ETF MATF FON GRF TMF FORUM

Prijemni ispit na Tehnološko-metalurškom fakultetu u Beogradu

jun 2018.


Test ima [inline]20[/inline] zadataka na [inline]2[/inline] stranice. Zadaci [inline]1–3[/inline] vrede po [inline]3[/inline] poena, zadaci [inline]4–7[/inline] vrede po [inline]4[/inline] poena, zadaci [inline]8–13[/inline] vrede po [inline]5[/inline] poena, zadaci [inline]14–17[/inline] vrede po [inline]6[/inline] poena i zadaci [inline]18–20[/inline] vrede po [inline]7[/inline] poena. Pogrešan odgovor donosi [inline]−10\%[/inline] od broja poena 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 Rešenje nejednačine [inline]\displaystyle x\le3-\frac{1}{x-1}[/inline] je skup:
[inline]\text{A)}[/inline] [inline](-\infty,1)[/inline];      [inline]\text{B)}[/inline] [inline](-\infty,1)\cup\{2\}[/inline];      [inline]\text{C)}[/inline] [inline](-\infty,2)[/inline];      [inline]\text{D)}[/inline] [inline](-\infty,1)\cup(2,+\infty)[/inline];      [inline]\text{E)}[/inline] [inline]\emptyset[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline](-\infty,1)[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline](-\infty,1)\cup\{2\}[/inline];      [inline]\text{C)}[/inline] [inline](-\infty,2)[/inline];      [inline]\text{D)}[/inline] [inline](-\infty,1)\cup(2,+\infty)[/inline];      [inline]\text{E)}[/inline] [inline]\emptyset[/inline];              [inline]\text{N)}[/inline] ne znam.

2.Link zadatka Sistem jednačina [inline]ax-y=a+1[/inline]; [inline]-x+ay=-2[/inline], nema rešenja ako je:
[inline]\text{A)}[/inline] [inline]a=-1[/inline];      [inline]\text{B)}[/inline] [inline]a=0[/inline];      [inline]\text{C)}[/inline] [inline]a=1[/inline];      [inline]\text{D)}[/inline] [inline]a=-2[/inline];      [inline]\text{E)}[/inline] [inline]a=2[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]a=-1[/inline];      [inline]\text{B)}[/inline] [inline]a=0[/inline];      [inline]\text{C)}[/inline] [inline]a=1[/inline];      [inline]\text{D)}[/inline] [inline]a=-2[/inline];      [inline]\text{E)}[/inline] [inline]a=2[/inline];              [inline]\text{N)}[/inline] ne znam.

3.Link zadatka Lovac i po za dan i po ulovi zeca i po. Broj zečeva koji ulovi [inline]9[/inline] lovaca za [inline]8[/inline] dana je:
[inline]\text{A)}[/inline] [inline]9[/inline];      [inline]\text{B)}[/inline] [inline]48[/inline];      [inline]\text{C)}[/inline] [inline]36[/inline];      [inline]\text{D)}[/inline] [inline]40[/inline];      [inline]\text{E)}[/inline] [inline]72[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]9[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]48[/inline];      [inline]\text{C)}[/inline] [inline]36[/inline];      [inline]\text{D)}[/inline] [inline]40[/inline];      [inline]\text{E)}[/inline] [inline]72[/inline];              [inline]\text{N)}[/inline] ne znam.

4.Link zadatka Proizvod rešenja jednačine [inline]\displaystyle\left(\frac{1}{4}\right)^\frac{4-x^2}{2}=8^x[/inline] je:
[inline]\text{A)}[/inline] [inline]7[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\text{E)}[/inline] [inline]-4[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]7[/inline];      [inline]\text{B)}[/inline] [inline]4[/inline];      [inline]\text{C)}[/inline] [inline]9[/inline];      [inline]\text{D)}[/inline] [inline]0[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-4[/inline];              [inline]\text{N)}[/inline] ne znam.

