9-sinf o’quvchilari uchun matematikadan masala va misollar

317) burchakni gradus o`lchovida ifodalang.

318) ni hisoblang

319) 3cos2x +sin²x+5 sinx cosx = 0 tenglamani yeching.

320) tenglama ildizlarining o`rta arifmetik qiymatini toping.

321) 9^x+1=3^x+1+3^x-1 va 2^2x+1=2,5*2^x tenglamalar teng kuchlimi?

322) Ifodani soddalashtiring

323) 4^x-5*2^x+6=0 tenglama katta ildizning kichik ildiziga nisbatini ko`rsating

324) arcsin x = bo`lsa, arcos x ni toping

325) log₃(x+1) + log₃(x+3) = 1 Tenglamani yeching

326) Agar bo’lsa , , ni hisoblang.

327) Muntazam oltiburchakka tashqi chizilgan aylananing radiusi 12ga teng bo’lsa, oltiburchakning kichik diagonalini toping.

328) АВС uchburchakda ga teng. A uchidan tushirilgan balandlik uzunligini toping.

329) Bir nuqtadan tekislikka 4 va 8 uzunlikdagi og’malar o’tkazilgan. Agar ularning proyeksiyalari nisbatlari 1:7 bo’lsa, nuqtaning tekislikkacha masofasi qanchaga teng bo’ladi?

330) Aylanaga tashki chizilgan teng yonli trapetsiyanig asoslari 54 va 24 ga teng. Aylananing radiusini toping.

331) Kesma uchlarining koordinatalari A (1;-2,4) va B (3;-4,2). Kesma o’rtasining koordinatasini toping.

332). у = 0,5 х + 6 chiziqli funksiya berilgan. Agar х = -1,5 bo’lsa y ning qiymatini toping.

333). у = -3 х + 1,5 chiziqli funksiya berilgan. Agar у = -7,5 bo’lsa x ning qiymatini toping

334). Tenglamalar sistemasini yeching:

335). х+у ning yigindisini toping, agar bir juft son (х; у) tenglamalar sistemasining yechimi bo’lsa

336). Tengsizlikni hadma-had qo’shing: 6 > -1 и 3 > 2

337). Tengsizliklarni ko’paytiring: и

338). Tengsizlikni yeching: 12 + 6x 27 + x.

339). Tengsizlikni yeching: 12(3x –1) – 18(2x + 2) > 2

340). Tengsizliklar sistemasini yeching:

341). Ildizni qiymatini toping.

342). Ifodani soddalashtiring:

343). Tenglamani yeching: 5x²–13x + 6 = 0

344). Tenglamani ildizini toping: 8x(1 + 2x) = - 1.

345). Ildizlari -8 va -2. ga teng bo’lgan kvadrat tenglama tuzing.

346). Ko’paytuvchilarga ajrating: х³ –3х²+ 2х.

347). Tenglamalar sistemasini yeching:

348). Bikvadrat tenglamani yeching: х⁴ –13х² + 36 = 0.

349). To’g’ri to’rtburchakning tomonlari 25 sm va 60 sm. Uning diagonalini toping.

350). Uchburchakning uchta tomoniga 4, 13,15 ko’ra uchburchakning yuzini toping .

351). Doiraga ichki chizilgan АВС burchak 70^о ga teng. AB yoyning qiymatini toping, agar ВC yoy 130^о ga teng bo’lsa.

352). АС va BД vatarlar kesishadi. САД burchakni toping, АВД burchak 40^о ga , АДС burchak 70^о ga teng bo’lsa.

353). To’g’ri burchakli uchburchakning katetlari 5 sm va 12 sm. Uchburchakka ichki chizilgan aylanani radiusini toping.

354). To’g’ri burchakli uchburchakning kateti 7 sm va gipotenuzasi 25 sm, tashqi chizilgan doiraning radiusini toping.

355). Vektor m(-2;1), vektor n(-3; -4) berilgan. а·b ko’paytmasini toping..

356).Vektor а(-1; -2), vector b(2;5) berilgan. 3а + b vektorning koordinatalarini toping.

