9-sinf Matematika olimpiada №2

Avgust 19, 2024

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9-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

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1. 60⁰ li burchakka bir-biriga tashqaridan urinuvchi ikkita aylana ichki chizilgan. Kichik aylananing radiusi ga teng. Katta aylananing radiusini toping.

A) 2r

B) 5r

C) 3r

D) 4r

2 / 25

2. Parallellogrammning 5 ga teng bo‘lgan diagonali uning 12 ga teng bo‘lgan tomoniga perpendikulyar. Parallelogrammning perimetrini toping.

A) 48

B) 34

C) 50

D) 44

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3. Geometrik progressiyada dastlabki to‘rtta hadlari mos ravishda 6; 24; 96; bo‘lsa, ni toping.

A) 14

B) 16

C) 15

D) 22

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4. Agar sin x + cos x = 1,04 tenglik o’rinli bo’lsa, x qaysi chorakda joylashgan?

A) II

B) III

C) I

D) IV

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5. Agar f(x) = (a + b − 4)x³+ 2x²+ (b − 3)x +6 juftfunksiyaberilganbo’lsa, f(b) ningqiymatini toping.

A) 20

B) 27

C) 24

D) 7

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6. Bahodir o`zidagi 411 dona yong`oqni 4 ta bolaga bo`lib berdi. Agar Sanjar va O`ktamning olgan yong`oqlari soni 2 va 3 sonlariga to`g`ri proporsional ,O`ktam va Sohibning yong`oqlari 7 va 5 sonlariga teskari proporsional , Sanjar va G`anisherning yong`oqlari esa 9 va 4 sonlariga teskari proporsional ekanligi ma`lum bo`lsa, G`anisher nechta yong`oq olgan?

A) 135

B) 145

C) 180

D) 126

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7. tengsizlikni yeching.

A) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

B) (-∞;3)∪(3;∞)

C) xℇR

D) (-∞;-1/2)∪(-1/2;∞)

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8. Tenglamalar sistemasi nechta yechimga ega?

A) 4

B) 2

C) 6

D) 1

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9. Birinchi quvurdan ikkinchi quvurga qaraganda ikki barobar ko’p suv oqadi.Ikkalasi birgalikda bo’sh hovuzni 12 soatda to’ldiradi.Birinchi quvur hovuzning uchdan bir qismini necha soatda to’ldiradi?

A) 9

B) 6

C) 4

D) 12

10 / 25

10. ABC uchburchakda O nuqta AD medianava BE bissektrisalar kesishishnuqtasi. AOEva BOD uchburchaklar yuzlari mos ravishda 1 va 3 ga teng bo`lsa, EOC uchburchakning yuzini toping.

A) 4

B) 2

C) 3

D) 5

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11. Sonlarni o`sish tartibida yozing.

A) a

B) c

C) c

D) b

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12. Funksiya berilgan. f(f(−1)) ni toping.

A) 29

B) 18

C) 15

D) 5

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13. Agar bo’lsa , x va y sonlarning ko’paytmasini toping.

A) -4

B) 6

C) 8

D) -2

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14. ABCD parallelogramda AB=10, AD=16. BC tomonga AE va DF bissektrisalar o`tkazilganbo`lib, ular G nuqtada kesishadi. E va F nuqtalar BC tomonda bo`lsa, AGD va FGE uchgburchaklar yuzalari nisbatini toping.

A) 16

B) 4

C) 64

D) 36

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15. Agar x²−8x+20z+4z²+41=0 tenglik o`rinli bo`lsa, xz ni toping.

A) -10

B) -40

C) -20

D) -5

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16. ABC uchburchakning AB tomonidan M va N nuqtalar shunday tanlab olinganki, BN=NM=MA. AC tomonidan K va L nuqtalar shunday tanlab olindiki AK=3KL=1,5LC bo'ldi. S_MNLK: S_MNLK=?

A) 3

B) 2

C) 1

D) 0,5

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17. x₀soni tenglamani ildizi bo`lsa, x²₀ -64 ni toping.

A) 8

B) 0

C) 20/69

D) -48

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18. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 39

B) 48

C) 33

D) 30

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19. f(x) funksiyani toping.

A) 1/x

B) (1+x)/(1-x)

C) 1/(1-x)

D) (1-x)/(1+x)

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20. ax²+bc+c=0 kvadrat tenglama bitta manfiy, bitta musbat ildizga ega bo`lsa, quyidagilardan qaysibiri to`g`ri?(D=b²−4ac)

A) 3

B) 2

C) 4

D) 1

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21. Agar cheksiz kamayuvchi geometrik progressiyaning hadlari yig`indisi ga teng bo`lsa, uning hadlari kublari yig`indisining hadlari kvadratlari yig`indisiga nisbatini toping.

A) 1

B) 4

C) 2

D) 3

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22. ABCD trapetsiyaning yuzi 36 gateng, asoslari DC=6, AB=2. BC tomonidan E nuqta olingan bo’lib, BE=2EC bo’lsa, ADE uchbutchakning yuzini toping.

A) 21

B) 14

C) 16

D) 12

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23. (a²- 9)x = a²+ 2a - 3 tenglama a ningqandayqiymatidacheksizko’pyechimgaega?

A) a ≠1

B) a = 1

C) a=2 ; a = -3

D) a=−3

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24. Kataklarning chiziqlari bo’yicha A dan B ga olib boruvchi eng qisqa yo’llar soni nechta?

A) 58

B) 56

C) 55

D) 57

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25. To’rt xonali son “yoqimli” deyiladi, agar sonning o‘zi 25 ga bo‘linsa, uning raqamlari yig‘indisi 25 ga bo‘linsa va uning raqamlari ko‘paytmasi 25 ga bo‘linsa. Barcha “yoqimli” sonlarning yig‘indisini toping.

A) 14450

B) 13450

C) 450

D) 14455

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