2

3

bo'lsa, sin -1-

                    +Sin —          ning qiymatini

20

1                 30

cos a

15

sin 120 — sin 72 0                       toping.
42 0 ifodaning qiymatini toping. cos
7
0-1              D)vQ                                                                                16
Center (t.me/idcuz)
4— bo'lsa, cos — 2 cos — ning qiymatini
5
8

cos a — cos 50                                              sin
540
ni
soddalashtiring.

cos a — cos 20 eos 30
A)tg3a cp D) - 2
A) tga B)ctga
C) —tga   D) —ctg a
Ifodani
soddalashtiring: sin a -l- cos(600 — a) cosa — sin(600 —
a)
A)tg150
B)ctg150 C)ctga D)tga
18a;
= 7T bo'lsa,

tga•tg — Q) •tg + cos 20 cos a — 2 sin2 a cos I
ifodani soddalashtiring.

Hisoblang:
  cos 10 0 • sin 40 0 • COS 70 0

B)

c)Šl

1
D)-

4

4

cos

2

— sin (T + ŽQ)

Soddalashtiring:
cos(27r

cos(qr -l- 20)

B) 1 — 2tg3ct C) 2tg3a D) 1
ctg5 0 • ctg55 0 • ctg65 9
ni hisoblang.
1

4
'2m 2 — 3
C)
4

4m2 — I
B)

4
D)
4

256 • sin 2 5

• sin2 55

sin2 60

Sino 65

ni

sin
100 = m bo'lsa, cos 400 • cos 20 0 ni m orqali
ifodalang.
hisoblang.
a; {3 bir-biriga teng
bo'lmagan qo'shni burchaklar 13 sin — + sin — bo'lsa, 2 ni soddalashtiring. sin
+ sin 2:r + sin 4x + sin 5x      sin — L— sin —(3
ifodaning      2     2
cos -l- cos 2.1' + cos 4a: -l- cos 5cc qiymatini toping,
2

cos 180 — COS 12 -I-COS 480 — COS 54
 sin 570 sin
9 0 sin 30 cos 9 hisoblang.
Hisoblang:
sin 14 0 -k
sin 28 0 + sin 420 cos 140 + COS 28 0 -k
COS 42 0 • ctg28 0
                     A)tg280                             C)ctg280             D)ctg2280
Hisoblang: cos 360 — cos 720
                 1           1
                             B)-
                            2                   4
                                     2
bo'lsa, cos ( 2                                   ning
qiymatini toping.
B)
2
C) cosD)sin (t
sin(3a: + y) + sin y sin ning
qiymatini
cos y —
cos(3a: -I- y)         2 toping.
A)tgë£
              2      B)tã
3m
C)cos — 2
8. YARIM
BURCHAK

S. Yarim bUrchak formulalari
ning
qiymatini toping. D)16
+ cos 51 • cos 390 ning
qiymatini toping. 3
qiymatini
sin a
                                                                                +              ning
qiymatini
sin2 22 0
                                              0
— sin 680 ning qiymatini toping.
2 sin2 11
1
cos2 42 0
2 sire 24 0 —
cos 48 0 — 1 ning qiymatini
1
2
sin 80 a bo'lsa, sin2 41 0
1   — 2a 2 B)
2
2
D)
                                2                         4
cos 760 m bo'lsa ifodalang.
I — cos — + sin —
8
ni soddalashtiring.
1 + cos — + sin — 8
B) — ctg %
8
                      C)tg                D) ctg;
16

9. rfrigonornetrik funksiyalar
1
a = sin 16 0 — sin 2160 ;          — funksiyaning b cos
1300 cos ?960 • c tg1400 tg'220 C sonlarining
ishoralarini aniqlang.
Juft funksiyalarni ko'rsating:

Quyidagi funksiyalardan qaysi birining grafigi koordinata, boshidan o'tmaydi?
sin a:
— 1 — cos x C)y = lg(a; -l- 1)  — tg:r -l- a:
6 cos a; + 7
3 funksiyaning
eng katta butun qiymatini toping.
y (7 -- cos -l- cos x)
funksiyaning eng kichik qiymati yo bo'lsa, yo ning eng katta tub bo'luvchisini
toping.kichik A)2
a = ctg240 ;b ctg32 0 va c =
ctg202 0 sonlarini
             O'sish tartibida joylashtiring.                                                                                eng
katta

2 sin 2x
2a;) sire a; +                    funksiya
cos toping.

sin              + 1) + cos
               + I)

2
qiymatlar sohasini toping.
(00

8cÓs       funksiyaning qiŸmatlar
(0; 4]
(0; 81
+ 24 cos2 2a;
  funksiyaning eng toping.
      C) 21         D) 27
ning qiymatlar sohasini toping.
[O; cos I]

(I ctg qiymatlar sohasini  funksiyaning
qiymati o'zgaruvchining qiymatiga bog'liq bo'lmaydigan q, ning barcha
qiyrnatlari ko'paytmasini toping.

funksiyaning

V = lg (6 sin c — to'plamini toping. A)
(—00;4] B) C) (-00,8] D)

y = 18 sin 2:r cos 2x katta qiymatini A) 24 B) 42
f( ) = cos(cosa;)
C)
[cos 1; 1]         D) Y — cos2n -l- sin funksiyaning eng kichik
qiyrnatini toping. 1 1       1
Y = I cosa + Il va y = I cosm — Il funksiyalar [0; 27r]
oraliqda nechta nuqtada kesishadi?
f (x) = 16 sin4 8:r cos4 8a:
funksiyaning eng kichik musbat davrini toping.
f(m) = sin 2a: funksiyani OX o'qi
bo'yicha
2 birlik chapga siljitishdan qanday
funksiya hosil bo'Iadi? A) — sin 2œ B)— cos 2a:

C)sin 2x                          D)cos
2a;

10. TESKARI

10. Teskari trigonometrik funksiyalar
       +
arccos              2 ) ning qiymatini                                                                      arctg(VS)
toping.
27T
                               B)
                3             6
Hisoblang: — arcsin — -l- —
arccos — 2
                          57                       3
D)-
                                   66                                2
nechtasi to'g'ri?
1
Hisoblang: 3arctg5 + 3arctg— 5
3
Quyidagi tengliklardan nechtasi to'g'ri?
) — arcsinx
= — arctga;
3)arctga; -V- arcctg:t =yeching.
4) arcsin + arccos
ko'rsating:
y = arccos (tr — 10) funksiya aniqlanish sohasiga
tegishli butun sonlar yig'indisini toping.
             A) 9         B) 10         C) 30         D) 27
y = 4 -l- — arcsina:
funksiyaning eng kichik
"Ir bo'lsa, 8 arccos(a
                                                                                B)47r                             D)
77r

arcsin(sin 1400 ) ni hisoblang. B) -400
ning qiymatini toping.
7
4
7
+ ctg  arctg— ning qymatini
04, 5
10. TESKARI

-10

m
0 arccosO.4 , b z arccos0,7 va c arcsinO, 8 sonlarini o'sish tartibida
joylashtiring. A)b, c, a B)a, c, b
y z arcsin (12 — 31 + 3) sohasini
toping.
 3
arcsin(5c2 — 41 — 0,5) — ildizIarİ kolpaytmasini toping.
90,1
 sin (2arctg—) — cos (2arctg—) ni hisoblang.
arcsin(:c—2) tengsizlikni
A) (1; 00)
          C) (1;3]            D)
(2; 00)
32
y 8-4- — arcsin (c) funksiyaning
eng kichik va eng katta qiymatlari ko'paytmasini toping.
A) 192          B) O
C) —128             D)
—192
1
sin x —                   arcsinc — —
funksiyaning
OX o'qi bilan kesishish nuqtalari absissasining eng kichik
qİymatinİ topİng.
                   2           3     D) 6
arcsin x — — + funksiyaning qiymatlari
sohasİni ko'rsating.

1  funksiyaning
aniqlanish tg (arcsinx) sohasini toping.

