ETF MATF FON GRF TMF FORUM

Prijemni ispit na Tehnološko-metalurškom fakultetu u Beogradu

jun 2021.


Test ima [inline]20[/inline] zadataka na [inline]2[/inline] stranice. Zadaci [inline]1–3[/inline] vrede po [inline]3[/inline] poena, zadaci [inline]4–7[/inline] vrede po [inline]4[/inline] poena, zadaci [inline]8–13[/inline] vrede po [inline]5[/inline] poena, zadaci [inline]14–17[/inline] vrede po [inline]6[/inline] poena i zadaci [inline]18–20[/inline] vrede po [inline]7[/inline] poena. Pogrešan odgovor donosi [inline]−10\%[/inline] od broja poena za tačan odgovor. Zaokruživanje [inline]N[/inline] ne donosi ni pozitivne ni negativne poene. U slučaju zaokruživanja više od jednog, kao i u slučaju nezaokruživanja nijednog odgovora, dobija se [inline]-1[/inline] poen.

1.Link zadatka Rešenje jednačine [inline]\displaystyle\frac{\displaystyle0,24x}{\displaystyle\left(\frac{17}{40}-\frac{5}{24}\right)\cdot2\frac{4}{13}}=\frac{\displaystyle4\frac{3}{8}:7-3\frac{3}{10}:11}{\displaystyle2-\frac{3}{20}\cdot9}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{24}{25}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{25}{24}[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{24}{25}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{25}{24}[/inline];      [inline]\text{C)}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] ne znam.

2.Link zadatka Izraz [inline]\displaystyle\left\{\left[3^{-1}\cdot\left(\frac{3}{4}\right)^{-5}\right]:6^{-2}\right\}^\frac{1}{4}[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{8}{3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{8}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]8[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{8}{3}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{8}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline];      [inline]\text{D)}[/inline] [inline]1[/inline];      [inline]\text{E)}[/inline] [inline]8[/inline];              [inline]\text{N)}[/inline] ne znam.

3.Link zadatka Rešenje jednačine [inline]7x^2-\left[(4x-3)^2-1\right]=11x-(3x-5)^2[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline](0,1)[/inline];      [inline]\text{B)}[/inline] [inline][1,2][/inline];      [inline]\text{C)}[/inline] [inline](2,3)[/inline];      [inline]\text{D)}[/inline] [inline][-1,0][/inline];      [inline]\text{E)}[/inline] [inline](3,+\infty)[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline](0,1)[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline][1,2][/inline];      [inline]\text{C)}[/inline] [inline](2,3)[/inline];      [inline]\text{D)}[/inline] [inline][-1,0][/inline];      [inline]\text{E)}[/inline] [inline](3,+\infty)[/inline];              [inline]\text{N)}[/inline] ne znam.

4.Link zadatka Broj rešenja jednačine [inline]\left|2x^2-x-1\right|=2x+1[/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.

5.Link zadatka Ako je polinom [inline]ax^4+bx^3+1[/inline] deljiv polinomom [inline](x-1)^2[/inline] onda je zbir koeficijenata [inline]a[/inline] i [inline]b[/inline] jednak:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]0[/inline];      [inline]\text{C)}[/inline] [inline]-1[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]-2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]0[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-1[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]-2[/inline];              [inline]\text{N)}[/inline] ne znam.

6.Link zadatka Broj pozitivnih, celobrojnih rešenja nejednačine [inline]\displaystyle x\le3-\frac{1}{x-1}[/inline] je:
[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]0[/inline];      [inline]\text{D)}[/inline] beskonačno;      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]3[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]0[/inline];      [inline]\text{D)}[/inline] beskonačno;      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] ne znam.

7.Link zadatka Trgovac je prodao [inline]500\text{ kg}[/inline] dve vrste kafe cene [inline]80\text{ din.}[/inline] i [inline]60\text{ din.}[/inline] po kilogramu, kao mešavinu po [inline]68\text{ din.}[/inline] kilogram. Kafe, čija je cena [inline]80\text{ din.}[/inline] po kilogramu, je tada prodao:
[inline]\text{A)}[/inline] [inline]100\text{ kg}[/inline];      [inline]\text{B)}[/inline] [inline]200\text{ kg}[/inline];      [inline]\text{C)}[/inline] [inline]150\text{ kg}[/inline];      [inline]\text{D)}[/inline] [inline]300\text{ kg}[/inline];      [inline]\text{E)}[/inline] [inline]220\text{ kg}[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]100\text{ kg}[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]200\text{ kg}[/inline];      [inline]\text{C)}[/inline] [inline]150\text{ kg}[/inline];      [inline]\text{D)}[/inline] [inline]300\text{ kg}[/inline];      [inline]\text{E)}[/inline] [inline]220\text{ kg}[/inline];              [inline]\text{N)}[/inline] ne znam.

