Test-2019 1-Variant
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2019 yil 30 ta lik variant
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- GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI
- 14 – Variant.
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13 – Variant.
1. Merganning bitta otgan o’qining nishonga tegishi ehtimoli 0,9 ga teng bo’lsa, otilgan uchta o’qning ikkitasi nishonga tegishi va bittasi tegmasligi ehtimolini toping. A) 0,27 B) 0,18 C) 0,243 D) 0,729
2. Agar 𝑓(𝑥) = 𝑘𝑥 + 𝑏 bo’lsa, 𝑓(−3) − 𝑓(0) ni toping. A) -3k+b B) -3k+2b C) -3k D) -3
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 3. |4𝑥 − 25| = 𝑥 2 + 3𝑥 + 7 tenglama nechta haqiqiy yechimga ega? A) 0 B) 1 C) 2 D) 3
4. 𝑥
2 − (𝑏 + 2)𝑥 + 𝑏 − 4 = 0 kvadrat tenglamaning ildizlaridan biri b ga teng bo’lsa, ildizlari kvadratlarining yig’indisini toping. A) 10 B) 15 C) 20 D) 25
5. Sohaning necha foizi bo’yalgan?
A) 25 B) 35 C) 40 D) 30 6. Tenglamani yeching: √(𝑥 + 3) 2 3 − 2 √(𝑥 − 1) 2 3 + √𝑥 2 + 2𝑥 − 3 3 = 0
A) ∅ B) 5 9
C) -3 D) 1
7. 𝑓(𝑥) = arcsin(3 − 2𝑥) bo’lsa, 𝑓 −1 (𝑥)
ni toping.( bu yerda 𝑓 −1 (𝑥)
funksiya 𝑓(𝑥) funksiyaning teskari funksiyasi) A) sin (3 − 2𝑥) B) arccos(3 − 2𝑥) C)
3 2 − sin 𝑥 2 D) 3 2 − 1 2 sin 𝑥
8. Hisoblang: 𝑎𝑟𝑐𝑡𝑔√2 + 𝑎𝑟𝑐𝑡𝑔 1 √2
A) 45° B) 30° C) 90° D) 𝑎𝑟𝑐𝑡𝑔 (√2 + 1 √2 )
9. Hisoblang: √12 − 2√11 − √11 − 1 A) 2√11 B) – 2 C) -1 D) 1
10. Geometrik progressiyada 𝑏 6 − 𝑏 3 = 84 𝑣𝑎 𝑏 5 − 𝑏
2 = 42
bo’lsa, 𝑏 1 + 𝑏 4 =? A) 36 B) 15 C) 51 D) 27
11. 𝐴 = {1; 4; 5; 7; 8}; 𝐵 = {1; 2; 3; 5; 8; 9; 10; 11; 12} va
𝐶 = {𝑎; 𝑏; 𝑐; 𝑑; 𝑓} bo’lsa, 𝑛((𝐵\𝐴) ∪ 𝐶) ni aniqlang. A) 6 B) 9 C) 11 D) 15
12.
