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.

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

2

\[2\sqrt {\frac{a}{b}} \]

\[2\sqrt {ab} \]

\[2\sqrt {\frac{b}{a}} \]

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

\(\sqrt {10} \)

12\(\sqrt {30} \)

\(\sqrt {30} \)

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

50

52

49

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

7

5

9

3

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

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

\(\frac{\pi }{{12}} + \pi k;\;\;\;k \in Z\)

\(\;\;\frac{\pi }{6} + \pi k;\;\;\;k \in Z\)

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

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

3

5

0

7

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

3\(\sqrt[3]{x} + \frac{3}{8}{x^2}\sqrt[3]{{{x^2}}}\)−\({5^x}ln5 + 2x + C\)

3\(\sqrt[3]{x} + \frac{3}{8}{x^2}\sqrt[3]{{{x^2}}}\)−\(\frac{{{5^x}}}{{ln5}} + 2x + C\)

3\(\sqrt[3]{x} + \frac{3}{8}{x^2}\sqrt[3]{{{x^2}}}\)−\({5^x} + 2x + C\)

\(\sqrt[3]{x} + 3{x^2}\sqrt[3]{{{x^2}}}\)−\({5^x} + 2x + C\)

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

0

6

3

1

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

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

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

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

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

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.

\[y = - {x^2} + 2x\]

\[y = - {x^2} + 1\]

\[y = - {x^2} - 2x\]

\[y = {x^2} - 2x\]

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

0

1−\(\sqrt {a - 1} \)

1+\(\sqrt {a + 1} \)

\(\sqrt {{a^2} - 1} \)

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.

18

324

288

72

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

2

1

3

4

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

3(1−a)(1+b)

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

3(1−a)

1+b

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.

\(\frac{{25}}{{12}}\)

2

2\(\sqrt 2 \)

\(\frac{{15}}{7}\)

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

(2;1)

(1;-2)

(-2;1)

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

4

2

8

16

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

\(\frac{\pi }{2}\)

\(\frac{\pi }{3}\)

0

\(\frac{\pi }{4}\)

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

7

12

14

9

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?

18

20

10

15

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

−7cos5x−5cos7x+c

7sin5x−5sin7x+c

7sin5x+5sin7x+C

7cos5x−5cos7x+c

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

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

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

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

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

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

0,75

0,5

0,25

0,125

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

2\(\sqrt 2 \)−1

4\(\sqrt 3 - 6\)

1

\(6 - 2\sqrt 3 \)

. Beshyulduzning uchidagi burchaklarining yig‘indisini toping.

240

90

270

180

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

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

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

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

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

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

10

11

13

12

y=6sin2x+sin12x funksiyaninghosilasini toping.

−24sin7xcos5x

24sin7xsin5x

24cos7xcos5x

24sin5xcos7x

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

6

10

-6

-2

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

πk; π−arcctg4+πk; k\( \in Z\)

arccos0,8+2πk; k\( \in Z\)

π −arcctg4+πk; k\( \in Z\)

πk; −arcctg4+πk; k\( \in Z\)

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.

1019

1519

2519

5039

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

[−2;0]

[2;∞)

[−2;∞)

(−∞;−2]

\[{3^{2017}}\] sonning oxirgi ikkita raqamini toping.

03

83

13

63

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.

216

100

45

27

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

(0;3)

a>3, a=0

a=3

1<a<3

\[ABC\] 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.

15

16

12

14

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

\[\frac{{{h^2}}}{{{a^2}{b^2}}}\]

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

\[{a^2} + {b^2}\]

\[\frac{1}{{{h^2}}}\]

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

5va7

−5 va 7

−7va 5

−7 va −5

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

\(4\sqrt 3 + 7\)

\(\frac{{\sqrt 3 - 1}}{2}\)

\(\frac{{1 + \sqrt 3 }}{2}\)

\(7 - 4\sqrt 3 \)

\[{x^2} - {y^2} = 36\] tenglama nechta natural yechimga ega?

1

3

4

2

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