Algebra Yozma ish 11 – sinf 1- nazorat ishi 1 variant

1. Sharning katta doirasi yuzi 16 ga teng. Shar sirtining yuzini toping.

2. Sharga tashqi chizilgan kubning hajmi 8 ga teng. Sharning radiusini toping.

3. O‘q kesimi kvadratdan iborat silindrga ichki chizilgan sharning hajmi 9π/16 ga teng. Silindrning yon sirtini toping.

4. Sharga ichki chizilgan konusning asosi sharning katta doirasiga teng. Konus o‘q kesimining yuzi 9 ga teng. Sharning hajmini toping.

5. Sharga ichki chizilgan konusning o‘q kesimi teng yonli to‘g‘ri burchakli uchburchakdan iborat. Konus hajmi shar hajmining qanday qismini tashkil etadi?
2-variant

1. Sharning katta doirasi yuzi 18 ga teng. Shar sirtining yuzini toping.

2. Sharga tashqi chizilgan kubning hajmi 6 ga teng. Sharning radiusini toping.

3. O‘q kesimi kvadratdan iborat silindrga ichki chizilgan sharning hajmi 9π/8 ga teng. Silindrning yon sirtini toping.

4. Sharga ichki chizilgan konusning asosi sharning katta doirasiga teng. Konus o‘q kesimining yuzi 12 ga teng. Sharning hajmini toping.

5. Sharga ichki chizilgan konusning o‘q kesimi teng yonli to‘g‘ri burchakli uchburchakdan iborat. Konus hajmi shar hajmining qanday qismini tashkil etadi?

Yakuniy nazorat test.

1-variant

1. Uchta nuqta berilgan: A (1; 1; 1), B (–1; 0; 1), C (0; 1; 1). Shunday D (x; y; z) nuqtani topingki, AB va CD vektorlar teng bo‘lsin.

A) D (2; 0; 1); B) D (–2; 0; 1); C) D (–2; 1; 1); D) D (2; 0; 0).

2. Skalar ko‘paytmasi 0,5 ga teng bo‘lgan birlik vektorlar orasidagi burchakni toping.

A) 60°; B) 30°; C) 120°; D) 45°.

3. Kubning ikkita qarama-qarshi yoqlarining diagonallari orqali o‘tkazilgan kesimning yuzi 16 2 ga teng. Kubning qirrasini toping.

A) 4; B) 2 2 ; C) 4 2 ; D) 8.

4. Muntazam uchburchakli prizmaning hajmi 27 3 ga, asosiga tashqi chizilgan aylananing radiusi esa 2 ga teng. Prizmaning balandligini toping.

A) 12; B) 8; C) 6; D) 9.

5. Oktaedrning qirrasi a ga teng. Uning to‘la sirtini hisoblang.

A) 2a2 3 ; B) a2 3 ; C) 2 3a2 / 3; D) 4a2 3 .

6. To‘rtburchakli muntazam kesik piramidaning balandligi 16 ga, asoslarining tomonlari 24 va 40 ga teng. Kesik piramidaning diagonalini toping.

A) 48; B) 24; C) 36; D) 40.

7. Konusning balandligi 10 ga, o‘q kesimi uchidagi burchagi 120° ga teng. Konus hajmini toping.

A) 1000p; B) 1200p; C) 900p; D) 600p.

8. Shar katta doirasining yuzi 25π ga teng. Sharning markazidan qanday masofada o‘tkazilgan tekislik shardan doirasining yuzi 9π ga teng bo‘lgan kesim ajratadi?

A) 3,8; B) 3,6; C) 3,5; D) 4.

9. Piramidaning hajmi 25 ga, unga ichki chizilgan sharning radiusi 1,5 ga teng. Piramidaning to‘la sirtini toping.

A) 20; B) 15; C) 25; D)50.

10. Balandligi 3 ga, yasovchisi 6 ga teng bo‘lgan konusga tashqi chizilgan sharning radiusini toping.

A) 3 3 ; B) 5; C) 6; D) 4 2 .