53 13 + 77 19 − 93 23 ifodaning qiymati quyidagi oraliqlardan qaysi biriga tegishli? A) (1;2) B) (2;3) C) (3;4) D) (4;5)
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 13. Ishchi birinchi kuni ish normasining 1 8
qismini bajardi. Ikkinchi kuni birinchi kunda bajargan ishning 1 8
ish bajardi. Ishchi shu ikki kunda ish normasining qancha qismini bajargan? A) 17
B) 1 4 C) 9 64 D) 17 64
14. Tengsizlikni nechta butun son qanoatlantiradi:
𝑥 3
≤ 16𝑥
𝑥−2
A) 5 B) 7 C) 3 D) cheksiz ko’p
15. 𝑦 = 2𝑥 2 − 4𝑥 + 6
funksiyani ordinatalar o’qiga nisbatan simmetrik funksiyasini aniqlang. A) 𝑦 = 2𝑥 2 + 4𝑥 + 6
B) 𝑦 = −2𝑥 2 − 4𝑥 − 6
C) 𝑦 = −2𝑥 2 + 4𝑥 − 6
D) 𝑦 = −2𝑥 2 − 4𝑥 + 6
16. 𝑓(𝑥) = 15 4𝑥
+ 12𝑥
2 5 funksiyaning eng kichik qiymatini aniqlang. A) 3 B) 6 C) 18 D) 36
17. 𝑥
𝑥 𝑛 = 𝑛, 𝑛 ∈ 𝑁 tenglamani yeching. A) n B) √𝑛 C) √𝑛 𝑛
3
18. 𝑓(𝑥) = (𝑥 2 − 3𝑥 + 4) ∙ (𝑥 − 4) funksiyaning 𝑥 0 = 4
nuqtadagi hosilasini toping. A) 5 B) 8 C) 12 D) 17
19. Aniq integralni hisoblang: ∫ (2𝑥 + 5) ∙ cos(𝑥 2 + 5𝑥) 𝑑𝑥 1 0
A) sin 5 B) − sin 5 C) − sin 6 D) sin 6
20. {𝑎 = 16 − 𝑥 2 𝑏 = 𝑥
2 − 4
bo’lsa, 𝑎 ∙ 𝑏 ko’paytmaning eng katta qiymatini toping. A) -64 B) 36 C) 64 D) -36
21. Teng yonli trapetsiyaning diogonali o’tkir burchagining bisektrissasi va katta asosi 24 ga, perimetri 54 ga teng bo’lsa, o’rta chizig’ini toping. A) 15 B) 16 C) 17 D) 18
22. Uchburchakli piramida asosining ikki tomoni uzunligi 9 dm va 10 dm ga teng. Ular orasidagi burchak 45°. Yon qirrasi uzunligi 16 dm ga teng. Agar yon qirrasi va asos tekisligi orasidagi burchak 30° ni tashkil etsa, piramidaning hajmini toping. A)
58√3 3 B) 30√2 C)90√2 D) 60√2 GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 23. Muntazam oltiburchakli piramidaga konus ichki chizilgan. Piramidaning yon yoqlari bilan asosi 60° li burchak hosil qiladi. Agar piramidaning asosiga ichki chizilgan aylananing radiusi 16 ga teng bo’lsa, konusning yon sirtini toping. A) 512𝜋 B) 256𝜋 C) 300𝜋 D) 450𝜋
24. 3 ta tengdosh prizmaning balandliklari nismati mos ravishda 4:9:12 kabi nisbatda bo’lsa, prizmalar asos yuzalari nisbatini aniqlang. A) 12:9:4 B) 9:4:3 C) 16:81:144 D) 8:18:24
25. Uchlari A(-1;1) ; B(3;1) ; C(-1;7) nuqtalarda bo’lgan uchburchakning yuzini toping. A) 12 B) 6 C) 18 D) 24
