1.Link zadatka Neka su [inline]a[/inline] i [inline]b[/inline] proizvoljni realni brojevi. Koliko je od sledećih tvrđenja uvek tačno?
[inline](I)[/inline] ako je [inline]a\lt b[/inline] i [inline]ab\ne0[/inline], onda je [inline]\displaystyle\frac{1}{a}>\frac{1}{b}[/inline];
[inline](II)[/inline] ako je [inline]a\lt b[/inline], onda je [inline]a^2\lt b^2[/inline];
[inline](III)[/inline] ako je [inline]a\lt b[/inline], onda je [inline]2a\lt a+b[/inline];
[inline](IV)[/inline] ako je [inline]a\lt b[/inline], onda je [inline]-a>-b[/inline].
[inline]\text{A)}[/inline] nijedno [inline]\text{B)}[/inline] jedno [inline]\text{C)}[/inline] dva [inline]\text{D)}[/inline] tri [inline]\text{E)}[/inline] četiri [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] nijedno [inline]\text{B)}[/inline] jedno [inline]\enclose{circle}{\text{C)}}[/inline] dva [inline]\text{D)}[/inline] tri [inline]\text{E)}[/inline] četiri [inline]\text{N)}[/inline] ne znam
2.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\left(2019x^2+1\right)\left(x^2-y-1\right)\left(x^2-y^2\right)}{(x-y)(2019x-1260y)\left(2x^2-3y\right)}[/inline] za [inline]x=\sqrt3[/inline] i [inline]y=2[/inline]:
[inline]\text{A)}[/inline] manja je od [inline]0[/inline] [inline]\text{B)}[/inline] jednaka je [inline]0[/inline] [inline]\text{C)}[/inline] pripada intervalu [inline](0,1][/inline] [inline]\text{D)}[/inline] veća je od [inline]1[/inline] [inline]\text{E)}[/inline] nije definisana [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] manja je od [inline]0[/inline] [inline]\text{B)}[/inline] jednaka je [inline]0[/inline] [inline]\text{C)}[/inline] pripada intervalu [inline](0,1][/inline] [inline]\text{D)}[/inline] veća je od [inline]1[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] nije definisana [inline]\text{N)}[/inline] ne znam
3.Link zadatka Sistem jednačina [inline]2x+ay=3[/inline], [inline](a+2)x+4y=-3[/inline] ima beskonačno mnogo rešenja ako i samo ako za parametar [inline]a[/inline] važi:
[inline]\text{A)}[/inline] [inline]a=4[/inline] [inline]\text{B)}[/inline] [inline]a=2[/inline] [inline]\text{C)}[/inline] [inline]a\in\{-4,2\}[/inline] [inline]\text{D)}[/inline] [inline]a=-4[/inline] [inline]\text{E)}[/inline] takvo [inline]a[/inline] ne postoji [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]a=4[/inline] [inline]\text{B)}[/inline] [inline]a=2[/inline] [inline]\text{C)}[/inline] [inline]a\in\{-4,2\}[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]a=-4[/inline] [inline]\text{E)}[/inline] takvo [inline]a[/inline] ne postoji [inline]\text{N)}[/inline] ne znam
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4.Link zadatka Ako kvadratna jednačina [inline]x^2-ax+4=0[/inline] ima realna rešenja [inline]x_1[/inline] i [inline]x_2[/inline], pri čemu je [inline]x_1\lt x_2[/inline], a kvadratna jednačina [inline]x^2-9x+b=0[/inline] ima rešenja [inline]x_1[/inline] i [inline]2x_2[/inline], tada je proizvod [inline]abx_1x_2[/inline] jednak:
[inline]\text{A)}[/inline] [inline]20[/inline] [inline]\text{B)}[/inline] [inline]40[/inline] [inline]\text{C)}[/inline] [inline]80[/inline] [inline]\text{D)}[/inline] [inline]160[/inline] [inline]\text{E)}[/inline] [inline]272[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]20[/inline] [inline]\text{B)}[/inline] [inline]40[/inline] [inline]\text{C)}[/inline] [inline]80[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]160[/inline] [inline]\text{E)}[/inline] [inline]272[/inline] [inline]\text{N)}[/inline] ne znam
5.Link zadatka Teme parabole [inline]y=kx^2-7x+4k[/inline], [inline]k\ne0[/inline], leži u drugom kvadrantu ako i samo ako je:
[inline]\text{A)}[/inline] [inline]\displaystyle k\in\left(-\frac{7}{4},0\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle k\lt-\frac{7}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle|k|>\frac{7}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle k\in\left(-\frac{7}{4},0\right)\cup\left(0,\frac{7}{4}\right)[/inline] [inline]\text{E)}[/inline] [inline]k\lt0[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle k\in\left(-\frac{7}{4},0\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle k\lt-\frac{7}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle|k|>\frac{7}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle k\in\left(-\frac{7}{4},0\right)\cup\left(0,\frac{7}{4}\right)[/inline] [inline]\text{E)}[/inline] [inline]k\lt0[/inline] [inline]\text{N)}[/inline] ne znam