3 arcsin — 5 24 ifodaning qiymatini
toping. arctg — 7
TESKARI

15

5m
arcsin x + 4 arccos = — tenglamaning ildizi bo'lsa, ning qiymat,ini toping.
 arcsin(sin6) ni
hisoblang. A)2T — 6
            — 4) < arccos(x           2)
tengisizlikni
yeching.
arcsin(a; + y) + arccos(3x — 4y)bo'lsa,
ning qiymatini toping.
— ning qiymatini toping.
24
C)
25

arccos
cos               ni soddalashtiring.
D)—
arcsin                                       tengsizlikni
qanoatlantiruvchi butun sonlar yig'indisini toping.
sin (2  ning qiymatini
toping,
3v/i
 16
cos
arcsin  — arccos —  ning        qiymatini 13
toping.
33
        65
Qaysi javobda y = arcsin x
funksiyaning grafigi -tasvirlangan?
          B)
C)      D)

II. Trigonometrik tenglamalar
sin 20 3 tenglama a
ning qandaÿ qiymatlarida yechimga ega bo'ladi? A)[—l; 1)
Quyidagi tenglamalardan qaysi biri ildizga ega
3
A)cos sin x —
8
1 sin x — 2
             C)cos 2 a,'
— sin2             3
5
D)cos a,' sin
x = — 2

O tenglamani yeching.
cos2 2a,•
sin 2x -1- sin2 2xO tenglamani yeching.
[El tg4a• = 1
tenglamaning e [0; T] kesmadagi eng katta ildizini
ko'rsating.
                                      13T                                     15T
 B)  D)
16  16

sin2 a; — (I -F   sin:c +O tenglamani yeching.
                       -1-
'2TT1               D) 2Tn
m ning qanday qiymatlarida 4 cos sina 10 tenglama
yechimga ega bo tladi?
A) [—14; —6] B) (—60; —14] U [—6; x) C) [—12; -8]
D) (—oo; —12]
U [—8; N)
cos X (cos X' + I)-l-sİnx (sin c — 1) 1 tenglamani
yeching
A)                Z      B) — +
mı, 11      Z       C)
4
cos 2 z:
şinx(2vQcosx: — sin x) tenglama
3T
[O; 2 da necht,a ildizga ega?
4 sin 21 -l- 4 sin — 10 5 tenglama [—T; T] oraliqda nechta
yechimga ega?

2 cos 2T + 7 coşm z: O tenglama T] oraliqda nechta yechimga ega?
cos X' -l- sin '21
O tenglamani yeching.
cos
a ning nechta butun qiymatida 3 sin
+4 cos z:
(12 4 tenglama yechimga ega bo'ladi? A)5
coşa 2.17
— sin4 — 2 tenglamaning eng kichik musbat ildizini toping'
48
coş (x -I-       —        tenglamani yeching.
2
5T
         12               12
B)Tk; — +             k G Z
12

—l— 277 k; — 12

Z

D)—— -l- 2Tk; — -l-

Z

12

— O tenglamaning [O; IO] oraliqdagi
                  3               3
2
— tenglama €-
sin 4x sin 2x = 2cos370 cos 70
= sin — tenglamani yeching.
O tenglamaning e (0; 4T) mavjud?

a; ning qanday qiymatlarida cos(600 — sin
rt', cos(600 +a;) sonlari arifmetik progressiya tashkil qiladi?
               -l-
rrn           D) T -l- 2ûrn,
cos2 — 3 cos rt sin a: 4- I = O tenglamani
yeching.
Ah -4- Tn, a.rctg— + TO, n, Z
B) a -l- -n-n„ arctg2 + Tn, n
e Z
C) — -1- Tn, arctg2 -l- 7rn, n
Z
1))±— -l- rrn, arctg— + Tn, n e Z
cos2 + cos Ž 3x — I
tenglama kesmada nechta yechimga ega? A)2
logcosa. sin a; -l- logsm COS           2 tenglamani yeching.

20

tga: -b- tg3a: -l- = 1 tenglamaning
kesmadagi eng katta ildizini toping.
57r
C)
     16                                    12

12

25Sin¼ -l- 25cos2 = 10 tenglamani yeching.
4 — 6 sin a; = 4sinc — I tenglama a: e
[—27G 27r] da nechta ildizga ega?
                             3           3
cos2 a; — —
cosa• + — 2              2
tenglamani yeching.
-l- 27rn,n e Z
+ Žqrn, 27rn, n G Z
cos4:r — 8 cos4 a• -l- 1
0 tenglamaning eng kichik musbat va eng katta manfiy yechimlari ko'paytmasini
toping.
                  2                                 2
          4                     9
                 2                                  2
D)— 36
1
sin —x) •sin(600 -I-c) = — tenglamaning 8 eng
kichik musbat ildizini toping.
6

T tenglama nechta
yechimga ega?
log25_x2 sin tenglama
sin 3C -F sinr cos 3$ -l- cosa; tenglamaning a; E IO;
27rl kesmadagi eng katta va eng kichik qiymatlari yig'indisni toping.
137r
8    3 toping.
4 cos 2c vrŽ(cosc — sina)
tenglamani yeching. tenglamani
           Aů
-l- 2łrn             B)—— -l- 2łrn
'2łrn„.n
€ Z
arctg— + 27tn, n
C- Z 2tc
                                   2
              O tenglamani yeching.
4
va   e + ning qiymatini toping.
n Z
Nechta o'tkir burchak sin 4a• — cos
2x tenglikni qanoatlantiradi?            sin          COS
12
                                                                        ců
       (-1) ii+—; k e z
                                                                                k
                Trk
12 tg2x — ctg4c tenglama CO;
Tj oraliqda nechta yechimga ega? A)3
sin 9T — sin 33 cos 6T tenglamaning IO; kesmadagi
yechimlari sonini toping. C) 10 D) 11

13

sinc + siny I tenglamalar
sistemasini
3 yeching.
2

18

A)
+ 2łrn; —sina — — tenglamaning nechta ildizi bor.

9 B) +
2rn; — — Trn            AP
6
T trn
tgm z: a; tenglamaning 1—10; IO)
oraligida nechta yechimi bor.
D)10
cos + cos 6x             2 cos      tenglamaning IO;
271 kesmadagi ildizlari sonini toping.
         A)12ta        B)ll
ta
010 ta                                                                                ta    2
sin 3x + (2sinm — I)2-2—0         tenglamani yeching.
B)
(—1)n-FIE

k ning nechta butun qiymatida                                                     D)
                       n e Z

1

sin ka; + cos km                 tenglama   1—27r; 2łrl
oraliqda 12 ta yechimga ega bo'ladi?
A) I ta           B) 2 ta          C) 3 ta         D)

12.
TRIGONOMETRIK TENGSIZLIKLAR
12. frigonometrik tengsizliklar
cos æ < O tengsizlikni
yeching.
2
O tegsizlikni
yeching.
,nez
sin2 x
> 3sinx tengsizlikni yeching. A) [— 2 -E- 27rk•, 27rk] , k € Z
+ '27Tk; 2Tk], k Z
377
D) -l- 2Tk,7r -l- 2Tk] k Z
                                                                                <
O tengsizlikni yeching.

Hosila
1. Hosila
olish qoidalari
                         3a3 — 5a;2 +  7 bo'lsa,
f/ (a;) ni toping. bo'lsa, f' (4) ning qiymatini toping.
         — IOx +6                            B)-4
B)6T2
C)9c2
D)9T — 10z -1-6
5.c—3
vag(a;) bo'lsa, f/ (c) —g'(x) ning
qiymatini toping.
                         + —  + 4 bo'lsa,                              D)9
3
tenglarnani
yeching.
bo'lsa, f/ (n2 )
ni toping.
f (x) +7'.E va f  9 bo'lsa, m-l-n D)n2n+1 ning qiymatini toping.
—
ex bo'lsa, f' (In 2) ni toping. 1
2 — 4ax -1- 5a2 bo'lsa,     c)l qiyrnatini toping.
                                    C)2a     D)8a
bo'lsa, f' (8) ning
qiymatini toping.
 va
— —1 bo'lsa, f' (To) ni a; -1- 2 toping.
D)13
330

                                f z: 7z bo'lsa,
 (I
log7 10) ning qiymatini                                                                     2
75 bo'lsa, f' (x)             0
In 7 toping.
                         A)7          B)10
        C)71n7          D)70
1
1082
a; bo'lsa, f'             ning qiymatini 71n2           toping.
1               f(l) — — 4 bo'lsa, 7           01
                                                                                12         D)
14
x bo'lsa, f' (m)        log3
e tengsizlikni yeching.
A) (—oo; I)ning qiymatini
C)
(1; 00)    D) (e;
00)
D)
21
sin a; bo'lsa, f' (x)
ning qiymatini toping.
                                cos — 3 sin T                                                                                f'
(4) ning qiymatini
                            a; sin 4-3 cos tc                                                                                1                 1
B)   16           D)
4 a;
cos x + 3 sin C)
x sin c + 3 sin :ž',

f —
.3a;a va g(T) -1- 2.T bo'lsa, f' (x) g' (x) tengsizlikni yeching.
4
3
          3                        4
5
4
D)
             4                      3
— cos T bo'lsay f' (x) —
tengsizlikning 10; oraliqdagi yechimlarini toping.
2łr
6
                                      27T                                            57r
D)
          3           3                          6'
6
T
— 3) 4 bo'lsa, f (x) + f' (a:) + 0 tenglamaning ildizi nechaga teng.
A)-27 B) -3                                       D)27
a: sin c + cos:r bo'lsa, ning qiymatini toping.