357). y=x² parabolaning y=2x to’g’ri chiziq bilan kesishish nuqtasining koordinatalarini toping.

358). y=x²-3x+2 funksiyaning OX o’qi bilan kesishish nuqtalarining koordinatalarini toping .

359). x²- 16< 0 tengsizlikni yeching

360). Ifodani soddalashtiring: ;

361). Hisoblang: .

362). Funksiyaning aniqlanish sohasini toping :

363). Funksiyalarning qaysilari juft funksiyalar?

1). 2) 3) 4)

364). 2 π/ 3 radianli burchakni gradusda ifodalang.

365). Ko’paytmaning qaysi biri musbat?

A) sin2cos2sin1sin1⁰ B) tg8⁰ctg8ctg10⁰ C) sin9⁰sin9cos9⁰cos9

D) cos10⁰cos10 cos11⁰cos√11 E) tg7,5⁰tg7,5ctg3⁰ctg3

366).cosα=0,6 bo’lsa, sinα ni toping 0< α< π/2

367). Hisoblang : .

368). Soddalashtiring:

369). Arifmetik progressiyada bo’lsa, uning dastlabki 50 ta hadi yig’indisini toping.

370). Arifmetik progressiyada d=-3 va bo’lsa, uning birinchi hadini toping.

371). Geometrik progressiyada bo’lsa, progressiyaning hadlari soni n ni toping.

372). Agar geometrik progressiyada =9 va b₆=20 bo’lsa , uning 5-hadini toping.

373). -25; -5; -1 cheksiz kamayuvchi geometrik progressiya yig’indisini toping.

374). O’xshash uchburchaklarning perimetrlari nisbati nimaga teng?

375). Ikkita o’xshash ko’pburchak uchun noto’g’ri tasdiqni toping:

A) Perimetrlari nisbati tomonlar nisbatiga teng; B) Yuzlarini nisbati tomonlar nisbatining kvadratiga teng; D) Ularning burchaklari soni teng; E) Perimetrlari nisbati o’xshashlik koeffitsentining kvadratiga teng.

376). Cos 60⁰ nimaga teng?

377). AgarAB=6cm, AC= 4cm, 0 bo’lsa, ABC uchburchak yuzini toping. 378). Aylanaga ichki chizilgan muntazam ko’pburchakning bir tomoni aylanadan 18⁰ ga teng yoy ajratadi. Ko’pburchakning nechta tomoni bor?

379).Tomoni 7sm bo’lgan kvadratga tashqi chizilgan aylananing radiusini toping.

380). Uzunliklari 2sm va 8 sm bo’lgan kesmalarning o’rta proporsionali nimaga teng?

381). Yarim aylanadagi C nuqtadan AB diametrga tushirilgan CD perpendikulyar AB kesmada 6 va 24 ga teng kesmalar ajratadi. CD kesmani toping.

382). Parabola uchining kordinatalarini toping: y=(x-2)²-4.

383). y=2x² funksiyaning o’sish oralig’ini ko’rsating.

384). tengsizlikning butun yechimlari yig’indisini toping

385). Hisoblang:

386). Soddalashtiring: 13*2³-9*2³+2³

387). Funksiyaning aniqlanish sohasini toping: y=

388). Funksiyalarning qaysilari toq funksiya?

1) y=6x 2) 3) y=4x+7 4) y=2x²-10.

389). 45⁰ li burchakning radian o‘lchovini toping.

390). Ko‘paytmaning qaysi biri manfiy?

A) cos314^osin147^o B) tg200^octg201^o C) cos215^o cos295^o D) sin170^octg250^o E) cos215^otg315^o

391). Soddalashtiring: .

392). bo‘lsa, ni toping.

393). Agar va bo‘lsa, ni toping.

394). 7, 9, 11, … , - arifmetik progressiyaning 12- hadini toping.

395). Agar arifmetik progressiyada , n=8 bo‘lsa, uning dastlabki 10 ta hadining yig‘indisini toping.