5.Link zadatka Peti član aritmetičke progresije je [inline]a_5=16[/inline] a jedanaesti [inline]a_{11}=31[/inline]. Zbir prvih [inline]17[/inline] članova te progresije [inline]S_{17}[/inline] je:
[inline]\text{A)}[/inline] [inline]444[/inline];      [inline]\text{B)}[/inline] [inline]442[/inline];      [inline]\text{C)}[/inline] [inline]368[/inline];      [inline]\text{D)}[/inline] [inline]468[/inline];      [inline]\text{E)}[/inline] [inline]455,5[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]444[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]442[/inline];      [inline]\text{C)}[/inline] [inline]368[/inline];      [inline]\text{D)}[/inline] [inline]468[/inline];      [inline]\text{E)}[/inline] [inline]455,5[/inline];              [inline]\text{N)}[/inline] ne znam.

6.Link zadatka Neka je [inline]n[/inline] broj stranica pravilnog mnogougla. Ako se on poveća za [inline]3[/inline], tada se ugao pravilnog mnogougla poveća za [inline]4^\circ[/inline]. Tada je [inline]n[/inline] jednako:
[inline]\text{A)}[/inline] [inline]12[/inline];      [inline]\text{B)}[/inline] [inline]14[/inline];      [inline]\text{C)}[/inline] [inline]15[/inline];      [inline]\text{D)}[/inline] [inline]16[/inline];      [inline]\text{E)}[/inline] [inline]17[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]12[/inline];      [inline]\text{B)}[/inline] [inline]14[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]15[/inline];      [inline]\text{D)}[/inline] [inline]16[/inline];      [inline]\text{E)}[/inline] [inline]17[/inline];              [inline]\text{N)}[/inline] ne znam.

7.Link zadatka Stranice trougla su [inline]5\text{ cm}[/inline], [inline]7\text{ cm}[/inline] i [inline]9\text{ cm}[/inline]. Ako se produže za jednake dužine [inline]x[/inline] trougao postaje pravougli. Tada je [inline]x[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]3\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]7\text{ cm}[/inline];      [inline]\text{D)}[/inline] [inline]1\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]2\text{ cm}[/inline];      [inline]\text{B)}[/inline] [inline]3\text{ cm}[/inline];      [inline]\text{C)}[/inline] [inline]7\text{ cm}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]1\text{ cm}[/inline];      [inline]\text{E)}[/inline] [inline]4\text{ cm}[/inline];              [inline]\text{N)}[/inline] ne znam.

8.Link zadatka Posle dva uzastopna jednaka procentualna povećanja cene proizvoda od [inline]100[/inline] dinara, ona sada iznosi [inline]125,44[/inline] dinara. Procenat povećanja je:
[inline]\text{A)}[/inline] [inline]12\%[/inline];      [inline]\text{B)}[/inline] [inline]9\%[/inline];      [inline]\text{C)}[/inline] [inline]15\%[/inline];      [inline]\text{D)}[/inline] [inline]14\%[/inline];      [inline]\text{E)}[/inline] [inline]25\%[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]12\%[/inline];      [inline]\text{B)}[/inline] [inline]9\%[/inline];      [inline]\text{C)}[/inline] [inline]15\%[/inline];      [inline]\text{D)}[/inline] [inline]14\%[/inline];      [inline]\text{E)}[/inline] [inline]25\%[/inline];              [inline]\text{N)}[/inline] ne znam.

9.Link zadatka Ako je [inline]\log_a27=b[/inline] onda je [inline]\log_{\sqrt3}\sqrt[3]a[/inline] jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3(1-a)}{b+1}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{b+1}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{b}[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3(1-a)}{b+1}[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]3[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{b+1}[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{2}{b}[/inline];              [inline]\text{N)}[/inline] ne znam.

