11-sinf matematika fanidan online test

11-sinf o'quvchilari uchun mo'ljallangan matematika fanidan online test savollari.

Fan olimpiadasining birinchi bosqichi (maktab bosqichi) ni o'tkazish uchun

Test savollar soni: 40 ta

Bajarish uchun ajratilgan vaqt: 100 daqiqa

Barcha ma'lumotlarni to'g'ri kiriting.

${\left( {\frac{1}{3}} \right)^{ - 40{x^2}}} < {3^{4{x^2} - 3x + 0,5}}$ tengsizlik yechimlari joylashgan interval uzunligini toping.

0,75

0,5

0,25

0,125

Ifodaning oxirgi raqamini aniqlang: ${3^{279}} \cdot {7^{298}} - {3^{178}} \cdot {7^{197}}$

6

1

0

3

Koordinata boshidan o‘tuvchi, simmetriya o‘qi ordinata o‘qiga parallel, cho‘qqisi $y = x$ va $x + y - 2 = 0$ to‘g‘ri chiziqlar kesishgan nuqtada bo‘lgan parabolaning tenglamasini toping.

$y = {x^2} - 2x$

$y = - {x^2} + 1$

$y = - {x^2} - 2x$

$y = - {x^2} + 2x$

. To‘g‘ri burchakli uchburchakka ichki va tashqi chizilgan aylanalar radiuslari 2 va 5 ga teng. Katetlarning yig‘indisini toping.

7

14

12

9

2, 3, 4, 5, 6, 7, 8, 9, 10 sonlariga bo‘lganda mos ravishda 1, 2, 3, 4, 5, 6, 7, 8, 9 qoldiqlar hosil bo‘ladigan eng kichik natural sonni toping.

2519

1519

1019

5039

Agar $lg5 = a\;\;va\;\;lg3 = b$ bo`lsa, ${\log _{30}}8$ ni toping.

1+b

3(1−a)(1+b)

3(1−a)

$\frac{{3\left( {1 - a} \right)}}{{1 + b}}$

$\left( {2{{\cos }^2}\frac{x}{2} - 1} \right)\sqrt {25 - 4{x^2}} = 0$ tenglama nechta ildizga ega?

4

1

3

2

$y = {\log _{\frac{2}{3}}}\left| {6x - 8} \right|$ funksiyaning aniqlanish sohasini toping.

$\left( { - \infty ;\frac{4}{3}} \right)$

$\left( { - \infty ;\frac{2}{3}} \right) \cup \left( {\frac{2}{3};\infty } \right)$

$\left( { - \infty ;\frac{4}{3}} \right) \cup \left( {\frac{4}{3};\infty } \right)$

$\left( {\frac{2}{3};\infty } \right)$

Doiraga ichki chizilgan kvadrat undan yuzasi $2\pi - 4$ ga teng bo‘lgan segmentni ajratadi. Kvadratning yuzasini toping.

16

8

4

2

$\left| {{x^2} + 2x - 8} \right| = 3a$ tenglama a ning qanday qiymatlarida 3 ta haqiqiy yechimga ega bo`ladi.

(0;3)

a=3

a>3, a=0

1<a<3

Perimetri 4 gao`tkirburchagi 30oga vashuburchakqarshisidagitomoni $\sqrt 3$ ga teng bo`lgan uchburchakka ichki chizlgan aylana radiusini toping.

$4\sqrt 3 + 7$

$7 - 4\sqrt 3$

$\frac{{1 + \sqrt 3 }}{2}$

$\frac{{\sqrt 3 - 1}}{2}$

Ifodanisoddalashtiring. $1 - \frac{{\frac{1}{{\sqrt {a - 1} }} - \sqrt {a + 1} }}{{\frac{1}{{\sqrt {a + 1} }} - \frac{1}{{\sqrt {a - 1} }}}}$ :

1−

$\sqrt {a - 1}$

1+

$\sqrt {a + 1}$

$\sqrt {{a^2} - 1}$

0

y= $\frac{1}{{\sqrt[3]{{{x^2}}}}} + x\sqrt[3]{{{x^2}}}$ − ${5^x} + 2$ funksiyaning boshlang`ich funksiyasini toping.