2-variant

1. Uchta nuqta berilgan: A (2 1; –1), B (–3; 1; 1), C (2; 0; 1). ShundayD(x; y; z) nuqtani topingki, AB va CD vektorlar teng bo‘lsin.

A) D (3; 0; 1); B) D (–3; 0; 1); C) D (–3; 0; 3); D) D (–3; 0; 0).

2. Skalar ko‘paytmasi 22ga teng bo‘lgan birlik vektorlar orasidagi burchakni toping.

A) 60°; B) 30°; C) 120°; D) 45°.

3. To‘rtburchakli muntazam prizma asosining tomoni 2 ga, diagonali bilan yon yog‘i orasidagi burchak esa 30° ga teng. Prizmaning hajmini toping.

A) 8 2 ; B) 4; C) 16; D) 4 2 .

4. Silindrning balandligi 5 ga, uning asosiga ichki chizilgan muntazam uchburchakning tomoni 3 3 ga teng. Silindrning hajmini toping.

A) 25π; B) 35π; C) 45π; D) 40π.

5. To‘rtburchakli muntazam piramidaning yon qirrasi 3 2 ga, yon qirra va asos tekisligi orasidagi burchak 45° ga teng. Piramidaning hajmini toping.

A) 12 2 ; B) 18; C) 9 2 ; D) 24.

6. Konusning yasovchisi 15 ga, yon sirti yoyilmasining uchidagi burchagi 120° ga teng. Konus asosining diametrini toping.

A) 10; B) 15; C) 20; D) 25.

7. Asoslarning radiuslari 2 va 7 ga, o‘q kesimining diagonali 15 ga teng bo‘lgan kesik konus yon sirtining yuzini toping.

A) 112π; B) 115π; C) 117π; D) 120π.

8. Kubga tashqi chizilgan sharning hajmi unga ichki chizilgan sharning hajmidan necha marta katta?

A) 8; B) 4; C) 4 2 ; D) 3 3 .

9. Silindrga shar ichki chizilgan. Silindrning hajmi 16π ga teng bo‘lsa, sharning hajmini toping.

A) 32π/3; B) 16π/3; C) 64π/3; D) π.

10. Qirrasi 12 ga teng bo‘lgan kubga konus ichki chizilgan. Konusning asosi

kubning quyi asosiga ichki chizilgan, uchi esa kubning yuqoridagi asosining

markazida. Konusning hajmini toping.

A) 120π; B) 132π; C) 126π; D) 144π.

1. A(x₁; y₁; z₁) va B(x₂; y₂; z₂) nuqtalar berilgan. z₂– z₁ nimani anglatadi?

A) AB kesma o‘rtasining koordinatasini; B) AB kesma uzunligini;

C) AB vektor uzunligini; D) AB vektor koordinatalaridan birini.

2. 64- rasmda AB⊥α, a⊂a, AO=OB bo‘lsa,

A) A va B nuqtalar O nuqtaga nisbatan simmetrik bo‘ladi;

B) A va B nuqtalar a to‘g‘ri chiziqqa nisbatan simmetrik bo‘ladi;

C) A va B nuqtalar a tekislikka nisbatan simmetrik bo‘ladi;

D) AB kesma a to‘g‘ri chiziqqa nisbatan simmetrik bo‘ladi.

64 65 66

3. 65- rasmda B nuqta AOC tekislikda yotmaydi. Unda OA, OB va OC

vektorlar …

A) kollinear; B) komplanar;

C) bir xil yo‘nalishli; D) komplanar emas.

4. M(–7; 1; 4) va N(–1; –3; 0) nuqtalar berilgan. MN kesma o‘rtasining

koordinatalarini toping.

A) (–4; –1; 4); B) (–4; –1;2); C) (–4; –2; 2); D) (–3; 2; 2).

5. A(0; –3; 2) va B(4; 0; –2) nuqtalar berilgan. AB kesma o‘rtasi nimaga

tegishli?

A) Ox o‘qiga; B) Oy o‘qiga; C) Oz o‘qiga; D) Oxy tekisligiga.

6. A(3; 4; –3) nuqtadan Oz o‘qigacha bo‘lgan masofani toping.

A) 3; B) 5; C) 2 3; D) 34 .

