Бөлшекті қысқартыңыз: 5 + 5 4 5 \frac{\sqrt{5}+5}{4\sqrt{5}} 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 5

1 + 5 4 \frac{1+\sqrt{5}}{4} 4 1 + 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

5 4 \frac{\sqrt{5}}{4} 4 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

5 \sqrt{5} 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 5 − 1 -\sqrt{5}-1 − 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 1

Функцияның анықталу облысын табыңыз: у = ( 10 − x ) ( x + 21 ) у=\sqrt{\left(10-x\right)\left(x+21\right)} у = ( 1 0 − x ) ( x + 2 1 ) <path d="M263,681c0.7,0,18,39.7,52,119c34,79.3,68.167, 158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067 c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84, 175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71 c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3, -252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26 s76,-59,76,-59s76,-60,76,-60z M1001 80H40000v40H1012z">

− 21 ≤ x ≤ 10 -21\le x\le10 − 2 1 ≤ x ≤ 1 0

21 ≤ x ≤ 10 21\le x\le10 2 1 ≤ x ≤ 1 0

10 ≤ x ≤ 21 10\le x\le21 1 0 ≤ x ≤ 2 1

− 21 < x ≤ 10 -21<x\le10 − 2 1 < x ≤ 1 0

10 < x < − 21 10<x<-21 1 0 < x < − 2 1

Теңсіздікті шешіңіз: x − 2 4 − 2 x + 1 3 < 3 − x \frac{x-2}{4}-\frac{2x+1}{3}<3-x 4 x − 2 − 3 2 x + 1 < 3 − x

( 6 4 7 ; + ∞ ) \left(6\frac{4}{7};\ +\infty\right) ( 6 7 4 ; + ∞ )

( − ∞ ; 6 4 7 ) \left(-\infty;\ 6\frac{4}{7}\right) ( − ∞ ; 6 7 4 )

Бөлшектің бөліміндегі иррационалдықтан арылтыңыз: 4 3 + 1 \frac{4}{\sqrt{3}+1} 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1 4

2 ( 3 − 1 ) 2\left(\sqrt{3}-1\right) 2 ( 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 1 )

4 4 + 1 \frac{\sqrt{4}}{4}+1 4 4 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1

3 − 1 4 \frac{\sqrt{3}-1}{4} 4 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 1

2 3 − 1 4 \frac{2\sqrt{3}-1}{4} 4 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 1

2 3 + 1 4 \frac{2\sqrt{3}+1}{4} 4 2 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1

Теңдеуді шешіңіз: x 4 – 13x 2 +36 =0

x = ± 2 ; x = ± 3 x=\pm2;\ x=\pm3 x = ± 2 ; x = ± 3

x = ± 1 ; x = ± 4 x=\pm1;\ x=\pm4 x = ± 1 ; x = ± 4

x = 5 ; x = 6 x=5;\ x=6 x = 5 ; x = 6

x = 2 x=\sqrt{2} x = 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

x = ± 10 ; x = ± 1 x=\pm10;\ x=\pm1 x = ± 1 0 ; x = ± 1

Функция нөлдерін табыңыз: y = 2 3 x − 4 0 , 3 x − 3 y=\frac{\frac{2}{3}x-4}{0,3x-3} y = 0 , 3 x − 3 3 2 x − 4

1 6 ; 10 \frac{1}{6};\ 10 6 1 ; 1 0

2 3 ; 4 \frac{2}{3};\ 4 3 2 ; 4

Рационалды бөлшек түрінде жазыңыз: 1 1 + 1 1 + 1 x \frac{1}{1+\frac{1}{1+\frac{1}{x}}} 1 + 1 + x 1 1 1

x + 1 2 x + 1 \frac{x+1}{2x+1} 2 x + 1 x + 1

x + 2 x + 1 \frac{x+2}{x+1} x + 1 x + 2

x + 1 2 x \frac{x+1}{2x} 2 x x + 1

"Жас математик" қалалық олимпиада. 9 сынып

Authored by Mereke Suleimenova

Mathematics

9th Grade

Used 12+ times

"Жас математик" қалалық олимпиада. 9 сынып

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Бөлшекті қысқартыңыз:
$\frac{\sqrt{5}+5}{4\sqrt{5}}$

1,25

$\frac{\sqrt{5}}{4}$

$\sqrt{5}$

$\frac{1+\sqrt{5}}{4}$

$-\sqrt{5}-1$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Теңдеуді шешіңіз: -50a² + 5a +1 = 0

a₁=1, a₂=2

a₁=-1, a₂=0,2

a₁=5, a₂=1

a₁=0,5, a₂=0,2

a₁=-0,1, a₂=0,2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Функцияның анықталу облысын табыңыз:
$у=\sqrt{\left(10-x\right)\left(x+21\right)}$

