ETF MATF FON GRF FORUM

Prijemni ispit na Građevinskom fakultetu u Beogradu

30. jun 2020.


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-\sqrt2}{1+\sqrt2}-\frac{1+\sqrt2}{1-\sqrt2}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]16[/inline]      [inline]\text{B)}[/inline] [inline]4\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]-2\sqrt2[/inline]      [inline]\text{D)}[/inline] [inline]2-4\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2-2\sqrt2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]16[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]4\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]-2\sqrt2[/inline]      [inline]\text{D)}[/inline] [inline]2-4\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2-2\sqrt2[/inline]              [inline]\text{N)}[/inline] Ne znam

2.Link zadatka Ako je [inline]f(x)=x+1[/inline] i [inline]\displaystyle g(x)=\frac{1}{x-1}[/inline], onda je [inline]g\bigl(f(1)\bigr)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]-4[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]0[/inline]      [inline]\text{E)}[/inline] [inline]1[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]-4[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]0[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]1[/inline]              [inline]\text{N)}[/inline] Ne znam

3.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja jednačine [inline]\sqrt2x^2+x+1=0[/inline], onda je [inline]\displaystyle\frac{1}{x_1^2x_2}+\frac{1}{x_1x_2^2}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]-\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]2[/inline]      [inline]\text{D)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]-\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]2[/inline]      [inline]\text{D)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam

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

5.Link zadatka Ako je [inline](a_n)[/inline] aritmetički niz takav da je [inline]a_5+a_{10}+a_{12}=3[/inline] i [inline]a_{11}+a_6=0[/inline], onda je zbir [inline]a_1+a_2+a_3[/inline] jednak:
[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]-9[/inline]      [inline]\text{C)}[/inline] [inline]-17[/inline]      [inline]\text{D)}[/inline] [inline]-11[/inline]      [inline]\text{E)}[/inline] [inline]-39[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]-9[/inline]      [inline]\text{C)}[/inline] [inline]-17[/inline]      [inline]\text{D)}[/inline] [inline]-11[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]-39[/inline]              [inline]\text{N)}[/inline] Ne znam

6.Link zadatka Zbir rešenja jednačine [inline]4\cdot2^{2x}-17\cdot2^x+4=0[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]8[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [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]4[/inline]      [inline]\text{B)}[/inline] [inline]8[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]0[/inline]      [inline]\text{E)}[/inline] [inline]3[/inline]              [inline]\text{N)}[/inline] Ne znam

7.Link zadatka Prave [inline]5x-y=-1[/inline] i [inline]6x-y=19[/inline] seku se u tački [inline]M(a,b)[/inline]. Tada je [inline]a\cdot b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2021[/inline]      [inline]\text{B)}[/inline] [inline]1010[/inline]      [inline]\text{C)}[/inline] [inline]101[/inline]      [inline]\text{D)}[/inline] [inline]202[/inline]      [inline]\text{E)}[/inline] [inline]2020[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2021[/inline]      [inline]\text{B)}[/inline] [inline]1010[/inline]      [inline]\text{C)}[/inline] [inline]101[/inline]      [inline]\text{D)}[/inline] [inline]202[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]2020[/inline]              [inline]\text{N)}[/inline] Ne znam

8.Link zadatka Vrednost parametra [inline]a[/inline] za koju je polinom [inline]P(x)=3ax^3+2ax^2+ax+1[/inline] deljiv polinomom [inline]Q(x)=x+1[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]      [inline]\text{E)}[/inline] [inline]-3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{C)}[/inline] [inline]3[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]      [inline]\text{E)}[/inline] [inline]-3[/inline]              [inline]\text{N)}[/inline] Ne znam

9.Link zadatka Ako jednačina [inline]x^2+ax+1=0[/inline] nema realnih rešenja, onda parametar [inline]a[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline](-1,1)[/inline]      [inline]\text{B)}[/inline] [inline](-3,3)[/inline]      [inline]\text{C)}[/inline] [inline](-5,5)[/inline]      [inline]\text{D)}[/inline] [inline](-2,2)[/inline]      [inline]\text{E)}[/inline] [inline](-6,6)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-1,1)[/inline]      [inline]\text{B)}[/inline] [inline](-3,3)[/inline]      [inline]\text{C)}[/inline] [inline](-5,5)[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline](-2,2)[/inline]      [inline]\text{E)}[/inline] [inline](-6,6)[/inline]              [inline]\text{N)}[/inline] Ne znam

10.Link zadatka Ako prava [inline]ax+y=0[/inline] dodiruje kružnicu [inline]x^2+2x+y^2+2y+1=0[/inline], onda je [inline]a[/inline] jednako:
[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]\enclose{box}{\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