396). Geometrik progressiyada bo‘lsa, uning mahrajini toping.

397). Agar geometrik progressiyada , q=2 bo‘lsa 6-hadini toping.

398).Cheksiz kamayuvchi geometrik progressiyada , bo‘lsa,progressiyaning yig’indisini toping.

399). Ikkita o’xshash uchburchak yuzlarining nisbati nimaga teng?

400). Ikkita o’xshash ko’pburchak uchun noto’g’ri tasdiqni toping:

A) Ularning tomonlari soni teng; B) Ularning burchaklari soni teng;

C) Perimetrlari nisbati o’xshashlik D) Mos tomonlari proportsional

koeffitsentlariga teng

E) Yuzlarining nisbati o’xshashlik koeffitsentlariga teng.

401). tgα=√3 bo’lgan α o’tkir burchakni ko’rsating

402). To’g’ri burchakli uchburchakning bir burchagi 30⁰ga, shu burchak qarshisidagi katet 2√3 ga teng. Uning gipotenuzasini toping.

403). Istalgan muntazam ko’pburchak uchun noto’g’ri tasdiqni toping

A) Ichki aylana chizish mumkin; B) Diagonallari teng;

C) Tashqi аylana chizish mumkin; D) Tomonlari teng;

E) Burchaklari teng.

404).Radiusi 5sm bo’lgan aylanaga ichki chizilgan muntazam oltiburchakning perimetrini toping.

405).Uzunliklari 4 va 16 bo’lgan kesmalarning o’rta proporsionali nimaga teng?

406). Yarim aylanadagi C nuqtadan AB diametrga tushirilgan CD perpendikulyar AB kesmada 4 va 9 ga teng kesmalar ajratadi. CD kesmani toping.

407). ning shundaz qiymatini topingki, ² parabola bilan y=5x+1 to`g`ri chiziqning kesishish nuqtalaridan birining absissasi x=1bo`lsin .

408). ning shundaz qiymatini topingki, ² parabola bilan y=2x+b to`g`ri chiziqning kesishish nuqtalaridan birining absissasi x=1bo`lsin .

409). k ning shundaz qiymatini topingki, ² parabola bilan y=kx-6 to`g`ri chiziqning kesishish nuqtalaridan birining absissasi x=2bo`lsin .

410).. y=x²-2x+4 Parabolaning koordinata o`qlari bilan kesishgan nuqtalarining koordinatalarini toping.

411).y=-x²-4x-5 Parabolaning koordinata o`qlari bilan kesishgan nuqtalarining koordinatalarini toping.

412).y=6x²-5x+1 Parabolaning koordinata o`qlari bilan kesishgan nuqtalarining koordinatalarini toping.

413).y=-x²+6x+7 Parabolaning kordinata o`qlari bilan kesishgan nuqtalarining koordinatalarini toping.

414).y=x²-4x.Parabola uchining koordinatalarini toping.

415).y= +2x. Parabola uchining koordinatalarini toping.

416).y= x²+6x+5.Parabola uchining koordinatalarini toping.

417).Tengsizlikni yeching

2 x²-8 0

418).-3 x²+27 0 Tengsizlikni yeching.

419).3x²-9 0 Tengsizlikni yeching

420). ­­­­­ x²+7x 0 Tengsizlikni yeching

421). x²+3x 0 Tengsizlikni yeching

422).Ikkita o`xshash uchburchak uchun noto`g`ri tasdiqni toping?

a)yuzlari nisbati o`xshashlik koefisentiga teng

b)Mos medianalar nisbati o`xshashlik koefisentiga teng

c)mos bissektrisalar nisbati oxshashlik koefisentiga teng

d)mos balandliklar nisbati o`xshashlik koefisentiga teng

423).Ikkita geometrik ko`pburchak uchun to`gri tasdiqni toping

a)Ular teng

b)ular o`xshash

c) Ular teng dosh

d)yo`q

424).Uchburchak medianalari uchun noto`g`ri tasdiqni ko`rsating?