26. To’g’ri burchakli parallelepipedning tomonlarining nisbati 2:5:3 kabi va to’la sirti yuzi 248 ga teng bo’lsa, uning hajmini toping. A)120 B) 240 C) 320 D) 480
27. To’g’ri konusning balandligi 10 ga, asosining radiusi 6 ga teng va asosining markazidan yasovchisiga eng qisqa masofadagi nuqtalardan asosga parallel tekislik o’tkazildi. Hosil bo’lgan kesik konusning kichik asosi radiusini toping. A)
75 34 B) 75 17 C) 150 17 D) 97 34
28. O’nbir burchakli prizmaning nechta turli dioganal kesimi mavjud? A) 11 B) 33 C) 44 D) 22
29. ABC uchburchakda BD bisektrissa va AB=7; BC=9 bo’lsa, AC:AD=? A)
7 16 B) 9 16 C) 16 7 D) 16 9
30. (4;0) va (0;3) nuqtalardan o’tuvchi to’g’ri chiziq tenglamasining burchak koeifitsiyentini toping. A) 3
B) 4 3 C) − 4 3 D) − 3 4
1. Ko’phadlarni ko’paytiring: (3𝑎 + 2) ∙ (𝑎 − 4)
A) 3𝑎
2 + 14𝑎 − 8 B) 3𝑎 2 − 10𝑎 − 8 C) 3𝑎
2 + 10𝑎 − 8 D) 3𝑎 2 − 14𝑎 − 8 2. 𝑎 + 𝑏 ∙ √6 6
bo’lsa, 𝑎 2 + 𝑏 2 ning qiymatini toping. A) 6 B) 24 C) 30 D) 36
3. 𝑎 3 + 𝑏
3 = 15 𝑣𝑎 𝑎 2 𝑏 + 𝑎𝑏
2 = 4
bo’lsa, 𝑎 + 𝑏
ni toping. A) 2 B) 1 C) 3 D) 4
4. 520 ni 20 foiz oshirib, so’ngra uning 25 foizini toping. A) 144 B) 132 C) 156 D) 168
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 5. Hisoblang: 18𝑠𝑖𝑛224°+3𝑐𝑜𝑠134° 𝑐𝑜𝑠46°
A) -21 B) 21 C) -15 D) 15
6. 𝑠𝑖𝑛2𝑥 = 𝑐𝑜𝑠𝑥 tenglamaning eng kichik musbat ildizini toping. A)
𝜋 3 B) 𝜋 2 C) 𝜋 4 D) 𝜋 6
7. Hisoblang: √28 − 10√3 − 1 √7+4√3 A 7 B) 2√3 C) 3 D) 7 − 2√3
8. 𝑦 = −𝑥 2 + 6𝑥 − 5
funksiyaning qiymatlar sohasini toping. A) [4; ∞) B) (−∞; 4] C) (−∞; −5] D) [−5; ∞)
9. 𝑓(𝑥) = 3 𝑥+1
+3 𝑥+2
+3 𝑥+3
5 𝑥+2
+14∙5 𝑥 𝑏𝑜 ′ 𝑙𝑠𝑎,
9𝑓(−1) =?
A) 15 B) 9 C) 25 D) 39 10. Aniqmas integralni hisoblang: ∫ 𝑥 2
3 ) 𝑑𝑥
A)
sin(4−𝑥 3 ) 3 + 𝐶
B) cos(4−𝑥
3 ) 3 + 𝐶
C) − sin(4−𝑥 3 ) 3 + 𝐶
D) − cos(4−𝑥
3 ) 3 + 𝐶
11. Parallelogrammning o’tmas burchagi 150°
ga, tomonlari 12 va 18 ga va burchaklari bisektrissalari kesishishidan hosil bo’lgan to’g’ri to’rtburchakning yuzini toping. A) 12 B) 9 C) 8 D) 10
12. Tengsizlikni yeching: (𝑥 + 1) ∙ (|𝑥| − 1) ≤ 8
A) (−∞; 0] B) [0; 3] C) (−∞; 3] D) [3; ∞)
13. Tenglamani yeching: |𝑥| + |2𝑥| = 3𝑥 A) 0;1 B) 0;2 C) 0;1;2 D) [0; ∞)
14. Tenglamalar sistemasini yeching: { 𝑦 + |𝑥 + 1| = 1 |𝑥 − 𝑦| = 5
A) ( 5 2 ; − 5 2 ) B) (− 5 2 ; − 5 2 )
C) ( 5 2 ; 5 2 ) D) (− 5 2 ; 5 2 )
15. Butun yechimlari sonini toping. { |4 + 𝑥| ≤ 7 |2𝑥 + 3| ≥ 9