A (T — I) 2; B va C
(T 4- 1)2 sonlari uchun f AB -1- BC + CA bo'lsin. U hołda — O
tenglama ildizlari yig'indisi nechaga teng?
bo'Isa, f/
y 3 arcsinc
+ 2 arccosc bo'lsa, y' (O) ning qiymatini toping. B)3
64 bo'lsa, a
ning qiymatini toping.
                            BP 04                 D)16
f(x)
łga•, bo'lsa, f' (T) z: — tenglarnani yeching.
                  +
'27rn                      D) —— -1- 2nn
cos a:
I 3 Sin bo'lsa, f' ning qiymatini
toping.
1
2

2. MURAKKAB                         HOSILASI

2. Murakkab funksiya hosilasi

               f(2x)       sin4x bo'lsa, f/ (x) ni toping.
             A)
—2 cos             B)2 cos
               C)—2
cos               1))2 cos (Ix
bo'lsa, y/ (1) ning
qiymatini toping. C)4e     D)5e
bo 'Isa, f/(1) ning Aiymatini toping.
              A)
-48             B) -36            C)36          D)48
 bo'lsa, f/ (6) ning qiymatini toping.
             C)6         D)mavjud emas
bo'lsa, (2) ning qiymatini
hosilasini toping.
— 3C)3
(+6) ning
bo?lsa, f' (2) ning qiymatini
ning qiymatini

3.                             TEKSHIRISH

3. Funksiyani tekshirish
                         3      7
—
—cŽ + 6x funksiya qanday uzunlikdagi 2
kesmada kamayadi?
3
5
— —a;2 2 + 4a; — 4 funksiyaning [0;3] kesmadagi
eng katta qiymati nechaga teng? A)-4 B)-y
66

f (x) = — 9x2 -l- 24x
+ 7 funksiyaning minimum qiymatini toping.
               A)
21         B)23         C) 27         D) 30
Chizmada f(œ) funksiya
hosilasi berilgan. funksiyaning o'sish oralig'ini toping.

2
1

o

     1

               3] U [4; 00)        U [3;4]
                       C)                oo;
2] U [4; 00) IJ {3}

x5 — 80x-1-20 funksiyaning
kama,yish oralig'ini toping.

           C) [2; 00) D)
(-oo; -2] U [2; 00)
B)(—oo; —5] IJ [1; 00)
-1] U [5; 00)
00)
—3] IJ [1 ; 00)

                                                                                3.                                   TEKSHIRISH
— x •          funksiyaning
minimum nuqtasi        3 —5x2-1-7 funksiyaning kamayish absissasini toping.              oralig'ini
toping.
                                                                                1                        10
C)—
log.2 e                                                                                3                         3
                                                                                10                            1 10
D)
3
y             3
sin       — 2 funksiyaning o'sish oralig'ini toping.
           4        2                                                                                1
m ning qanday
               + rrn;                                                                                qiymatlarida
y — 3
           2                                                                                4x
-i- 7 funksiya doim o'suvchi bo'ladi?
C)(—oo; 00)
Trn 2
—4) U (—4', 00)
—4] U [4; 00)
Chizmada
f (œ) funksiyani grafigi berilgan. f' (x) Iar uchun quyidagilardan qaysi
biri to'g'ri?

2:r) funksiyaning kamayish oralig'ini
toping.
A)(—oo; O) IJ [I ; 2)
                                                                                C)
[1;2)                    00)
>
f'(2)                    >
f'(l)
> f'(l)
f (x) funksiya
o'zining aniqlanish sohasida musbat va kamayuvchi funksiya bo'lsa,
quyidagilardan qaysi bir o'suvchi bo'ladi?

ning qanday
qiymatlarida
funksiya
o'zining aniqlanish sohasida qat'iy kamayuvchi bo'ladi.
A)         00)
C) (-4;oo)                         0)
Quyida
berilgan funksiyalardan nechtasi o'zining aniqlanish sohasida doimo o'suvchi?
5
In
x funksiyaning kamayish 2        1
oralig'ini toping.                                                                                3)
f (x) = sin3 4) f (æ) C -l- —;
A) (0; 00)                                                                                =
c4 -l- :t2; 6)f(Œ) =

1-test                4. HOSILANING GEOMETRIK VA MEXANIK MA'NOSI
4.
Hosilaning geometrik va mexanik ma'nosi

ning
qanda,y qiymatida y funksiyaga o'tkazilgan urinma, Or; o'qiga parallel bo'ladi?
AP B)3
3
—a;4 + — 32 funksiya
grafigiga o 'tkazilgan urinrna OT o'qining musbat yo'nalishi bilan tashkil
qilgan burchagi kosinusi — ga teng bo'lsa.
Urinish nuqtasining
koordinatalarini toping.
   1 1  1 1
B)
1 1
C)
'ż;8A      D)
32
1
Ushbu
y 2/ 4 funksiya grafigining absissa o'qi bilan kesishgan nuqtasiga o'tkazilgan
urinma oenglamasini tuzing.
               2               2   2
Agar moddiy nuqtaning
harakat tenglamasi 2t3 — 12t2 + 4t + 6 ko'rinishda
bo'lsa, tezlanish qancha vaqtdan keyin nolga teng bo'ladi? AP 13)3
Harakat tenglamasi 20
+ łot + t2 bo'lgan jismning tezligi qancha vaqtda 36rn/s ga
erishadi?
A)9           C)13    D)15
Harakat
tenglamasi 3T2 + 4 bo'lgan jismning tezligi 30111/s bo'lgan vaqtda
koordinatasini aniqlang.
A)56    B)60   C)68   D)72
f
(T) funksiyaniňg nuqtasidan O'tkazilgan urinma (—1; 2) va (5; —4)
nuqtalardan o'tsa,
(To)
ning qiymatini toping, B)-yž 1
2
y er funksiya
grafigiga absissasi au.) 1 bo'lgan nuqtada o'tkazilgan urinma tenglamasini
tuzing.
a;
e
y funksiya grafigiga
absissasi —2 bo'lgan nuqtada o'tkazilgan urinma tenglamasini tuzing. A)y —— 5,
1, 75
— 1, 25T+ 5,5
1, 75z +
y aa; + b to'g'ri
chiziq y 5T3 — 4a;2 4- — 3 funksiya grafigiga
absissaši 1 bo'lgan nuqtadan o'tkazilgan urinma bo'lsa, a + b ning
qiymatini toping.
                                    C)17    D)23

      4,
HOSILANING GEOMETRIK VA MEXANIK MA SNOSI                                               1-test
funksiyaga o'tkazilgan urinma OT o'qining
musbat yo'nalishi bilan 1350 burchak
tashkil qiladigan nuqtalarning absissalarini toping.
A)-2; 12            13)0; 3 D)4;
12
e absissali nuqtadan
funksiya grafigiga absissasi 1
nuqtadan o'tkazilgan urinma, Occ o'qining musbat yo'nalishi
bilan a burchak cosa ning qiymatini toping.
13)-2
5

1  2 C)        D) funksiya grafigiga
absissasi — o'tkazilgan urinma va Or bilan hosil qilgan
—0, 25$4 funksiya
grafigiga  z: I bo'lgan nuqtada o'tkazilgan
Ox o'qining musbat yo'nalishi bilan hosil qilgan
burchakni toping.
                    A)450         B)600           C)1200           D)1350
grafigiga — burchak
                                     16                                                                                D)ll
— + 5 funksiyaning
grafigiga To 2 nuqtada O'tkazilgan urinmasining koeffitsiyentini toping.
burchak
k ning
qanday qiyrnatida f (T) z: 3ka3 5 funksiyaning To       2 nuqtada
urinmaning burchak koeffitsiyenti bo'laźli?              1             1
9
2-test                                           4.
HOSILANING GEOMETRIK VA MEXANIK MA'NOSI

f (T) +
funksiya grafigiga o'tkazilgan urinmaning burchak koeffitsiyenti 4 ga teng
bo'lsa, urinish nuqtasi
absissasini toping.
               1          1
8
Moddiy nuqtaning harakat tenglarnasi t3 —
9t2 -1- 30t -4-4 ko'rinishida bo'lsa, uning eng kichik bo'lgan
vaqtni toping.
y z: f(T) funksiya grafigiga ato —1
nuqtasidan urinma o'tkazilgan. Agar g (m) g' (—1) ning qiymatini toping.
 f (x) 2$3 —9+4-123-1-6
funksiyaning OT
parallel bo'lgan urinmalari nechta?
 f va f2a;
— 6 funksiyalar orasidagi eng qisqa masofani toping.
(Dy o'qini (O; 3) nuqtada kesuvchi parabolaning absissasi 2
nuqtasida o'tkazilgan urinma y z: — I bo'lsa, parabolaning OT o'qi bilan
kesishish nuqtalari orasidagi masofani toping. A)l
f (a) 2x,G funksiya grafigiga o'tkazilgan urinma (6; 5)
nuqtadan o'tadi. Urinish nuqtasining absissalari qabul qilishi murnkin bo 'Igan
qiymatlar yig'indisini toping. A)5 B)10 C)13
Chizmada y f (T) funksiya
hosilasining grafigi tasvirlangan. y J funksiya grafigiga 1—5; 51 kesmadagi
nechta nuqtadan o'tkazilgan urinmasi 1
 — —„r + $ to'g'ri
chiziqqa parallel bo'ladi?
2

