Matematika (07.03.2026) 1-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;

Agar

m = 24^3 \cdot 6^{12} \cdot 20^3

bo'lsa,

\frac{m^2}{2^n}

kasrning qiymati natural son bo'ladigan

n

ning eng katta qiymatini toping.

Agar

a = \lg 3

b = \cos 3

c = \ln 3

bo'lsa,

\frac{|a-b| + |b-c| - |a-c|}{|a+b| + |b-c| - |c+a|}

ifodani soddalashtiring.

Mug'ombir soddadilga ushbu ko'prikdan har bir o'tishingda cho'ntagingdagi pulni 2 barobar (marta) oshirib beraman deydi. Lekin sen menga har safar o'tganingda 36000 so'm berasan. Agar soddadil 3 marta ko'prik ustidan o'tgandan so'ng puli tugagan bo'lsa, boshida soddadilda necha so'm puli bo'lgan?

Tarkibida 60 litr suv bo'lgan suv va neft aralashmasi tarkibidan 15 litr neft ajratib olindi. Qolgan birikma tarkibida

4\%

neft qoldi. 60 litr aralashmaning tarkibida necha

\%

neft bo'lgan?

Hisoblang.

\frac{(a^2)^{-3} \cdot (-a^2)^7}{(-a^3)^2}

Hisoblang.

\frac{1}{\sqrt{2} + 2} - \frac{1}{2 - \sqrt{2}} - \sqrt{2}

Hisoblang.

\frac{8(\sqrt{3} - \sqrt{15})}{\sqrt{3} + \sqrt{7} + \sqrt{11} + \sqrt{15}} + \frac{8(\sqrt{3} - \sqrt{15})}{\sqrt{3} - \sqrt{7} - \sqrt{11} + \sqrt{15}}

\log_{12}162

\log_{12}x

\log_{12}y

\log_{12}z

\log_{12}1250

sonlari arifmetik progressiyaning ketma-ket hadlari bo'lsa,

z - x - y

ning qiymatini toping.

Agar

q < 1

geometrik progressiyada

b_1 + b_2 + b_3 = 21

b_1 \cdot b_2 \cdot b_3 = 216

bo'lsa, geometrik progressiyada

S_5

ni toping.

10.

Soddalashtiring.

\frac{a^3 - b^3}{(2a+b)^2 - 3a(a+b)} + \frac{(a^2+b)(b^2+a) - ab(ab+1)}{a^2 - ab + b^2}

11.

Soddalashtiring.

(a \ge 3)

\left(\frac{a + \sqrt{a^2 - 3a}}{a - \sqrt{a^2 - 3a}} - \frac{a - \sqrt{a^2 - 3a}}{a + \sqrt{a^2 - 3a}}\right) \cdot \frac{3}{4}

12.

Sonlarni kamayish tartibida joylashtiring.

a = \sin 17^\circ,\quad b = \sin 167^\circ,\quad c = \sin 375^\circ

13.

2(\sin^2 x + \operatorname{tg}^2 x) + 3 = 4\operatorname{tg}x + 2\sqrt{2}\sin x

tenglamaning

[0; 4\pi]

oraliqdagi ildizlari yig'indisini toping.

14.

Tenglamaning haqiqiy ildizlari yig'indisini toping.

\left(\sqrt{7 + 4\sqrt{3}}\right)^x + \left(\sqrt{7 - 4\sqrt{3}}\right)^x = 14

15.

Tenglamani yeching.

\left(\frac{2}{3}\right)^{\log_3(x+1)} \cdot \left(\frac{4}{9}\right)^{\log_{\frac{1}{9}}(x-1)} = \frac{2}{3}

16.

Tenglamalar sistemasining yechimlari

(x_1; y_1)

;

(x_2; y_2)

; ...;

(x_n; y_n)

bo'lsa,

x_1 + x_2 + x_3 + \ldots + x_n

ni toping.

\begin{cases} x^2 + y^2 = 34 \\ x + xy + y = 7 \end{cases}

17.

Tenglamaning haqiqiy ildizlari yig'indisini toping.

(x^2 - 8x + 12) \cdot \sqrt{10 + 3x - x^2} = 0

18.

