Matematika (01.03.2026) 2-smena

45 ta savol · saqlash uchun kiring

Matematika formulalar varaqasi / Лист формул по математике

Tenglamalar / Уравнения

ax^{2}+bx+c=0; \quad x_{1:2}=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}; \quad \begin{cases}x_{1}+x_{2}=-\frac{b}{a}\\ x_{1}\cdot x_{2}=\frac{c}{a}\end{cases}

|f(x)|+|g(x)|=|f(x)+g(x)|\Rightarrow f(x)\cdot g(x)\ge0;

\frac{Ax}{ax^{2}\pm bx-c}\pm\frac{Bx}{ax^{2}\pm dx+c}=k \quad \Rightarrow \quad \frac{A}{ax-\frac{c}{x}\pm b}\pm\frac{B}{ax+\frac{c}{x}\pm d}=k;

(ax^{2}\pm bx-c)(ax^{2}\pm dx+c)=Ax^{2} \quad \Rightarrow \quad (ax-\frac{c}{x}\pm b)(ax+\frac{c}{x}\pm d)=A;

ax+\frac{c}{x}=z

o'zgaruvchi kiritib yechiladi / решается c помошью замены

(x-a)(x-b)(x-c)(x-d) = A \quad \Rightarrow \quad a+b=c+d

bo'lsa,

t=x^{2}-(a+b)x

o'zgaruvchi kiritib yechiladi / решается c помошью замены

Qisqa ko'paytirish formulalari / Формулы сокращённого умножения

a^{2}-b^{2}=(a-b)(a+b)

(a\pm b)^{2}=(a^{2}\pm2ab+b^{2})

(a\pm b)^{3}=a^{3}\pm3a^{2}b+3ab^{2}\pm b^{3}

a^{3}\pm b^{3}=(a\pm b)(a^{2}\mp ab+b^{2})

a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+...+ab^{n-2}+b^{n-1})

a^{2n}\pm b^{2n}=(a\pm b)(a^{2n-1}\mp a^{2n-2}b+...+ab^{2n-2}\mp b^{2n-1})

a^{2n+1}\pm b^{2n+1}=(a\pm b)(a^{2n}\mp a^{2n-1}b+...+ab^{2n-1}\mp b^{2n})

(a+b)^{n}=a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+...

...+\frac{n(n-1)(n-2)\cdot...\cdot(n-(k-1))}{k!}+...+nab^{n-1}+b^{n}

Arifmetik progressiya / Арифметическая прогрессия

a_{n}=a_{n-1}+d=a_{1}+(n-1)d;

a_{n}=\frac{a_{n-k}+a_{n+k}}{2} \quad (1\le k\le n-1);

S_{n}=\frac{a_{1}+a_{n}}{2}\cdot n=\frac{2a_{1}+d(n-1)}{2}\cdot n

Geometrik progressiya / Геометрическая прогрессия

b_{n}=b_{1}\cdot q^{n-1}; \quad b_{n}^{2}=b_{n-m}\cdot b_{n+m} \quad (1\le m\le n-1);

S_{n}=\frac{b_{1}(1-q^{n})}{1-q} \quad (|q|>1);

S_{n}=\frac{b_{1}}{1-q} \quad (|q|<1);

Logarifmning xossalari / Свойства логарифмов

log_{a}1=0; \quad log_{a}(x_{1}\cdot x_{2})=log_{a}|x_{1}|+log_{a}|x_{2}|;

log_{a}\frac{x_{1}}{x_{2}}=log_{a}|x_{1}|-log_{a}|x_{2}|; \quad log_{a}b=\frac{log_{c}b}{log_{c}a};

log_{a^{q}}x^{p}=\frac{p}{q}\cdot log_{a}x; \quad log_{a}b=\frac{1}{log_{b}a};

lg10^{n}=n; \quad lne^{n}=n;

Daraja va ildiz / Степень и корень

a^{n}\cdot a^{m}=a^{m+n}; \quad a^{n}:a^{m}=a^{m-n}; \quad (a^{m})^{n}=a^{m\cdot n};

(a\cdot b)^{n}=a^{n}\cdot b^{n}; \quad (\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}; \quad a^{-n}=\frac{1}{a^{n}};

(\frac{a^{n}}{b^{m}})^{-k}=(\frac{b^{m}}{a^{n}})^{k}; \quad (-a)^{2n}=a^{2n}; \quad (-a)^{2n+1}=-a^{2n+1};

