1.Link zadatka Za [inline]|m|\ne1[/inline], izraz [inline]\displaystyle\frac{m^2-1}{m^4-1}\cdot\left[(m+1)^3-\frac{2m\left(m^2-1\right)}{m-1}\right][/inline] je identički jednak izrazu:
[inline]\text{A)}[/inline] [inline]m-1[/inline]; [inline]\text{B)}[/inline] [inline]m-2[/inline]; [inline]\text{C)}[/inline] [inline]m+1[/inline]; [inline]\text{D)}[/inline] [inline]m[/inline]; [inline]\text{E)}[/inline] [inline]m+2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]m-1[/inline]; [inline]\text{B)}[/inline] [inline]m-2[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]m+1[/inline]; [inline]\text{D)}[/inline] [inline]m[/inline]; [inline]\text{E)}[/inline] [inline]m+2[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Prošle godine je u jednom voćnjaku zasađeno ukupno [inline]95[/inline], a ove godine ukupno [inline]108[/inline] sadnica jabuka i krušaka. Ako je ove godine broj zasađenih sadnica jabuka uvećan za [inline]8\%[/inline], a krušaka za [inline]20\%[/inline] u odnosu na prošlu godinu, onda je broj sadnica krušaka zasađenih prošle godine jednak:
[inline]\text{A)}[/inline] [inline]51[/inline]; [inline]\text{B)}[/inline] [inline]50[/inline]; [inline]\text{C)}[/inline] [inline]47[/inline]; [inline]\text{D)}[/inline] [inline]45[/inline]; [inline]\text{E)}[/inline] [inline]48[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]51[/inline]; [inline]\text{B)}[/inline] [inline]50[/inline]; [inline]\text{C)}[/inline] [inline]47[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]45[/inline]; [inline]\text{E)}[/inline] [inline]48[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Ako je [inline]\displaystyle f(x)=\frac{x-1}{x+1}[/inline] za [inline]x\ne-1[/inline], [inline]\displaystyle g(x)=\frac{x+2}{x-2}[/inline] za [inline]x\ne2[/inline] i [inline]f^{-1}[/inline] i [inline]g^{-1}[/inline] odgovarajuće inverzne funkcije, onda je [inline]g^{-1}\left(f^{-1}(2)\right)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{2}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Vrednost izraza [inline]\displaystyle\sqrt{2^2-\left(\frac{8}{5}\right)^2}+\left[1.5-0.5\cdot\left(\frac{16}{25}:0.8\right)\right]:\left(2-\frac{5}{8}\right)[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]2[/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]1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]2[/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]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Ako je [inline](\overline z+\text{Im }z)\cdot(2+i)=6\cdot\text{Re }z-i[/inline], [inline]i^2=-1[/inline], onda je [inline]|z|[/inline] jednako:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]2\sqrt5[/inline]; [inline]\text{E)}[/inline] [inline]2\sqrt6[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]2\sqrt5[/inline]; [inline]\text{E)}[/inline] [inline]2\sqrt6[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Broj svih realnih rešenja nejednačine [inline]\log_\frac{1}{3}x\le\log_3(2-x)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]0[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]0[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
7.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle x^2+x-1\le\frac{3}{x^2+x+1}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Neka su [inline]a[/inline], [inline]b[/inline], [inline]a\sqrt b[/inline] i [inline]b\sqrt a[/inline] pozitivni realni brojevi različiti od [inline]1[/inline]. Ako je [inline]\log_{a\sqrt b}a=m[/inline], onda je [inline]\log_{b\sqrt a}b[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4(1-m)}{1-3m}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4(1-m)}{4-3m}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1-m}{m}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4(1-m)}{m}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1-m}{1-3m}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4(1-m)}{1-3m}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{4(1-m)}{4-3m}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1-m}{m}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{4(1-m)}{m}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1-m}{1-3m}[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Vrednost izraza [inline]\sin2022^\circ+\cos2022^\circ+\sin48^\circ+\cos48^\circ[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]0[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]0[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{1}{2}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle-\frac{1}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Ako je polinom [inline]P(x)=x^{2022}-a\cdot x^{1011}+b[/inline], [inline]a,b\in\mathbb{R}[/inline], deljiv polinomom [inline]x^2+2x+1[/inline], tada je zbir [inline]2a+b[/inline] jednak:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]-1[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]-3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]0[/inline]; [inline]\text{C)}[/inline] [inline]-1[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]-3[/inline]; [inline]\text{N)}[/inline] Ne znam.
11.Link zadatka Količnik najveće i najmanje vrednosti funkcije [inline]f(x)=4\cos x-\sin^2x+8[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{12}{5}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{11}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{12}{5}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{11}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{5}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
12.Link zadatka Dat je pravougaonik [inline]ABCD[/inline] takav da je [inline]|AB|=6\text{ cm}[/inline] i [inline]|BC|=3\text{ cm}[/inline]. Simetrala ugla kod temena [inline]A[/inline] seče stranicu [inline]CD[/inline] u tački [inline]E[/inline]. Ako je [inline]AE\cap BD=\{F\}[/inline] i [inline]BE\cap AC=\{G\}[/inline], tada je obim trougla [inline]EFG[/inline] jednak:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{2}\left(2+\sqrt2\right)\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]2\left(\sqrt2+1\right)\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]2\left(\sqrt3+1\right)\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]2+\sqrt2\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]5\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{3}{2}\left(2+\sqrt2\right)\text{ cm}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2\left(\sqrt2+1\right)\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]2\left(\sqrt3+1\right)\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]2+\sqrt2\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]5\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.