Tengsizlikni yeching.

\begin{cases} \dfrac{36}{x} - x \le 0 \\[2mm] \dfrac{|12 - 2x| \cdot (x^2 + 5x + 25)}{|x| - 3} \le 0 \end{cases}

19.

Tengsizlikni yeching.

\sqrt{x - 11} + \sqrt{12 - x} > 0

20.

Agar

f(x) = \begin{cases} 8 + x, & \text{agar } x < 0 \\ 2 - x, & \text{agar } x \ge 0 \end{cases}

bo'lsa,

f\bigl(f(f(-5))\bigr)

ni toping.

21.

Aniq integralni hisoblang.

\int_3^6 \frac{x + 1}{x^2 + x - 6}\,dx

22.

Agar

f(x) = \frac{x + x^2 + x^3 + \ldots + x^{2024}}{x + x^2 + x^3 + \ldots + x^{1012}}

bo'lsa,

f'(1)

ni toping.

23.

Agar

O_1

aylana radiusi 5 ga,

O_2

aylana radiusi 2 ga teng bo'lsa,

AB

kesmani toping.

24.

f(x) = x^2 - 2ax - a - 6

funksiya

Ox

o'qini kesib o'tuvchi nuqtalar orasidagi masofa 10 ga teng bo'lsa,

a

ning qiymatlari yig'indisini toping. (Agar u bitta bo'lsa shu sonni toping.)

25.

ABC

uchburchak berilgan.

BDC

bir to'g'ri chiziqda yotadi va

|AC| = |AD|

|AE| = |DE|

tengliklar o'rinli bo'lsa,

\angle FLB = \beta

ni toping.

26.

ABC

muntazam uchburchakning tomoni 8 ga teng.

AD

kesma asosini 5 va 3 ga teng kesmalarga ajratadi.

ADC

ABD

uchburchakka ichki chizilgan doira yuzalari yig'indisini toping.

27.

ABCD

trapetsiyaning diagonallari

O

nuqtada kesishadi.

BOC

uchburchak yuzasi 3 ga teng. Agar

\frac{S_{BOC}}{S_{COD}} = \frac{1}{3}

bo'lsa,

AOB

uchburchak yuzini toping.

28.

Muntazam oltiburchakning tomoni 1 ga teng. Uning tomonlari o'rtalari tutashtirilib yana oltiburchak hosil qilindi. Hosil bo'lgan oltiburchakka yana shunday tomonlari tutushtirildi va bu jarayon cheksiz davom etdi. Hosil bo'lgan oltiburchaklar yuzini toping.

29.

A(6; 4; -2)

B(x; y; 0)

\overrightarrow{CD}(4; -3; 1)

vektor berilgan.

\overrightarrow{AB}

\overrightarrow{CD}

vektorlar kollinear bo'lsa,

\overrightarrow{AB}

ning koordinatalari yig'indisini toping.

30.

Rombning 60 va 80 ga teng diagonallari va unga romb tekisligiga tegishli bo'lmagan

P

nuqtasidan rombning diagonallari kesishgan nuqtasiga uzunligi 45 ga teng perpendikulyar tushirildi. Shu

P

nuqtadan rombning tomonigacha bo'lgan eng yaqin masofani toping.

31.

A = \{1; 2; 3; 4; 5; 6\}

to'plam berilgan. To'plamning nechta qism to'plamida 3 yoki 5 dan kamida bittasi qatnashadi?

32.

C_n^4 - C_n^3 = 14

bo'lsa,

C_n^2

ni toping.

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

33-35.

Agar silindr balandligi 8 ga teng bo'lsa, to'la sirti

232{,}5\pi

bo'lsa, quyidagilarni hisoblang:

Javob variantlari:

\frac{\sqrt{161}}{2}

\frac{\sqrt{161}}{4}

\frac{17}{2}

\frac{3\sqrt{21}}{2}

\frac{3\sqrt{21}}{4}

\frac{19}{2}

Savol	A	B	C	D	E	F
33. 10 cm kesma silindrning har xil asosida yotsa, silindr o'qidan shu kesmagacha eng qisqa masofa qanday?
34. Silindr o'qiga parallel kesim o'tkazilgan. U kvadrat bo'lsa, shu kesimgacha eng qisqa masofani toping.
35. Silindrga tashqi chizilgan shar radiusini toping.

