ETF MATF FON GRF FORUM

Prijemni ispit na Građevinskom fakultetu u Beogradu

2. jul 2013.


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]\left(x^2+x\sqrt2+1\right)\left(x^2-x\sqrt2+1\right)[/inline] za [inline]x=\sqrt[4]2[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]3+2\sqrt2[/inline]      [inline]\text{B)}[/inline] [inline]3-2\sqrt2[/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]3+2\sqrt2[/inline]      [inline]\text{B)}[/inline] [inline]3-2\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]1[/inline]      [inline]\text{D)}[/inline] [inline]2[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]3[/inline]              [inline]\text{N)}[/inline] Ne znam

2.Link zadatka Ako je [inline]\log_32=p[/inline], onda je [inline]\log_372[/inline] jednak:
[inline]\text{A)}[/inline] [inline]2p+3[/inline]      [inline]\text{B)}[/inline] [inline]3p+2[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2p+3}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3p+2}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{p}{3p+2}[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2p+3[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]3p+2[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{2p+3}[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3p+2}[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{p}{3p+2}[/inline]              [inline]\text{N)}[/inline] Ne znam

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3.Link zadatka Rešenje nejednačine [inline]\displaystyle\frac{1}{x}\lt5[/inline] je skup oblika:
[inline]\text{A)}[/inline] [inline](a,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline][a,+\infty)[/inline]      [inline]\text{C)}[/inline] [inline](-\infty,a)\cup[b,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)[/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][a,+\infty)[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline](-\infty,a)\cup[b,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline](a,b)[/inline]      [inline]\text{E)}[/inline] [inline][a,b)[/inline]              [inline]\text{N)}[/inline] Ne znam

4.Link zadatka Koliko različitih četvorocifrenih brojeva može da se napiše koristeći cifre [inline]2,0,1,3[/inline] pri čemu se cifre ne ponavljaju?
[inline]\text{A)}[/inline] [inline]6[/inline]      [inline]\text{B)}[/inline] [inline]12[/inline]      [inline]\text{C)}[/inline] [inline]18[/inline]      [inline]\text{D)}[/inline] [inline]24[/inline]      [inline]\text{E)}[/inline] [inline]48[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]6[/inline]      [inline]\text{B)}[/inline] [inline]12[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]18[/inline]      [inline]\text{D)}[/inline] [inline]24[/inline]      [inline]\text{E)}[/inline] [inline]48[/inline]              [inline]\text{N)}[/inline] Ne znam

5.Link zadatka U krug poluprečnika [inline]r[/inline] upisan je pravilan osmougao. Njegova površina jednaka je:
[inline]\text{A)}[/inline] [inline]4r^2\sqrt2[/inline]      [inline]\text{B)}[/inline] [inline]2r^2\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4}{3}r^2\sqrt2[/inline]      [inline]\text{D)}[/inline] [inline]4r\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2\sqrt3r^2[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4r^2\sqrt2[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]2r^2\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{4}{3}r^2\sqrt2[/inline]      [inline]\text{D)}[/inline] [inline]4r\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2\sqrt3r^2[/inline]              [inline]\text{N)}[/inline] Ne znam

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6.Link zadatka Ako je [inline]\sin11^\circ=a[/inline], onda je [inline]\sin2013^\circ[/inline] jednak:
[inline]\text{A)}[/inline] [inline]3a-4a^3[/inline]      [inline]\text{B)}[/inline] [inline]3a[/inline]      [inline]\text{C)}[/inline] [inline]4a^3[/inline]      [inline]\text{D)}[/inline] [inline]3a^3-4a[/inline]      [inline]\text{E)}[/inline] [inline]4a^3-3a[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]3a-4a^3[/inline]      [inline]\text{B)}[/inline] [inline]3a[/inline]      [inline]\text{C)}[/inline] [inline]4a^3[/inline]      [inline]\text{D)}[/inline] [inline]3a^3-4a[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]4a^3-3a[/inline]              [inline]\text{N)}[/inline] Ne znam

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7.Link zadatka Tačke [inline]A(1,1)[/inline], [inline]B(3,4)[/inline], [inline]C(4,6)[/inline] i [inline]D(a,b)[/inline] su redom temena paralelograma [inline]ABCD[/inline]. Tada je [inline]a-b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]1[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]-1[/inline]      [inline]\text{D)}[/inline] [inline]-2[/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{box}{\text{C)}}[/inline] [inline]-1[/inline]      [inline]\text{D)}[/inline] [inline]-2[/inline]      [inline]\text{E)}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam

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8.Link zadatka Broj celobrojnih rešenja nejednačine [inline]\sqrt{x^2-1}\lt x+1[/inline] koja pripadaju segmentu [inline][-100,100][/inline] jednak je:
[inline]\text{A)}[/inline] [inline]99[/inline]      [inline]\text{B)}[/inline] [inline]100[/inline]      [inline]\text{C)}[/inline] [inline]101[/inline]      [inline]\text{D)}[/inline] [inline]200[/inline]      [inline]\text{E)}[/inline] [inline]201[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]99[/inline]      [inline]\enclose{box}{\text{B)}}[/inline] [inline]100[/inline]      [inline]\text{C)}[/inline] [inline]101[/inline]      [inline]\text{D)}[/inline] [inline]200[/inline]      [inline]\text{E)}[/inline] [inline]201[/inline]              [inline]\text{N)}[/inline] Ne znam