A) [-11;3] B) [-11;-6] C) [−11; −3] ∪ {3} D) [−11; −6] ∪ {3}
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 16. ∫
𝑑𝑥 √𝑥 2 +1 1 0 aniq integralni hisoblang. A) 1
ln(1 + √2) B) ln(1 + √2) C) 1
ln(1 + √2) + 1 4 D) ln(1 + √2) + 1 17. 𝐹(𝑥) = 𝑥 3 + 𝐴𝑥
2 + 𝐵𝑥 + 𝐶
ko’phad uchun 𝐹(𝑥 + 1) = 𝑥 3 + 𝐷𝑥
2 + 54𝑥 + 37
bo’lsa A+B+C ning qiymatini toping. A) 54 B) 53 C) 36 D) 37
18. Tengsizlikni yeching: 100𝑥 > √10 3 lg 𝑥
A) (0;10000) B) (10; 1000) C) (1; 100) D) (10; 100)
19. n natural sonning qanday qiymatlarida 2 + 1 𝑛+ 2 3 = 13 5 tenglik o’rinli bo’ladi? A) 3 B) 4 C) 2 D) 1
20. Arifmetik progressiyani tashkil etuvchi 𝑛 + 3; 𝑛 + 9; 𝑛 + 15; … ; 𝑛 + 123 ketma-ketlikning o’n birinchi hadi 67 ga teng bo’lsa, bu ketma-ketlikning to’rtinchi hadini toping. A) 25 B) 19 C) 24 D) 22
21. Teng yonli trapetsiyaning diogonali o’tkir burchagining bisektrissasi va katta asosi 22 ga, perimetri 52 ga teng bo’lsa, o’rta chizig’ini toping. A) 15 B) 16 C) 17 D) 18
22. ABC uchburchakda BD bisektrissa va AB=7; BC=9 bo’lsa, AD:DC=? A)
7 9 B) 9 16
C) 9 7 D) 16 9
23. Tenglamani yeching: 𝑥+4 6 −3 2 3 +4 − 𝑥−3
3 +2 2+ 1 3 = 𝑥 8 +2 3 4 ( 4 7 ) −1
A) -14 B) 30 C) 14 D) -30
24. Silindrning to’la sirti 192𝜋 ga teng bo’lsa, silindr hajmining eng katta qiymatini toping. A) 192𝜋 B) 192√2𝜋 C) 200𝜋 D) 256√2𝜋
25. 𝑥
2 + 𝑦
2 + 𝑧
2 ≤ 4𝑥 + 6𝑦 + 10𝑧
tengsizlk bilan chegarlangan jismning sirtini toping. A) 148𝜋 B) 140𝜋 C) 152𝜋 D) 150𝜋
26. Teng yonli trapetsiyaning katta asosi 25 cm, perimetri esa 55 cm ga teng. Agar uning diogonali o’tkir burchagining bissektrissasi bo’lsa, o’rta chizig’ini toping.
A) 16,5 B) 17,5 C) 18,5 D) 19,5
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 27. ABCD parallelogramda D o’tmas burchak. E nuqta AB tomonda yotadi. Agar AE:EB nisbat 4:3 kabi bo’lsa, BCDE to’rtburchak yuzini DAE uchburchak yuziga nisbatini toping. A) 5:1 B) 5:2 C) 6:1 D) 7:2
28. To’g’ri burchakli uchburchakning kichik burchagi 30° va unga yopishgan kateti 4 cm bo’lsa, uchburchakning eng katta bisektrissa uzunligini toping. A)
4 √3 B) 4√2 − √3 C) 8√2 + √3 D) 8√2 − √3
29. O’lchamlari 𝑎; 𝑏; 𝑐 bo’lgan parallelepipedning to’la sirtining yuzasi 288 ga teng. Agar 1 𝑎
1 𝑏 + 1 𝑐 = 1 3 o’rinli bo’lsa, parallelepipedning hajmini toping.