$-21\le x\le10$

$21\le x\le10$

$10\le x\le21$

$-21<x\le10$

$10<x<-21$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Теңдеуді шешіңіз: x⁵+x⁴+3x³+3x²+2x+2=0

x= 1

x= -2

x= - 1

x₁=0, x₂=-2

x₁=1, x₂=-2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Қаңтар айында -106 өнім, әр келесі айда алдыңғы айға қарағанда 12 өнім артық жасалды. Маусым және желтоқсан айларында қанша өнім жасалды?

маусым айында – 166, желтоқсан айында – 238

маусым айында – 126, желтоқсан айында – 248

маусым айында – 136, желтоқсан айында – 258

маусым айында – 116, желтоқсан айында – 228

маусым айында – 186, желтоқсан айында – 218

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$Есептеңіз:\ \frac{\left(2^8\right)^2\cdot2^6\cdot2^2}{2^{22}}$

$\frac{1}{7}$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$Өрнекті\ ықшамдаңыз:\ \ \left(x^5-5xy^2\right)+\left(x^5-y^2x\right)$

$6x^{10}-6x^2y^4$

$-8x^2y^4$

$x^5-6xy^2$

$2x^{10}-8xy$

$2x^5-6xy^2$

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Теңсіздікті шешіңіз:
$\frac{x-2}{4}-\frac{2x+1}{3}<3-x$

$(-∞;-6)$

$\left(6\frac{4}{7};\ +\infty\right)$

$\left(-\infty;\ 6\frac{4}{7}\right)$

(-6; 6)

(-6; 0)

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Шахмат турниріне 14 шахматшы қатысты, олар әрқайсысымен бір партиядан ойнады. Барлығы қанша партия ойнады?

$91$

$82$

$98$

$100$

$74$

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"Жас математик" қалалық олимпиада. 9 сынып

Бөлшекті қысқартыңыз: 5+545\frac{\sqrt{5}+5}{4\sqrt{5}}45​5​+5​

Теңдеуді шешіңіз: -50a2 + 5a +1 = 0

Функцияның анықталу облысын табыңыз: у=(10−x)(x+21)у=\sqrt{\left(10-x\right)\left(x+21\right)}у=(10−x)(x+21)​

Теңдеуді шешіңіз: x5+x4+3x3+3x2+2x+2=0

Қаңтар айында -106 өнім, әр келесі айда алдыңғы айға қарағанда 12 өнім артық жасалды. Маусым және желтоқсан айларында қанша өнім жасалды?

Есептеңіз: (28)2⋅26⋅22222Есептеңіз:\ \frac{\left(2^8\right)^2\cdot2^6\cdot2^2}{2^{22}}Есептеңіз: 222(28)2⋅26⋅22​

Өрнекті ықшамдаңыз: (x5−5xy2)+(x5−y2x)Өрнекті\ ықшамдаңыз:\ \ \left(x^5-5xy^2\right)+\left(x^5-y^2x\right)Өрнекті ықшамдаңыз: (x5−5xy2)+(x5−y2x)

Теңсіздікті шешіңіз: x−24−2x+13<3−x\frac{x-2}{4}-\frac{2x+1}{3}<3-x4x−2​−32x+1​<3−x

Зауыт өнімдерінің 0,01% ақаулы екені белгілі. Зауыттың 1000 өнімінің арасында орташа есеппен қанша өнім ақаулы болады?

Шахмат турниріне 14 шахматшы қатысты, олар әрқайсысымен бір партиядан ойнады. Барлығы қанша партия ойнады?

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Бөлшекті қысқартыңыз:
$\frac{\sqrt{5}+5}{4\sqrt{5}}$

Теңдеуді шешіңіз: -50a² + 5a +1 = 0

Функцияның анықталу облысын табыңыз:
$у=\sqrt{\left(10-x\right)\left(x+21\right)}$

Теңдеуді шешіңіз: x⁵+x⁴+3x³+3x²+2x+2=0

$Есептеңіз:\ \frac{\left(2^8\right)^2\cdot2^6\cdot2^2}{2^{22}}$

$Өрнекті\ ықшамдаңыз:\ \ \left(x^5-5xy^2\right)+\left(x^5-y^2x\right)$

Теңсіздікті шешіңіз:
$\frac{x-2}{4}-\frac{2x+1}{3}<3-x$