a)bir nuqtadan kesishadi

b)Kesishish nuqtasida 2/1 nisbatda bo`linadi.

c)o`zi tushgan tomoni qolgan 2 tomonga proporsianal kesma ajratadi

d)har bir uchburchakning tengdosh qismlarga ajratadi

425).Uchburchak bissektrisalari uchun to`gri tasdiq?

a)1 nuqtada kesishadi

b)kesishish nuqtasida 2:1 nisbatda bo`ladi

d)O`zi tushgan tomoni qolgan 2tomonga proporsianal kesma ajratadi

e)O`zi chiqqan uchdagi burchak teng 2 ga bo`linadi

426). Ikkita o`xshash ,ko`p burchak uchun noto`g`ri tasdiqni toping?

a)uni tomonlari soni teng?

b)ularni burchaklari soni teng

d)proporsianal

e)yuzalari nsbati o`xshashlik kofissentiga teng

427) 2 ta o`xshash ko`pburchak uchun to`g`ri tasdiq?

a)perimetrlar nisbati tomonlari nisbatiga teng

b)yuzlar nisbati tomonlar nisbatiga teng

d)yuzlar nisbati o`xshashlik koffisentiga teng

e)perimetrlar nisbati o`xshashlik kofiissenti kvadratiga teng

428).tomonlari a,b,c mos burchaklari α β yuzi S bo`lgan 3 burchak uchun qaysi fo`rmula noto`g`ri

a)a²=b²+c²-2bc cos ; B. /sin=b/ =c/sin/ ;

b)S=1/2 absin ;

d)S=1/2absin

e)S=1/2bcsin

429).Noto`g`ri fo`rmulani top?

a)sin² +cos² =1

b)sin(180^o- )=sin

d)cos(180^o- )=cos

e)sin(90^o- )=cos

f)cos(90^o- )=sin

430).Uchburchakning uchta tomoni ma`lum bo`lsa qaysi teoremadan foydalanib uning burchaklarini topamiz

431).(x+3)(x-4)>0 Tengsizlikni yeching

432).(x-1)(x+7)<0 Tengsizlikni yeching

433).6 x²+5x-6>0 Tengsizlikni yeching

434). -4x²+8x-3>0 Tengsizlikni yeching

435). Tengsizlikni yeching

436).Hisoblang:(-8)²-(-5)³-(12)^-1.

437).Hisoblang: (-0.2)^-3+(0.2)^-2-(-2)^-2.

438).Hisoblang: 439).Hisoblang:

440).Hisoblang:

441).Hisoblang:

442). Hisoblang: .

443). Hisoblang. .

444). Hisoblang. .

445). Hisoblang. .

446).To`g`ri javobni aniqlang .Istalgan aylana uzunligini shu aylana diametriga nisbati

a) aylanaga bog`liq

b) radiusga proporsianal

d) ga teng

e) radiusning kvadratiga proporsianal

447).Noto`g`risini toping. Istalgan doira yuzining uning radiusga nisbat

a) radiusga teng

b) radiusga proporsianal

d) diametrga proporsianal

e) o`zgarmas son

448).Istalgan muntazam ko`pburchak uchun noto`g`ri tasdiqni toping.

a) Ichki aylana chizish mumkin

b) diaganallari teng

d) tomonlaari teng

e) burchaklari teng

449). Noto`g`ri tasdiqni toping.

a) aylana yoyining uzunligi uning radius o`lchoviga proprsianal

b) doira sektorining yuzi sektorning gradus o`lchoviga proporsianal

d) doira yuzi radiusining kvadratiga proporsianal

e) segmentning yuzi uning yoyiga proporsianal

450). To`g`ri javobni toping. Doiraning vektori uni

a) 2ta segmentga

b) 2ta sektorga

d) 2ta yoyga

e) tengdosh sektorga

451).To`g`ri burchak uchburchakning gipotenuzasiga tushirilgan balandlik haqida noto`g`ri tasdiqni topìng.

a) katetlardan kichik

b) uchburchakni 2ta o`xshash uchburchaklarga ajratadi

d) katetlar gipotenuzasiga proyeksiyalari orasida o`rta proporsianal

e) gipotenuza yarmiga teng.