\sqrt[n]{a^{k}}=a^{\frac{k}{n}}; \quad \sqrt[n]{a^{k}\cdot b^{m}}=\sqrt[n]{a^{k}}\cdot\sqrt[n]{b^{m}};

\sqrt[n]{\frac{a^{k}}{b^{m}}}=\frac{\sqrt[n]{a^{k}}}{\sqrt[n]{b^{m}}}; \quad (\sqrt[n]{a^{m}})^{k}=\sqrt[n]{a^{mk}}; \quad \sqrt[n]{a^{n+k}}=a\sqrt[n]{a^{k}};

a^{-\frac{k}{n}}=\frac{1}{\sqrt[n]{a^{k}}}; \quad \sqrt[n]{\sqrt[m]{a^{k}}}=\sqrt[nm]{a^{k}};

\sqrt[n]{a^{k}}\cdot\sqrt[m]{b^{p}}=\sqrt[nm]{a^{km}\cdot b^{pn}}; \quad \sqrt[n]{a^{n}}=|a| \quad (n=2k);

\sqrt[2n]{(a-b)^{2n}}=\begin{cases}a-b, & a\ge b\\ b-a, & b\ge a\end{cases}

Urinma va normal tenglamasi / Уравнение касательной и нормали

y=f(x_{0})+f^{\prime}(x_{0})(x-x_{0});

y=f(x_{0})-\frac{1}{f^{\prime}(x_{0})}(x-x_{0});

Hosilaga doir formulalar va xossalari / Таблица производных и свойства

(x^{a})^{\prime}=ax^{a-1}; \quad (a^{x})^{\prime}=a^{x}ln a; \quad (e^{x})^{\prime}=e^{x};

(log_{a}x)^{\prime}=\frac{1}{x ln a}; \quad (ln x)^{\prime}=\frac{1}{x}; \quad (sin x)^{\prime}=cos x;

(cos x)^{\prime}=-sin x; \quad (tg x)^{\prime}=\frac{1}{cos^{2}x}; \quad (ctg x)^{\prime}=-\frac{1}{sin^{2}x};

(u\pm v)^{\prime}=u^{\prime}\pm v^{\prime}; \quad (k\cdot u)^{\prime}=k\cdot u^{\prime};

(u\cdot v)^{\prime}=u^{\prime}\cdot v+u\cdot v^{\prime}; \quad (\frac{u}{v})^{\prime}=\frac{u^{\prime}\cdot v-u\cdot v^{\prime}}{v^{2}};

Integralga doir formulalar va xossalari / Таблица и свойства интегралов

\int x^{n}dx=\frac{x^{n+1}}{n+1}+C; \quad \int\frac{dx}{x}=ln|x|+C;

\int e^{x}dx=e^{x}+C; \quad \int a^{x}dx=\frac{a^{x}}{lna}+C;

\int sinx dx=-cosx+C; \quad \int cosx dx=sinx+C;

\int k\cdot f(x)dx=k\cdot\int f(x)dx;

\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx;

\int_{a}^{b}f(x)dx=F(b)-F(a); \quad \int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx;

\int_{a}^{b}f(x)dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}f(x)dx \quad (a\le c\le b);

O'rta arifmetik va o'rta geometrik / Среднее арифметическое и среднее геометрическое

A=\frac{a_{1}+a_{2}+...+a_{n}}{n}; \quad G=\sqrt[n]{a_{1}\cdot a_{2}\cdot...\cdot a_{n}}

Ba'zi trigonometrik formulalar / Основные формулы тригонометрии

Asosiy trigonometrik ayniyatlar / Основные тригонометрические свойства:

sin^{2}\alpha+cos^{2}\alpha=1; \quad tg\alpha=\frac{sin\alpha}{cos\alpha}; \quad ctg\alpha=\frac{cos\alpha}{sin\alpha};

tg^{2}\alpha+1=\frac{1}{cos^{2}\alpha}; \quad ctg^{2}\alpha+1=\frac{1}{sin^{2}\alpha};

cos(\alpha\pm\beta)=cos\alpha\cdot cos\beta\mp sin\alpha\cdot sin\beta;

sin(\alpha\pm\beta)=sin\alpha\cdot cos\beta\pm cos\alpha\cdot sin\beta;

tg(\alpha\pm\beta)=\frac{tg\alpha\pm tg\beta}{1\mp tg\alpha\cdot tg\beta}; \quad ctg(\alpha\pm\beta)=\frac{ctg\alpha\cdot ctg\beta\mp1}{ctg\alpha\pm ctg\beta};

sin\alpha+sin\beta=2sin\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

sin\alpha-sin\beta=2sin\frac{\alpha-\beta}{2}cos\frac{\alpha+\beta}{2};

cos\alpha+cos\beta=2cos\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

cos\alpha-cos\beta=-2sin\frac{\alpha+\beta}{2}sin\frac{\alpha-\beta}{2};

