1.Link zadatka Neka je [inline]f(x)=x-1[/inline] i [inline]g(x)=|x+1|[/inline]. Skup rešenja jednačine [inline](f\circ g)(x)=(g\circ f)(x)[/inline] je:
[inline]\text{A)}[/inline] [inline](0,+\infty)[/inline] [inline]\text{B)}[/inline] [inline]\{0,1\}[/inline] [inline]\text{C)}[/inline] [inline][0,+\infty)[/inline] [inline]\text{D)}[/inline] [inline](-\infty,+\infty)[/inline] [inline]\text{E)}[/inline] [inline](-\infty,0][/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline](0,+\infty)[/inline] [inline]\text{B)}[/inline] [inline]\{0,1\}[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline][0,+\infty)[/inline] [inline]\text{D)}[/inline] [inline](-\infty,+\infty)[/inline] [inline]\text{E)}[/inline] [inline](-\infty,0][/inline] [inline]\text{N)}[/inline] ne znam
2.Link zadatka Kvadratna funkcija data sa [inline]f(x)=ax^2+bx+c[/inline] je takva da važi [inline]f(-3)=12[/inline], [inline]f(-1)=6[/inline], [inline]f(2)=12[/inline]. Ako su [inline]x_1[/inline] i [inline]x_2[/inline] obe nule ove funkcije, tada je [inline]x_1^3+x_2^3[/inline] jednako:
[inline]\text{A)}[/inline] [inline]-19[/inline] [inline]\text{B)}[/inline] [inline]-17[/inline] [inline]\text{C)}[/inline] [inline]-7[/inline] [inline]\text{D)}[/inline] [inline]17[/inline] [inline]\text{E)}[/inline] [inline]19[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]-19[/inline] [inline]\text{B)}[/inline] [inline]-17[/inline] [inline]\text{C)}[/inline] [inline]-7[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]17[/inline] [inline]\text{E)}[/inline] [inline]19[/inline] [inline]\text{N)}[/inline] ne znam
3.Link zadatka Realnih rešenja jednačine [inline]\displaystyle\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt2[/inline] ima:
[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]4[/inline] [inline]\text{E)}[/inline] beskonačno mnogo [inline]\text{N)}[/inline] ne znam[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]4[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] beskonačno mnogo [inline]\text{N)}[/inline] ne znam
4.Link zadatka Prvi, drugi i treći član geometrijskog niza su, redom, prvi, četvrti i šesti član aritmetičkog niza. Ako je zbir svih članova geometrijskog niza jednak [inline]12[/inline], onda je prvi član geometrijskog niza jednak:
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] [inline]5[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]3[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] [inline]5[/inline] [inline]\text{N)}[/inline] ne znam
5.Link zadatka Figura u ravni koja je u pravouglom Dekartovom koordinatnom sistemu određena sa [inline]x^2+y^2\le1+2|x|[/inline] ima površinu jednaku:
[inline]\text{A)}[/inline] [inline]3\pi+2[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{10}{3}\pi+\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]3\pi-2[/inline] [inline]\text{D)}[/inline] [inline]4\pi-2[/inline] [inline]\text{E)}[/inline] [inline]4\pi[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]3\pi+2[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\frac{10}{3}\pi+\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]3\pi-2[/inline] [inline]\text{D)}[/inline] [inline]4\pi-2[/inline] [inline]\text{E)}[/inline] [inline]4\pi[/inline] [inline]\text{N)}[/inline] ne znam
6.Link zadatka Najmanje pozitivno rešenje jednačine [inline]2\sin(2x-70^\circ)=3\text{ tg }(x-35^\circ)[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline](0^\circ,10^\circ)[/inline] [inline]\text{B)}[/inline] [inline][10^\circ,30^\circ][/inline] [inline]\text{C)}[/inline] [inline](30^\circ,45^\circ)[/inline] [inline]\text{D)}[/inline] [inline][45^\circ,60^\circ][/inline] [inline]\text{E)}[/inline] [inline](60^\circ,90^\circ)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline](0^\circ,10^\circ)[/inline] [inline]\text{B)}[/inline] [inline][10^\circ,30^\circ][/inline] [inline]\text{C)}[/inline] [inline](30^\circ,45^\circ)[/inline] [inline]\text{D)}[/inline] [inline][45^\circ,60^\circ][/inline] [inline]\text{E)}[/inline] [inline](60^\circ,90^\circ)[/inline] [inline]\text{N)}[/inline] ne znam
