ETF MATF FON GRF TMF FORUM

Prijemni ispit na Građevinskom fakultetu u Beogradu

26. jun 2018.


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{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{9}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5}{11}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4}{9}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{10}{11}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5}{7}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{9}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{5}{11}[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\frac{4}{9}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{10}{11}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5}{7}[/inline]              [inline]\text{N)}[/inline] Ne znam

2.Link zadatka Ako je [inline]f(x)=\sqrt{x+1}[/inline] i [inline]g(x)=\sqrt{x-1}[/inline], onda je [inline](g\circ f)(24)+(f\circ g)(1)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-1[/inline]      [inline]\text{B)}[/inline] [inline]3[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [inline]\text{D)}[/inline] [inline]4[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-1[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]3[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [inline]\text{D)}[/inline] [inline]4[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam

3.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja kvadratne jednačine [inline]x^2-x+1=0[/inline], onda je [inline]x_1^3+x_2^3[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]-2[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]-3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]-2[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]-3[/inline]              [inline]\text{N)}[/inline] Ne znam

4.Link zadatka Koliko celobrojnih rešenja ima nejednačina [inline]\displaystyle\frac{x^2-2x+2}{x^2+4x}\ge0[/inline]?
[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] beskonačno mnogo      [inline]\text{D)}[/inline] [inline]0[/inline]      [inline]\text{E)}[/inline] [inline]3[/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] beskonačno mnogo      [inline]\text{D)}[/inline] [inline]0[/inline]      [inline]\text{E)}[/inline] [inline]3[/inline]              [inline]\text{N)}[/inline] Ne znam

5.Link zadatka Ako je u geometrijskom nizu zbir prvog i drugog člana jednak [inline]4[/inline], a zbir četvrtog i petog člana jednak [inline]108[/inline], onda je sedmi član ovog niza jednak:
[inline]\text{A)}[/inline] [inline]216[/inline]      [inline]\text{B)}[/inline] [inline]128[/inline]      [inline]\text{C)}[/inline] [inline]81[/inline]      [inline]\text{D)}[/inline] [inline]729[/inline]      [inline]\text{E)}[/inline] [inline]243[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]216[/inline]      [inline]\text{B)}[/inline] [inline]128[/inline]      [inline]\text{C)}[/inline] [inline]81[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]729[/inline]      [inline]\text{E)}[/inline] [inline]243[/inline]              [inline]\text{N)}[/inline] Ne znam

6.Link zadatka Zbir rešenja jednačine [inline]9^x-12\cdot3^x+27=0[/inline] jednak 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] [inline]7[/inline]      [inline]\text{E)}[/inline] [inline]5[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]3[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]7[/inline]      [inline]\text{E)}[/inline] [inline]5[/inline]              [inline]\text{N)}[/inline] Ne znam

7.Link zadatka Na Svetskom prvenstvu u fudbalu [inline]32[/inline] ekipe podeljene su u [inline]8[/inline] grupa od po [inline]4[/inline] ekipe. U prvom krugu svaka ekipa igra protiv svake ekipe iz svoje grupe. Ukupan broj odigranih utakmica u prvom krugu jednak je:
[inline]\text{A)}[/inline] [inline]92[/inline]      [inline]\text{B)}[/inline] [inline]96[/inline]      [inline]\text{C)}[/inline] [inline]24[/inline]      [inline]\text{D)}[/inline] [inline]72[/inline]      [inline]\text{E)}[/inline] [inline]48[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]92[/inline]      [inline]\text{B)}[/inline] [inline]96[/inline]      [inline]\text{C)}[/inline] [inline]24[/inline]      [inline]\text{D)}[/inline] [inline]72[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]48[/inline]              [inline]\text{N)}[/inline] Ne znam

8.Link zadatka Polinom [inline]P(x)=x^4+ax^3+b[/inline] deljiv je polinomom [inline]Q(x)=x^2+1[/inline]. Ostatak pri deljenju polinoma [inline]P(x)[/inline] polinomom [inline]x+1[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]10[/inline]      [inline]\text{B)}[/inline] [inline]-50[/inline]      [inline]\text{C)}[/inline] [inline]80[/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]10[/inline]      [inline]\text{B)}[/inline] [inline]-50[/inline]      [inline]\text{C)}[/inline] [inline]80[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]0[/inline]      [inline]\text{E)}[/inline] [inline]-10[/inline]              [inline]\text{N)}[/inline] Ne znam