7. CD+DE+EF vektorlar yig‘indisini toping.

A) O; B) CF; C) DF; D) CE.

8. m ning qaysi qiymatida a(m; 4; –3) va b(4; 8; –6) vektorlar kollinear

bo‘ladi?

A) 2; B) 5; C) 1; D) 3.

9. O nuqta α tekislikda yotmaydi. Markazi O nuqtada bo‘lgan gomotetiyada

α tekislik undan farqli bo‘lgan β tekislikka o‘tadi. Agar a to‘g‘ri chiziq α

tekislikka tegishli bo‘lsa, …

A) α || β bo‘ladi; B) α tekislik β tekislik bilan kesishadi;

C) a ⊂ β bo‘ladi; D) α ⊥ β bo‘ladi.

10. AB to‘g‘ri chiziq BCD tekislikka perpendikular. Qaysi vektorlarning

skalar ko‘paytmasi nolga teng bo‘ladi?

A) CA va CB; B) BD va AD; C) AC va BC; D) AB va CD.

11. Qirrasi 1 ga teng bo‘lgan ABCDA1B1C1D1 kub berilgan (66- rasm).

(AB+BC) ∙ BB ni toping.

A) 1; B) 0; C) –1; D) 0,5.

12. p ning qaysi qiymatida a(1; 1; 0) va b(0; 4; p) vektorlar orasidagi

burchak 60° ga teng bo‘ladi?

A) 4; B) 4 yoki –4; C) 16; D) 16 yoki –16.

13. ABCDA1B1C1D1 kub berilgan. Parallel ko‘chirishda A1D kesma D1C

kesmaga o‘tadi. Bu ko‘chirishda AA1B1 tekislik qaysi tekislikka o‘tadi?

A) DB1B; B) DCC1; C) AA1C1; D) ABC.

14. a tekislik unda yotmaydigan ABC uchburchakning simmetriya tekisligidir.

Qaysi tasdiq to‘g‘ri?

A) (ABC)⊥α;

B) ABC uchburchak teng yonli;

C) ABC uchburchakning simmetriya markazi bor;

D) ABC uchburchakning simmetriya o‘qi bor.

15. ABCDA1B1C1D1 kub berilgan. A1B1+BC–DD1 ni toping.

A) A1C; B) BD1 ; C) B1D; D) AC1 .

16. Qaysi geometrik almashtirish ikki ayqash to‘g‘ri chiziqlardan birini

ikkinchisiga o‘tkazadi?

A) parallel ko‘chirish; B) tekislikka nisbatan simmetriya;

C) burish; D) gomotetiya.

17. M(–1; 2; –4) nuqtaga Oyz tekislikka nisbatan simmetrik bo‘lgan nuqtani

toping.

A) (1; –2; 4); B) (1; 2; –4); C) (–1; –2; –4); D) (–1; 2; 4).

18. Parallel ko‘chirishda AB vektor DC vektorga o‘tadi. Qaysi tasdiq

noto‘g‘ri?

A) AB=DC; B) AC va BD kesma o‘rtalari ustma-ust tushadi;

C) AB, AC va DC vektorlar komplanar; D) ABCD parallelogramm.

19. В(–3; 2; –5) nuqta Oxz tekislikdan qanday masofada yotibdi?

A) 2; B) 5; C) 3; D) 34 .

20. А(1; –2; 0), В(1; –4; 2), С(3; 2; 0) nuqtalar ABC uchburchakning uchlari.

CM mediana uzunligini toping.

A) 2√3; B) 3√2; C) 6 ; D) 18.

21. Agar a(1; m; 2) va b(0,5m+1; 3; 1) vektorlar kollinear bo‘lsa, m+n ni

toping.

A) 3; B) 5; C) –4; D) 9.

22. А(–1; –9; –3) va В(0; –2; 1) nuqtalar berilgan. vektorni koordinata

vektorlari (ortlar) bo‘yicha yoying.

A) (BA) = i + 9j – k ; B) (BA) = i – 9j + k ;

C) (BA) = –i – 9j – 4k ; D) (BA) = i + 9j – 4k .

