1.Link zadatka Vrednost izraza [inline]\displaystyle\left[\left[(0.2)^{-1}\cdot2^{0.5}\right]:\frac{5}{3}\right]^2\cdot(-3)^{-2}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]1[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Za [inline]a\in(0,4)[/inline], izraz [inline]\displaystyle\sqrt{\frac{1}{4}a+4a^{-1}-2}+\sqrt{\frac{1}{4}a+\frac{1}{4}a^{-1}+\frac{1}{2}}[/inline] identički je jednak izrazu:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{7}{2\sqrt a}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{\sqrt a}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{5}{2\sqrt a}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{2\sqrt a}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{\sqrt a}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{7}{2\sqrt a}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{3}{\sqrt a}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{5}{2\sqrt a}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{3}{2\sqrt a}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{2}{\sqrt a}[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Ako je [inline]\displaystyle f\left(\frac{x+1}{x-1}\right)=x[/inline] za [inline]x\ne1[/inline], [inline]\displaystyle g(x)=\frac{2}{f(x)-1}[/inline] i [inline]g^{-1}[/inline] inverzna funkcija funkcije [inline]g[/inline], tada je vrednost izraza [inline]f\left(g^{-1}(1)\right)[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Ako je [inline]\displaystyle z=\left(5-\frac{3+7i}{1+i}\right)^{2022}[/inline], [inline]i^2=-1[/inline], onda je [inline]z+\overline z[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-2^{2023}[/inline]; [inline]\text{B)}[/inline] [inline]2^{2023}[/inline]; [inline]\text{C)}[/inline] [inline]-2^{2022}[/inline]; [inline]\text{D)}[/inline] [inline]2^{2022}[/inline]; [inline]\text{E)}[/inline] [inline]-2^{2021}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-2^{2023}[/inline]; [inline]\text{B)}[/inline] [inline]2^{2023}[/inline]; [inline]\text{C)}[/inline] [inline]-2^{2022}[/inline]; [inline]\text{D)}[/inline] [inline]2^{2022}[/inline]; [inline]\text{E)}[/inline] [inline]-2^{2021}[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Ako se uvećanjem dužine jedne stranice kvadrata za [inline]25\%[/inline] i druge za [inline]p\%[/inline] dobija pravougaonik čija površina je dvostruko veća od površine kvadrata, tada je:
[inline]\text{A)}[/inline] [inline]p=75[/inline]; [inline]\text{B)}[/inline] [inline]p=60[/inline]; [inline]\text{C)}[/inline] [inline]p=65[/inline]; [inline]\text{D)}[/inline] [inline]p=50[/inline]; [inline]\text{E)}[/inline] [inline]p=70[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]p=75[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]p=60[/inline]; [inline]\text{C)}[/inline] [inline]p=65[/inline]; [inline]\text{D)}[/inline] [inline]p=50[/inline]; [inline]\text{E)}[/inline] [inline]p=70[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Za članove rastućeg geometrijskog niza [inline]a_1,a_2,a_3,\ldots[/inline] važe jednakosti [inline]a_1^3=2a_2[/inline] i [inline]\displaystyle\frac{a_4}{a_2}-\frac{a_2}{a_1}=2[/inline]. Proizvod prvih pet članova datog niza je:
[inline]\text{A)}[/inline] [inline]2^{10}[/inline]; [inline]\text{B)}[/inline] [inline]2^{15}[/inline]; [inline]\text{C)}[/inline] [inline]2^5[/inline]; [inline]\text{D)}[/inline] [inline]2^{20}[/inline]; [inline]\text{E)}[/inline] [inline]2^{25}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]2^{10}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2^{15}[/inline]; [inline]\text{C)}[/inline] [inline]2^5[/inline]; [inline]\text{D)}[/inline] [inline]2^{20}[/inline]; [inline]\text{E)}[/inline] [inline]2^{25}[/inline]; [inline]\text{N)}[/inline] Ne znam.