6.Link zadatka Ako je [inline](x,y)[/inline] rešenje sistema jednačina [inline]2^x+3\cdot2^y=2[/inline], [inline]4^x-9\cdot4^y=1[/inline], onda je [inline]x-y[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\log_23[/inline] [inline]\text{B)}[/inline] [inline]\log_25[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]\log_25-2[/inline] [inline]\text{E)}[/inline] [inline]\log_27-2[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\log_23[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\log_25[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]\log_25-2[/inline] [inline]\text{E)}[/inline] [inline]\log_27-2[/inline] [inline]\text{N)}[/inline] ne znam
7.Link zadatka Vrednost izraza [inline]\log_2\left(\log_{\sqrt2}9\cdot\log_{\sqrt3}2\right)[/inline] je:
[inline]\text{A)}[/inline] [inline]-1[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]2[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]-1[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]3[/inline] [inline]\text{C)}[/inline] [inline]4[/inline] [inline]\text{D)}[/inline] [inline]2[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline] [inline]\text{N)}[/inline] ne znam
8.Link zadatka Tetiva jednaka poluprečniku kruga deli krug na dva dela. Odnos površine većeg dela prema površini manjeg je:
[inline]\text{A)}[/inline] [inline]32:1[/inline] [inline]\text{B)}[/inline] [inline]\left(6\pi+2\sqrt3\right):\left(3\pi-2\sqrt3\right)[/inline] [inline]\text{C)}[/inline] [inline]\left(10\pi+3\sqrt3\right):\left(2\pi-3\sqrt3\right)[/inline] [inline]\text{D)}[/inline] [inline]\left(5\pi+\sqrt3\right):\left(\pi-\sqrt3\right)[/inline] [inline]\text{E)}[/inline] [inline]16:1[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]32:1[/inline] [inline]\text{B)}[/inline] [inline]\left(6\pi+2\sqrt3\right):\left(3\pi-2\sqrt3\right)[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\left(10\pi+3\sqrt3\right):\left(2\pi-3\sqrt3\right)[/inline] [inline]\text{D)}[/inline] [inline]\left(5\pi+\sqrt3\right):\left(\pi-\sqrt3\right)[/inline] [inline]\text{E)}[/inline] [inline]16:1[/inline] [inline]\text{N)}[/inline] ne znam
9.Link zadatka Površina osnove pravilne trostrane piramide je [inline]180\text{ cm}^2[/inline], a površina preseka te piramide sa ravni koja je paralelna osnovi i udaljena je [inline]6\text{ cm}[/inline] od vrha piramide iznosi [inline]45\text{ cm}^2[/inline]. Zapremina te piramide je:
[inline]\text{A)}[/inline] [inline]480\text{ cm}^3[/inline] [inline]\text{B)}[/inline] [inline]600\text{ cm}^3[/inline] [inline]\text{C)}[/inline] [inline]720\text{ cm}^3[/inline] [inline]\text{D)}[/inline] [inline]960\text{ cm}^3[/inline] [inline]\text{E)}[/inline] [inline]1440\text{ cm}^3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]480\text{ cm}^3[/inline] [inline]\text{B)}[/inline] [inline]600\text{ cm}^3[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]720\text{ cm}^3[/inline] [inline]\text{D)}[/inline] [inline]960\text{ cm}^3[/inline] [inline]\text{E)}[/inline] [inline]1440\text{ cm}^3[/inline] [inline]\text{N)}[/inline] ne znam
10.Link zadatka Broj rešenja jednačine [inline]\sin(2\cos x+2)=0[/inline] u intervalu [inline][0,2\pi][/inline] je:
[inline]\text{A)}[/inline] veći od [inline]4[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] [inline]3[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] veći od [inline]4[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\text{C)}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]3[/inline] [inline]\text{N)}[/inline] ne znam
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11.Link zadatka Funkcija [inline]f\colon(-1,1)\to\mathbb{R}[/inline], takva da za sve [inline]x\ne k\pi[/inline], [inline]k\in\mathbb{Z}[/inline] važi [inline]\displaystyle\frac{\sin4x}{\sin x}=f(\cos x)[/inline], data je izrazom:
[inline]\text{A)}[/inline] [inline]f(t)=4t\left(2t^2-1\right)[/inline] [inline]\text{B)}[/inline] [inline]f(t)=4t\left(t^2-1\right)[/inline] [inline]\text{C)}[/inline] [inline]f(t)=2t\left(1-t^4\right)[/inline] [inline]\text{D)}[/inline] [inline]f(t)=4t\left(1+2t^2\right)[/inline] [inline]\text{E)}[/inline] [inline]f(t)=2t\left(2t^2-1\right)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]f(t)=4t\left(2t^2-1\right)[/inline] [inline]\text{B)}[/inline] [inline]f(t)=4t\left(t^2-1\right)[/inline] [inline]\text{C)}[/inline] [inline]f(t)=2t\left(1-t^4\right)[/inline] [inline]\text{D)}[/inline] [inline]f(t)=4t\left(1+2t^2\right)[/inline] [inline]\text{E)}[/inline] [inline]f(t)=2t\left(2t^2-1\right)[/inline] [inline]\text{N)}[/inline] ne znam
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12.Link zadatka Neka je [inline]ABCD[/inline] paralelogram u [inline]xOy[/inline] ravni, [inline]S[/inline] presek njegovih dijagonala i [inline]E[/inline] središte stranice [inline]CD[/inline]. Ako je [inline]A(1,1)[/inline], [inline]S(6,4)[/inline], [inline]E(4,2)[/inline], [inline]B(x_1,y_1)[/inline] i [inline]D(x_2,y_2)[/inline], tada je [inline]x_1+2y_1+3x_2+4y_2[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-24[/inline] [inline]\text{B)}[/inline] [inline]-16[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\text{D)}[/inline] [inline]16[/inline] [inline]\text{E)}[/inline] [inline]10[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]-24[/inline] [inline]\text{B)}[/inline] [inline]-16[/inline] [inline]\text{C)}[/inline] [inline]0[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]16[/inline] [inline]\text{E)}[/inline] [inline]10[/inline] [inline]\text{N)}[/inline] ne znam
13.Link zadatka Parabola [inline]y=(x-1)^2[/inline] i prava [inline]y=kx[/inline] imaju bar jednu zajedničku tačku ako i samo ako za realni parametar [inline]k[/inline] važi:
[inline]\text{A)}[/inline] [inline]k\ge0[/inline] [inline]\text{B)}[/inline] [inline]k\le-4[/inline] [inline]\text{C)}[/inline] [inline]k\ge0[/inline] ili [inline]k\le-4[/inline] [inline]\text{D)}[/inline] [inline]-4\le k\le0[/inline] [inline]\text{E)}[/inline] [inline]k\ge-4[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]k\ge0[/inline] [inline]\text{B)}[/inline] [inline]k\le-4[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]k\ge0[/inline] ili [inline]k\le-4[/inline] [inline]\text{D)}[/inline] [inline]-4\le k\le0[/inline] [inline]\text{E)}[/inline] [inline]k\ge-4[/inline] [inline]\text{N)}[/inline] ne znam
14.Link zadatka Niz [inline](a_n)[/inline] određen je uslovima [inline]a_1=3[/inline], [inline]a_2=15[/inline] i [inline]\displaystyle a_{n+2}=\frac{a_{n+1}}{a_n}[/inline] za [inline]n\in\mathbb{N}[/inline]. Član [inline]a_{2019}[/inline] tog niza jednak je:
[inline]\text{A)}[/inline] [inline]3[/inline] [inline]\text{B)}[/inline] [inline]5[/inline] [inline]\text{C)}[/inline] [inline]15[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{5}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]3[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]5[/inline] [inline]\text{C)}[/inline] [inline]15[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{5}[/inline] [inline]\text{N)}[/inline] ne znam
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15.Link zadatka Ako za aritmetički niz [inline](a_n)[/inline] važi [inline]a_1+a_7=22[/inline] i [inline]a_3a_4=88[/inline], onda je [inline]a_7[/inline] jednako:
[inline]\text{A)}[/inline] [inline]17[/inline] [inline]\text{B)}[/inline] [inline]18[/inline] [inline]\text{C)}[/inline] [inline]19[/inline] [inline]\text{D)}[/inline] [inline]20[/inline] [inline]\text{E)}[/inline] [inline]21[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]17[/inline] [inline]\text{B)}[/inline] [inline]18[/inline] [inline]\text{C)}[/inline] [inline]19[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]20[/inline] [inline]\text{E)}[/inline] [inline]21[/inline] [inline]\text{N)}[/inline] ne znam