Trigonometrik funksiyaning ba'zi burchaklardagi qiymatlari / Значения тригонометрической функции под некоторыми углами

$\alpha$	0	$\frac{\pi}{6}$	$\frac{\pi}{4}$	$\frac{\pi}{3}$	$\frac{\pi}{2}$
$\sin\alpha$	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1
$\cos\alpha$	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0

To'g'ri burchakli uchburchak uchun formulalar / Формулы для прямоугольного треугольника

a^2 + b^2 = c^2;

a = c \cdot \sin\alpha

b = c \cdot \cos\alpha;

a = b \cdot \text{tg}\alpha

Ixtiyoriy uchburchak uchun formulalar / Формулы для произвольного треугольника

S = \frac{1}{2}ab\sin\gamma

S = \sqrt{p(p - a)(p - b)(p - c)}

p = \frac{1}{2}(a + b + c); \quad S = \frac{1}{2}h_c \cdot c

\frac{\sin\alpha}{a} = \frac{\sin\beta}{b} = \frac{\sin\gamma}{c}

a^2 = b^2 + c^2 - 2bc\cos\alpha

Uchburchak uchun formulalar (umumiy) / Формулы для треугольника (общие)

S=\frac{1}{2}ab sin\gamma; \quad S=\sqrt{p(p-a)(p-b)(p-c)};

p=\frac{1}{2}(a+b+c); \quad S=\frac{1}{2}h_{c}\cdot c;

\frac{a}{sin\alpha}=\frac{b}{sin\beta}=\frac{c}{sin\gamma}=2R; \quad a^{2}=b^{2}+c^{2}-2bc cos\alpha;

To'g'ri burchakli uchburchak / прямоугольный треугольник:

a^{2}+b^{2}=c^{2}; \quad a=c\cdot sin\alpha; \quad b=c\cdot cos\alpha; \quad a=b\cdot tg\alpha;

Uchburchakka ichki va tashqi chizilgan aylana radiuslarini hisoblash formulasi /
Формула вычисления радиусов окружности, вписанной внутрь и вне треугольника

r=\frac{2S}{a+b+c}; \quad R=\frac{abc}{4S};

To'rtburchakning yuzlari uchun formulalar / Формулы граней четырехугольника

Parallelogramm / параллелограмм:

S=a\cdot h_{a}; \quad S=a\cdot b\cdot sin\alpha;

Romb / ромб:

S=\frac{1}{2}\cdot d_{1}\cdot d_{2}; \quad S=a^{2}\cdot sin\alpha;

Trapetsiya / трапеция:

S=\frac{a+b}{2}\cdot h;

Aylana va doira Doiraviy sektor va segment yuzi / Круговой сектор и сегментная грань

l=2\pi R; \quad S=\pi R^{2};

S_{sektor}=\frac{\pi R^{2}}{360}\cdot\alpha; \quad S_{segment}=\frac{R^{2}}{2}(\alpha-sin\alpha);

Vektorlar / Векторы

|\vec{a}|=\sqrt{x^{2}+y^{2}+z^{2}}

vektorning uzunligi / длина вектора

\vec{a}\cdot\vec{b}=|\vec{a}|\cdot|\vec{b}|\cdot cos\varphi

skalyar ko'paytmasi / скалярное умножение

\vec{a}\cdot\vec{b}=x_{1}\cdot x_{2}+y_{1}\cdot y_{2}

vektorlarning skalyar ko'paytmasi / скалярное произведение векторов

\vec{a}\cdot\lambda=\vec{c}(x\cdot\lambda;y\cdot\lambda;z\cdot\lambda)

Stereometriya formulalari / Формулы стереометрии

Prizma / призма | Piramida / пирамида:

V=S\cdot H; \quad V=\frac{1}{3}S\cdot H;

Kesik piramida / усеченная пирамида:

V=\frac{1}{3}h(S_{1}+\sqrt{S_{1}\cdot S_{2}}+S_{2});

Silindr / цилиндр:

S_{yon}=2\pi RH; \quad V=\pi R^{2}H;

Konus / конус:

S_{yon}=\pi R l; \quad V=\frac{1}{3}\pi R^{2}H;

Kesik konus / усеченный конус:

V=\frac{1}{3}\pi h(R_{1}^{2}+R_{1}\cdot R_{2}+R_{2}^{2});

Shar / шар:

S=4\pi R^{2}; \quad V=\frac{4}{3}\pi R^{3};

Shar segmentining hajmi / объем шар сегмента:

V=\pi H^{2}(R-\frac{H}{3});

Shar segmentining sirtining yuzi / площадь поверхности шарового сегмента:

S_{sirt}=2\pi RH;

\overline{8962ab}

ko'rinishidagi son 12 ga qoldiqsiz bo'linsa,

a \cdot b

ning eng katta qiymatini toping.

Hisoblang.

\{3 \cdot [\lg 5] + 5 \cdot \{\lg 0{,}1\} - 7[\ln 3]\}

A

punktdan

B

punktga piyoda yo'lga chiqdi. Oradan 3 soat o'tgach, uning ortidan velosipedchi yo'lga chiqdi. Velosipedchi yo'lning yarmiga yetganida piyodani quvib o'tdi. Agar velosipedchining tezligi piyodaning tezligidan 4 marta katta bo'lsa, piyoda

A

dan

B

gacha bo'lgan masofani necha soatda bosib o'tadi?

Tadbirkor bitta ko'ylak va bitta shimni mos ravishda bir xil tannarxda sotib oldi (ya'ni ko'ylaklar o'zaro bir xil narxda, shimlar ham o'zaro bir xil narxda olingan). Agar u ko'ylakni

40\%

ga, shimni

45\%

ga qimmatlatib sotsa, 215 000 so'm foyda ko'radi. Agar aksincha, ko'ylakni

45\%

ga, shimni

40\%

ga qimmatlatib sotsa, 210 000 so'm foyda ko'radi. Ko'ylakning tannarxini toping.

Hisoblang.

\left(1 + \left(2 - \left(3 + (4-1)^{-1}\right)^{-1}\right)^{-1}\right)^{-1}

Hisoblang.

\left(9{,}4 \cdot \sqrt[3]{6^2\sqrt{6}} - 3{,}4\sqrt{6\sqrt[3]{6^2}}\right)^{\frac{6}{11}}

Hisoblang.

\sqrt[3]{26 + 15\sqrt{3}} + \sqrt[3]{26 - 15\sqrt{3}}

a_n

arifmetik progressiyada

a_2 = 2a_1

a_{10} = 20

bo'lsa,

S_6 - S_5

ni hisoblang.

\{a_n\}

arifmetik progressiya va

\{b_n\}

geometrik progressiya berilgan. Agar

a_1 + a_2 + a_3 + \ldots + a_n = 820

b_1 + b_2 + b_3 = 217

b_1 = a_2

b_2 = a_9

b_3 = a_{44}

(d \ne 0)

bo'lsa,

n

ni toping.

10.

Agar

\frac{x-2}{y} = 1

bo'lsa,

\frac{2x + 4y + 2}{x + y}

ning qiymatini toping. Bunda

(y \ne -1)

11.

Soddalashtiring.

\frac{1}{a + \cfrac{1}{b + \cfrac{1}{c}}} : \frac{1}{a + \cfrac{1}{b}} - \frac{1}{b(abc + a + c)}

12.

Hisoblang.

\frac{\sin 11^\circ - \sin 49^\circ}{1 - 2\cos^2 54{,}5^\circ}

13.

Tenglama

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

oraliqda nechta yechimga ega?

\sqrt{3}\sin^2 x + \sin^2 2x = \frac{\sqrt{3}}{2} - \frac{1}{2} - \sqrt{3}\cos 2x

14.

Tengsizlikni yeching.

(0{,}75)^{\frac{x^2 + x - 8}{x + 1}} > 0{,}6 \cdot (1{,}25)^{x - \frac{8}{x+1}}

15.

Tengsizlikni nechta butun son qanoatlantiradi?

\log_{0{,}5}\log_2\log_{x-1} 9 > 0

16.