9.Link zadatka Ako je [inline]z=x+iy[/inline] ([inline]x,y\in\mathbb{R}[/inline], [inline]i^2=-1[/inline]), proizvod rešenja jednačine [inline]|z|+i\overline z=z+2-i[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]-1+i[/inline]      [inline]\text{C)}[/inline] [inline]-i[/inline]      [inline]\text{D)}[/inline] [inline]-1[/inline]      [inline]\text{E)}[/inline] [inline]i[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]-1+i[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]-i[/inline]      [inline]\text{D)}[/inline] [inline]-1[/inline]      [inline]\text{E)}[/inline] [inline]i[/inline]              [inline]\text{N)}[/inline] Ne znam

10.Link zadatka Jednačina kružnice [inline]k[/inline] koja dodiruje [inline]x[/inline]-osu i čiji je centar tačka [inline](0,1)[/inline] glasi:
[inline]\text{A)}[/inline] [inline]x^2+y^2=y[/inline]      [inline]\text{B)}[/inline] [inline]x^2+y^2=2[/inline]      [inline]\text{C)}[/inline] [inline]x^2+y^2=x[/inline]      [inline]\text{D)}[/inline] [inline]x^2+y^2=2y[/inline]      [inline]\text{E)}[/inline] [inline]x^2+y^2=2x[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]x^2+y^2=y[/inline]      [inline]\text{B)}[/inline] [inline]x^2+y^2=2[/inline]      [inline]\text{C)}[/inline] [inline]x^2+y^2=x[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]x^2+y^2=2y[/inline]      [inline]\text{E)}[/inline] [inline]x^2+y^2=2x[/inline]              [inline]\text{N)}[/inline] Ne znam

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

12.Link zadatka Rešenje nejednačine [inline]\sqrt{2x+4}\lt x-2[/inline] je skup:
[inline]\text{A)}[/inline] [inline](-\infty,0)\cup(6,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,-2)[/inline]      [inline]\text{C)}[/inline] [inline](-1,0)\cup(4,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline](4,+\infty)[/inline]      [inline]\text{E)}[/inline] [inline](6,+\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,0)\cup(6,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,-2)[/inline]      [inline]\text{C)}[/inline] [inline](-1,0)\cup(4,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline](4,+\infty)[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline](6,+\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam

13.Link zadatka Količnik imaginarnog i realnog dela kompleksnog broja [inline]\left(1-i\sqrt3\right)^{2018}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-2^{2017}\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{C)}[/inline] [inline]-2^{2018}[/inline]      [inline]\text{D)}[/inline] [inline]2^{2018}[/inline]      [inline]\text{E)}[/inline] [inline]2^{1009}\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-2^{2017}\sqrt3[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]\sqrt3[/inline]      [inline]\text{C)}[/inline] [inline]-2^{2018}[/inline]      [inline]\text{D)}[/inline] [inline]2^{2018}[/inline]      [inline]\text{E)}[/inline] [inline]2^{1009}\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam

14.Link zadatka U jednakokraki trapez dužine kraka [inline]5\text{ cm}[/inline] upisan je krug prečnika [inline]4\text{ cm}[/inline]. Ako su [inline]a[/inline] i [inline]b[/inline] osnovice trapeza, onda je [inline]a\cdot b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]84[/inline]      [inline]\text{B)}[/inline] [inline]72[/inline]      [inline]\text{C)}[/inline] [inline]36[/inline]      [inline]\text{D)}[/inline] [inline]40[/inline]      [inline]\text{E)}[/inline] [inline]16[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]84[/inline]      [inline]\text{B)}[/inline] [inline]72[/inline]      [inline]\text{C)}[/inline] [inline]36[/inline]      [inline]\text{D)}[/inline] [inline]40[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]16[/inline]              [inline]\text{N)}[/inline] Ne znam

15.Link zadatka Ako je [inline]m[/inline] najmanja, a [inline]M[/inline] najveća vrednost funkcije [inline]f(x)=-x^2+2x-2[/inline] na segmentu [inline][0,3][/inline], onda je [inline]m\cdot M[/inline] jednako:
[inline]\text{A)}[/inline] [inline]10[/inline]      [inline]\text{B)}[/inline] [inline]-10[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]5[/inline]      [inline]\text{E)}[/inline] [inline]-5[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]10[/inline]      [inline]\text{B)}[/inline] [inline]-10[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]5[/inline]      [inline]\text{E)}[/inline] [inline]-5[/inline]              [inline]\text{N)}[/inline] Ne znam

