9-sinf Matematika olimpiada №2

Avgust 19, 2024

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9-sinf Matematika olimpiada №2

2019-yil tuman bosqichida tushgan savollar

1 / 25

1. Asoslari 18 va 12 ga teng bo‘lgan teng yonli trapetsiyaning diagonallari o‘zaro perpendikulyar. Trapetsiyaning yuzini toping

A) 150

B) 400

C) 225

D) 125

2 / 25

2. Hovuzga uchta quvur o‘tkazilgan. Birinchisi hovuzni 12 soatda, ikkinchisi 8 soatda to‘ldiradi. Uchinchisi hovuzni 1 sutkada bo‘shatadi. Agar uchala quvur birgalikda ochib qo‘yilsa, bo‘sh hovuzning yarmi qancha vaqt(soat)da to‘ladi?

A) 1,5

B) 3

C) 2

D) 2,5

3 / 25

3. 60⁰ li burchakka bir-biriga tashqaridan urinuvchi ikkita aylana ichki chizilgan. Kichik aylananing radiusi ga teng. Katta aylananing radiusini toping.

A) 2r

B) 3r

C) 5r

D) 4r

4 / 25

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

A) -40

B) -5

C) -10

D) -20

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5. 20 dan 250 gacha sonlarichida 4 ga bo`linadigan, lekin 6 ga bo`linmaydigan nechta natural son bor?

A) 48

B) 33

C) 39

D) 30

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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) 145

B) 180

C) 126

D) 135

7 / 25

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

A) II

B) III

C) I

D) IV

8 / 25

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

A) 27

B) 24

C) 7

D) 20

9 / 25

9. Muntazam uchburchakning ichidagi nuqtadan tomonlarigacha bo`lgan masofalar yig`indisi 6 ga teng bo`lsa, uchburchak yuzini toping.

A) 99

B) 12√3

C) 84

D) 55

10 / 25

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

A) -4

B) 8

C) -2

D) 6

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11. Tenglamalar sistemasi nechta yechimga ega?

A) 6

B) 2

C) 4

D) 1

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

A) 4

B) 1

C) 2

D) 3

13 / 25

13. 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) 36

B) 4

C) 16

D) 64

14 / 25

14. 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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15. Agar arifmetik progressiyada bo`lsa, ayirmani toping.

A) 4

B) 2

C) 1

D) 3

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

A) a=−3

B) a = 1

C) a ≠1

D) a=2 ; a = -3

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17. 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) 4

B) 6

C) 12

D) 9

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

A) 20/69

B) 8

C) 0

D) -48

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19. f(x) funksiyani toping.

A) (1-x)/(1+x)

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

C) 1/(1-x)

D) 1/x

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20. Hisoblang: cos 10^o− 2 cos 50^o− cos 70^o

A) cos40°

B) –cos40°

C) –sin40°

D) sin40°

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21. tengsizlikni yeching.

A) (-∞;-1/2)∪(-1/2;∞)

B) (-∞;-1/2)∪(-1/2;3)∪(3;∞)

C) xℇR

D) (-∞;3)∪(3;∞)

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22. Sonlarni o`sish tartibida yozing.

A) a

B) b

C) c

D) c

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23. 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) 1

B) 2

C) 0,5

D) 3

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

A) 56

B) 55

C) 57

D) 58

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25. bo‘lsa, 4? + 3? + 2? yig‘indini toping. (Bunda, ?, ?, ?- raqamlar)

A) 12

B) 16

C) 4

D) 8

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