1-qism. Har bir topshiriq 0,9 balldan baholanadi
Ayirmasi noldan farqli bo‘lgan arifmetik progressiyaning 4-hadidan boshlab 14hadigacha bo‘lgan hadlar yig‘indisi 77 ga teng. Progressiyaning 7 ga teng bo‘lgan had
nomerini toping.
A) 8
B)9
C) 11
D) 10
x3
x2
2. Tenglamani yeching: 3  8  3  33
A) -2
B) 0
C) 1
D) -1
3. Tenglamalar sistemasi nechta yechimga ega?
(𝑥 + 1)(𝑥 − 2)(𝑥 + 6)(𝑦 − 1)(𝑦 + 9) = 0
A) 6
B) 8
C) 10 D) 12
(𝑥2 − 9)(𝑦2 − 8) = 0
4. Agar 𝑠𝑖𝑛𝑥 + 𝑐𝑜𝑠𝑥 = √0,8 bo‘lsa, (𝑠𝑖𝑛4𝑥 − 𝑐𝑜𝑠4𝑥)2 ni toping.
A) 0,8
B) 0,9
C) 0,96
D) 0,81
1.
5. Tenglama nechta yechimga ega?
(𝑥2 − 𝑥 − 6)√
𝑥2−1
=0
2𝑥
A) 2 B) 3
C) 4
D) 5
6. Agar 𝑦1 = 6𝑥 − 6 va у2//𝑦1 hamda у2 to‘g‘ri chiziq 𝐴(6; 6) nuqtadan o‘tsa, 𝑦2 ni
toping.
A) 6𝑥 − 24
B) −6𝑥 + 42
C) −6𝑥 + 6
D) 6𝑥-30
7. (𝑥2 − 4𝑥 + 3)√𝑐𝑜𝑠𝑥 = 0 tenglama nechta yechimga ega, agar 𝑥 ∈ (0; 50)?
A) 17
B) 14
C) 15
D) 16
8. 𝑚 kasr (𝑚, 𝑛 −natural sonlar)— qisqarmas kasr va 7𝑚+6𝑛 kasr esa qisqaradi. Ushbu
𝑛
3𝑚+2𝑛
kasr qanday songa qisqaradi? 𝐴)5
B)2
𝐶) 8
𝐷) 3
9. 𝑃(𝑥) = 𝑥5 − 7𝑥4 + 3𝑥3 − 𝑥 + 2 ko‘phadni 𝑥2 + 𝑥 ga bo‘lgandagi qoldiqni aniqlang.
A) 10𝑥 +2
𝐵) 8𝑥 + 2
𝐶) 6𝑥 + 2
𝐷) 4𝑥 + 2
−2021𝑥 + 2021𝑥, 𝑥 < 3
bo‘lsa, 𝑓(0) − 𝑓(5) ayirmani toping.
10. Agar 𝑓(𝑥) =
√𝑥 + 20 + 21, 𝑥 ≥ 4
𝐵) − 25
𝐶) − 24
A) -27
𝐷) − 26
2-qism. Har bir topshiriq 1,5 balldan baholanadi
11. 𝐴𝐵𝐶 uchburchakning 𝐴𝐶 tomonida 𝐷 nuqta olingan, bunda ∠𝐴𝐵𝐶 = ∠𝐵𝐷𝐶. Agar
𝐴𝐷 = 10, 𝐶𝐷 = 8 bo‘lsa, 𝐵𝐶 ni toping. A) 9 B) 15
C) 10
D) 12
2022
2021
12. 10
−2
ayirmani 24 ga bo‘lgandagi qoldiqni toping. 𝐴)8 𝐵) 16 𝐶) 12 𝐷) 0
D) 2 cos2 9
13. Soddalashtiring: (4 cos2 9  3)(4 cos2 27  3)  ctg9. A) tg9 B) 1 C) sin18
14. ABCD to‘rtburchakda АВ = CD = 9 va bu to‘rtburchakka radiusi 4 ga teng aylana ichki
chizilgan. ABCD to‘rtburchak yuzini toping. A) 36
B) 72
C) 144
D) 81
1
5 1∙3
.
15. 1
+
A) 25
1
+ ⋯+
3∙5
B) 12
1
(2𝑛−1)(2𝑛+1)
C) 37
= 0,48 bo‘lsa 𝑛 ning qiymatini toping.
D) 40
16. (𝑥2 − 2𝑥 + 3)(𝑦2 + 6𝑦 + 12) = 6 bo‘lsa, 𝑥 + 𝑦 ni toping.
A) 2
B) −2
C) 3
D) −3
17.ABC – gipotenuzasi AB bo‘lgan to‘g‘ri burchakli uchburchak. Gipotenuzaning ikki
tomon davomida AB to‘g‘ri chiziqda AK = AC va BM = BC shartlar bilan kesmalar
ajratilgan. KCM burchakni toping.
A) 90°
B) 120°
C) 135°
D) 150°
x2 + 2y2 − 2yz = 100
18.Agar
bo‘lsa, |𝑥𝑦𝑧| ni toping.
2xy − z2 = 100
A) 1000
B) 100
C) 500
D) 800
19.Agar cos ∠A = 1 va sin∠B = 1 bo‘lsa, АВС uchburchakning mos ravishda А va В
5
2
uchlaridan tushirilgan balandliklar nisbatini toping.
2
5√2
5 √6
5√3
A)5 B) 24
C)
D)
24
12
20.АВС uchburchakning АС tomonida М nuqta shunday olinganki, bunda ∠ABM = 45°
va ∠CBM = 30°. Agar АВ =4 va ВС = 5 bo‘lsa, МA : МС ni toping.
A)
𝟒√𝟐
B)
2√2
C)
5
𝟓
4√3
D)
5
2√3
5
3-qism. Har bir topshiriq 2,6 balldan baholanadi
21.𝑥2 + |𝑥 − 3| ≤ |𝑥2 + 𝑥| − 3 tengsizlikni yeching.
22.𝑓(𝑥 − 1) = 2𝑔(5𝑥 + 4) va 𝑔(2𝑥 − 1) = 4𝑥 + 4 bo‘lsa, 𝑓(𝑥) ni toping
1
23.

