Yechim va ko‘rsatmalar

Yechim va ko‘rsatmalar
9- sinf uchun test
1. (m-n)²∙(n²-m)=4m²n tenglama nechta butun (n;m) yechimlarga ega?
+A. 3 ta B) 2 ta C) 5 taD) 4 ta

2. Ushbu (a-2)! + 2b!=22c-1 tenglikni qanoatlantiruvchi a, b, c, tub sonlar yig’indisini toping.

+A) 18 yoki 19 B) 14 yoki 15 C) 18 yoki 15 D) 14 yoki 23

3. Aytaylik ABC uchburchakda A=70º va bu uchburchakka ichki chizilgan aylana markazi O nuqta bo’lsin. Agar AC+AO=BC bo’lsa, u holda ni toping.

+A) 35º B) 45º C) 14º D) 28º

4. Agar f(x)=x²+14x+42 bo‘lsa, f(f(f(f(x)))))=0 tenglamani yeching.

A) ildizi yo‘q +B) ± –7 C) ± +7
D) ± +7

5. Agar arifmetik progressiyaning dastlabki n hadi yig‘indisi 2n²-3n ga teng bo’lsa, uning n-hadi formulasini toping.

+A) a_n=-5+4n B) a_n=5+5n C) a_n=5-4n D) a_n=-5-5n

6. Tenglamalar sistemasining bir vaqtda x>0 va y>0 bo’ladigan yechimlaridan x+y yig’indini toping.

+A) 118 B) 4 C) 14 D) 105

7. 1+2∙3+3∙3²+... + 2010∙3²⁰⁰⁹+ 2011∙3²⁰¹⁰+ 2012∙3²⁰¹¹ yig‘indini hisoblang.

A) 1006∙3²⁰¹²- 1 +B) (4023∙3²⁰¹² +1) C) (1006∙3²⁰¹²+1) D) 2012.

8. Agar ABC uchburchakda A burchagi 120⁰ bo‘lsa, cos3A+cos 3B+cos3C ni toping.

A)0; +B) 1; C) D)
9. AC va BD diagonallari o‘zaro perpendikulyar bo‘lgan ABCD to‘rtburchakka radiusi 2 ga teng bo‘lgan aylana tashqi chizilgan. Agar AB = 3 bo‘lsa, CD ni toping.
A) +B) C) D)
10. ABC uchburchakda AC tomonga tushirilgan balandligi 2 ga AB tomoni 5 ga, ABC uchburchakka tashqi chizilgan aylana radiusi 5 ga teng bo‘lsa, BC tomonining uzunligini toping.
A) 2 B)5 +C) 4 D)
11. Agar birinchi chorakdagi α, β va γ burchaklar ayirmasi bo‘lgan arifmetik progressiya tashkil qilishi, ularning tangenslari esa geometrik progressiya tashkil qilishi ma’lum bo‘lsa, ularnining yig‘indisini toping.
A) B) +C) D) .
12. x²-6px+q=0 kvadrat tenglama har xil x₁ va x₂ ildizlarga ega agar p, x₁, x₂, q sonlar biror geometrik progressiyaning ketma-ket to‘rtta hadi bo‘lsa, u holda barcha ildizlar ko‘paytmasini toping.
A) 54 +B) -256 C) -72 D) 108.
13. Cheksiz kamayuvchi geometrik progressiyaning yig‘indisi bo‘lib, uning qaysidir hadi ga teng. Agar shu haddan oldingi barcha hadlar yig‘indisining undan keyingi hadlar yig‘indisiga nisbati 30 bo‘lsa, u holda o‘sha hadning nomeri n ni toping.
A) 6 B) 8 C) 4 +D) 5.
14. Bo’luvchilari orasida ixtiyoriy raqam bilan tugaydigani (0 dan 9 gacha) albatta bor bo‘lgan eng kichik natural sonni toping.
A) 729 +B) 270 C) 360 D) 810

15. BD ABC uchburchakning medianasi, BC=14 hamda ∠ABD=45º va ∠ABD=30º bo’lsa, BD medianani toping.

A) B) 5
+C) D) .
9-sinf yozma ish