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9.Link zadatka Broj kompleksnih brojeva [inline]z=x+iy[/inline] ([inline]x,y\in\mathbb{R}[/inline]), za koje važi jednakost [inline]|z+3|-\overline z=2-i[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]3[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]4[/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]3[/inline]      [inline]\text{B)}[/inline] [inline]2[/inline]      [inline]\text{C)}[/inline] [inline]4[/inline]      [inline]\text{D)}[/inline] [inline]1[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]0[/inline]              [inline]\text{N)}[/inline] Ne znam

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10.Link zadatka Prava [inline]x+y=2013[/inline] je tangenta parabole [inline]y=x^2+19x+m[/inline]. Tada je [inline]m[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2003[/inline]      [inline]\text{B)}[/inline] [inline]2103[/inline]      [inline]\text{C)}[/inline] [inline]2013[/inline]      [inline]\text{D)}[/inline] [inline]2113[/inline]      [inline]\text{E)}[/inline] [inline]2130[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]2003[/inline]      [inline]\text{B)}[/inline] [inline]2103[/inline]      [inline]\text{C)}[/inline] [inline]2013[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline]2113[/inline]      [inline]\text{E)}[/inline] [inline]2130[/inline]              [inline]\text{N)}[/inline] Ne znam

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11.Link zadatka Zbir prvih [inline]50[/inline] neparnih prirodnih brojeva je:
[inline]\text{A)}[/inline] [inline]1275[/inline]      [inline]\text{B)}[/inline] [inline]1500[/inline]      [inline]\text{C)}[/inline] [inline]2500[/inline]      [inline]\text{D)}[/inline] [inline]2550[/inline]      [inline]\text{E)}[/inline] [inline]2750[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]1275[/inline]      [inline]\text{B)}[/inline] [inline]1500[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]2500[/inline]      [inline]\text{D)}[/inline] [inline]2550[/inline]      [inline]\text{E)}[/inline] [inline]2750[/inline]              [inline]\text{N)}[/inline] Ne znam

12.Link zadatka Ako polinom [inline]P(x)=x^4+ax^3+x^2+b[/inline] pri deljenju polinomom [inline]Q(x)=x^2+2x[/inline] daje ostatak [inline]R(x)=-2x+1[/inline], onda je [inline]a+b[/inline] jednako:
[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]-1[/inline]      [inline]\text{E)}[/inline] [inline]-2[/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]1[/inline]      [inline]\text{D)}[/inline] [inline]-1[/inline]      [inline]\text{E)}[/inline] [inline]-2[/inline]              [inline]\text{N)}[/inline] Ne znam

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13.Link zadatka Ako je [inline]i^2=-1[/inline], onda je [inline]\displaystyle\frac{(1-i)^{11}}{(1+i)^5}[/inline] jednako:
[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]4i[/inline]      [inline]\text{C)}[/inline] [inline]-8i[/inline]      [inline]\text{D)}[/inline] [inline]8i[/inline]      [inline]\text{E)}[/inline] [inline]8[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]4[/inline]      [inline]\text{B)}[/inline] [inline]4i[/inline]      [inline]\text{C)}[/inline] [inline]-8i[/inline]      [inline]\text{D)}[/inline] [inline]8i[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]8[/inline]              [inline]\text{N)}[/inline] Ne znam

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14.Link zadatka Ako je [inline]\displaystyle f\left(\frac{x-1}{x+1}\right)=x[/inline], onda je [inline]f\bigl(f(1/2)\bigr)[/inline] jednako:
[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]-1[/inline]      [inline]\text{E)}[/inline] [inline]-2[/inline]              [inline]\text{N)}[/inline] Ne znam[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]-1[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline]-2[/inline]              [inline]\text{N)}[/inline] Ne znam

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15.Link zadatka Ako je [inline](a_n)[/inline] rastući geometrijski niz, takav da je proizvod prva tri člana [inline]1000[/inline], a njihov zbir [inline]35[/inline], onda je [inline]a_6[/inline] jednako:
[inline]\text{A)}[/inline] [inline]160[/inline]      [inline]\text{B)}[/inline] [inline]80[/inline]      [inline]\text{C)}[/inline] [inline]180[/inline]      [inline]\text{D)}[/inline] [inline]80[/inline]      [inline]\text{E)}[/inline] [inline]100[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]160[/inline]      [inline]\text{B)}[/inline] [inline]80[/inline]      [inline]\text{C)}[/inline] [inline]180[/inline]      [inline]\text{D)}[/inline] [inline]80[/inline]      [inline]\text{E)}[/inline] [inline]100[/inline]              [inline]\text{N)}[/inline] Ne znam