11.Link zadatka Broj rešenja jednačine [inline]\sin x-\cos2x=0[/inline] koja pripadaju intervalu [inline](-\pi,\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]3[/inline]      [inline]\text{C)}[/inline] [inline]5[/inline]      [inline]\text{D)}[/inline] [inline]7[/inline]      [inline]\text{E)}[/inline] [inline]9[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]3[/inline]      [inline]\text{C)}[/inline] [inline]5[/inline]      [inline]\text{D)}[/inline] [inline]7[/inline]      [inline]\text{E)}[/inline] [inline]9[/inline]              [inline]\text{N)}[/inline] Ne znam

12.Link zadatka Na koliko se različitih načina mogu poređati sva slova reči [inline]ISPIT[/inline]?:
[inline]\text{A)}[/inline] [inline]60[/inline]      [inline]\text{B)}[/inline] [inline]30[/inline]      [inline]\text{C)}[/inline] [inline]90[/inline]      [inline]\text{D)}[/inline] [inline]20[/inline]      [inline]\text{E)}[/inline] [inline]12[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]60[/inline]      [inline]\text{B)}[/inline] [inline]30[/inline]      [inline]\text{C)}[/inline] [inline]90[/inline]      [inline]\text{D)}[/inline] [inline]20[/inline]      [inline]\text{E)}[/inline] [inline]12[/inline]              [inline]\text{N)}[/inline] Ne znam

13.Link zadatka Vrednost izraza [inline]\displaystyle\frac{2^{1010}+(1+i)^{2020}}{2^{1010}-(1-i)^{2020}}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]2^{2020}(1+i)[/inline]      [inline]\text{B)}[/inline] [inline]2^{2020}i[/inline]      [inline]\text{C)}[/inline] [inline]2^{1010}[/inline]      [inline]\text{D)}[/inline] [inline]2^{1010}i[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2^{2020}(1+i)[/inline]      [inline]\text{B)}[/inline] [inline]2^{2020}i[/inline]      [inline]\text{C)}[/inline] [inline]2^{1010}[/inline]      [inline]\text{D)}[/inline] [inline]2^{1010}i[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam

14.Link zadatka Proizvod realnih rešenja jednačine [inline]\sqrt{2x+4}=2-x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]6[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]-2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]6[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\text{E)}[/inline] [inline]-2[/inline]              [inline]\text{N)}[/inline] Ne znam

15.Link zadatka Četvorostrana piramida čija je osnova pravougaonik stranica [inline]6[/inline] i [inline]8[/inline] ima međusobno jednake bočne ivice. Ako je dužina bočne ivice [inline]13[/inline], dužina visine piramide je jednaka:
[inline]\text{A)}[/inline] [inline]5[/inline]      [inline]\text{B)}[/inline] [inline]6[/inline]      [inline]\text{C)}[/inline] [inline]12[/inline]      [inline]\text{D)}[/inline] [inline]2\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]5[/inline]      [inline]\text{B)}[/inline] [inline]6[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]12[/inline]      [inline]\text{D)}[/inline] [inline]2\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam

16.Link zadatka Rešenje nejednačine [inline]\displaystyle\frac{x+1}{x-1}>\frac{x-2}{x+2}[/inline] je skup oblika:
[inline]\text{A)}[/inline] [inline](a,b]\cup(c,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline][a,+\infty)[/inline]      [inline]\text{C)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)[/inline]      [inline]\text{E)}[/inline] [inline](a,b)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline](a,b]\cup(c,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline][a,+\infty)[/inline]      [inline]\text{C)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)[/inline]      [inline]\text{E)}[/inline] [inline](a,b)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam

17.Link zadatka Najveća vrednost funkcije [inline]f(x)=2x-x^2[/inline] iznosi:
[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]-3[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]-3[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]1[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam

18.Link zadatka Krug [inline]k[/inline] upisan u pravougli trougao [inline]ABC[/inline], dodiruje katete [inline]AC[/inline] i [inline]BC[/inline] u tačkama [inline]P[/inline] i [inline]Q[/inline]. Ako je [inline]AC=6[/inline] i [inline]BC=8[/inline], površina figure ograničene dužima [inline]PC[/inline], [inline]QC[/inline] i manjim od lukova [inline]PQ[/inline] kruga [inline]k[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]4+\pi[/inline]      [inline]\text{B)}[/inline] [inline]4-\pi[/inline]      [inline]\text{C)}[/inline] [inline]4\pi[/inline]      [inline]\text{D)}[/inline] [inline]4+4\pi[/inline]      [inline]\text{E)}[/inline] [inline]5-\pi[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4+\pi[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]4-\pi[/inline]      [inline]\text{C)}[/inline] [inline]4\pi[/inline]      [inline]\text{D)}[/inline] [inline]4+4\pi[/inline]      [inline]\text{E)}[/inline] [inline]5-\pi[/inline]              [inline]\text{N)}[/inline] Ne znam

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

20.Link zadatka Vrednost izraza [inline]4\sin^32020^\circ-3\sin2020^\circ[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{\sqrt3}{2}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt2}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\frac{\sqrt3}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{\sqrt3}{2}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{\sqrt2}{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.