10.Link zadatka Ako se dužina poluprečnika lopte poveća za [inline]3[/inline] njena zapremina se poveća za [inline]252\pi[/inline]. Tada se njena površina poveća za:
[inline]\text{A)}[/inline] [inline]108\pi[/inline];      [inline]\text{B)}[/inline] [inline]102\pi[/inline];      [inline]\text{C)}[/inline] [inline]100\pi[/inline];      [inline]\text{D)}[/inline] [inline]106\pi[/inline];      [inline]\text{E)}[/inline] [inline]98\pi[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]108\pi[/inline];      [inline]\text{B)}[/inline] [inline]102\pi[/inline];      [inline]\text{C)}[/inline] [inline]100\pi[/inline];      [inline]\text{D)}[/inline] [inline]106\pi[/inline];      [inline]\text{E)}[/inline] [inline]98\pi[/inline];              [inline]\text{N)}[/inline] ne znam.

11.Link zadatka Ako nejednačina [inline]\displaystyle\frac{x^2+(p+1)x+1}{x^2-x+1}\lt3[/inline] važi za svako [inline]x\in\mathbb{R}[/inline] onda [inline]p[/inline] pripada skupu:
[inline]\text{A)}[/inline] [inline](-\infty,-8)[/inline];      [inline]\text{B)}[/inline] [inline](-\infty,0)[/inline];      [inline]\text{C)}[/inline] [inline](-8,+\infty)[/inline];      [inline]\text{D)}[/inline] [inline](-8,0)[/inline];      [inline]\text{E)}[/inline] [inline](-\infty,1)[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline](-\infty,-8)[/inline];      [inline]\text{B)}[/inline] [inline](-\infty,0)[/inline];      [inline]\text{C)}[/inline] [inline](-8,+\infty)[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline](-8,0)[/inline];      [inline]\text{E)}[/inline] [inline](-\infty,1)[/inline];              [inline]\text{N)}[/inline] ne znam.

12.Link zadatka Zbir [inline]1+i+i^2+\cdots+i^{2000}[/inline], gde je [inline]i^2=-1[/inline], jednak je:
[inline]\text{A)}[/inline] [inline]i[/inline];      [inline]\text{B)}[/inline] [inline]-i[/inline];      [inline]\text{C)}[/inline] [inline]1[/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]i[/inline];      [inline]\text{B)}[/inline] [inline]-i[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]1[/inline];      [inline]\text{D)}[/inline] [inline]-1[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.

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13.Link zadatka Ako je [inline]f(x-2)=x^2-2x+3[/inline] onda je [inline]f(x+2)-2f(x+1)+f(x)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]x^2[/inline];      [inline]\text{B)}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]x^2+1[/inline];      [inline]\text{D)}[/inline] [inline]x^2-1[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]x^2[/inline];      [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2[/inline];      [inline]\text{C)}[/inline] [inline]x^2+1[/inline];      [inline]\text{D)}[/inline] [inline]x^2-1[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.

14.Link zadatka Celobrojno [inline]x[/inline] u razvoju [inline]\left(x+x^{\log x}\right)^5[/inline] takvo da treći član (u smislu razvoja binomne formule) iznosi [inline]10^6[/inline] jednako je:
[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]8[/inline];      [inline]\text{D)}[/inline] [inline]9[/inline];      [inline]\text{E)}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]7[/inline];      [inline]\text{C)}[/inline] [inline]8[/inline];      [inline]\text{D)}[/inline] [inline]9[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]10[/inline];              [inline]\text{N)}[/inline] ne znam.

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15.Link zadatka Dužina stranice romba je [inline]a=15[/inline] a zbir njegovih dijagonala je [inline]d_1+d_2=36[/inline]. Tada mu je površina jednaka:
[inline]\text{A)}[/inline] [inline]99[/inline];      [inline]\text{B)}[/inline] [inline]100[/inline];      [inline]\text{C)}[/inline] [inline]125[/inline];      [inline]\text{D)}[/inline] [inline]64[/inline];      [inline]\text{E)}[/inline] [inline]81[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]99[/inline];      [inline]\text{B)}[/inline] [inline]100[/inline];      [inline]\text{C)}[/inline] [inline]125[/inline];      [inline]\text{D)}[/inline] [inline]64[/inline];      [inline]\text{E)}[/inline] [inline]81[/inline];              [inline]\text{N)}[/inline] ne znam.