452).AB va CD vatarlar O nuqtada kesishadi.Noto`g`ri tasdiqni toping?

a) DAB= DCB

b) AOD va COB 3burchaklar o`xshash

d) AO.OB=CO.OD

e) AO=CO

453).To`g`ri tasdiqni toping.

a) teng kesmalar proyeksiyalari ham teng.

b) katta kesma proyeksiyasi ham teng

d) bir to`g`ri chiziqdagi teng kesmalarning proyeksiyasi teng

e) proyeksiya uzunligi proyeksiyalanuvchi kesma uzunligiga teng emas

454).To`g`ri burchakli uchburchakning gipotenuzasiga tushirilgan balandlik uni 2ta uchburchakka bo`ladi. Bu uchburchaklar

a) teng

b) tengdosh

d) o`xshash

e) teng yonli

455).Funksiyaning aniqlanish sohasini toping. y=

456). Funksiyaning aniqlanish sohasini toping. y= .

457). Funksiyaning aniqlanish sohasini toping y= .

458).Quyidagi funksiyalarning qaysilari o`suvchi.?

1)y=-x ; 2)y=-2/3 ; 3)y= ; 4)y= .

459). Quyidagi funksiyalarning qaysilari o`suvchi.?

1)y= ; 2) y= ; 3)y=-2x+7; 4) y=- .

460). Quyidagi funksiyalarning qaysilari pasayuvchi.?

1)y=-1/x ; 2)y=-3x+4; 3)y=x -27; 4)y= .

461). Quyidagi funksiyalarning qaysilari pasayuvchi.?

1)y= 2)y= 3)y= 4)y= ;

462).Funksiyalarning qaysilari juft funksiya.?

1)y=x+1/x 2)y=x + 3)y=-3+5/x 4)y=x -3/x.

463). Funksiyalarning qaysilari juft funksiya.?

1)y=3x -7x +5x +9. 2)y=(x+1)

3)y=1+4x 4)y= .

464). Funksiyalarning qaysilari toq funksiya.?

1)y=6x 2)y= 3) y=4x+7 4)y=2x -10.

465).153 ning radian o`lchovini toping.

466).0,65 ning gradus o`lchovini toping.

467).Kordinatalarining qaysi biri manfiy?

A)cos 314 sin 147 B)tg 200 C)cos 163 cos295 D)sin 170 E)cos 215 tg 315

468).Ko’paytmaning qaysi biri musbat?

A)sin 2cos 2sin 1sin 1 B)tg 8 ctg 8ctg 10 ctg ; C)sin 9 sin 9cos 9 cos 9 D)cos 10 cos 10cos 11 cos E)tg7.5 tg7.5ctg3 ctg3

469).( ; ) nuqtaga tushish uchun(1;0) nuqtani burish kerak bo’lgan barcha burchaklarni toping.

470).Tomonlari a,b,c bo`lgan uchburchakning m_a medianasini quyidagi formulalardan qaysilari bilan hisoblash mumkin

a) m_a=1/2

b) ma=1/2

d) m_a=1/2

e) m_a

471).To`g`ri javobni aniqlang .Istalgan aylana uzunligini shu aylana diametriga nisbati

a) aylanaga bog`liq

b) radiusga proporsianal

d) ga teng

e) radiusning kvadratiga proporsianal

472).Noto`g`risini toping. Istalgan doira yuzining uning radiusga nisbati

a) radiusga teng

b) radiusga proporsianal

d) diametrga proporsianal

e) o`zgarmas son

473).Istalgan muntazam ko`pburchak uchun noto`g`ri tasdiqni toping.

a) Ichki aylana chizish mumkin

b) diaganallari teng

d) tomonlaari teng

e) burchaklari teng

474). Noto`g`ri tasdiqni toping.