A) 432 B) 216 C) 288 D) 504
30. Qirrasi 2√3 ga teng bo’lgan tetraedrning hajmini toping. A) 3√2 B) 2√6 C) 4√3 D) 4√6
3
15 – Variant. 1. Arifmetik progressiyada 𝑎 4 = 5 va 𝑎 𝑛+1 = 𝑎 𝑛 + 4 bo’lsa, progressiyaning dastlabki 14 ta hadi yig’indisini toping. A) 348 B) 336 C) 376 D) 330
2. 𝐴 = {𝑥|𝑥 ≥ 6; 𝑥 ∈ 𝑁} ; 𝐵 = {𝑥|𝑥 < 18; 𝑥 ∈ 𝑄}
bo’lsa, 𝑛(𝐴 ∩ 𝐵) ni toping. A) 10 B) 11 C) 12 D) 13
3. Tengsizlikni yeching: 7 𝑥−1 ∙(𝑥−2) 𝑥−3
> 0
A) (−∞; 2) ∪ (3; ∞) B) (2;3) C) (1; 2) ∪ (3; ∞) D) (2; 7) ∪ (3; ∞)
4. 6 3 + 8 ∙ 11 + 4 ifodani 6 ga bo’lgandagi qoldiqni toping. A) 1 B) 0 C) 2 D) 4
5. ∫ (𝑥 − 8) 7 ∙ 𝑥𝑑𝑥
9 8
aniq integralni hisoblang. A) 0 B) 1
C) 1 1 8 D) 1 1 9
6. 1 𝑥(𝑥+4)
+ 1 (𝑥+4)(𝑥+8) + 1 (𝑥+8)(𝑥+12) ifodani soddalashtiring. A) 1
B) 4 𝑥(𝑥+12) C)
12 𝑥(𝑥+12)
D) 3 𝑥(𝑥+12)
7. ABC uchburchakda ∠𝐵𝐴𝐶 = 33°.AC tomondan shunday D nuqta olinganki, bunda BD=DC. Agar ∠𝐵𝐷𝐶 = 42° bo’lsa, ∠𝐴𝐵𝐶 ning qiymatini toping. A) 48° B) 57° C) 69° D) 78°
8. Soatning soat mili 19° ga burilsa, minut mili necha gradusga buriladi? A) 112° B) 172° C) 228° D) 212°
9. 𝑐𝑜𝑠 4 11𝑥 − 𝑠𝑖𝑛 4 11𝑥 = cos 20𝑥 tenglamani yeching. A) 𝜋𝑛; 𝑛 ∈ 𝑍 B) 𝜋𝑛 11 ; 𝑛 ∈ 𝑍
C) 𝜋𝑛 21 ; 𝑛 ∈ 𝑍 D) 𝜋𝑛 22 ; 𝑛 ∈ 𝑍
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 10. 𝑦 = ln 𝑥 𝑥−1 funksiyaning hosilasini toping. A) ln 𝑥 − 1 + 1 𝑥
1 𝑥
C) ln 𝑥 − 1 𝑥 D) ln 𝑥 + 1 − 1 𝑥
11. Merganning bitta otgan o’qining nishonga tegishi ehtimoli 0,9 ga teng bo’lsa, otilgan uchta o’qning ikkitasi nishonga tegishi va bittasi tegmasligi ehtimolini toping. A) 0,27 B) 0,18 C) 0,243 D) 0,729
12. = 𝑘𝑥
2 + 3
funksiyaga A(3;12) nuqta tegishli bo’lsa, k ning qiymatini toping. A) -1 B) 1 C) 2 D) 3
13. Markazi (0;0) nuqtada bo’lgan aylanadagi A(0;2) nuqtani soatyo’nalishida 60° ga burganda hosil bo’lgan nuqtaning koordinatalari yig’indisini toping. A) −1 − √3 B) −1 + √3 C) 1 + √3 D) 1 − √3
14. Sonning oxirgi raqamini toping: 819 12 13 A) 9 B) 1 C) 7 D) 3
15. Aniqmas integralni hisoblang: ∫ 𝑥𝑠𝑖𝑛2𝑥𝑑𝑥 A)
𝑐𝑜𝑠2𝑥 2 ∙ 𝑥 + 𝑠𝑖𝑛2𝑥 4 + 𝐶 𝐵)
𝑐𝑜𝑠𝑥 2 ∙ 𝑥 + 𝑠𝑖𝑛𝑥 4 + 𝐶 C) −
𝑐𝑜𝑠2𝑥 2 ∙ 𝑥 + 𝑠𝑖𝑛2𝑥 4 + 𝐶 D)
𝑐𝑜𝑠2𝑥 2 + 𝑠𝑖𝑛2𝑥 4 + 𝐶
16. Tenglamani haqiqiy ildizlarini toping: (2 + √3) 𝑥 2
𝑥 2 = 4 A) -1 B) 1;0 C) 0;-1;1 D) -1; 1