13.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\sqrt{2x^2-7x+3}\le3-x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]6[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]6[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka Zbir svih realnih rešenja jednačine [inline]\left(1+2\sqrt2\right)^{2\left(x^2-5x+2\right)+4}=4\left(1+2\sqrt2\right)^{x^2-5x+2}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]6[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]7[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.
15.Link zadatka Data je jednačina [inline]\displaystyle2\cos2x+2\sin^2\frac{x}{2}+4\cos^2x-7\cos x-5=0[/inline]. Zbir kvadrata najvećeg negativnog i najmanjeg pozitivnog rešenja date jednačine je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{8\pi^2}{9}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4\pi^2}{3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{10\pi^2}{9}[/inline]; [inline]\text{D)}[/inline] [inline]\pi^2[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2\pi^2}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{8\pi^2}{9}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{4\pi^2}{3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{10\pi^2}{9}[/inline]; [inline]\text{D)}[/inline] [inline]\pi^2[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2\pi^2}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka U tetraedru [inline]ABCD[/inline] tačke [inline]E[/inline] i [inline]F[/inline] predstavljaju središta ivica [inline]AC[/inline] i [inline]CD[/inline]. Ako je površina trougla [inline]EFB[/inline] jednaka [inline]\sqrt{11}\text{ cm}^2[/inline], tada je zapremina datog tetraedra jednaka:
[inline]\text{A)}[/inline] [inline]6\sqrt2\text{ cm}^3[/inline]; [inline]\text{B)}[/inline] [inline]5\sqrt2\text{ cm}^3[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{14\sqrt2}{3}\text{ cm}^3[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{16\sqrt2}{3}\text{ cm}^3[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{13\sqrt2}{3}\text{ cm}^3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]6\sqrt2\text{ cm}^3[/inline]; [inline]\text{B)}[/inline] [inline]5\sqrt2\text{ cm}^3[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{14\sqrt2}{3}\text{ cm}^3[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\frac{16\sqrt2}{3}\text{ cm}^3[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{13\sqrt2}{3}\text{ cm}^3[/inline]; [inline]\text{N)}[/inline] Ne znam.
17.Link zadatka Ako u razvoju [inline]\displaystyle\left(\frac{y}{\sqrt[5]x}+\frac{\sqrt x}{y^2}\right)^n[/inline], [inline]x>0[/inline], [inline]y\ne0[/inline], postoji član oblika [inline]C\cdot y^m[/inline], gde je [inline]C[/inline] konstanta i [inline]m\in\mathbb{N}[/inline], onda je:
[inline]\text{A)}[/inline] [inline]n=11m[/inline]; [inline]\text{B)}[/inline] [inline]n=13m[/inline]; [inline]\text{C)}[/inline] [inline]n=9m[/inline]; [inline]\text{D)}[/inline] [inline]n=7m[/inline]; [inline]\text{E)}[/inline] [inline]n=15m[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]n=11m[/inline]; [inline]\text{B)}[/inline] [inline]n=13m[/inline]; [inline]\text{C)}[/inline] [inline]n=9m[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]n=7m[/inline]; [inline]\text{E)}[/inline] [inline]n=15m[/inline]; [inline]\text{N)}[/inline] Ne znam.
18.Link zadatka Dužine stranica pravouglog trougla predstavljaju uzastopne članove geometrijske progresije, a dužina jedne od kateta jednaka je [inline]1[/inline]. Proizvod površina svih takvih, međusobno nepodudarnih trouglova, jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}\sqrt\frac{\sqrt5-1}{2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}\sqrt\frac{\sqrt5+1}{2}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt5+1}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{2}\sqrt\frac{\sqrt5-1}{2}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}\sqrt\frac{\sqrt5+1}{2}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{4}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{\sqrt5+1}{4}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
19.Link zadatka Broj svih četvorocifrenih brojeva koji ne sadrže cifru [inline]0[/inline] i koji imaju bar dve susedne cifre iste, jednak je:
[inline]\text{A)}[/inline] [inline]1980[/inline]; [inline]\text{B)}[/inline] [inline]1953[/inline]; [inline]\text{C)}[/inline] [inline]2007[/inline]; [inline]\text{D)}[/inline] [inline]1926[/inline]; [inline]\text{E)}[/inline] [inline]2034[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1980[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1953[/inline]; [inline]\text{C)}[/inline] [inline]2007[/inline]; [inline]\text{D)}[/inline] [inline]1926[/inline]; [inline]\text{E)}[/inline] [inline]2034[/inline]; [inline]\text{N)}[/inline] Ne znam.
20.Link zadatka Neka su [inline]k_1[/inline] i [inline]k_2[/inline] koeficijenti pravca tangenti iz tačke [inline]A(-1,3)[/inline] na elipsu [inline]\displaystyle\frac{x^2}{4}+\frac{y^2}{11}=1[/inline]. Tada je [inline]k_1^2+k_2^2[/inline] jednako:
[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{8}{3}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{10}{3}[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{8}{3}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{10}{3}[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.
Izvor: LINK
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