3

$\sqrt[3]{x} + \frac{3}{8}{x^2}\sqrt[3]{{{x^2}}}$ −

${5^x} + 2x + C$

3

$\sqrt[3]{x} + \frac{3}{8}{x^2}\sqrt[3]{{{x^2}}}$ −

${5^x}ln5 + 2x + C$

3

$\sqrt[3]{x} + \frac{3}{8}{x^2}\sqrt[3]{{{x^2}}}$ −

$\frac{{{5^x}}}{{ln5}} + 2x + C$

$\sqrt[3]{x} + 3{x^2}\sqrt[3]{{{x^2}}}$ −

${5^x} + 2x + C$

Agar f(g(x))= − x+13 bo`lsa, f(x) va g(x) to`g`ri chiziqlar orasidagi burchakni toping.

0

$\frac{\pi }{3}$

$\frac{\pi }{4}$

$\frac{\pi }{2}$

Asosi $\sqrt[3]{{18}}$ ga teng bo`lgan muntazam to`rtburchakli piramidaning uchidan o`tkazilgan kesma asos tomonini 2:4 nisbatda bo`ladi va asos tekisligi bilan 60o li burchakhosilqiladi. Piramidahajmini toping.

6

12

$\sqrt {30}$

$\sqrt {10}$

$\sqrt {30}$

Agar ${2^a} = 27$ , ${3^c} = 16$ bo’lsa a ∙ ? ning qiymatini toping.

11

13

12

10

. ${\rm{1}}! + {\rm{2}}! + {\rm{3}}! + \ldots + {\rm{1}}0!$ sonining oxirgi raqamini toping.

7

5

3

0

Bitta tekislikda yotuvchi n ta turli tog`ri chiziq o`tkazilgan. Ularning ixtiyoriy ikkitasi parallel emas va ixtiyoriy uchtasi bitta nuqtadan o`tmaydi ,ya`ni bitta nuqtada kesishmaydi. Bu to`g`ri chiziqlar tekislikni 1276 qismga ajratadi. n ni aniqlang?

51

49

50

52

$ABC$ uchburchakka aylana tashqi chizilgan. Uchburchakning $AM$ medianasi aylana bilan $K$ nuqtada kesishguncha davom ettirilgan. Agar $AM = 18,\,MK = 8,\,BK = 10$ bo‘lsa, $AC$ tomonini toping.

12

16

15

14

. Beshyulduzning uchidagi burchaklarining yig‘indisini toping.

90

180

270

240

Radiusi 6 ga teng bo`lgan uchta aylana o`zaro tashqi urinishidan hosil bo`lgan egri chiziqli uchburchakka ichki chizilgan aylana radiusini toping.

4

$\sqrt 3 - 6$

$6 - 2\sqrt 3$

1

2

$\sqrt 2$ −1

. $\left| {{{\left( {x - 6} \right)}^3} + 28} \right| = 36$ tenglamaning ildizlari yig‘indisini toping.

-2

6

-6

10

ABCD tetraedrning D uchidagi barcha yassi burchaklari to`g`ri. Shu tetraedrda kub shunday ichki chizilganki, kubning bitta uchi D nuqtada, unga qarama−qarshi uchi esa ABC yoqda yotibdi. Agar DA=5, DB=6 va DC=10 bo`lsa, kub qirrasining uzunligini toping.

$\frac{{25}}{{12}}$

$\frac{{15}}{7}$

2

$\sqrt 2$

a+b=−1 a+c=6 va b+c=1 bo`lsa, ${a^2}\left( {3b + 3c + 2a} \right) + {b^2}\left( {3a + 3c + 2b} \right) + {c^2}\left( {3a + 3b + 2c} \right)$ = ning son qiymatini toping.

45

100

216

27

. $a \le x \le y \le z \le t \le b$ va $a,b > 0$ bo‘lsa, $\frac{x}{y} + \frac{z}{t}$ ifodaning eng kichik qiymatini toping.

