ETF MATF FON GRF FORUM

Prijemni ispit na Građevinskom fakultetu u Beogradu

29. jun 2021.


Test ima [inline]20[/inline] zadataka na dve stranice. Zadaci [inline]1–3[/inline] vrede po [inline]4[/inline] poena, zadaci [inline]4–17[/inline] vrede po [inline]5[/inline] poena i zadaci [inline]18–20[/inline] vrede po [inline]6[/inline] poena. Pogrešan odgovor donosi [inline]−10\%[/inline] poena od broja poena predviđenih 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 Vrednost izraza [inline]\displaystyle\frac{2}{3\sqrt3+5}+5[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]3\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]5\sqrt3[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]10[/inline]      [inline]\text{E)}[/inline] [inline]5[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]3\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]5\sqrt3[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]10[/inline]      [inline]\text{E)}[/inline] [inline]5[/inline]              [inline]\text{N)}[/inline] Ne znam

2.Link zadatka Ako je [inline]\log_32=a[/inline] i [inline]\log_35=b[/inline], onda je [inline]\log_{27}20[/inline] jednak:
[inline]\text{A)}[/inline] [inline]3(a+b)[/inline]      [inline]\text{B)}[/inline] [inline]3(2a+b)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{2a+b}{3}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a+b}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2a+b}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]3(a+b)[/inline]      [inline]\text{B)}[/inline] [inline]3(2a+b)[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\frac{2a+b}{3}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{a+b}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2a+b}[/inline]              [inline]\text{N)}[/inline] Ne znam

3.Link zadatka Ako je [inline]\displaystyle f\left(\frac{2x+7}{3-x}\right)=x[/inline], onda je [inline]f(2)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam

4.Link zadatka Poluprečnik kruga [inline]x^2+y^2-6x+8y=0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]7[/inline]      [inline]\text{B)}[/inline] [inline]5[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]7[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]5[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam

5.Link zadatka Skup rešenja nejednačine [inline]\displaystyle\frac{2}{x^2}\lt\frac{1}{x^3}[/inline] je oblika:
[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a)[/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a)[/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline](a,b)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam

6.Link zadatka Ako je [inline](a_n)[/inline] aritmetički niz takav da je [inline]a_2+a_7=36[/inline] i zbir prvih sedam članova niza je [inline]100[/inline], onda je [inline]a_1[/inline] jednako:
[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]3[/inline]      [inline]\text{E)}[/inline] [inline]-8[/inline]              [inline]\text{N)}[/inline] Ne znam[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]3[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]-8[/inline]              [inline]\text{N)}[/inline] Ne znam

7.Link zadatka Skup rešenja nejednačine [inline]\sqrt{x+6}>x[/inline] je oblika:
[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\text{D)}[/inline] [inline][a,b)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,a]\cup[b,\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a][/inline]      [inline]\text{C)}[/inline] [inline][b,\infty)[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline][a,b)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam

8.Link zadatka Imate šest različitih romana pisca Borisa Vijana. Na koliko načina možete da ih poređate na policu za knjige?
[inline]\text{A)}[/inline] [inline]24[/inline]      [inline]\text{B)}[/inline] [inline]120[/inline]      [inline]\text{C)}[/inline] [inline]160[/inline]      [inline]\text{D)}[/inline] [inline]420[/inline]      [inline]\text{E)}[/inline] [inline]720[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]24[/inline]      [inline]\text{B)}[/inline] [inline]120[/inline]      [inline]\text{C)}[/inline] [inline]160[/inline]      [inline]\text{D)}[/inline] [inline]420[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]720[/inline]              [inline]\text{N)}[/inline] Ne znam

9.Link zadatka Polinom [inline]P(x)=ax^4+bx^3-4x+1[/inline] je deljiv polinomom [inline]Q(x)=x^2-1[/inline]. Onda je [inline]a+3b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]17[/inline]      [inline]\text{B)}[/inline] [inline]15[/inline]      [inline]\text{C)}[/inline] [inline]13[/inline]      [inline]\text{D)}[/inline] [inline]11[/inline]      [inline]\text{E)}[/inline] [inline]3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]17[/inline]      [inline]\text{B)}[/inline] [inline]15[/inline]      [inline]\text{C)}[/inline] [inline]13[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]11[/inline]      [inline]\text{E)}[/inline] [inline]3[/inline]              [inline]\text{N)}[/inline] Ne znam

10.Link zadatka Ako je [inline]z=x+iy[/inline] kompleksan broj takav da je [inline]|z-2i|-\overline z=i+3[/inline], onda je [inline]3xy[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-1[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]-4[/inline]      [inline]\text{D)}[/inline] [inline]5[/inline]      [inline]\text{E)}[/inline] [inline]-6[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-1[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]-4[/inline]      [inline]\text{D)}[/inline] [inline]5[/inline]      [inline]\text{E)}[/inline] [inline]-6[/inline]              [inline]\text{N)}[/inline] Ne znam

11.Link zadatka Prava koja prolazi kroz tačke [inline]A(1,-1)[/inline] i [inline]B(0,2)[/inline] sa koordinatnim osama gradi trougao čija je površina:
[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]      [inline]\text{C)}[/inline] [inline]4[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{6}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]      [inline]\text{C)}[/inline] [inline]4[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{6}[/inline]              [inline]\text{N)}[/inline] Ne znam