-2
-2

        a:

 + aa:2 4a + 2
funksiyaning (I; 3) nuqtasidan o'tkazilgan urinmaning burchak koeffitsiyentini
topiing.
D)12
y '2x2 funksiyaga, uning y 1 funksiya bilan
kesishish nuqtasi orqali o'tkazilgan urinma tenglamasini tuzing.
A)y 2x —

4, HOSILANING GEOMETRIK VA MEXANIK MA'NOSI
ax3 + bT2 + 7
funksiyaning A(I; 10) nuqtasidan O'tkazilgan urinmaning burcha,k koeffitsiyenti
11 ga teng bo'lsa a ning qiymatini toping. A)2
 Agar f (T) 2a;3
-1- ax2 + 2ba; + 4 funksiyaning absissasi 1 va 3 bo'lgan
nuqtalardan o'tkazilgan urinmalarning burchak koefftsiyentlari teng bo'lsa, a
ning qiymatini toping.
                            13)-12              C)12
         D)16
2 — 2a; -1- 3 funksiya grafigiga nuqtadan
o'tkazligan urinma tenglamasini tuzing.
A)
y 6 — zim; y 2 — 43
B)
y 6 — 4a;; y         — 6 C)y                — 6; y 2 —
D)y 3— 5a;y z 4 — 6z
f (x) a:r2 +
br + c funksiyaning OT o'qi bilan kesishish nuqtalari orqali o'tkazilgan
urinmalar o'zaro perpendikulyar bo 'Isa, quyidagilardan qaysi biri o 'rinli?
A)
b2 + 4aC 1           B)b2 — 4ac — 1     C)b2 4ac
— —1      D)ab        O
y ka: + b to'g'ri
chiziq y f (T) funksiyaga nuqtada urinadi. f' (I) ning qiymatini toping.

-3

-2

2

              3                        4
                  4                                        3
2-test
2
+ '2t — 2(m) va
bilan tezlanishlari teng masofani toping.

Integral
1.
Integral(l-qism)
— ; 8 funksiyasini
100d:r ni toping.
       A) 100x + C B)îáö
+ c
C)50x2 + C
5 — 4a ning boshlang'ich funksiyasini toping.
A)5a: — 4a2 C B)5x - 2x2 + c D)5x  + C
 f(c) ex ning (In 6; 9) nuqtadan
o'tuvchi boshlang'ich funksiyasini toping.
f(c) = 2 cos
.c+4œ ning boshlang'ich funksiyasini toping.
A) —2 sin +
4x ln 4 + C
B)2sinœ -l- — + C
C)2cosc + —
ln x + C
D)2sinœ+4œ1n4+C
348

JC             -l-          1) ni toping,
A)2X + 3
3
3x2
8
                 2 x funksiyaning
2;                 nuqtasidan
ln 2

4
A)2œ ln 2 + —

4

In 2

ln2

1112

4

8

21112 ln2

ln2

1112

o'tuvchi boshlang'ich funksiyasini
toping.
Agar f (x)             f (2 cosa• + 3)d:r bo'lsa,     (x)
ni toping.
        cos         3
C) —2 sin .T                       D)2
sin X + 3
3 da ni toping.
2
ni toping.
f (2x -l- 1) (3x -p 2)d.r ni toping.
B)2cg + 27
+ + C
+ 27 +
+ c

3
da; ni toping.
2
2
2
2 sin ni toping.
cos c
A)4 sin x -l- C                 13)—4
sin œ -l- C C)4 cos X -l- C D) —4 cos â' + C
— 2vG)da; ni toping.

2
f (2 sin •
ctgœ + sin 1
A)2 sin c + ctgx + C B)2 sin x —
ctga; -f- C

A)œ3 —

3

2

2

_D)c2 -
  2c+C

3
f (œ -l- 1)4 dx ni toping.
5

sin œ +
ctgœ + C sin — ctga; -l- C        D)           3

2.

2, Integral(2-qism)

5 (a; -l- 2) 2 da; ni toping.

2 da; ni toping.
32x—3

2)t +C f 230+ 4da; ni toping.

-pc

27 B)-
2           1 C)      D)
        32x—3 ln 2               2 . 32x—3 In 3

'23x4-4

f (2x + ni toping.

ln 2                        3
1112

3-2
              .
                    1112 + C                     D)
ni toping.
13)21n
12œ + II + C ln 12x + Il + C
4
da: ni toping.
1
2(3a; --1- 5)2
2
B)-
2
3(3a• +
6

f (3x2 -l- sin

ni toping.

— cos

C

D)-
1
B)a;[2] —
cos
2
3

A)sin '2x-1-C B)cos 2x+C sin 2c + C
fcos (     da; ni toping. 5— 7x

C) — sin 2x-1-C

2

A) — sin

5 — 7x
2

B)sin

2

C) — sin

2

sin

5— 7x
2

sin

cos 3 œ

ni toping.

f (cos2 a: — sin2 x)dx
ni toping.

1
— cos 2a -l- C
3     2
sin a; -l- cos
A)a,' — cos 2a; -4- C
-h — cos '2a +
C
1
— — cos —F C
2
-l- — cos 2a; + C

                1                                                                         2             4
— sin 3a; + 2 funksiyaning         da: ni toping. sin2 (3c)        cos2
2x nuqtadan o'tuvchi boshlang'ich funksiyasini toping.                ctg3:r
— 2tg2:r + C
1

— cos 3a; -l- '2a; -k —

B) cos

— 6

C) — Sin
12
D) — cos

— 2

          12                           6
3
cos(4rr -l-
6)dm ni hisoblang.
f e5x +6 da• ni toping.
A)e5x + 6 +C       B)
-e5x+6 + C
In 5
4x2 + 2a: + 1
da: ni toping.
8x3 —
1
A)ln 12a; — 1 C
B)21n       — II + C
C)) ln 12a: —
Il + C
D)-21n 12x - 1 +C
f (a: + ctg2 2x)da• ni toping,
2 A) —
—ctg2ïL' +

ctg3 2:r 02 B)
6
2
C) —ctg2a; —         C
— —ctg3a; — 2tg2c + C
— 8tgœ
-l- C
D) —ctg3œ + 2tg2x + C
f Tr e x da: ni toping•
In 'Ir err
f sin(2 —             ni toping.
cos(4:r — 2) +
C
B)) cos(2 - 4c) + c
C) a sin(2 — 4x) + C cos(2 —
f (c) (3a; -l- + — + — 4 funksiyaning (—1; 3)
a; 3x nuqtadan o'tuvchi boshlang'ich
funksiyasini toping.
+ ln — 1
             9                           9x3
1 B)            + ln — 3
1
C)      9
4
D)
             3                           3x5
Agar f(a;)             F (x) + c
bo?lsa, f                ni hisoblang.

D) —ctg2œ -l- -b- C

                                ni
toping.                                                             tg:vda; ni
toping.
A)ln I cos cl + C    B)— ln Icosxl -l- C
A)ln 1x 2                11 + C   C)ln I sin {Tl + C           D)ln
Itgxl + C
1
C)
1
D)

1
da: ni toping.
A)ln                                         B)- ln

      (:r 2 — 2a: -l- 3) 3          ni
hisoblang.                                                                                +
C D)41n
1
1
B)
1
C)                                                                                f
cos 3a; • cos 5',rda• ni toping.
2(až2 — 2C-1_
                        1                                                                                sin
2a: — — 1 sin 5a: -t- C
D)-                                                                                A)
                   16
sin 2C-l- — sin 8C + C
16
C)— sin 2x -l- — sin 8c + C
16