8.Link zadatka Količina vode, u litrima, koju treba sipati u [inline]12[/inline] litara [inline]4\%[/inline]-ne slane vode da bi se dobila [inline]2,5\%[/inline]-na slanoća je:
[inline]\text{A)}[/inline] [inline]5,5[/inline];      [inline]\text{B)}[/inline] [inline]6[/inline];      [inline]\text{C)}[/inline] [inline]7[/inline];      [inline]\text{D)}[/inline] [inline]7,2[/inline];      [inline]\text{E)}[/inline] [inline]8[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]5,5[/inline];      [inline]\text{B)}[/inline] [inline]6[/inline];      [inline]\text{C)}[/inline] [inline]7[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]7,2[/inline];      [inline]\text{E)}[/inline] [inline]8[/inline];              [inline]\text{N)}[/inline] ne znam.

9.Link zadatka Zbir svih celobrojnih rešenja nejednačine [inline]\sqrt{x+3}+\sqrt{x+15}\lt6[/inline] je:
[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]-3[/inline];      [inline]\text{D)}[/inline] [inline]-2[/inline];      [inline]\text{E)}[/inline] [inline]-6[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]0[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]-3[/inline];      [inline]\text{D)}[/inline] [inline]-2[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-6[/inline];              [inline]\text{N)}[/inline] ne znam.

10.Link zadatka Zbir svih rešenja jednačine [inline]\log_3x=1+\log_x9[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{28}{3}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{28}{3}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]3[/inline];              [inline]\text{N)}[/inline] ne znam.

11.Link zadatka Ako je [inline]\text{tg }x=2[/inline], onda je vrednost izraza [inline]\sin^4x+\cos^4x[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4}{25}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{7}{25}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4}{5}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{17}{25}[/inline];      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4}{25}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{7}{25}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4}{5}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{17}{25}[/inline];      [inline]\text{E)}[/inline] [inline]1[/inline];              [inline]\text{N)}[/inline] ne znam.

12.Link zadatka Ako je [inline]x[/inline] stranica kvadrata upisanog u jednakostranični trougao stranice [inline]a[/inline], onda je [inline]x[/inline] jednako:
[inline]\text{A)}[/inline] [inline]a\left(3\sqrt3-2\right)[/inline];      [inline]\text{B)}[/inline] [inline]a\left(3\sqrt3+2\right)[/inline];      [inline]\text{C)}[/inline] [inline]a\left(2\sqrt3-3\right)[/inline];      [inline]\text{D)}[/inline] [inline]a\left(2\sqrt3-2\right)[/inline];      [inline]\text{E)}[/inline] [inline]a\left(3\sqrt3+3\right)[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]a\left(3\sqrt3-2\right)[/inline];      [inline]\text{B)}[/inline] [inline]a\left(3\sqrt3+2\right)[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]a\left(2\sqrt3-3\right)[/inline];      [inline]\text{D)}[/inline] [inline]a\left(2\sqrt3-2\right)[/inline];      [inline]\text{E)}[/inline] [inline]a\left(3\sqrt3+3\right)[/inline];              [inline]\text{N)}[/inline] ne znam.

13.Link zadatka Dužina osnovne ivice pravilne četvorostrane piramide je [inline]a=16\text{ cm}[/inline], dok je bočna visina za [inline]2\text{ cm}[/inline] duža od visine piramide. Njena zapremina je:
[inline]\text{A)}[/inline] [inline]1200\text{ cm}^3[/inline];      [inline]\text{B)}[/inline] [inline]1280\text{ cm}^3[/inline];      [inline]\text{C)}[/inline] [inline]1300\text{ cm}^3[/inline];      [inline]\text{D)}[/inline] [inline]1400\text{ cm}^3[/inline];      [inline]\text{E)}[/inline] [inline]1150\text{ cm}^3[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1200\text{ cm}^3[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1280\text{ cm}^3[/inline];      [inline]\text{C)}[/inline] [inline]1300\text{ cm}^3[/inline];      [inline]\text{D)}[/inline] [inline]1400\text{ cm}^3[/inline];      [inline]\text{E)}[/inline] [inline]1150\text{ cm}^3[/inline];              [inline]\text{N)}[/inline] ne znam.