7.Link zadatka Ostatak koji se dobija deljenjem polinoma [inline]P(x)=x^{2022}-2x^{2021}+4[/inline] polinomom [inline]Q(x)=x^2-x-2[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-2x+5[/inline]; [inline]\text{B)}[/inline] [inline]-3x+4[/inline]; [inline]\text{C)}[/inline] [inline]-5x+2[/inline]; [inline]\text{D)}[/inline] [inline]-x+6[/inline]; [inline]\text{E)}[/inline] [inline]-4x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-2x+5[/inline]; [inline]\text{B)}[/inline] [inline]-3x+4[/inline]; [inline]\text{C)}[/inline] [inline]-5x+2[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]-x+6[/inline]; [inline]\text{E)}[/inline] [inline]-4x+3[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Vrednost izraza [inline]\left(\log_{\sqrt[3]3}\sqrt3\right)^2\cdot\log_{\left(\sqrt3+1\right)}\left(4+2\sqrt3\right)+\log_{\sqrt[3]2}2\sqrt2[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]9[/inline]; [inline]\text{D)}[/inline] [inline]10[/inline]; [inline]\text{E)}[/inline] [inline]15[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]12[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]9[/inline]; [inline]\text{D)}[/inline] [inline]10[/inline]; [inline]\text{E)}[/inline] [inline]15[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle\frac{11-16x}{4x^2-8x-21}\ge1[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\text{B)}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]3[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]1[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]5[/inline]; [inline]\text{C)}[/inline] [inline]3[/inline]; [inline]\text{D)}[/inline] [inline]4[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Proizvod svih realnih rešenja jednačine [inline]28\cdot\sqrt3^{x^2-x}-3^{x^2-x+2}=3[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-10[/inline]; [inline]\text{B)}[/inline] [inline]-6[/inline]; [inline]\text{C)}[/inline] [inline]-2[/inline]; [inline]\text{D)}[/inline] [inline]-4[/inline]; [inline]\text{E)}[/inline] [inline]-8[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-10[/inline]; [inline]\text{B)}[/inline] [inline]-6[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-2[/inline]; [inline]\text{D)}[/inline] [inline]-4[/inline]; [inline]\text{E)}[/inline] [inline]-8[/inline]; [inline]\text{N)}[/inline] Ne znam.
11.Link zadatka Broj svih rešenja jednačine [inline]\displaystyle2\left(\cos^3x+\sin^2\frac{x}{2}\right)=1+\cos2x[/inline] na intervalu [inline](-\pi,\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]5[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]5[/inline]; [inline]\text{B)}[/inline] [inline]4[/inline]; [inline]\text{C)}[/inline] [inline]6[/inline]; [inline]\text{D)}[/inline] [inline]2[/inline]; [inline]\text{E)}[/inline] [inline]3[/inline]; [inline]\text{N)}[/inline] Ne znam.
12.Link zadatka Proizvod svih realnih rešenja jednačine [inline]\log_3x\cdot\log_39x=\log_33x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{9}[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{1}{9}[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle\frac{1}{3}[/inline]; [inline]\text{N)}[/inline] Ne znam.
13.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\cos10^\circ-\sin10^\circ}{\cos95^\circ+\cos205^\circ}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{2}{\sqrt3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{\sqrt2}{3}[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle-\frac{\sqrt2}{\sqrt3}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle-\frac{2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle-\frac{2}{\sqrt3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle-\frac{\sqrt2}{3}[/inline]; [inline]\text{D)}[/inline] [inline]-1[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]\displaystyle-\frac{\sqrt2}{\sqrt3}[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka Neka su [inline]B[/inline] i [inline]C[/inline] dodirne tačke tangenti iz tačke [inline]A(6,0)[/inline] na kružnicu [inline](x-1)^2+y^2=9[/inline]. Dužina duži [inline]BC[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{23}{5}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{24}{5}[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{22}{5}[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{23}{5}[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\displaystyle\frac{24}{5}[/inline]; [inline]\text{C)}[/inline] [inline]5[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{22}{5}[/inline]; [inline]\text{E)}[/inline] [inline]4[/inline]; [inline]\text{N)}[/inline] Ne znam.
15.Link zadatka Zbir kvadrata svih celobrojnih rešenja nejednačine [inline]\sqrt{4x^2-4x+1}+2\sqrt{-2x^2+10x-8}\le4x-3[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]30[/inline]; [inline]\text{B)}[/inline] [inline]21[/inline]; [inline]\text{C)}[/inline] [inline]17[/inline]; [inline]\text{D)}[/inline] [inline]10[/inline]; [inline]\text{E)}[/inline] [inline]26[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]30[/inline]; [inline]\text{B)}[/inline] [inline]21[/inline]; [inline]\text{C)}[/inline] [inline]17[/inline]; [inline]\text{D)}[/inline] [inline]10[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]26[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Iz kvadrata [inline]ABCD[/inline], čija stranica je dužine [inline]2\text{ cm}[/inline], isečena su dva trougla čija su temena tačka [inline]B[/inline] i središta stranica [inline]AB[/inline] i [inline]BC[/inline], odnosno tačka [inline]D[/inline] i središta stranica [inline]CD[/inline] i [inline]DA[/inline]. Zapremina tela nastalog rotacijom preostalog dela kvadrata oko prave koja sadrži stranicu [inline]AB[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]4\pi\text{ cm}^3[/inline]; [inline]\text{B)}[/inline] [inline]5\pi\text{ cm}^3[/inline]; [inline]\text{C)}[/inline] [inline]6\pi\text{ cm}^3[/inline]; [inline]\text{D)}[/inline] [inline]7\pi\text{ cm}^3[/inline]; [inline]\text{E)}[/inline] [inline]8\pi\text{ cm}^3[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4\pi\text{ cm}^3[/inline]; [inline]\text{B)}[/inline] [inline]5\pi\text{ cm}^3[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]6\pi\text{ cm}^3[/inline]; [inline]\text{D)}[/inline] [inline]7\pi\text{ cm}^3[/inline]; [inline]\text{E)}[/inline] [inline]8\pi\text{ cm}^3[/inline]; [inline]\text{N)}[/inline] Ne znam.
