Мavzu:”Olimpiada masalalarini yecyishni o’rgatish”

Yozma ish, X sinf
I-tur I-variant

1) Quyidagini isbotlang: tg20ºtg40ºtg80º=

2) Taqqoslang:
3). Ko’paytuvchilarga ajrating:
4) To’rtburchakka aylana ichki chizilgan. To’rtburchakning ketma-ket uchta tomoni uzunliklarining nisbati 1:2:5 kabi, uning perimetri esa 60 sm ga teng. To’rtburchakning barcha tomonlarini toping.
5) Katetlari 18 sm va 24 sm bo’lgan to’g’ri burchakli uchburchak o’tkir burchaklarining bissektrisalarini toping.


X sinf, Matematika
II-tur II-variant
1) 279 ni 16 ga bo’lganda qoldiq 7 bo’ladi. Bo’linma nechaga teng ?
A) 12 B) 13 C) 11 D) 17
2) ga teskari sonni toping. A) -0,75 B) 1,5 C) D)
3) 1 soat 160 minut 5 sekund necha sekunddan iborat. A)12205 B)106005 C)13205 D) 14205
4) 3,3; x ; va -2,1 sonlarining o’rta arifmetigi 0,6 ga teng. x ni toping.
A) -0,6 B) 0,6 C) 2 D) 0,8
5) tenglamaning ildizlari manfiy bo’ladigan k ning barcha musbat qiymatlari yig’indisini toping. A) 13 B) 10 C) 8 D) 11
6) tenglamaning ildizlari bo’lib, tenglikni qanoatlantirsa, a ning qiymatini toping . A) 9 B) -1 C) 3 D) -3
7) tejngsizlikni yeching. A) [-7;5) B) ( C) (- D) (-7;5]
8) 24 ning barcha natural bo’luvchilari yig’indisini toping. A) 48 B) 60 C) 124 D) 108
9) y= funksiya grafigining Oy o’qi bilan kesishish nuqtasi ordinatasini toping.
A) -1 B) -2 C) 1 D) 0
10) Ikkita to’g’ri chiziqning kesishishidan hosil bo’lgan qo’shni burchaklarning ayirmasi 50⁰ ga
teng.Shu burchaklardan kichigini toping. A) 65⁰ B) 60⁰ C) 70⁰ D) 50⁰
11) = tenglamaning barcha natural yechimlari yig’indisini toping.
A) 1 B) 12 C) 10 D) 15
12) Yuzi 156 sm² ,balandliklari 4 sm va 12 sm bo’lgan parallelogrammning perimetrini toping.
A) 73 B) 104 C)96 D) 108
13) ni soddalashtiring. A) sin4α B) 2tg4α C) cos4α D) tg4α
14) y= funksiyaning aniqlanish sohasini toping. A) (-4;4) B) C) D)
15) 842 sonining o’ng tomoniga qanday raqam yozilsa, hosil bo’lgan son 36 ga qoldiqsiz bo’linadi?
A) 2 B) 4 C) 8 D) 6
16) y = 3x² +8x-8 funksiyaning grafigi qaysi choraklarda joylashgan?
A) Barcha choraklarda B) II, III, IV C) I,II,III D) III, IV
17) tengsizliklar sistemasining butun yechimlari yig’indisini toping
.A) 5 B) 30 C) 21 D) 20
18) log₂(4-2x)- > tengsizlikni yeching.
A) (-∞;1) B) (- ∞;0,5) C) (0; 1) D) (-4;-1)
19) funksiyaning eng katta qiymatini toping.
A) 1,5 B) C) D) 3
20) Muntazam oltiburchakka tashqi chizilgan aylananing radiusi bo’lsa ,unga ichki chizilgan aylananing radiusini toping. A) B) 1,5 C) 1,2 D)
21) M(x,y) nuqtaning koordinatalari yig’indisi 6ga teng. Bu nuqta va koordinat boshi orasidagi eng qisqa masofa qanchaga teng bo’ladi? A)2 B)3 C)4,5 D)1,5
22) To’g’ri burchakli uchburchakning katetlari 48 va 14 ga teng. Kichik katetning gipotenuzadagi proyeksiyasini toping.Javob:____________________________________

23) Yig’indisi 38 va 62 sonlarining o’rta arifmetigiga teng bo’lishi uchun 62 ning 60% olinsa, 38 ning necha foizini olish kerak?Javob:____________________________________

24) Uchburchakning burchaklari 45⁰ va 60⁰ ga,unga tashqi chizilgan aylananing radiusi R ga teng. Uchburchakning yuzini topingJavob:____________________________________

25) sin 5x tenglamaning ildizlarini ko’rsating.

Javob:_________________________________