16.Link zadatka Proizvod [inline]\cos20^\circ\cos40^\circ\cos60^\circ\cos80^\circ[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline];      [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{6}[/inline];      [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{16}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{8}[/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}{4}[/inline];      [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{6}[/inline];      [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{1}{16}[/inline];      [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{8}[/inline];              [inline]\text{N)}[/inline] ne znam.

17.Link zadatka Broj načina na koji je moguće razmestiti [inline]10[/inline] gostiju hotela po sobama ako su dobili po jednu jednokrevetnu, dvokrevetnu, trokrevetnu i četvorokrevetnu sobu jednak je:
[inline]\text{A)}[/inline] [inline]12800[/inline];      [inline]\text{B)}[/inline] [inline]24000[/inline];      [inline]\text{C)}[/inline] [inline]360[/inline];      [inline]\text{D)}[/inline] [inline]3600[/inline];      [inline]\text{E)}[/inline] [inline]12600[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]12800[/inline];      [inline]\text{B)}[/inline] [inline]24000[/inline];      [inline]\text{C)}[/inline] [inline]360[/inline];      [inline]\text{D)}[/inline] [inline]3600[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]12600[/inline];              [inline]\text{N)}[/inline] ne znam.

18.Link zadatka Razlika najveće i najmanje vrednosti koju funkcija [inline]y=2x^3-15x^2+36x+2[/inline] dostiže na segmentu [inline][1,4][/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]9[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]5[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]9[/inline];      [inline]\text{B)}[/inline] [inline]1[/inline];      [inline]\text{C)}[/inline] [inline]5[/inline];      [inline]\text{D)}[/inline] [inline]4[/inline];      [inline]\text{E)}[/inline] [inline]0[/inline];              [inline]\text{N)}[/inline] ne znam.

19.Link zadatka Broj rešenja jednačine [inline]2\sin^4x-2\cos^4x-1=0[/inline] koja pripadaju intervalu [inline][-\pi,\pi][/inline] je:
[inline]\text{A)}[/inline] [inline]6[/inline];      [inline]\text{B)}[/inline] [inline]3[/inline];      [inline]\text{C)}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]5[/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]3[/inline];      [inline]\enclose{circle}{\text{C)}}[/inline] [inline]4[/inline];      [inline]\text{D)}[/inline] [inline]5[/inline];      [inline]\text{E)}[/inline] [inline]2[/inline];              [inline]\text{N)}[/inline] ne znam.

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20.Link zadatka Tačka [inline]P[/inline] na hiperboli [inline]3x^2-4y^2=72[/inline] koja je najbliža pravoj [inline]3x+2y+1=0[/inline] je:
[inline]\text{A)}[/inline] [inline]P(-3,6)[/inline];      [inline]\text{B)}[/inline] [inline]P(-6,-6)[/inline];      [inline]\text{C)}[/inline] [inline]P(6,-3)[/inline];      [inline]\text{D)}[/inline] [inline]P(6,6)[/inline];      [inline]\text{E)}[/inline] [inline]P(-6,3)[/inline];              [inline]\text{N)}[/inline] ne znam.[inline]\text{A)}[/inline] [inline]P(-3,6)[/inline];      [inline]\text{B)}[/inline] [inline]P(-6,-6)[/inline];      [inline]\text{C)}[/inline] [inline]P(6,-3)[/inline];      [inline]\text{D)}[/inline] [inline]P(6,6)[/inline];      [inline]\enclose{circle}{\text{E)}}[/inline] [inline]P(-6,3)[/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.