a) aylana yoyining uzunligi uning radius o`lchoviga proprsianal

b) doira sektorining yuzi sektorning gradus o`lchoviga proporsianal

d) doira yuzi radiusining kvadratiga proporsianal

e) segmentning yuzi uning yoyiga proporsianal

475). To`g`ri javobni toping. Doiraning vektori uni

a) 2ta segmentga

b) 2ta sektorga

d) 2ta yoyga

e) tengdosh sektorga

476).To`g`ri burchak uchburchakning gipotenuzasiga tushirilgan balandlik haqida noto`g`ri tasdiqni topìng.

a) katetlardan kichik

b) uchburchakni 2ta o`xshash uchburchaklarga ajratadi

d) katetlar gipotenuzasiga proyeksiyalari orasida o`rta proporsianal

e) gipotenuza yarmiga teng.

477).AB va CD vatarlar O nuqtada kesishadi.Noto`g`ri tasdiqni toping?

a) DAB= DCB

b) AOD va COB 3burchaklar o`xshash

d) AO.OB=CO.OD

e) AO=CO

478).To`g`ri tasdiqni toping.

a) teng kesmalar proyeksiyalari ham teng.

b) katta kesma proyeksiyasi ham teng

d) bir to`g`ri chiziqdagi teng kesmalarning proyeksiyasi teng

e) proyeksiya uzunligi proyeksiyalanuvchi kesma uzunligiga teng emas

479).To`g`ri burchakli uchburchakning gipotenuzasiga tushirilgan balandlik uni 2ta uchburchakka bo`ladi. Bu uchburchaklar

a) teng

b) tengdosh

d) o`xshash

e) teng yonli

480).(1;0)nuqtani 5 z. burchakka burishdan hosil bo`ladigan nuqtaning koordinatalarini toping.

481).Sonlarni o`sish tartibida yozing:a=sin1,57; b=cos1,58; c=sin3.

482).Sonlarni kamayish tartibida yozing:

a=cos2; b=cos20; c=sin2; d=sin20.

483).Hisoblang: sin136

484). Hisoblang: ;

485).Arifmetik progressiyada a­­­₁=3,d=-2 S₁₀₁ ni toping.

486). Arifmetik progressiyada d=4, S₅₀=5000 bo’lsa a₁ ni toping.

487). Arifmetik progressiyada a₁=1,a₁₀₁=301 bo’lsa d ni toping.

488) Arifmetik progressiyada a₂+a₉=20 bo’sa ,S₁₀ ni toping.

489). 8 ga bo’lganda 7 qoldiq beradigan ketma-ketlikni toping 5-hadini tiping .

490).701 soni 1.8,15,22… progressiyaning nechanchi nomerli hadi?

491). 1002,999,996… progressiyaning nechanchi nomerli hadidan boshlab, uning hadlari manfiy sonlar bo’ladi?

492). Arifmetik progressiyada a₂+a₆=44,a₅-a₁=20 bo’lsa a₁₀₀ ni toping.

493).Arifmetik progressiyada a₁=7, d=5, S_n=25450 bo`lsa, n ni toping.

494). Arifmetik progressiya a₁₂+a₁₅=20 bo`lsa, S₂₆ ni toping.

495).Uzunligi A va B bo`lgan kesmalar o`rta proporsianali nimaga teng

496).Agar to`gri burchakli uchburchakning balandligi gipotenuzasini 6 sm va 5/4 sm kesmalarga ajratsa bu uchburchakning yuzini toping

497).C nuqtadan o`tkazilgan bir kesuvchi aylanani A va B 2-si esa D va E nuqtalarda kesadi.Agar CD=18 sm CB=4sm CA=8sm bo`lsa, AE kesma uzunligi?

498).Agar A(-5; ) B(-4;2 ) C (-2; ) D(0;2) bo`lsa ABCD to`rtburchakning diaganallari orasidagi burchakni top?

499).Agar parallegramning diagonallari 10 sm va 8 sm ga teng va ular orasidagi burchak 45^obo`lsa parallelogramni tomonlari?

500).Radiusi 8 sm bo`lgan aylanaga ichki chizilgan muntazam oltiburchakning yuzi?