1
f (sin(2x) +                              Ili toping.                                                     —
cos 2a; — — cos 8a: -l- C
16
1
— cos 4a: + C
4
B)a: -l- — sin 4a; C
— 4 sin 4a; + C sin4 (2a:)
cos4 (2a;) J ni toping. D)
          8              8
2
1 f 4-—žd.c ni toping.             2
8
A)ln — 21 + C                                                             -
ln ex — 21 + C                                                                                —
                  -1- 4) g + c
                        —
21 + C        D)ln le c
J f'           • f           ni toping.                                                                f
(c) funksiya uchun f' (a;)                   a sin 2C +
                                                                                1                             19
                                                                                bcos
3a;; f                                                  — Šhartlar
2
o'rinli bo'lsa, a — b ning
qiymatini toping. D)
3
           7              5
   sin 21: • sin4 a.•da; ni
toping.                                                                                —
+ C
D)a 2 ln œ —
2x -l- C A) — sin6 + C B) — sin6 as + C cos6
tr + C D)—— sin6 C
+ C ni toping.      -l- C
A)ln — Il + In Ix — 31 + C
B)21n — Il + In IX — 31 + C C)ln — Il +2 ln — 31 -I-C
ni toping.
da
ni toping.
                      +
C            B) —arctg-s- + C                                                                   2ctga;
                        +
C         D) —arctg— + C                                                               sin
.rr
toping.
                            + C ni toping.                                                    A)xarctga;
-l- — ln 1x2 -l- Il + C
—9x2 + 16
— + In -l- Il -l- C
A) 73
arcsin — + C B) 73 arcsin — + C                                                          —
ln la:2 + Il -F C
C) arcsin — + C D) arcsin — + C                                                                  —
arctga; + C
              ln œd:r ni toping.                                                                                ni

2
B) Ina;
2
         2                2
C) ln                                                                       In2
—
                         4                                      2
sina; • eœda; ni toping.
A)sin me — COS C
B) (sin x -l- cos                                                                                -l-
C
-l- cos æ)
+ C
D) —ex (sin
— cos œ) + C
cos2 da: ni toping.

A)œtgx + ln I cos al -h- C -l- ln I sin -l- C — In I cos
cl + C
D)xctgx — In
Ictgxl + C
 ni toping. sin x

A)ln Itga:l
  + C' ln Itg;l + C

B)2 ln Itg;l + C
D)ln Itg;l + C

dm ni toping.
(C + 4) LOI

101

'25

(Œ + 4) 100
B)

(x + 4) 100

101

100

-l- 4) 100
C)

(x + 4)99

25

99

(x + 4) 100
D)

(x + 4)x99

99

25

f(2 + Œ)eœda: ni toping.

+ 2eœ +C
— 6x -l- 10 ni toping,
C)ln       +
101 D)arctg 2
clœ
ni toping.
B)arcsin x 2 2) C) arcsin œ 2 2)
D)2 arcsin 32)
A)x2 arcsin -l- C
B)c2 -jr- T, arcsin x
-l- C
- l)ex +
C
ni toping.

C).T2 arcsina; + a;
arcsin (c + C

3. ANIQ INTEGRAL

3.
Aniq integral
                   sin  ni hisoblang.
A)—2
1
U
cos2 da ni hisoblang. 1     2

 ni
hisoblang.

J rlogg log3 48 ni
hisoblang.
               1      2
                        B)
               3      4
C)
 In 3
f
4 2 cos xdx ni hisoblang.
        A)-2N/î  13)0
 C)vQ

4 D)

—dm ni hisoblang.
-+-
cos2 ni hisoblang. B)2TÏ C)37r D)47r
123
(4:r -F 2)dŽr ni hisoblang. 13)12     C)16
ni hisoblang.
13)1
(4x
— 2x)dx ni hisoblang.
                 B)74   C)80
  D)81
f (3x3 +
3œ2 + 4a)dx ni hisoblang.           D)16
= 24 bo'lsa, a ni toping. cp D)-2

f (4x3 -l- 2x -l- I)dx ni hisoblang. ni hisoblang.
ni hisoblang.
                        B) 36
        C) 46           D) 56

1-test                                                                          4.
EGRI CHIZIQLI TRAPETSIYA YUZI

4. Egri
chiziqli trapetsiya yuzi
y + 2', y =              I va = 3 to'g'ri chiziqlar bilan
chegaralangan soha yuzini toping.
 Y = œ2 ;y
 I va 2 chiziqlar chegaralangan soha
yuzini toping. D)3
Chizmada berilganlarga ko'ra
bo'yalgan yuzani toping.

3
7

                                                  4

2

       1       2

                                  C)10      D)12
y = VE, y = O; a; = I va = 9 chiziqlar bilan chegaralangan
soha yuzini toping.
                            B)14                             D)26
y & ; y = O;a; ln 2 va ln 4 chiziqlar bilan
chegaralangan soha yuzini toping.
                B)ln2
                               3             2
chegaralangan soha yuzini toping.
chegaralangan soha yuzini toping.
C)
chegaralangan soha yuzini toping.
chegaralangan soha yuzini toping.
yuzani toping.

    4. ECRI
CHIZIQLI TRAPETSIYA YUZI                                                                           I-test
funksiyalar bilan
D) 2, 4v/ä
4 chiziqlar bilan
ko'ra bo'yalgan soha
2 + 5x —
2-test                                                                             4.
EGRI CHIZIQLI TRAPETSIYA YUZI

37r
2 chegaralangan soha yuzini
toping.
y = 3x ; y = 61C — 3 chiziqlar bilan
chegaralangan
Agar SI = 6; S2 = 4 bo Isa, ning qiymatini toping.
                                        C)vQ
     D)2v/i
1 va c 2 chiziqlar
bilan chegaralangan sohani Ox o'qi atrofida 360 0 ga aylantirishdan
hosil bo'lgan jism hajmini toping.
              A)2T          13)7+                                                                                D)47r

Kombinatorika.
Ehtimollar nazariyasi. To'plam
1. Kombinatorika
Savatda 6 ta
olma va 5 ta nok bor. Savatdan A shahardan B shaharga 6 xil, B shahardan C bitta
mevani necha xil usulda tanlab olish shaharga esa 4 xil yo'l bilan boorish
mumkin. mumkin? A shahardan C shaharga B orqali
borish kerak
A) 5                                                                                B)
6           C) 11      D) 30     bo'lsa, buni necha xil usulda amalga oshirsa
bo'ladi?
                                                                                A)
12      B) 24      C) 32      D) 48
"Matbuot tarqatuvchi"
do'konida 5 xil konvert va 8 xil marka sotilmoqda. I ta konvert va 1 ta markani
necha xil usulda sotib olish mumkin? A shahardan B shaharga 8 xil yo'l orqali
borish C) 13 D) 40 murnkin. Yo'lovchi borgan
yo'lidan qaytmaslik sharti bilan, A shahardan B shaharga necha xil usulda
borib-kelishi mumkin?
                                                                                A)
49         B) 56         C) 64         D) 72
Birinchi o'quvchida matematika faniga Oid 6 ta
kitob, ikkinchi o'quvchida esa geometriya
                   faniga
Oid 4 ta kitob bor. Ular necha xil usul                                 Savatda
5 ta olma, 4 ta nok va 6 ta anor bor.
bilan birining bitta kitobini
ikkinchisining bitta          Savatdan ikki Xil nomdagi mevani necha xil usul
kitobiga almashtirishi mumkin?              bilan tanlash mumkin?
                A)
6         B) 10         C) 12         D) 24                                         A)
74          B) 80       C) 90          D) 120
 Do'konda
4 Xil ruchka, 5 2; 5; 6; 7; 8 raqamlari yordamida, ularni chizg'ich sotilmoqda.
O'quvchi bitta ruchka, takrorlamasdan nechta ikki xonali son yozish bitta
daftar va 1 ta chizg'ichni necha xil usulda mumkin?
sotib olishi mumkin?A) 10 B) 20 C) 25 C) 30 A) 15
B) 24 C) 120
O; 2; 3; 5; 6 raqamlari yordamida, ularni
6 ta savolga
"ha" yoki "yo'q" deb necha xil takrorlamasdan nechta uch
xonali son tuzish usulda javob berish mumkin? mumkin?
A)   12           B)
36     C) 64      A) 24     B) 48      C) 60      D) 72
366

uchburchak
mavjud.                                                                        uchburchak
mavjud.
G
B)    100         C)110
(23 — y) 7 standart shaklga keltirilganda
a5 y 6 oldidagi koefftsiyentni toping. ifodaning ozod hadini toping.
A) —672 B) —336 B) —120 C) 336 D) 672           D) 240
(Z' — 2y + 3z) 5 soddalashtirilganda x2 yż
z oldidagi
                + -1- + + C9 yig'indini hisoblang.                                koeffitsiyentni
toping.
A)   62 B) 63 C) 126
D) 127 B) —120 D) 360
(a; + 2) n ifoda standart shaklga
keltfrilganda Shunday eng kichik natural sonni topingki, oldidagi koefitsiyent
240 bo'lsa, n ning qiymatini bunda (my ifoda toping, soddalashtirilganda
karnida 200 ta haddan iborat
B)
14     C) 15       D)
16
Kitob javonida kimyo faniga oid 2
ta, matematika Asadbekda 4 ta turli matematika va 3 ta turli faniga oid 3 ta va
fizika faniga oid 4 ta kitob fizika kitoblari mavjud. U matematika kitoblari
mavjud. Tarkibida har bir fanga oid kamida yonma-yon turishi sharti bilan, bu 7
ta kitobni bitta kitob bo'ladigan kitoblar to'plarnini necha javonga necha xil
usulda joylashtirishi mumkin? xil usulda tanlash mumkin?
A) 24         B) 36         C) 144         D) 576                                                         B)
315         C) 360        D) 512