Tenglama nechta haqiqiy ildizga ega?

|x^2 - 5x - 6| + |7 + 6x - x^2| = x + 1

17.

Tenglama nechta haqiqiy ildizga ega?

8x^3 - 6x^2 + 3x - 1 = 0

18.

Tengsizlikni yeching.

\frac{1}{x+1} + \frac{2}{x+3} - \frac{3}{x+2} > 0

19.

Tengsizlikni qanoatlantiruvchi butun sonlar yig'indisini toping.

(2x^2 - x - 2)^2 < (x^2 + 5x + 4)^2

20.

Rasmda

f(x) = ax^3 + bx^2 + cx + d

funksiya grafigi tasvirlangan. Rasmdagi ma'lumotlar asosida

f(-3)

ni toping.

21.

Aniqmas integralni hisoblang.

\int \frac{x}{\sqrt{3x+1}}\,dx

22.

Agar

f(x) = \left|\ln x - \log_{\sin x}\cos x\right|

bo'lsa,

f'\left(\frac{\pi}{4}\right)

ni toping.

23.

Uchburchakning eng katta tomoni 8 ga, yon tomonlari esa

3x - 4

2x + 1

ga teng. Agar uchburchakning tomonlari butun sonlardan iborat bo'lsa, uchburchak perimetrini toping.

24.

Agar

f(x)

noldan farqli juft funksiya va

g(x)

noldan farqli toq funksiya bo'lsa, quyidagilardan nechtasi toq funksiya bo'ladi?

I.

y_1 = f(x) \cdot g(x)

II.

y_2 = f(x) + g(x)

III.

y_3 = \frac{f(x)}{g(x)}

25.

ABC

muntazam uchburchakka radiuslari teng bo'lgan

O_1

O_2

O_3

markazli aylanalar ichki chizilgan.

ABC

uchburchak yuzining

O_1O_2O_3

uchburchak yuziga nisbatini toping.

26.

ABC

teng yonli uchburchakda

AB = BC

AC = 64

. Uchburchakka radiusi 16 ga teng bo'lgan aylana va radiusi

r

ga teng bo'lgan kichik aylana ichki chizilgan bo'lsa,

r

ni toping.

27.

Chizmada

ABCD

trapetsiyaning

AC

BD

diagonallari

O

nuqtada kesishadi. Agar

BOC

AOD

uchburchak yuzalari mos ravishda 2 va 8 ga teng bo'lsa, bo'yalgan soha yuzini toping.

28.

Rasmda

ABCD

kvadrat va

CED

BCP

muntazam uchburchaklar tasvirlangan. Shunga ko'ra

\angle DKE

burchakni toping.

29.

A(-2; 5; -4)

B(-2; 7; -1)

C(4; 7; 2)

nuqtalar koordinatalari berilgan.

ABC

uchburchakda

AC

tomonga

BD

mediana o'tkazilgan.

\sin\angle CBD

ni toping.

30.

ABC

teng yonli to'g'ri burchakli uchburchakning

BC

kateti

\alpha

tekislikda yotadi.

AC

kateti

\alpha

tekislik bilan

45^\circ

li burchak tashkil qiladi.

AB

gipotenuza va

\alpha

tekislik orasidagi burchakni toping.

31.

Sinfda jami 25 nafar o'quvchi bor. Ulardan 9 nafari biologiya to'garagiga, 8 nafari kimyo to'garagiga qatnashadi. 10 nafar o'quvchi esa hech qaysi to'garakka qatnashmaydi. Ikkala to'garakka ham qatnashadigan o'quvchilar sonini toping.

32.

Ikkita kesishmaydigan to'g'ri chiziqlardan 3 ta va 4 ta nuqtalar olingan. Shu nuqtalarni tutashtirishdan nechta uchburchak hosil qilish mumkin?

Topshiriqlar (33-35) va javob variantlari (A-F) ni o'zaro moslashtiring.

33-35.

Prizma asosi teng yonli trapetsiyadan iborat va prizmaga shar ichki chizish mumkin. Trapetsiya asoslari 8 va 18 ga teng. Prizmaning

AA_1D_1D

BB_1C_1C

yon yoqlariga

KK_1N_1N

LL_1M_1M

parallel kesimlar o'tkazilgan.