23. А(1; –2; 2), В(1; 4; 0), С(–4; 1; 1) va D(–5; –5; 3) nuqtalar berilgan. АС

va ВD vektorlar orasidagi burchakni toping

A) 150°; B) 30°; C) 45°; D) 90°.

24. |a̅| = 6, |a̅+b̅| =11, |a̅–b̅| = 7 ekanligi ma’lum bo‘lsa, |b̅| ni toping.

A) 11; B) 18; C) 20 ; D) 7.

25. Asoslari ВС va АD bo‘lgan АВСD trapetsiya berilgan. Agar AB(–7; 4; 5),

AC(3; 2; –1), AD(20; –4; –12), М va N – mos ravishda АВ va СD tomonlar

o‘rtasi bo‘lsa, MN vektor koordinatalari yig‘indisini toping.

A) 1; B) 2 ; C) 3; D) 4.

5 nazorat ishi.1 variant

1. Uchburchakli muntazam piramidaning balandligi 4 ga, asosining balanligi esa 4,5 ga teng. Pirmidaning yon qirrasini toping.

2. To’rtburchakli muntazam piramidaning balandligi 15 ga, dioganali kesimining yuzi120 ga teng. shu piramidaning hajmini toping.

3. To’rtburchakli muntazam kesik piramidaning asoslari 3 sm va 5 sm, dioganali 9 sm. Kesik piramidaning balandligini toping.

4. konus asosining radiusi 6 ga, balandligi 8 ga teng. konus yoyilmasining uchidagi burchagini toping.

5. Konusning yon sirti 96 ga teng. Shu konus balandligining o’rtasidan unga perpendikulyar tekislik o’tkazish natijasida hosil bo’lgan kesik konusning yon sirtini toping.

2 variant

1. Uchburchakli muntazam piramidaning balandligi 8 ga, asosining balanligi esa 4,5 ga teng. Pirmidaning yon qirrasini toping.

2. To’rtburchakli muntazam piramidaning balandligi 30 ga, dioganali kesimining yuzi 240 ga teng. shu piramidaning hajmini toping.

3. To’rtburchakli muntazam kesik piramidaning asoslari 6 sm va 10 sm, dioganali 18 sm. Kesik piramidaning balandligini toping.

4. konus asosining radiusi 3 ga, balandligi 4 ga teng. konus yoyilmasining uchidagi burchagini toping.

5. Konusning yon sirti 48 ga teng. Shu konus balandligining o’rtasidan unga perpendikulyar tekislik o’tkazish natijasida hosil bo’lgan kesik konusning yon sirtini toping.

6 - nazorat ishi 1 – variant

1. Sharning katta doirasi yuzi 16 ga teng. shar sirtining yuzini toping.

2. Sharga tashqi chizilgan kubning hajmi 8 ga teng. sharning radiusini toping.

3. O’q kesimi kvadratdan iborat silindrga ichki chizilgan sharning hajmi ga teng. Silindrning yon sirtini toping.

4. Sharga ichki chizilgan konusning asosi sharning katta doirasiga teng. Konus o’q kesimining yuzi 9 ga teng. sharning hajmini toping.

5. sharga ichki chizilgan konusning o’q kesimi teng yonli to’g’ri burchakli uchburchakdan iborat. Konus hajmi shar hajmining qanday qismini tashkil etadi?

6- nazorat ishi 2 – variant

1. Sharning katta doirasi yuzi 4 ga teng. shar sirtining yuzini toping.

2. Sharga tashqi chizilgan kubning hajmi 8 ga teng. sharning radiusini toping.

3. O’q kesimi kvadratdan iborat silindrga ichki chizilgan sharning hajmi 18 ga teng. Silindrning yon sirtini toping.

4. Sharga ichki chizilgan konusning asosi sharning katta doirasiga teng. Konus o’q kesimining yuzi 16 ga teng. sharning hajmini toping.

5. sharga ichki chizilgan konusning o’q kesimi teng yonli to’g’ri burchakli uchburchakdan iborat. Konus hajmi shar hajmining qanday qismini tashkil etadi?