ETF MATF FON GRF FORUM

Prijemni ispit na Građevinskom fakultetu u Beogradu

30. jun 2015.


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\sqrt\frac{2+\sqrt3}{2-\sqrt3}+\sqrt\frac{2-\sqrt3}{2+\sqrt3}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]4\sqrt3[/inline]      [inline]\text{B)}[/inline] [inline]4[/inline]      [inline]\text{C)}[/inline] [inline]14\sqrt3[/inline]      [inline]\text{D)}[/inline] [inline]14[/inline]      [inline]\text{E)}[/inline] [inline]4+2\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4\sqrt3[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]4[/inline]      [inline]\text{C)}[/inline] [inline]14\sqrt3[/inline]      [inline]\text{D)}[/inline] [inline]14[/inline]      [inline]\text{E)}[/inline] [inline]4+2\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam

2.Link zadatka Ako su [inline]x_1[/inline] i [inline]x_2[/inline] rešenja kvadratne jednačine [inline]-x^2+2x-p^2=0[/inline], onda je [inline]x_1^2+x_2^2[/inline] jednako:
[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]4-p^2[/inline]      [inline]\text{C)}[/inline] [inline]4-2p^2[/inline]      [inline]\text{D)}[/inline] [inline]4-p^4[/inline]      [inline]\text{E)}[/inline] [inline]4-2p^4[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]4-p^2[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]4-2p^2[/inline]      [inline]\text{D)}[/inline] [inline]4-p^4[/inline]      [inline]\text{E)}[/inline] [inline]4-2p^4[/inline]              [inline]\text{N)}[/inline] Ne znam

3.Link zadatka Ako je [inline]\displaystyle f(x)=\frac{1}{x+1}[/inline] i [inline]\displaystyle g(x)=\frac{x}{x+2}[/inline], onda je [inline]g\bigl(f(1)\bigr)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{5}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5}{3}[/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}{3}[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{5}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5}{3}[/inline]              [inline]\text{N)}[/inline] Ne znam

4.Link zadatka Ako su [inline]a[/inline], [inline]b[/inline] i [inline]c[/inline] međusobno različiti realni brojevi, onda je rešenje nejednačine [inline]\displaystyle\frac{1}{x^3}>1[/inline] skup oblika:
[inline]\text{A)}[/inline] [inline](a,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a)[/inline]      [inline]\text{C)}[/inline] [inline](a,b)\cup(c,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]      [inline]\text{E)}[/inline] [inline](a,b)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](a,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline](-\infty,a)[/inline]      [inline]\text{C)}[/inline] [inline](a,b)\cup(c,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline](a,b)[/inline]              [inline]\text{N)}[/inline] Ne znam

5.Link zadatka Minimum funkcije [inline]f(x)=2x^2-5x+7[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]10[/inline]      [inline]\text{B)}[/inline] [inline]0[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{31}{8}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{31}{4}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{31}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]10[/inline]      [inline]\text{B)}[/inline] [inline]0[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle\frac{31}{8}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{31}{4}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{31}{2}[/inline]              [inline]\text{N)}[/inline] Ne znam

6.Link zadatka Rešenje nejednačine [inline]\log_x(3x-2)>2[/inline] je skup oblika: ([inline]a[/inline], [inline]b[/inline], [inline]c[/inline] i [inline]d[/inline] su međusobno različiti realni brojevi)
[inline]\text{A)}[/inline] [inline](a,b)\cup(b,c)[/inline]      [inline]\text{B)}[/inline] [inline](a,b)\cup[c,d)[/inline]      [inline]\text{C)}[/inline] [inline](a,b)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)\cup(c,+\infty)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline](a,b)\cup(b,c)[/inline]      [inline]\text{B)}[/inline] [inline](a,b)\cup[c,d)[/inline]      [inline]\text{C)}[/inline] [inline](a,b)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)\cup(c,+\infty)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,a)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam

7.Link zadatka Zbir rešenja jednačine [inline]3^{x^2-2x-11}=11^{x^2-2x-11}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]1[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]-2[/inline]      [inline]\text{E)}[/inline] [inline]2+\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]2[/inline]      [inline]\text{B)}[/inline] [inline]1[/inline]      [inline]\text{C)}[/inline] [inline]0[/inline]      [inline]\text{D)}[/inline] [inline]-2[/inline]      [inline]\text{E)}[/inline] [inline]2+\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam

8.Link zadatka Ako je polinom [inline]P(x)=ax^4-x^3+bx+2[/inline] deljiv polinomom [inline]Q(x)=x^2-4[/inline], onda je [inline]8a+b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]12[/inline]      [inline]\text{B)}[/inline] [inline]9[/inline]      [inline]\text{C)}[/inline] [inline]6[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]12[/inline]      [inline]\text{B)}[/inline] [inline]9[/inline]      [inline]\text{C)}[/inline] [inline]6[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam

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

10.Link zadatka Prava [inline]\displaystyle y=-\frac{x}{2}+5[/inline] normalna je na pravu:
[inline]\text{A)}[/inline] [inline]\displaystyle y=\frac{x}{2}+5[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle y=\frac{x}{2}-5[/inline]      [inline]\text{C)}[/inline] [inline]y=-x+5[/inline]      [inline]\text{D)}[/inline] [inline]y=2x+3[/inline]      [inline]\text{E)}[/inline] [inline]y=-2x+5[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle y=\frac{x}{2}+5[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle y=\frac{x}{2}-5[/inline]      [inline]\text{C)}[/inline] [inline]y=-x+5[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]y=2x+3[/inline]      [inline]\text{E)}[/inline] [inline]y=-2x+5[/inline]              [inline]\text{N)}[/inline] Ne znam