Javob variantlari:

12\sqrt{313}

132\frac{12}{13}

156\sqrt{13}

256\frac{11}{13}

156

6\sqrt{313}

Savol	A	B	C	D	E	F
33. Prizmaning $AA_1C_1C$ diagonal kesimi yuzini toping.
34. Trapetsiyaning diagonallari kesishish nuqtasidan o'tuvchi $LL_1M_1M$ kesim yuzini toping.
35. Trapetsiyaning o'rta chizig'i bilan bir to'g'ri chiziqda yotuvchi $KK_1N_1N$ kesim yuzini toping.

36.

r

s

t

haqiqiy sonlari

f(x) = x^3 + ax^2 + bx + 1

funksiyaning nollari,

r^2

s^2

t^2

haqiqiy sonlar

g(x) = x^3 + mx^2 + nx + p

funksiya nollari va

g(-1) = -5

bo'lsa,

n - m - p

ning qiymatini toping.

(a-1)^2 + (b-1)^2

ning qiymatini toping.

37.

Tenglamani yeching.

\sin^4 x + 2\sin^2 2x = 9\cos^4 x

a) Tenglama

\left[-\frac{\pi}{2}; \frac{5\pi}{2}\right]

oraliqda nechta ildizga ega?

b) Tenglamaning

[-\pi; \pi]

oraliqdagi ildizlari yig'indisini toping.

38.

y = f(x)

kvadrat funksiya uchun

f(0) = 2

bo'lsa,

f(x+5) = f(x) + x + 1

tenglik o'rinli bo'lsa,

f(2025)

ning qiymatini toping.

f(x-9) = f(x) + x - 3

tenglik o'rinli bo'lsa,

f(2025)

ning qiymatini toping.

39.

y = x^2 - 6x + 12

kvadrat funksiya berilgan. Parabolaga o'tkazilgan urinma

y = 2x + 1

to'g'ri chiziq bilan kesishmaydi.

a) Urinmani parabolaga urinish nuqtasini ordinatasini toping.

y = x^2 - 6x + 12

funksiya grafigidan

A

nuqta,

y = -2x + 2

funksiya grafigidan

B

nuqta olingan.

A

B

nuqtalar orasidagi mumkin bo'lgan eng qisqa masofani toping.

40.

y_1 = x^2

y_2 = \sqrt{x}

funksiyalar berilgan.

y_1

y_2

funksiyalar kesishishidan hosil bo'lgan soha yuzini toping.

y_1

y_2

funksiyalar kesishishidan hosil bo'lgan sohani

Ox

o'qi atrofida

360^\circ

aylantirishdan hosil bo'lgan jism hajmini toping. (

\pi \approx 3

deb olinsin.)

41.

ABC

uchburchakning

AC

BC

tomonidan chiquvchi o'rta perpendikulyar chiziqlar mos ravishda

B

A

burchak bissektrisalari bilan

E

F

nuqtalarda kesishadi. Agar

\angle AFO = 5^\circ

\angle BEO = 10^\circ

AC = 3

bo'lsa,

\angle ACB

burchak kattaligini toping.

OF

ning qiymatini toping.

42.

ABCD

trapetsiyaning kichik asosi 56 ga teng. Trapetsiyaga tashqi chizilgan aylanadagi

E

nuqtadan

DC

tomonga parallel urinma va trapetsiya asoslariga parallel

EF

kesma o'tkazilgan. Agar

EF = 70

va aylana radiusi

14\sqrt{7}

ga teng bo'lsa,

a) Trapetsiya diagonalini toping.

b) Trapetsiya yuzini toping.

43.

Muntazam sakkizburchakka aylana ichki chizilgan, aylanaga muntazam oltiburchak ichki chizilgan.

a) Aylana markazidan muntazam oltiburchak tomonigacha bo'lgan eng qisqa masofani muntazam sakkizburchakning tomonigacha bo'lgan eng qisqa masofaga nisbatini toping.

b) Muntazam oltiburchak yuzining muntazam sakkizburchak yuziga nisbatini toping.

44.

Muntazam to'rtburchakli kesik piramidaga shar ichki chizilgan. Piramidaning to'la sirti 312 ga teng. Piramida katta asosi yuzining kichik asos yuziga nisbati 9 ga teng.

a) Piramida hajmini toping.

b) Shar hajmi toping.

45.

Yon qirralari 2 ga teng bo'lgan muntazam to'rtburchakli piramida berilgan. Agar piramida eng katta hajmga ega bo'lsa,

a) Piramida asosining yuzini toping.

b) Piramida hajmini toping.