Uchlari berilgan
nuqtalarda bo'lgan nechta uchburchak mavjud.
c
          A)102          B)110          C)120          D)132
1;2;3;4;5;6
va 7 raqamlaridan foydalanib, raqarnlari o'sib borish tartibida bo'lgan nechta      soni
nechta? uch xonali son tuzish mumkin?
          A)
28          B) 35          C) 42          D) 56
soddalashtirilganda myzż a:yzt oldidagi  (va-
  ifoda      soddalashtirilganda, irratsional bo'lrnagan hadini toping.
A) -630 B)
-420 C) 420 D) 630
mumkin
bir nuqtada
hosil
10 ta odam
orasidan 6 łasini shunday tanlash ichida kerakki, bunda oldindan
belgilangan ikkita odam bir vaqtda tanlanmasin. Bunday tanlovni necha D) 990
xil usulda amalga oshirish mumkin?
        A)
120         B) 140         C) 180        D) 210
16 ta nechta
Turli raqamli, to'rt xonali juft
natural sonlar nechta?
A) 2240 B) 2296 C) 2520 D) 3645
2. EHTIMOLLAR
NAZARIYASI

2.
Ehtimollar nazariyasi
12 ta qizil va ta ruchkadan tavakkaliga olingan
ruchkanilłg ko'k rangli bo'lish ehtirnolini toping.
                                                          5
Anvar, Bahrołn, Dilnoza, Akrom va Maftuna o'yinni
birinchi boshlash uchun qur'a, tashlashdi.
O'yinni qiz bola boshlashi
ehtirnolini toping.
                                                                      4
D)
5
Zavodda ishlab chiqariladigan 500 ta mahsulotdan 15
łasi yaroqsiz, Zavodda ishlab chiqarilgan mahsulotdan tavakalliga
tanlangani yaroqli bo'lish ehtimolini toping. A)0, 95 B)0, 96
3 kishi Suxrob, Abduqodir, Diyor
yugurish musoboqasida ishtirok etishyapti. Suxrobning łolib bo
'lish ehtimoli — ga, Abduqodirning g
g'olib bo'lish elltimoli — ga teng.
Musobaqada Diyorning g'olib bo'lish ehtimolini toping.
Tala,baning imt,ihonda 160 bulldan yuqori ball Olish
ehtiłnoli 0,68 ga, 160 balldan kam ball Olish ehtimoli ga teng. Talabaning
aynan 160 ball Olish ehtimolini toping.
            A)0, 01         B)O, 02
D)0, 38
dan 10 gacha raqamlangan sharlardan
olingan shardagi son 3 ga bo'linish
kartochkalardan
Tanlangan bo'lish ehtimolini toping.
nishonga tegish ehtimoli
Mergan 2 marła o'q
uzganda ikkala tegish ehtimolini toping. D)0, 49
tashlanganda
kamida bir marła toping.
7
D)-
8
aylanalari radiuslari mos teng.
Mergan tavakkaliga tegdi. O'qning katta halqaga toping.
1
2

3. To'plamlar
               A                 Z; —2         K
6) bo'lsa,

A to'plarnning elementlar sonini aniqlang. B)7           D)9
Agar  va B 13; 4; 5; 6; 7) bo'lsa, A n B ni
toping.
B)łl; 2; 3; 4; 5; 6; 7)
C)ł3; 4;
5)
DNI; 2; 3; 4;
5)
Agar A C- R, —2 K a: K 4) b e R, —4
x K '2) bo'lsa, A IJ B ni toping.
A)łalx G R, —4  K —2)
B)łxlx e
R, -2                       21
D)łxIT                              4)
A (a; b; c; d; e) bo'lsa, A ning
nechta qism to'plamida b element qatnashadi ammo d element qatnashmaydi?
C)16
A                                14,6,
10, 12) va U
(2, 4, 6, 8, 10, 12, 10 bo'lsa, X n
13' ni toping.

AMIO; 12)      B)ł14ł
10, 12)  D)GO
Ir, y, k) bo'lsa, A n (B IJ C) ni
toping.
A)łc,
d, T, y, k)           B)łc, d, T, j) C)ła:, y, j, k)         D)fc, d,
y)
A (a; b; c; d; bo'lsa, A to'plarnning nechta qism
to'plamida c va e elementlari qatnashadi? C)16
n(A) — A toplamning elementlar soni. Agar n(A) 6; n(B)
4 bo'lsa, IJ B) fli toping.
                                   C)IO           D)12
Agar
A  N; F K 16) bo'lsa, A to'plamning qism to'plamlar sonini toping. A)4      C)16
      D)128
Agar A Ix a: N : — —10 K O) bo'lsa, A to'plarnning xos qism
to'plamlari sonini toping.
                13)14         C)30          D)32

3. TO'PLAMLAR

Agar A (Tl;r N; I c
5) bo'lsa, A to'plarnning 3 ta elementli qism to'plamlari sonini toping. A)3
C)10 D)20
 A to'plarn
elementlari 48 Hing, B to'plarn elementlari 60 ning natural bo'luvchilaridan
iborat. A n B ning elementlar sonini toping. C)12 D)19
A
to'plamda 12 ta, B to'plamda esa 16 ta element bor. A IJ B to'plamning
elementlari sonining eng katta va eng kichik qiymatlari yig'indisini toping.
A)28       B)40       C)44       D)48
A la; b; c; d; e) bo'lsa, A to'plamning nechta qłsm
to'plamida a va b dan faqat bittasi qatnashadi?
                 016
A to'plamning qism to'plamlari 32
ta, B to'plamning qism to'plamlari 16 ta, A LJ B to'plamniug qism to'plamlari
64 ta, bo'lsa, A n B to'plamning qism to'plamlari sonini toping.
D)16
Z, x 3) vaB ł:clr z, gł
U B') to'plamni toping.
to'plamga
amal
belgisi qo'yilsa, 17; 9) tenglik o'rinli

J avoblar
a ura son ar
Natural sonlar va Illar ustida amallar

Test raqami

1

2

3                                              8
  9 10 11 12 13 14

15

16

17

18

19

20

1-test

B

c

1)

D

B

c

B

c

B

2-t,est

c

13

Bo'linish belgilari, tub va murakkab sonlar

D

c

D

B

c

c

Test raqami
1-test
'2-test
Test raqmili

1
1

2
2

3                   4 5 6 7 8 9 10 11                      12
  13 14
Sonni tub ko'pavtuvchilarga ajrat,isll.
  EKUB va

15

17

18

19

20

3

(5

1-test

A

c

c

c

A

D

B

'2-tcst

c

c

B

D C A A B C 13 C B
Sonning bo'luvchilar solli va yig'indisi

c

B

D

12 13

14

15

16

17

18

19

20

1-test

c

B

c

B

D

B

B

B

c

2-test

A

B

B

Qoldiqli bo'lish, oxirgi raqarn

c

D

C

B

A

D

Tost raqami
1-test
2-test

'2

3

4

                        7
  s 9 10 11                12 13
asr ar
Oddiv kasrlar

14

15

17

18

19

20

Test raqami

1

2

3

4

5 G 7 8 9 10 11                             12
  13

15 c

16
B

17

18
A

19
B

20
B

'2-tesf

A

D

B

A C B C C C C: 1\ 13

c

A

c

D

B

B

3-test

c

c

c

Onli va cheksiz clavriy o'nli kasrlar

B

B

B

B

A

B

Test raqami

1

2

5

6 7 8 9 10 11                          12
  13

15

17

18

19

20

1-test

A

c

c

c

c

B

c

D

B

c

B

B

B

B B 13 C B C IX IX

A

D

B

B

D

B

B

3-test

B

A

Qism, foiz, nisbat va
  proporsiya

B

B

C

D

B

c

D

Test raqami

1

2

3

5

6 7 8 9 10 11                          12
  13

14

15

17

18

19

20

1-test
2-t,est

c

B

ge ral 1 0 a ar
Daraja va uning xossalari

C

c

B

13

c

B

B

Test raqallli
1-test
2-test
,l-test

3
c

4

5

6 7 8 9 10 11                          12
  13

14

15

16

17

18

19

20

376

Birhadlar va ko'phadlar ustida amallar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I-test

A

D

D

c

13

c

B

B

c

D

2-test

A

A

B

A

A

c

c

3-test

c

B

D

c

B

c

A

c

B

Qisqa ko'paytirish formulalari

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

D

c

D

c

D

D

13

B

1)

A

2-test

D

A

D

B

A

D

3-test

A

D

A

C B D

C,

B C!