$2\sqrt {ab}$

$2\sqrt {\frac{a}{b}}$

$2\sqrt {\frac{b}{a}}$

2

Bir savdogar 1 mеtrini 1200 tiyindan olgan matosini yuvib, kuritgandan so`ng 1800 tiyindan sotyapti. Mato yuvilib kuritilganidan so`ng 20 foizi qisqardi. Bularga ko`ra savdogar nеcha foiz foyda ko`radi?

10

20

18

15

Tenglamaniyeching: $\frac{{ct{g^2}x + 4ctgx}}{{5co{s^2}x - 4cosx}} = 0$

π −arcctg4+πk; k

$\in Z$

πk; π−arcctg4+πk; k

$\in Z$

πk; −arcctg4+πk; k

$\in Z$

arccos0,8+2πk; k

$\in Z$

${x^2} - {y^2} = 36$ tenglama nechta natural yechimga ega?

1

2

4

3

${3^{2017}}$ sonning oxirgi ikkita raqamini toping.

83

63

03

13

. $a,b$ -to‘g‘ri burchakli uchburchakning katetlari va $h$ -gipotenuzaga tushirilgan balandligi bo‘lsa, $\frac{1}{{{a^2}}} + \frac{1}{{{b^2}}}$ yig‘indini toping.

${a^2} + {b^2}$

$\frac{{2\left( {{a^2} + {b^2}} \right)}}{{ab}}$

$\frac{1}{{{h^2}}}$

$\frac{{{h^2}}}{{{a^2}{b^2}}}$

3cos2x-3 $\sqrt 3$ sin2x=0 trigonometrik tenglamani yeching.

$\;\;\frac{\pi }{6} + \pi k;\;\;\;k \in Z$

$\frac{\pi }{{12}} + \pi k;\;\;\;k \in Z$

$\;\frac{\pi }{{12}} + \frac{{\pi k}}{2};\;\;\;k \in Z$

$\frac{\pi }{{12}} + 2\pi k;\;\;\;k \in Z$

$y = 4{\sin ^4}x - {\cos ^2}2x$ funksiyaning qiymatlar to‘plamini toping.

$\left[ {1;3} \right]$

$\left[ { - 1;3} \right]$

$\left[ {1;4} \right]$

$\left[ { - 2;2} \right]$

GH kesmani O nuqta, G nuqtadan boshlab hisoblaganda, 5 : 7 kabi, P nuqta esa 5:11 kabi nisbatda bo’ladi. O va P nuqtalar orasidagi masofa 30 sm bo’lsa, GH kesmaning uzunligini toping.

324

18

288

72

tengsizlikniyeching. ${\log _{\sqrt 3 }}\left( {2x - 1} \right) < {\log _{\sqrt 3 }}\left( {{x^2} + 6x + 9} \right)$

$\left( {\frac{4}{3};3} \right)$

$\left( {\frac{1}{2};\infty } \right)$

$\left( {\frac{2}{3};2} \right)$

$\left( {\frac{5}{3};2} \right)$

Tenglamaniyeching: $\left| {{x^2} - 3x - 2} \right| = {x^2} + 3\left| {x + 2} \right| + 4$

[−2;∞)

[2;∞)

(−∞;−2]

[−2;0]

f(x)=70cosxcos6x uchunboshlang`ichfunksiya toping.

7sin5x−5sin7x+c

−7cos5x−5cos7x+c

7cos5x−5cos7x+c

7sin5x+5sin7x+C

$f\left( x \right) = \frac{{{x^3}}}{3} - {x^2} - 35x + 2$ funksiya uchun f `(x)=0 bo`lsa x ni toping.

−7 va −5

−7va 5

−5 va 7

5va7

. Tenglamani yeching: $2\left( {x + 2} \right) + {x^2} + 4y\left( {x + y} \right) = 0$

(-2;1)

(1;-2)

(2;1)

y=6sin2x+sin12x funksiyaninghosilasini toping.

24cos7xcos5x

24sin7xsin5x

24sin5xcos7x

−24sin7xcos5x

. $x - {x^{ - 1}} = 1$ bo‘lsa, ${x^4} + {x^{ - 4}}$ nimaga teng?

7

9

5

3

0%