🏆 Matematika bo‘yicha Online Olimpiada (6–8-sinf)

1
Agar \( x + \frac{1}{x} = 3 \) bo'lsa, \( x^2 + \frac{1}{x^2} \) ning qiymatini toping.
- A. 8
- B. 5
- C. 6
- D. 7
2
To'g'ri to'rtburchakning bo'yi enidan 4 sm uzun. Agar perimetri 32 sm bo'lsa, uning yuzini toping.
- A. 64 sm²
- B. 60 sm²
- C. 72 sm²
- D. 48 sm²
3
Agar \( \frac{a}{b} = \frac{2}{3} \) va \( \frac{b}{c} = \frac{4}{5} \) bo'lsa, \( \frac{a}{c} \) ning qiymatini toping.
- A. \frac{3}{5}
- B. \frac{5}{8}
- C. \frac{8}{15}
- D. \frac{2}{5}
4
Tenglamani yeching: \( 2x - 5 = 3x + 7 \).
- A. 12
- B. 2
- C. -2
- D. -12
5
Agar uchburchakning burchaklari nisbati 2:3:4 bo'lsa, eng kichik burchagini toping.
- A. 50°
- B. 40°
- C. 30°
- D. 60°
6
Agar \( 3^{x} = 27 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 2
- B. 4
- C. 5
- D. 3
7
Kvadratning perimetri 24 sm bo'lsa, uning diagonalini toping.
- A. 10\sqrt{2} sm
- B. 8\sqrt{2} sm
- C. 6\sqrt{2} sm
- D. 12\sqrt{2} sm
8
Agar \( y = 2x + 3 \) va \( y = 5x - 1 \) bo'lsa, \( x \) va \( y \) ni toping.
- A. x=1, y=5
- B. x=4, y=11
- C. x=3, y=9
- D. x=2, y=7
9
Agar sonning 40% 24 ga teng bo'lsa, bu sonni toping.
- A. 50
- B. 80
- C. 60
- D. 70
10
Agar \( \sqrt{x+5} = 3 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 5
- B. 3
- C. 4
- D. 2
11
To'g'ri burchakli uchburchakning katetlari 6 sm va 8 sm bo'lsa, gipotenuzasini toping.
- A. 10 sm
- B. 14 sm
- C. 12 sm
- D. 16 sm
12
Agar \( a + b = 10 \) va \( a - b = 4 \) bo'lsa, \( a \) va \( b \) ni toping.
- A. a=5, b=5
- B. a=8, b=2
- C. a=7, b=3
- D. a=6, b=4
13
Agar kubning hajmi 64 sm³ bo'lsa, uning to'la sirtini toping.
- A. 128 sm²
- B. 192 sm²
- C. 96 sm²
- D. 64 sm²
14
Agar \( \frac{2x-1}{3} = 5 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 8
- B. 7
- C. 9
- D. 10
15
Agar doiraning radiusi 7 sm bo'lsa, uning yuzini toping (\( \pi \approx 3.14 \)).
- A. 153.86 sm²
- B. 149.86 sm²
- C. 154.00 sm²
- D. 150.72 sm²
16
Agar \( 5^{x} = 125 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 3
- B. 5
- C. 4
- D. 2
17
Agar uchburchakning asosi 10 sm va balandligi 6 sm bo'lsa, uning yuzini toping.
- A. 60 sm²
- B. 30 sm²
- C. 50 sm²
- D. 40 sm²
18
Agar \( x^2 - 5x + 6 = 0 \) bo'lsa, tenglamaning ildizlarini toping.
- A. 2 va 4
- B. 3 va 4
- C. 2 va 3
- D. 1 va 6
19
Agar sonning 25% 15 ga teng bo'lsa, bu sonni toping.
- A. 80
- B. 50
- C. 60
- D. 70
20
Agar \( \frac{x}{2} + 3 = 7 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 6
- B. 12
- C. 10
- D. 8
21
Agar kvadratning yuzi 49 sm² bo'lsa, uning perimetrini toping.
- A. 36 sm
- B. 28 sm
- C. 32 sm
- D. 40 sm
22
Agar \( 2^{x} = 16 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 4
- B. 5
- C. 6
- D. 3
23
Agar to'g'ri to'rtburchakning bo'yi 12 sm va eni 5 sm bo'lsa, uning diagonalini toping.
- A. 15 sm
- B. 14 sm
- C. 16 sm
- D. 13 sm
24
Agar \( 3x + 4 = 19 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 5
- B. 4
- C. 6
- D. 7
25
Agar uchburchakning ikki burchagi 50° va 60° bo'lsa, uchinchi burchagini toping.
- A. 60°
- B. 70°
- C. 80°
- D. 90°
26
Agar \( \sqrt{9x} = 6 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 3
- B. 2
- C. 5
- D. 4
27
Agar kubning qirrasi 4 sm bo'lsa, uning hajmini toping.
- A. 16 sm³
- B. 48 sm³
- C. 64 sm³
- D. 32 sm³
28
Agar \( x + y = 15 \) va \( x - y = 5 \) bo'lsa, \( x \) va \( y \) ni toping.
- A. x=7, y=8
- B. x=8, y=7
- C. x=10, y=5
- D. x=9, y=6
29
Agar doiraning diametri 10 sm bo'lsa, uning uzunligini toping (\( \pi \approx 3.14 \)).
- A. 30.0 sm
- B. 31.4 sm
- C. 31.8 sm
- D. 32.0 sm
30
Agar \( 4^{x} = 64 \) bo'lsa, \( x \) ning qiymatini toping.
- A. 5
- B. 4
- C. 3
- D. 2