13

A

A

D

c

c

B

B

B

el-test

A

c

A

D

D

B

1)

5-test

A

D

c

D

B

c

B

B

B

c

B

B

Ko'phadni ko'paytuvchilarga ajrat,ish

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

B

D

c

D

B

B

B

A

A

D

A

A

c

2-test

D

D

c

D

B

A

A

B

B

D

A

A

c

3-test

c

D

A

A

c

c

1)

B

c

A

B

B

D

D

A

A

c

c

A

A

13

5-test

B

c

c

c

c

D

13

A

c

D

D

c

Algebraik kasrlar

Test raqami

1

2

3

4

5

7

8

9

10

11

12

14

15

17

18

19

20

I-test

B

B

B

B

B

c

B

A

D

C

13

c

1)

B

B

c

'2-test

c

A

D

B

B

c

c

B

3-test

D

B

A

A

B

D

B

B

c

D

D

A

B

4-test

B

B

c

B

B

D

B

c

A

D

B

B

D

5-test

A

B

B

c

c

D

D

B

B

D

B

IZ1q 1 teng ama va teng
  ama ar sisternasl, chiziqli tengsizlik va tengsizliklar sistemasi, chiziqli
  funksiya
Chiziqli tenglamalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

B

D

A

D

c

c

c

B

D

c

D

2-test

B

B

c

D

D

D

c

B

3-test

A

c

c

A

C'

13

C'

c

A

B

c

c

Chiziqli tenglamalar sistemasi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

1-test

A

B

D

A

c

B

D

D

B

2-test

D

c

c

D

B

A

B

3-test

c

B

1)

c

D

D

B

A

D

Chiziqli tenglama va tenglamalar sistemasi
  tuzishga doir masalalar

Test raqarni

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I -test

B

B ID

B C D

A D

C

B C'

B

B

c

2-test

c

D

B

Chiziqli tengsizlik

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

A

B

B

c

A

A

D

c

B

2-test

c

B

D

D

A

C

B

A

C C8

c

D

c

D

B

D

B

B

3-test

c

A

A

c

B

A

A

c

B

B

Chiziqli funksiya

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

1-test

D

B

A

c

B

D

B

c

c

B

A

c

2-test

A

C

c

D

c

B

A

A

c

B

3-test

c

B

c

D

c

c

B

c

A

B

A

B

c

IZ 1 1 0 a ar
Arifrnetik kvadrat ildiz va uning xossalari

Test raqami

1

2

3

4

5

6

7

10

11

12

14

15

16

17

18

19

20

I-test

B

B

c

A

A

c

B

c

B

B

c

A

D

2-test

c

D

B

B

B

B

B

A

B

A

B

B

c

3-test

A

B

D

c

B

c

c

A

B

c

c

c

B

D

c

c

B

13

B

A

D

D

D

C

Ildizli ifodalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

1-test

A

A

c

D

D

D

B

B

2-test

B

B

B

D

D

c

B

c

D

D

B

A

A

c

slon teng ama ar.  ar
Kvadrat tenglama

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

1-test

D

D

D

B

B

D

c

13

c

A

D

B

2-test

D

B

D

c

c

B

1)

c

1)

13

A

B

B

B

B

A

B

3-test

A

A

A

c

c

B

B

B

D

c

c

Ratsional tenglamalar

Test raqami

1

2

3

4

5

6

7

S

9

10

Il

12

14

15

17

18

19

20

Il-test,

c

B

D

B

c

c

B

B

D

A

B

2-test

c

A

B

C

C

D

13

c

B

B

C

D

B

D

3-test

B

A

A

D

D

c

c

13

A

c

B

B

B

c

c

B

D

Vivet teoremasi

Test raqami

1

2

3

4

5

6

7

10

11

12

13

14

15

16

17

18

19

20

1-test

1)

c

c

A

A

B

B

C'

C'

13

D

c

D

B

D

A

c

D

2-test

A

D

C

c

A

B

c

A

D

B

3-test

A

c

B

B

D

c

B

c

A

D

D

B

c

B

c

A

D

B

D

B

A

B

A

B

D

D

c

c

Ikkinchi va undan yuqori darajali
  tenglamalar sistemasi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

I-test

D

c

c

A

B

c

B

c

D

B

A

C

C

2-test

A

c

B

B

A

B

A

c

3-t,est

c

B

B

c

c

A

D

c

D

B

B

B

c

Ko'phadlar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

D

B

D

D

c

A

c

B

c

B

D

'2-test

B

c

c

D

D

A

A

D

D

D

c

D

B

3-test

A

B

c

D

D

D

B

A

D

c

                   atslona tengslz     ar
Ratsional tengsizliklar

Test raqami

1

2

3

4

5

6

9

10

11

12

14

15

16

1

18

19

20

I-test

A

B

B

c

c

c

A

A

B

C

A

B

2-test

c

B

B

D

B

D

c

D

B

A

c

D

3-test

c

c

B

D

D

B

c

c

D

c

B

B

B

4-test

A

B

D

B

B

D

B

D

13

13

D

c

A

c

B

C

5-test

A

B

A

B

13

1)

D

c

B

A

B

D

va rat un swa
Kvadrat funksiya

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

A

B

c

2-test

B

A

D

c

B

A

c

A

B

3-test

B

B

D

c

c

c

D

c

c

c

4-test

B

B

c

B

A

c c

c

c

B

D

B

B

c

c

o u 1 teng ama va tengslzl ar
Modulli tenglamalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I-test

A

D

c

B

B

C

13

A

B

D

B

D

A

B

2-test

B

D

A

c

c

A

13

A

B

c

A

c

D

c

3—test

A

B

c

D

A

c

A

A

B

B

D

D

B

B

B

B

13

A

D

c

c

B

c

D

c

B

Modulli tengsizlik

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

A

D

A

D

c

c

A

B

B

c

2-test

B

D

D

D

B

B

A

c

D

c

B

D

B

      1 .    atslon       o rsat IC 1 araJa
Ratsional ko'rsatkichli daraja

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

A

A

c

A

B

2-test

A

D

B

B

D B A

c

D

D

A

B

rratslona teng ama va tengslz 1 ar
Irratsional tenglamalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

A

c

B

B

B

D

D

B

2-test

B

B

B

c

D

c

c

c

D

c

A

c

c

3-test

B

c

c

B

D

B

A

c

D

c

B

Irratsional tengsizlik

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

1-test

B

B

c

B

c

c

A

c

D

A

B

c

c

2-test

c

D

c

A

D

c

A

B

c

B

rogress1Y ar
Arifmetik progressiya

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

B

c

B

c

A D D

B

D

C B I)

C

B

A

B

B

c

D

2-test

B

c

B

B

B A C A

B C

B B C

c

A

c

B

D

B

3-test

A

B

c

c

A B C

C

B B D

A C

B

D

B

c

B

B

c

Arifmetik progressiyaning yig'indisi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1 -test

c

B

A

A

B

c

B

D

c

D

c

2-test

c

A

D

D B

C

c

B

c

B

c

A

B

3-test

B

c

B

D

B

c

B

B

c

c

B

c

Geometrik progressiya

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

1-test

c

A

c

B

B

B

A

c

c

2-test

D

B

B

B

B B B

D

B

c

B

B

D

B

D

Geometrik progressiyaning yig'indisi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I-test

A

A

A

C C

B

B

A

(3

13

13

c

B

c

c

c

D

c

2-test

D

c

c

c

A

A

D

B

               1           atn masa ar
O'rta arifmetik va O'rta geometrik qiymatga
  oid masalalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

I-test

B

c

D

c

c

B

c

C

c

c

D

D

B

Foizga oid masalalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

A

c

c

B

D

D

C C

D

c

A

c

B

C

C

Harakatga oid masalalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

I-tcst

B

D

B

B

B

c

B

D

D

B

c

Ish va aralashmaga oid masalalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

c

B

A

B

c

C A

C

c

c

B

c

D

c

D

B

                         1 .           n Sly ar
Funksiya(l-qism)

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I -test

A

c

B

B

A

C

13

A

B

D

B

B

D

c

A

D

2-test

c

B

D

A

B

B

c

A

A

D

c

3-test

B

B

D

D

D

D

A

B

D

B

c

D

D

c

Funksiya(2-qism)

Test raqami

1

'2

3

4

5

6

7

8

9

10 11

12

14

15

16

17

18

19

20

1 -test

c

c

D

A

B

C

13

}3 A 1)

A

B

C

c

B

B

c

B

c

2-test

c

c

A

c

B

B

13

A

C

1)

c

A

D

A

B

D

c

3-test

D

D

c

B

D

B

A

D

c

D

B

B

D

B

C

ENmksiya(3-qism)