12.Link zadatka Broj rešenja jednačine [inline]\text{tg }x=\sqrt3[/inline] koja pripadaju intervalu [inline](0,3\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\infty[/inline]      [inline]\text{B)}[/inline] [inline]4[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]2[/inline]      [inline]\text{E)}[/inline] [inline]1[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\infty[/inline]      [inline]\text{B)}[/inline] [inline]4[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]2[/inline]      [inline]\text{E)}[/inline] [inline]1[/inline]              [inline]\text{N)}[/inline] Ne znam

13.Link zadatka [inline]\displaystyle\sin\left(\frac{\pi}{2}-x\right)[/inline] je jednak:
[inline]\text{A)}[/inline] [inline]-\sin x[/inline]      [inline]\text{B)}[/inline] [inline]-\cos x[/inline]      [inline]\text{C)}[/inline] [inline]\sin2x[/inline]      [inline]\text{D)}[/inline] [inline]\sin x[/inline]      [inline]\text{E)}[/inline] [inline]\cos x[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-\sin x[/inline]      [inline]\text{B)}[/inline] [inline]-\cos x[/inline]      [inline]\text{C)}[/inline] [inline]\sin2x[/inline]      [inline]\text{D)}[/inline] [inline]\sin x[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]\cos x[/inline]              [inline]\text{N)}[/inline] Ne znam

14.Link zadatka Kompleksni broj [inline]\displaystyle\frac{16+16i^{2021}}{(1+i)^9}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]-1[/inline]      [inline]\text{C)}[/inline] [inline]1-i[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]-1[/inline]      [inline]\text{C)}[/inline] [inline]1-i[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam

15.Link zadatka Broj rešenja jednačine [inline]\log_x(x+6)=2[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]1[/inline]      [inline]\text{C)}[/inline] [inline]2[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]4[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]1[/inline]      [inline]\text{C)}[/inline] [inline]2[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]4[/inline]              [inline]\text{N)}[/inline] Ne znam

16.Link zadatka Zapremina pravilnog tetraedra stranice [inline]a=6\text{ cm}[/inline] je:
[inline]\text{A)}[/inline] [inline]24\sqrt2\text{ cm}^3[/inline]      [inline]\text{B)}[/inline] [inline]16\sqrt2\text{ cm}^3[/inline]      [inline]\text{C)}[/inline] [inline]32\sqrt2\text{ cm}^3[/inline]      [inline]\text{D)}[/inline] [inline]18\sqrt2\text{ cm}^3[/inline]      [inline]\text{E)}[/inline] [inline]9\sqrt2\text{ cm}^3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]24\sqrt2\text{ cm}^3[/inline]      [inline]\text{B)}[/inline] [inline]16\sqrt2\text{ cm}^3[/inline]      [inline]\text{C)}[/inline] [inline]32\sqrt2\text{ cm}^3[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]18\sqrt2\text{ cm}^3[/inline]      [inline]\text{E)}[/inline] [inline]9\sqrt2\text{ cm}^3[/inline]              [inline]\text{N)}[/inline] Ne znam

17.Link zadatka Broj rešenja jednačine [inline]x^2-|x|-2=0[/inline] je:
[inline]\text{A)}[/inline] [inline]\infty[/inline]      [inline]\text{B)}[/inline] [inline]4[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]2[/inline]      [inline]\text{E)}[/inline] [inline]1[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\infty[/inline]      [inline]\text{B)}[/inline] [inline]4[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]2[/inline]      [inline]\text{E)}[/inline] [inline]1[/inline]              [inline]\text{N)}[/inline] Ne znam

18.Link zadatka Zbir rešenja jednačine [inline]6\cdot25^x-19\cdot15^x+10\cdot9^x=0[/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]3[/inline]      [inline]\text{E)}[/inline] [inline]27[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\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]3[/inline]      [inline]\text{E)}[/inline] [inline]27[/inline]              [inline]\text{N)}[/inline] Ne znam

19.Link zadatka Zbir najmanje i najveće vrednosti funkcije [inline]f(x)=x^2-x-6[/inline] na intervalu [inline][0,4][/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{25}{4}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]      [inline]\text{C)}[/inline] [inline]-6[/inline]      [inline]\text{D)}[/inline] [inline]6[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{25}{4}[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]      [inline]\text{C)}[/inline] [inline]-6[/inline]      [inline]\text{D)}[/inline] [inline]6[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam

20.Link zadatka Zbir rešenja jednačine [inline]\displaystyle\sin^4x+\cos^4x=\frac{3}{4}[/inline] koja pripadaju intervalu [inline](0,2\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]2\pi[/inline]      [inline]\text{B)}[/inline] [inline]4\pi[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{65\pi}{8}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{127\pi}{8}[/inline]      [inline]\text{E)}[/inline] [inline]8\pi[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2\pi[/inline]      [inline]\text{B)}[/inline] [inline]4\pi[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{65\pi}{8}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{127\pi}{8}[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]8\pi[/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.