16.Link zadatka Ako je kompleksan broj [inline]z[/inline] rešenje jednačine [inline]|z|+z=2+i[/inline], onda je [inline]\text{Re }z[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{5}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{2}{5}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{3}{5}[/inline] [inline]\text{E)}[/inline] takvo [inline]z[/inline] ne postoji [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{5}[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{3}{4}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{2}{5}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{3}{5}[/inline] [inline]\text{E)}[/inline] takvo [inline]z[/inline] ne postoji [inline]\text{N)}[/inline] ne znam
17.Link zadatka Ako polinom [inline]\left(3x^2+4x-5\right)(ax-2)[/inline] pri deljenju sa [inline]x+1[/inline] daje ostatak [inline]36[/inline], vrednost parametra [inline]a[/inline] je:
[inline]\text{A)}[/inline] [inline]-8[/inline] [inline]\text{B)}[/inline] [inline]-4[/inline] [inline]\text{C)}[/inline] [inline]-2[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\text{E)}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]-8[/inline] [inline]\text{B)}[/inline] [inline]-4[/inline] [inline]\text{C)}[/inline] [inline]-2[/inline] [inline]\text{D)}[/inline] [inline]1[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]4[/inline] [inline]\text{N)}[/inline] ne znam
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18.Link zadatka Funkcija [inline]f\colon\mathbb{R}\setminus\{-2\}\to\mathbb{R}[/inline] data je pomoću [inline]\displaystyle f(x)=\frac{x+1}{x+2}[/inline]. Zbir svih realnih brojeva [inline]x[/inline] za koje važi [inline]f\bigl(f(x)\bigr)=-x-1[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{10}{3}[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{4}{3}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{8}{3}[/inline] [inline]\text{E)}[/inline] takvo [inline]x[/inline] ne postoji [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4}{3}[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{10}{3}[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle-\frac{4}{3}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{8}{3}[/inline] [inline]\text{E)}[/inline] takvo [inline]x[/inline] ne postoji [inline]\text{N)}[/inline] ne znam
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19.Link zadatka Petocifrenih brojeva oblika [inline]\overline{a3cd2}[/inline] koji su deljivi sa [inline]4[/inline] i čije su sve cifre različite ima:
[inline]\text{A)}[/inline] [inline]210[/inline] [inline]\text{B)}[/inline] [inline]180[/inline] [inline]\text{C)}[/inline] [inline]168[/inline] [inline]\text{D)}[/inline] [inline]144[/inline] [inline]\text{E)}[/inline] [inline]120[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]210[/inline] [inline]\text{B)}[/inline] [inline]180[/inline] [inline]\text{C)}[/inline] [inline]168[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]144[/inline] [inline]\text{E)}[/inline] [inline]120[/inline] [inline]\text{N)}[/inline] ne znam
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20.Link zadatka Zbir [inline]\displaystyle{34\choose32}+{33\choose31}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle{34\choose31}^2[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}{33\choose32}^2[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle{34\choose33}^2[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}{32\choose31}^2[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle{33\choose32}^2[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle{34\choose31}^2[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}{33\choose32}^2[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle{34\choose33}^2[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}{32\choose31}^2[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle{33\choose32}^2[/inline] [inline]\text{N)}[/inline] ne znam
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Postupci: http://www.matf.bg.ac.rs/files/resenja_2019.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.