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

1-test

B

B

A

A

A

c

2-test

A

D

c

C

13

B

B

1)

A

A

D

A

A

c

     1 .     o rsa            •nng arn? va
Ko rsai Lljl tenglamaiac

Test raqami

1

2

3

5

6

7 8

10

11

12

13

14

15

17

18

19

20

1-test

A

c

B

c

B

c

A

D

B

D

2-test

D

c

c

B

B

B

D B

B

c

c

B

D

c

c

B

B

3-test

B

c

B

B

B

C

A

c

c

B

B

B

Ko'rsatkichli tengsizliklar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

1-test

A

B

c

c

B

B

c

B

D

c

c

2-test

c

A

B

c

c

ogorl m ar
Logarifmik hisoblaslllar va shakl
  almashtirishlar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

1-test

A

A

A

D

A

A

c

B

B

c

2-test

D

c

B

c

D

B

B

B

A

B

B

c

3-test

A

D

B

A

B

c

13

IX

A

13

A

B

c

A

c

B

D

B

B

c

D

A

D

D

c

c

D

D

B

c

D

Logarifmik funksiya

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

c

B

A

B

A

A

c

c

c

Logarifmik tenglamalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

1 -test

c

c

c

c

B

c

c

13

B

c

c

D

D

B

D

B

B

2-test

D

B

A

D

B

B

B

c

3-test

D

D

A

B

c

A

c

c

c

D

B

Logarifmik tengsizlik

Test raqarni

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

1-test

c

c

D

B

c

A

A

D

2-test

A

c

c

D

D

B

A

B

Igonometmya
Asosiy tushunchalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

c

D

B

D

c

c

A l)

A

C

13 13

A

B

B

B

D

c

D

2-test

B

B

c

c

c

B

D

B

c

c

B

B

B

Asosiy trigonometrik ayniyatlar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

1-test

A

c

A

B

B

B

B

B

c

B

A

B

2-test

B

B

A

B

c

D

B

c

c

Keltirish formulalari

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

1-test

A

c

D

D

B

D

C

13

C'

(J'

A

A

c

B

c

D

A

D

2-test

A

c

B

c

A

C

13

1)

A

B

A

c

c

D

Qo'shish formulalari

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

D

c

B

B

A

c c

c

B

D

A

D

2-test

A

A

B

B

A

B

A

c

Ikkilangan burchak formula,lari

Test raqami

1

2

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

B

c

A

B

D C A B

A C C

B

c

2-test

D

B

D

c

D

c

A

c

c

B

B

3-test

c

B

c

c

D

c

13 1)

1)

B

A

D

c

c

D

Geometrik masalalar

Test, raqarni

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1-test

A

D

D

c

c

B

IX

C

A

13 1)

13

B

A

A

c

D

2-test

B

c

D

A

A

A

c

Ko'payt,ma va yig'indi formulalari

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

A

B

A

B

c

A

B

D

2-test

c

D

B

c

c

c

D

B

B

Yarirn burchak formulalari

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

1-test

c

B

B

D

D

A

B

c

c

B

Thgonometrik funksiyalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

I-test

D

c

D

D

B

C

13

C,

13

13 13

A

B

D

c

B

B

B

B

c

2-test

D

c

A

c

c

c

3-test

A

c

c

A

D

c

c

B

B

Teskari trigonometrik funksiyalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

c

c

c

B

c

A

A

c

c

B

c

2-test

A

A

D

B

c

D

c

D

Trigonometrik tenglamalar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

1-test

c

D

c

B

B

B

B

B

B

c

2-test

B

c

c

D

B

c

c

c

A

c

D

D

3-test

D

D

D

D

c

c

A

D

B

c

4-test

B

B

c

c

A

B

B

A

D

Trigonometrik tengsizliklar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

I-test

A

D

B

A

A

A

D

c

D

D

2-test

c

c

A

c

c

D

A

A

J

OSI a
Hosila olish qoidalari

Test raqarni

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

1-test

A

B

c

A

c

B

B

2-test

A

B

D

A

A

D

c

3-test

D

B

A

c

c

D

B

A

A

B

Murakkab funksiya hosilasi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

17

18

19

20

1-test

B

B

D

D

D

B

D

A

B

2-test

c

A

B

c

A

D

c

B

B

D

B

D

Funksiyani tekshirish

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I-test

B

B

B

B

B

c

A

c

B

c

2-test

c

D

c

C

B

B

B

c

Hosilaning geometrik va mexanik ma'nosi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

B

B

A

c

c

B

D

B

c

c

A

D

B

2-test

c

A

c

c

B

c

B

c

B

D

c

c

c

c

c

1 . ntegra
Integral(l-qism)

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

17

18

19

20

I-test

A

B

B

A

B

A

c

B

B

D

D

2-test

B

B

B

B

B

B

c

B

c

A

D

B

B

c

B

Integral(2-qism)

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

1 -test

D

B

B

c

B

B

B

B

B

A

A

A

B

2-test

A

B

B

B

B

B

A

B

B

B

c

3-test

A

B

B

B

B

c

B

A

D

A

A

Aniq integral

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I-test

D

B

B

D

B

B

B

A

B

B

D

A

c

2-test

c

D

A

c

A

c

C'

c

13

A

c

B

D

c

A

B

Egri chiziqli trapetsiya yuzi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

D

B

B

c

A

A

D

B

B

c

2-test

A

D

B

B

c

A

B

D

A

D

c

om matorltimo ar nazarwasl.
Kombinatorika

o p am

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

14

15

16

17

18

19

20

I-test

c

D

D

c

c

B

B

c

B

c

D

B

A

c

2-test

D

c

D

D

B

c

B

A

B

D

B

D

A

c

3-test

c

D

c

c

D

c

D

A

B

B

B

B

D

c

c

Eht,imollar nazariyasi

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I-test

A

B

c

B

B

A

D

D

C

13

B

A

c

c

B

D

B

B

To' plamlar

Test raqami

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

I-test

B

c

c

B

B

D

B

A

c

c

A

c

c

D

B

UO'K
51(076.1)
22.1v6 M 31
M 31      Matematika
(Matnl : mavzulashtirilgan testlar to cplami / Sh. Jumayev Lva
boshq.j — Toshkent: Fan va ta'lim nashryoti.- 384 b.
KBK 22.1v6
ISBN-978-9943-8653-7-2
MATEMATIKA
mavzulashtirilgan
testlar to'plami
Muharrir X. Polatho (jayev
Badiiy
muharrir B. Irisboyev
Texnik
muharrir B. Irisboyev
Musahhih D.
Ismoilova
Sahifalovchi
B. Irisboyev
Lits. AI Ng 1
11. Bosishga 10.I l. 2023 yilda ruxsat etildi.
Bichimi
84X108 1 /g. Hajmi 24,0 6. T.
Adadi 1000
nusxa. Shartnoma Ne 50. Buyurtma Ng 103,
«FAN VA
TA'LIM» nashriyoti,
100115,
Toshkent sh., Chilonzor ko'chasi, I-uy.
«ADAD PLYUS»
MChJ bosmaxonasi,
Toshkent sh.,
Chilonzor ko'chasi, 28-uy.

[1]
< I Ina;l <
2 tengsizlikni yeching.
kJ (e; e2 )
IJ (e; e2 )                                                                     > O tengsizlikni qanoatlantiruvchi barcha natural sonlar yig'indisini
toping.

[2]
— cos 2a; + C

file_name: IDC To'plam 119-384 betgacha.pdf

alt: ARIFMETIK KVADRAT ILDIZ VA UNING

alt: Ildizli ifodalar 2.

alt: A) 11xy 3 B) —II:ry

alt: avfi+l av/ü- l

alt: D)a+l 2 D)—

alt: 2-test 2. ILD1zL1 IFODALÃR

alt: ILDIZLI IFODALAR 2-test

alt: Ratsional tenglamalar, Ko'phadlar 1

alt: O tenglamaning yechimlari 2x 2 + 3x — 5 = 0 tenglamaning qaysi ildizi — 9x +8 =

alt: katta İldİzİnİ toping.

alt: Ratsional tenglamalar — 17F + 16

alt: 2x — 8:r — 4

alt: tenglamaning — + 3

alt: 3. Viyet teoremasi

alt: O tenglarna ildizlari 4a 2 — ar -1- 9 0 tenglamaning ildizlari uchun

alt: IT — 3yl ning qiyrnatini toping

alt: Y 2 -I-4X — 23/ — 2 O tenglama nechta

alt: A) 3 ta B)2ta ta 9 -l- :v 2 y 2 + y4 — 189 tenglamalar — aty -l-

alt: 5. Ko'phadlar

alt: P(a) 2x 3 — -1-2T + 1 ko'phadning đarajasini aniqlang

title: k