36.

Tenglamalar sistemasi berilgan.

\begin{cases} x^2 + y^2 - 2(x - y)a = 9 - 6a - a^2 \\ x^2 + y^2 + 2(3x + 4y)a = 1 - 2a - 24a^2 \end{cases}

a) Tenglamalar sistemasi bitta haqiqiy yechimga ega bo'ladigan

a

ning nechta qiymati mavjud?

b) Tenglamalar sistemasi bitta haqiqiy yechimga ega bo'ladigan

a

ning eng katta qiymatini toping.

37.

Tenglamani yeching.

\sin^{10}x + \cos^{10}x = \frac{29}{16}\cos^4 2x

a) Eng kichik musbat ildizini toping.

b) Tenglama

[-\pi; \pi]

oraliqda ildizlar sonini toping.

38.

f(x) = a|x + b| + c

g(x) = kx + l

funksiya grafiklari

(6; 1)

nuqtada kesishadi.

f(x)

funksiya

(2; 3)

nuqtada maksimumga erishadi. Agar

(-\infty; 2)

oraliqda funksiyalar o'zaro parallel bo'lsa,

3 \cdot \frac{a + b + c}{k + l}

ni toping.

(-\infty; 2)

oraliqdagi

f(x)

g(x)

funksiya grafiklari orasidagi eng qisqa masofani toping.

39.

f(x) = \frac{x^5}{40} + \frac{x^4}{8} - \frac{x^3}{6} - x^2 + 2

funksiya berilgan.

a) Funksiyaning lokal maksimum nuqtalar sonini toping.

f(x)

funksiyaning

[-5; 2]

kesmadagi eng katta qiymatini toping.

40.

Rasmda

f(x) = ax^2 + bx + c

g(x) = kx + l

funksiya grafiklari tasvirlangan.

f(x) = ax^2 + bx + c

funksiya

Ox

o'qini

(-6; 0)

(2; 0)

nuqtalarda kesib o'tadi.

g(x) = kx + l

funksiya

f(x) = ax^2 + bx + c

funksiya bilan

(-4; 3)

(2; 0)

nuqtalarda kesishadi.

\frac{a + b + c}{k + l}

ning qiymatini toping.

b) Bo'yalgan soha yuzini toping.

41.

To'g'ri burchakli uchburchakning to'g'ri burchagidan gipotenuzaga balandlik va bissektrisa tushirilgan. Agar balandlik va bissektrisa uzunliklari mos ravishda 6 va 8 teng bo'lsa,

a) Uchburchak yuzini toping.

b) Uchburchak gipotenuzasini toping.

42.

ABCD

kvadratning

AC

diagonalidan

E

nuqta,

CD

tomonidan

F

nuqta olingan va

BE

EF

kesmalar o'zaro perpendikulyar. Agar

AE = 1

BE = \sqrt{3} + 1

bo'lsa,

DF

kesma uzunligini toping.

ABE

burchak kattaligini toping.

43.

Dekart koordinatalar sistemasida

y = \sqrt{x}

funksiya va muntazam

ABCDEFGH

sakkizburchak berilgan.

y = \sqrt{x}

funksiya sakkizburchakning

A

E

uchlarini kesib o'tadi.

a) Sakkizburchakning tomonini toping.

AE

kesma uzunligini toping.

44.

Asosi muntazam to'rtburchakli piramidaga silindr ichki chizilgan. Silindrning o'q kesimi piramida balandligidan o'tadi, piramida asosining yuzi 144 ga hajmi 288 ga teng bo'lsa, (

\pi \approx 3

deb olinsin.)

a) Eng katta hajmli silindr hajmini toping.

b) Silindr yon sirtining eng katta qiymatini toping.

45.

Anvar Bankdan yillik

20\%

foiz stavkasi bilan 2 yil muddatga 60 mln so'm miqdorida kredit oldi. Uning oylik to'lovi rasmdagi jadvalda ko'rsatilgan.

a) O'ninchi oyda to'lanadigan oylik to'lov (so'm) qancha bo'ladi?

b) Ikki yil mobaynidagi qo'shilgan foiz to'lovini (so'm) toping.