sin 45sin 46

1
1
1

 ... 
sin 47sin 48
sin133sin134 sin n

tenglikni qanoatlantiradigan
𝑛 ning eng kichik qiymatini toping.
24. 𝑎, 𝑏, 𝑐 − 𝐴𝐵𝐶 uchburchakning tomonlari.
Agar 𝑎4 + 𝑏4 + 𝑐4 + 32 = 2(𝑎2𝑏2 + 𝑏2𝑐2 + 𝑐2𝑎2) bo‘lsa, 𝐴𝐵𝐶 uchburchak yuzini
toping
25. Uchburchak tomonlarining uzunliklari berilgan tenglamaning ildizlariga mos keladi.
𝑥3 − 24𝑥2 + 183𝑥 − 440 = 0. Uchburchakning yuzini hisoblang.
26. Qavariq to‘rtburchakning diagonallari 3 va 4 ga teng. Agar qarama qarshi
tomonlarining o‘rtalarini tutashtirishdan hosil bo‘lgan kesmalar uzunliklari o‘zaro teng
bo‘lsa, qavariq to‘rtburchakning yuzini toping.
27.Agar 𝑦 > 0, 𝑥 + 𝑦2 = 7,25; 𝑦2 − 𝑧 = 2 va 𝑦2 = √𝑥 − 1 ∙ √2 − 𝑧 bo‘lsa,
𝑦(√𝑥 − 1 + √2 − 𝑧) ning qiymatini toping.
28.Agar 𝑥, 𝑦 ∈ (0; 𝜋2 ) va 𝑐𝑜𝑠2(𝑥 − 𝑦) = 𝑠𝑖𝑛2𝑥 ∙ 𝑠𝑖𝑛2𝑦 bo‘lsa, 𝑥 + 𝑦 ni toping.
29.ABCD to‘rtburchakda А va В burchaklar- to‘g‘ri, tg∠D = 3 va
4
ВС =
𝐴𝐷
2
= АВ + 2 bo‘lsa, АС ni toping.
30. 𝑥, 𝑦 sonlari (𝑥2 + 1)(𝑦2 + 1) + 2(𝑥 − 𝑦)(1 − 𝑥𝑦) = 4(1 + 𝑥𝑦) tenglikni qanoatlantiradi
|1 + 𝑥| ∙ |1 − 𝑦| ni toping.