17.Link zadatka Proizvod najmanje i najveće vrednosti funkcije [inline]\displaystyle f(x)=8^x-\frac{3}{2}16^x[/inline] na intervalu [inline][-4,4][/inline] jednak je:
[inline]\text{A)}[/inline] [inline]-23\cdot2^7[/inline]; [inline]\text{B)}[/inline] [inline]-3\cdot2^{10}[/inline]; [inline]\text{C)}[/inline] [inline]-5\cdot2^9[/inline]; [inline]\text{D)}[/inline] [inline]-21\cdot2^7[/inline]; [inline]\text{E)}[/inline] [inline]-25\cdot2^7[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]-23\cdot2^7[/inline]; [inline]\text{B)}[/inline] [inline]-3\cdot2^{10}[/inline]; [inline]\text{C)}[/inline] [inline]-5\cdot2^9[/inline]; [inline]\text{D)}[/inline] [inline]-21\cdot2^7[/inline]; [inline]\text{E)}[/inline] [inline]-25\cdot2^7[/inline]; [inline]\text{N)}[/inline] Ne znam.
18.Link zadatka Broj članova razvoja [inline]\left(\sqrt[6]{54}+\sqrt[3]{32}\right)^{2022}[/inline] koji su celi brojevi jednak je:
[inline]\text{A)}[/inline] [inline]337[/inline]; [inline]\text{B)}[/inline] [inline]674[/inline]; [inline]\text{C)}[/inline] [inline]675[/inline]; [inline]\text{D)}[/inline] [inline]338[/inline]; [inline]\text{E)}[/inline] [inline]1012[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]337[/inline]; [inline]\text{B)}[/inline] [inline]674[/inline]; [inline]\text{C)}[/inline] [inline]675[/inline]; [inline]\text{D)}[/inline] [inline]338[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]1012[/inline]; [inline]\text{N)}[/inline] Ne znam.
19.Link zadatka U oštrouglom trouglu [inline]ABC[/inline], simetrala unutrašnjeg ugla kod temena [inline]A[/inline] seče stranicu [inline]BC[/inline] u tački [inline]D[/inline]. Ako je [inline]|AB|=|AD|=|DC|=2\text{ cm}[/inline], onda je obim datog trougla jednak (u [inline]\text{cm}[/inline]):
[inline]\text{A)}[/inline] [inline]8[/inline]; [inline]\text{B)}[/inline] [inline]6+\sqrt5[/inline]; [inline]\text{C)}[/inline] [inline]4\sqrt5[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\text{E)}[/inline] [inline]4+2\sqrt5[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]8[/inline]; [inline]\text{B)}[/inline] [inline]6+\sqrt5[/inline]; [inline]\text{C)}[/inline] [inline]4\sqrt5[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]4+2\sqrt5[/inline]; [inline]\text{N)}[/inline] Ne znam.
20.Link zadatka Broj načina na koji se [inline]4[/inline] dečaka i [inline]6[/inline] devojčica mogu rasporediti u jednu vrstu, tako da nikoja dva dečaka ne budu raspoređeni jedan pored drugog, jednak je:
[inline]\text{A)}[/inline] [inline]140\cdot7![/inline]; [inline]\text{B)}[/inline] [inline]160\cdot7![/inline]; [inline]\text{C)}[/inline] [inline]150\cdot7![/inline]; [inline]\text{D)}[/inline] [inline]120\cdot7![/inline]; [inline]\text{E)}[/inline] [inline]180\cdot7![/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]140\cdot7![/inline]; [inline]\text{B)}[/inline] [inline]160\cdot7![/inline]; [inline]\text{C)}[/inline] [inline]150\cdot7![/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]120\cdot7![/inline]; [inline]\text{E)}[/inline] [inline]180\cdot7![/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.