16.Link zadatka U loptu poluprečnika [inline]R[/inline] upisan je valjak čija je visina jednaka prečniku osnove. Zapremina valjka jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\pi R^3\frac{\sqrt2}{2}[/inline]      [inline]\text{B)}[/inline] [inline]\pi R^3\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\pi R^2\frac{\sqrt2}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\pi R^2\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2\pi R^3[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\enclose{box}{\text{A)}}[/inline] [inline]\displaystyle\pi R^3\frac{\sqrt2}{2}[/inline]      [inline]\text{B)}[/inline] [inline]\pi R^3\sqrt2[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle\pi R^2\frac{\sqrt2}{2}[/inline]      [inline]\text{D)}[/inline] [inline]\pi R^2\sqrt2[/inline]      [inline]\text{E)}[/inline] [inline]2\pi R^3[/inline]              [inline]\text{N)}[/inline] Ne znam

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17.Link zadatka Broj parova prirodnih brojeva [inline](x,y)[/inline] koji su rešenja jednačine [inline]4^x-25^y=39[/inline] 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

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18.Link zadatka Skup svih rešenja nejednačine [inline]9^{|x-1|}-9^{|x-2|}\lt8\cdot3^{|x-1|+|x-2|-1}[/inline] je:
[inline]\text{A)}[/inline] [inline]\displaystyle\left(-\infty,\frac{3}{2}\right)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{3}{2},2\right)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle(-\infty,0]\cup\left(\frac{3}{2},2\right)[/inline]      [inline]\text{D)}[/inline] [inline](-\infty,2)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,+\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left(-\infty,\frac{3}{2}\right)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{3}{2},2\right)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle(-\infty,0]\cup\left(\frac{3}{2},2\right)[/inline]      [inline]\enclose{box}{\text{D)}}[/inline] [inline](-\infty,2)[/inline]      [inline]\text{E)}[/inline] [inline](-\infty,+\infty)[/inline]              [inline]\text{N)}[/inline] Ne znam

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19.Link zadatka Rešenje nejednačine [inline]\sin x>|\cos2x|[/inline] na intervalu [inline](0,2\pi)[/inline] je podskup oblika:
[inline]\text{A)}[/inline] [inline](a,b)\cup(b,c)\cup(d,e)[/inline]      [inline]\text{B)}[/inline] [inline](a,b)[/inline]      [inline]\text{C)}[/inline] [inline][a,b][/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]\text{A)}[/inline] [inline](a,b)\cup(b,c)\cup(d,e)[/inline]      [inline]\text{B)}[/inline] [inline](a,b)[/inline]      [inline]\text{C)}[/inline] [inline][a,b][/inline]      [inline]\text{D)}[/inline] [inline][a,b)[/inline]      [inline]\enclose{box}{\text{E)}}[/inline] [inline](a,b)\cup(b,c)[/inline]              [inline]\text{N)}[/inline] Ne znam

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20.Link zadatka Skup svih rešenja nejednačine [inline]\log_{|x|}\left(5x^2-1\right)>2[/inline] je:
[inline]\text{A)}[/inline] [inline](-\infty,-1)\cup(1,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{1}{\sqrt5},\frac{1}{2}\right)[/inline]      [inline]\text{C)}[/inline] [inline]\displaystyle(-\infty,-1)\cup\left(-\frac{1}{2},-\frac{1}{\sqrt5}\right)\cup\left(\frac{1}{\sqrt5},\frac{1}{2}\right)\cup(1,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\left(-\frac{1}{2},0\right)\cup\left(0,\frac{1}{2}\right)\cup(1,+\infty)[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle(-\infty,-1)\cup\left(-\frac{1}{\sqrt5},0\right)\cup\left(0,\frac{1}{\sqrt5}\right)[/inline]              [inline]\text{N)}[/inline] Ne znam[inline]\text{A)}[/inline] [inline](-\infty,-1)\cup(1,+\infty)[/inline]      [inline]\text{B)}[/inline] [inline]\displaystyle\left(\frac{1}{\sqrt5},\frac{1}{2}\right)[/inline]      [inline]\enclose{box}{\text{C)}}[/inline] [inline]\displaystyle(-\infty,-1)\cup\left(-\frac{1}{2},-\frac{1}{\sqrt5}\right)\cup\left(\frac{1}{\sqrt5},\frac{1}{2}\right)\cup(1,+\infty)[/inline]      [inline]\text{D)}[/inline] [inline]\displaystyle\left(-\frac{1}{2},0\right)\cup\left(0,\frac{1}{2}\right)\cup(1,+\infty)[/inline]      [inline]\text{E)}[/inline] [inline]\displaystyle(-\infty,-1)\cup\left(-\frac{1}{\sqrt5},0\right)\cup\left(0,\frac{1}{\sqrt5}\right)[/inline]              [inline]\text{N)}[/inline] Ne znam

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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.