11.Link zadatka Odnos zapremine lopte opisane oko date kocke i zapremine lopte upisane u istu kocku jednak je:
[inline]\text{A)}[/inline] [inline]2\sqrt2[/inline]      [inline]\text{B)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{C)}[/inline] [inline]2[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\text{E)}[/inline] [inline]3\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2\sqrt2[/inline]      [inline]\text{B)}[/inline] [inline]\sqrt3[/inline]      [inline]\text{C)}[/inline] [inline]2[/inline]      [inline]\text{D)}[/inline] [inline]3[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]3\sqrt3[/inline]              [inline]\text{N)}[/inline] Ne znam

12.Link zadatka Broj rešenja jednačine [inline]\sqrt{x+1}+\sqrt{x-2}=1[/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]\infty[/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]\infty[/inline]              [inline]\text{N)}[/inline] Ne znam

13.Link zadatka Imaginarni deo kompleksnog broja [inline]\displaystyle\frac{(1-i)^{2015}}{2-4i}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{2^{1007}}{5}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{2^{1006}}{5}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3\cdot2^{1006}}{5}i[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3\cdot2^{1006}}{5}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2^{1006}}{5}i[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{2^{1007}}{5}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{2^{1006}}{5}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3\cdot2^{1006}}{5}i[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]\displaystyle\frac{3\cdot2^{1006}}{5}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2^{1006}}{5}i[/inline]              [inline]\text{N)}[/inline] Ne znam

14.Link zadatka Dat je aritmetički niz kod koga je zbir prvih [inline]11[/inline] članova jednak [inline]22[/inline]. Ako je [inline]a_{12}=4[/inline], onda je [inline]a_6[/inline] jednako:
[inline]\text{A)}[/inline] [inline]16[/inline]      [inline]\text{B)}[/inline] [inline]-4[/inline]      [inline]\text{C)}[/inline] [inline]6[/inline]      [inline]\text{D)}[/inline] [inline]-8[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]16[/inline]      [inline]\text{B)}[/inline] [inline]-4[/inline]      [inline]\text{C)}[/inline] [inline]6[/inline]      [inline]\text{D)}[/inline] [inline]-8[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam

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

16.Link zadatka Dvocifrenih brojeva deljivih sa [inline]3[/inline] ima:
[inline]\text{A)}[/inline] [inline]25[/inline]      [inline]\text{B)}[/inline] [inline]24[/inline]      [inline]\text{C)}[/inline] [inline]27[/inline]      [inline]\text{D)}[/inline] [inline]30[/inline]      [inline]\text{E)}[/inline] [inline]33[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]25[/inline]      [inline]\text{B)}[/inline] [inline]24[/inline]      [inline]\text{C)}[/inline] [inline]27[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]30[/inline]      [inline]\text{E)}[/inline] [inline]33[/inline]              [inline]\text{N)}[/inline] Ne znam

17.Link zadatka Ako je [inline]\text{tg }x=m[/inline], onda je [inline]\cos2x[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{m}{\sqrt{m^2+1}}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1+m^2}{1-m^2}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{\sqrt{m^2+1}}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{m^2-1}{1+m^2}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1-m^2}{1+m^2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{m}{\sqrt{m^2+1}}[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1+m^2}{1-m^2}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{\sqrt{m^2+1}}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{m^2-1}{1+m^2}[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]\displaystyle\frac{1-m^2}{1+m^2}[/inline]              [inline]\text{N)}[/inline] Ne znam

18.Link zadatka Tangente parabole [inline]y=x^2[/inline] u tačkama [inline](1,1)[/inline] i [inline](-2,4)[/inline] seku se u tački [inline]M(a,b)[/inline]. Tada je [inline]ab[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-1[/inline]      [inline]\text{B)}[/inline] [inline]1[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/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]1[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]      [inline]\text{E)}[/inline] [inline]2[/inline]              [inline]\text{N)}[/inline] Ne znam

19.Link zadatka Zbir rešenja jednačine [inline]\sin x-|\sin x|+\sqrt2=0[/inline] na intervalu [inline](-2\pi,2\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi}{4}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3\pi}{4}[/inline]      [inline]\text{D)}[/inline] [inline]2\pi[/inline]      [inline]\text{E)}[/inline] [inline]3\pi[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]0[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\pi}{4}[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{3\pi}{4}[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]2\pi[/inline]      [inline]\text{E)}[/inline] [inline]3\pi[/inline]              [inline]\text{N)}[/inline] Ne znam

20.Link zadatka Data je jednačina [inline]\left|x^2-3x+2\right|=a[/inline]. Ova jednačina ima maksimalan broj rešenja ako realan parametar [inline]a[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline]\displaystyle\left(\frac{3}{2},\frac{7}{4}\right)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left[0,\frac{7}{4}\right)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\left(\frac{1}{4},\frac{7}{4}\right][/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{3}{4},\frac{7}{4}\right)[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\left(0,\frac{1}{4}\right)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left(\frac{3}{2},\frac{7}{4}\right)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left[0,\frac{7}{4}\right)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\left(\frac{1}{4},\frac{7}{4}\right][/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\left(\frac{3}{4},\frac{7}{4}\right)[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]\displaystyle\left(0,\frac{1}{4}\right)[/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.