14.Link zadatka Zbir svih vrednosti parametra [inline]A[/inline] za koje je prava [inline]p\colon Ax-2y-10=0[/inline] tangenta kružnice [inline]x^2+y^2=20[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]-4[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]-4[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] ne znam.

15.Link zadatka Vrednost izraza [inline]\displaystyle\left(\frac{1+i\sqrt3}{1+i}\right)^{30}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]2^{15}i[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]2^{15}[/inline];      [inline]\text{D)}[/inline] [inline]2^{30}[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]2^{15}i[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]2^{15}[/inline];      [inline]\text{D)}[/inline] [inline]2^{30}[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.

16.Link zadatka Zbir brojeva koje treba umetnuti između brojeva [inline]3[/inline] i [inline]96[/inline], tako da se dobije geometrijska progresija čija je suma zajedno sa datim brojevima [inline]189[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]86[/inline];      [inline]\text{B)}[/inline] [inline]80[/inline];      [inline]\text{C)}[/inline] [inline]88[/inline];      [inline]\text{D)}[/inline] [inline]90[/inline];      [inline]\text{E)}[/inline] [inline]100[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]86[/inline];      [inline]\text{B)}[/inline] [inline]80[/inline];      [inline]\text{C)}[/inline] [inline]88[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]90[/inline];      [inline]\text{E)}[/inline] [inline]100[/inline];              [inline]\text{N)}[/inline] ne znam.

17.Link zadatka Broj pravih određenih sa [inline]13[/inline] tačaka, od kojih nikoje tri nisu kolinearne, jednak je:
[inline]\text{A)}[/inline] [inline]87[/inline];      [inline]\text{B)}[/inline] [inline]118[/inline];      [inline]\text{C)}[/inline] [inline]78[/inline];      [inline]\text{D)}[/inline] [inline]140[/inline];      [inline]\text{E)}[/inline] [inline]120[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]87[/inline];      [inline]\text{B)}[/inline] [inline]118[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]78[/inline];      [inline]\text{D)}[/inline] [inline]140[/inline];      [inline]\text{E)}[/inline] [inline]120[/inline];              [inline]\text{N)}[/inline] ne znam.

18.Link zadatka Razlika najveće i najmanje vrednosti funkcije [inline]y=\sin x+\cos^2x+1[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{9}{4}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{9}{4}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{D)}[/inline] [inline]2[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline];              [inline]\text{N)}[/inline] ne znam.

19.Link zadatka Ako je [inline]f_1(x)=x[/inline], [inline]f_2(x)=1-x[/inline], [inline]f_{n+2}(x)=f_{n+1}\bigl(f_n(x)\bigr)[/inline] onda je [inline]f_{2021}(2021)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2020[/inline];      [inline]\text{B)}[/inline] [inline]-2021[/inline];      [inline]\text{C)}[/inline] [inline]2021[/inline];      [inline]\text{D)}[/inline] [inline]2002[/inline];      [inline]\text{E)}[/inline] [inline]-2020[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]2020[/inline];      [inline]\text{B)}[/inline] [inline]-2021[/inline];      [inline]\text{C)}[/inline] [inline]2021[/inline];      [inline]\text{D)}[/inline] [inline]2002[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-2020[/inline];              [inline]\text{N)}[/inline] ne znam.

20.Link zadatka Broj rešenja jednačine [inline]\displaystyle\sin^4x-\cos^4x=\frac{1}{2}[/inline] koja pripadaju intervalu [inline][-\pi,\pi][/inline] je:
[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]1[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.


Izvor: LINK


Napomena: Ukoliko vam treba pomoć oko rešavanja nekog od zadataka koji dosad nije obrađivan ni na jednoj temi, slobodno zatražite pomoć na forumu „Matemanija“, naravno uz poštovanje forumskih pravila.