17. Hisoblang: 21 √32−√11 + 9 √2−√11 A) 3√2 B) 2√11 C) 5√2 + 2√11 D) 0
18. 367𝑥75 ̅̅̅̅̅̅̅̅̅̅ sonni 75 ga bo’lganda qoldiq qolmaydi. x ni toping. A) 2; 8 B) 3;6;9 C) 2;5;8 D) 3;6
19. 𝑦 = √lg 3−𝑥 𝑥 funksiyaning aniqlanish sohasini toping. A) (0; 3] B) (0; 1,5) C) (0; 3) D) (0; 1,5]
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 20. 𝑥
2 − 2020𝑥 + 2019 < 0
tengsizlikning butun yechimlari yig’indisini toping? A) 2017201 B) 2037160 C) 2037170 D) 2137170
21. ABC uchburchakda BD bisektrissa va AB=7; BC=9 bo’lsa, AC:DC=? A)
7 16 B) 9 16 C) 16 7 D) 16 9
22. O’lchamlari 𝑎; 𝑏; 𝑐 bo’lgan parallelepipedning to’la sirtining yuzasi 288 ga teng. Agar 1 𝑎
1 𝑏 + 1 𝑐 = 2 5 o’rinli bo’lsa, parallelepipedning hajmini toping.
A) 432 B) 288 C) 360 D) 420
23. Qirrasi 6 ga teng bo’lgan tetraedrning to’la sirtini toping. A) 27√3 B) 18√3 C) 36√3 D) 54√3
24. O’q kesimi muntazam uchburchak bo’lgan konusning to’la sirti yuzi S ga teng bo’lsa, uning yon sirti yuzini toping.
A) 𝑆 2 B) 𝑆 3 C) 2𝑆 3 D) 3𝑆 4
25. Uchlari va yoqlari yig’indisi 38 ga teng bo’lgan piramidaning asosining diogonallari sonini toping. A) 225 B) 152 C) 135 D) 153
balandligi 5 cm. Yon sirtidan A va B nuqtalar olingan. A va B nuqtalardan asos tekisligigacha bo’lgan masofalar mos ravishda 2 cm va 3 cm. Agar AB kesma uzunligi 5 cm bo’lsa, silindr o’qidan AB kesmagacha bo’lgan masofani toping. A) 2√6 B) 2√3 C) √10 D) √8
27. A(−7; 11) nuqtaga koordinatalar boshiga nisbatan simmetrik nuqtani toping.
A) (−7; 11) B) (7; 11) C) (−7; −11) D) (7; −11)
28. ABCD parallelogramda BC va AD tomonlari o’rtalarida mon ravishda M va N nuqtalar olingan. AM va CN kesmalar BD dioganalni mos ravishda P va Q nuqtalarda kesib o’tadi. Agar DNQ uchburchak yuzi 15 ga teng bo’lsa, ABM uchburchakning yuzini toping. A) 36 B) 45 C) 60 D) 30
29. Chizmaga ko’ra x ni toping. A) 12 B) 18 C) 24 D) 20
GULISTON – 2019 MATEMATIKAFLY MADINABONU O’QUV MARKAZI Telegramdagi manzilimiz: https://telegram.me/matematikafly 30. Chizmaga ko’ra AO=15 cm, AB kichik yoy 5𝜋 cm bo’lsa, BC ning uzunligini toping.
A) 15 B) 12 C) 9 D) 6
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