16.Link zadatka Proizvod rešenja jednačine [inline]x+2\cdot|x-4|=7[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]6[/inline]      [inline]\text{B)}[/inline] [inline]5[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [inline]\text{D)}[/inline] [inline]-1[/inline]      [inline]\text{E)}[/inline] [inline]-6[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]6[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]5[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [inline]\text{D)}[/inline] [inline]-1[/inline]      [inline]\text{E)}[/inline] [inline]-6[/inline]              [inline]\text{N)}[/inline] Ne znam

17.Link zadatka Bočna strana pravilne četvorostrane piramide gradi sa osnovom piramide ugao od [inline]60^\circ[/inline]. Ako je dužina visine piramide jednaka [inline]\sqrt3[/inline], onda je njena zapremina jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4}{3}\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]3[/inline]      [inline]\text{C)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{D)}[/inline] [inline]4\sqrt3[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]\displaystyle\frac{4}{3}\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]3[/inline]      [inline]\text{C)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{D)}[/inline] [inline]4\sqrt3[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt3}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam

18.Link zadatka Tangenta parabole [inline]y=4-x^2[/inline] paralelna je pravoj [inline]y=4x[/inline]. Ako je jednačina tangente [inline]y=kx+n[/inline], onda je [inline]3k-n[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-12[/inline]      [inline]\text{B)}[/inline] [inline]-2[/inline]      [inline]\text{C)}[/inline] [inline]4[/inline]      [inline]\text{D)}[/inline] [inline]2[/inline]      [inline]\text{E)}[/inline] [inline]12[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]-12[/inline]      [inline]\text{B)}[/inline] [inline]-2[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]4[/inline]      [inline]\text{D)}[/inline] [inline]2[/inline]      [inline]\text{E)}[/inline] [inline]12[/inline]              [inline]\text{N)}[/inline] Ne znam

19.Link zadatka Rešenje nejednačine [inline]2\sin x-2\cos x\lt4\sin x\cos x-1[/inline] na intervalu [inline](-\pi,\pi)[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\left(-\frac{\pi}{3},\frac{\pi}{6}\right)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\frac{\pi}{3},-\frac{\pi}{6}\right)\cup\left(\frac{\pi}{3},\pi\right)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\left(\frac{\pi}{6},\pi\right)[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\left(-\frac{5\pi}{6},-\frac{\pi}{3}\right)\cup\left(-\frac{\pi}{6},\frac{\pi}{3}\right)[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\left(\frac{\pi}{2},\pi\right)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left(-\frac{\pi}{3},\frac{\pi}{6}\right)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left(-\frac{\pi}{3},-\frac{\pi}{6}\right)\cup\left(\frac{\pi}{3},\pi\right)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\left(\frac{\pi}{6},\pi\right)[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]\displaystyle\left(-\frac{5\pi}{6},-\frac{\pi}{3}\right)\cup\left(-\frac{\pi}{6},\frac{\pi}{3}\right)[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\left(\frac{\pi}{2},\pi\right)[/inline]              [inline]\text{N)}[/inline] Ne znam

20.Link zadatka Rešenje logaritamske nejednačine [inline]\displaystyle\log_{x^2}\left(\sqrt{x^2-1}-1\right)\lt0[/inline] je skup:
[inline]\text{A)}[/inline] [inline]\left(\sqrt2,\sqrt5\right)[/inline]      [inline]\text{B)}[/inline] [inline]\left(-\sqrt5,-\sqrt2\right)[/inline]      [inline]\text{C)}[/inline] [inline]\left(-\sqrt5,1\right)[/inline]      [inline]\text{D)}[/inline] [inline]\left(1,\sqrt2\right)[/inline]      [inline]\text{E)}[/inline] [inline]\left(-\sqrt5,-\sqrt2\right)\cup\left(\sqrt2,\sqrt5\right)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\left(\sqrt2,\sqrt5\right)[/inline]      [inline]\text{B)}[/inline] [inline]\left(-\sqrt5,-\sqrt2\right)[/inline]      [inline]\text{C)}[/inline] [inline]\left(-\sqrt5,1\right)[/inline]      [inline]\text{D)}[/inline] [inline]\left(1,\sqrt2\right)[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]\left(-\sqrt5,-\sqrt2\right)\cup\left(\sqrt2,\sqrt5\right)[/inline]              [inline]\text{N)}[/inline] Ne znam


Izvor: LINK

Postupci: https://www.grf.bg.ac.rs/p/docs/zadaci_prijemni/re_eni_zadaci_sa_prijemnog_ispita_iz_matematike__2018__1551440191530.pdf


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.