7.Link zadatka Ako je [inline]f\colon(-3,\infty)\to\mathbb{R}[/inline] definisana sa [inline]f(x)=x+\log_2(3+x)+4^x[/inline], onda je [inline]\displaystyle f^{-1}\left(\frac{1}{4}\right)+f^{-1}(7)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]0[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{29}{4}[/inline] [inline]\text{E)}[/inline] [inline]f^{-1}[/inline] ne postoji [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]0[/inline] [inline]\text{B)}[/inline] [inline]2[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\frac{7}{4}[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\frac{29}{4}[/inline] [inline]\text{E)}[/inline] [inline]f^{-1}[/inline] ne postoji [inline]\text{N)}[/inline] ne znam
8.Link zadatka Najmanji pozitivan realan broj [inline]r[/inline] za koji je broj [inline]r\cdot\left(3\sqrt3-4\sqrt2\right)[/inline] ceo je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{4}{5}\sqrt2+\frac{3}{5}\sqrt3[/inline] [inline]\text{B)}[/inline] [inline]4\sqrt2-3\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]4\sqrt2+3\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]\sqrt3-\sqrt2[/inline] [inline]\text{E)}[/inline] ne postoji takvo [inline]r[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline]\displaystyle\frac{4}{5}\sqrt2+\frac{3}{5}\sqrt3[/inline] [inline]\text{B)}[/inline] [inline]4\sqrt2-3\sqrt3[/inline] [inline]\text{C)}[/inline] [inline]4\sqrt2+3\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]\sqrt3-\sqrt2[/inline] [inline]\text{E)}[/inline] ne postoji takvo [inline]r[/inline] [inline]\text{N)}[/inline] ne znam
9.Link zadatka Celih brojeva [inline]x[/inline] za koje važi [inline]\displaystyle\frac{\log_4x+1}{|\log_2x-1|}>1[/inline] ima:
[inline]\text{A)}[/inline] [inline]2[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\text{C)}[/inline] [inline]13[/inline] [inline]\text{D)}[/inline] [inline]14[/inline] [inline]\text{E)}[/inline] beskonačno mnogo [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]13[/inline] [inline]\text{D)}[/inline] [inline]14[/inline] [inline]\text{E)}[/inline] beskonačno mnogo [inline]\text{N)}[/inline] ne znam
10.Link zadatka Dati su kompleksni brojevi [inline]\displaystyle z_1=1+\frac{i}{a}[/inline] i [inline]z_2=1-ia[/inline], gde je [inline]a\ne0[/inline] realan broj. Skup vrednosti parametra [inline]a[/inline] za koje važi [inline]|z_1|\lt|z_2|[/inline] je:
[inline]\text{A)}[/inline] [inline](-\infty,-1)\cup(1,+\infty)[/inline] [inline]\text{B)}[/inline] [inline](-1,0)\cup(0,1)[/inline] [inline]\text{C)}[/inline] [inline](1,+\infty)[/inline] [inline]\text{D)}[/inline] [inline](-\infty,0)\cup(0,+\infty)[/inline] [inline]\text{E)}[/inline] [inline](0,1)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\enclose{circle}{\text{A)}}[/inline] [inline](-\infty,-1)\cup(1,+\infty)[/inline] [inline]\text{B)}[/inline] [inline](-1,0)\cup(0,1)[/inline] [inline]\text{C)}[/inline] [inline](1,+\infty)[/inline] [inline]\text{D)}[/inline] [inline](-\infty,0)\cup(0,+\infty)[/inline] [inline]\text{E)}[/inline] [inline](0,1)[/inline] [inline]\text{N)}[/inline] ne znam
11.Link zadatka Poslastičarnica prodaje [inline]n[/inline] vrsta voćnih i [inline]n+2[/inline] vrste mlečnih sladoleda. Ako na [inline]175[/inline] načina možemo izabrati tri različite vrste sladoleda od kojih je bar jedna voćna i bar jedna mlečna, onda je [inline]n[/inline] jednako:
[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\text{C)}[/inline] [inline]5[/inline] [inline]\text{D)}[/inline] [inline]7[/inline] [inline]\text{E)}[/inline] [inline]9[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]1[/inline] [inline]\text{B)}[/inline] [inline]3[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]5[/inline] [inline]\text{D)}[/inline] [inline]7[/inline] [inline]\text{E)}[/inline] [inline]9[/inline] [inline]\text{N)}[/inline] ne znam
12.Link zadatka U kutiji se nalaze crvene, plave i bele kuglice, od čega je [inline]25\%[/inline] njih crvene boje, [inline]40\%[/inline] plave, a [inline]98[/inline] bele boje. Ako [inline]37,5\%[/inline] plavih kuglica obojimo u belo, a zatim [inline]45\%[/inline] belih kuglica obojimo u crveno, onda će broj crvenih kuglica u kutiji biti jednak:
[inline]\text{A)}[/inline] [inline]163[/inline] [inline]\text{B)}[/inline] [inline]140[/inline] [inline]\text{C)}[/inline] [inline]112[/inline] [inline]\text{D)}[/inline] [inline]136[/inline] [inline]\text{E)}[/inline] [inline]133[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]163[/inline] [inline]\text{B)}[/inline] [inline]140[/inline] [inline]\text{C)}[/inline] [inline]112[/inline] [inline]\text{D)}[/inline] [inline]136[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]133[/inline] [inline]\text{N)}[/inline] ne znam
13.Link zadatka Prirodnih brojeva [inline]n\le2022[/inline] takvih da se broj [inline]2^n[/inline] u dekadnom zapisu završava cifrom [inline]6[/inline] ima:
[inline]\text{A)}[/inline] [inline]500[/inline] [inline]\text{B)}[/inline] [inline]505[/inline] [inline]\text{C)}[/inline] [inline]550[/inline] [inline]\text{D)}[/inline] [inline]555[/inline] [inline]\text{E)}[/inline] [inline]55[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]500[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]505[/inline] [inline]\text{C)}[/inline] [inline]550[/inline] [inline]\text{D)}[/inline] [inline]555[/inline] [inline]\text{E)}[/inline] [inline]55[/inline] [inline]\text{N)}[/inline] ne znam
14.Link zadatka Najveći od brojeva [inline]2022^{2022}[/inline], [inline]2022![/inline], [inline]20^{\left(22^{20}\right)}[/inline], [inline]22^{\left(20^{20}\right)}[/inline] i [inline]20^{\left(20^{22}\right)}[/inline] je:
[inline]\text{A)}[/inline] [inline]2022^{2022}[/inline] [inline]\text{B)}[/inline] [inline]2022![/inline] [inline]\text{C)}[/inline] [inline]20^{\left(22^{20}\right)}[/inline] [inline]\text{D)}[/inline] [inline]22^{\left(20^{20}\right)}[/inline] [inline]\text{E)}[/inline] [inline]20^{\left(20^{22}\right)}[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]2022^{2022}[/inline] [inline]\text{B)}[/inline] [inline]2022![/inline] [inline]\text{C)}[/inline] [inline]20^{\left(22^{20}\right)}[/inline] [inline]\text{D)}[/inline] [inline]22^{\left(20^{20}\right)}[/inline] [inline]\enclose{circle}{\text{E)}}[/inline] [inline]20^{\left(20^{22}\right)}[/inline] [inline]\text{N)}[/inline] ne znam
15.Link zadatka Ako je [inline]\displaystyle x\in\left(0,\frac{\pi}{2}\right)[/inline] i važi [inline]\text{ctg}\left(\frac{3\pi}{2}-x\right)=\frac{4}{3}[/inline], onda broj [inline]\displaystyle\cos\frac{x}{2}\sin\frac{5x}{2}[/inline] pripada intervalu:
[inline]\text{A)}[/inline] [inline]\displaystyle\left[0,\frac{1}{5}\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left[\frac{1}{5},\frac{2}{5}\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left[\frac{2}{5},\frac{3}{5}\right)[/inline] [inline]\text{D)}[/inline] [inline]\displaystyle\left[\frac{3}{5},\frac{4}{5}\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left[\frac{4}{5},1\right)[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\displaystyle\left[0,\frac{1}{5}\right)[/inline] [inline]\text{B)}[/inline] [inline]\displaystyle\left[\frac{1}{5},\frac{2}{5}\right)[/inline] [inline]\text{C)}[/inline] [inline]\displaystyle\left[\frac{2}{5},\frac{3}{5}\right)[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]\displaystyle\left[\frac{3}{5},\frac{4}{5}\right)[/inline] [inline]\text{E)}[/inline] [inline]\displaystyle\left[\frac{4}{5},1\right)[/inline] [inline]\text{N)}[/inline] ne znam
16.Link zadatka Data je prava kupa sa vrhom [inline]V[/inline] i centrom osnove [inline]S[/inline]. Ako ravan paralelna osnovi kupe polovi njenu zapreminu i seče njenu visinu [inline]VS[/inline] u tački [inline]M[/inline], onda je [inline]VS:VM[/inline] jednako:
[inline]\text{A)}[/inline] [inline]\sqrt2[/inline] [inline]\text{B)}[/inline] [inline]\sqrt[3]2[/inline] [inline]\text{C)}[/inline] [inline]\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]\sqrt\pi[/inline] [inline]\text{E)}[/inline] [inline]2[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]\sqrt2[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]\sqrt[3]2[/inline] [inline]\text{C)}[/inline] [inline]\sqrt3[/inline] [inline]\text{D)}[/inline] [inline]\sqrt\pi[/inline] [inline]\text{E)}[/inline] [inline]2[/inline] [inline]\text{N)}[/inline] ne znam
17.Link zadatka Neka je [inline]ABCD[/inline] tetivni četvorougao takav da je [inline]AD=BC[/inline]. Ako je [inline]\angle BDC=20^\circ[/inline] i [inline]\angle CBD=50^\circ[/inline], tada je [inline]\angle ADB[/inline] jednak:
[inline]\text{A)}[/inline] [inline]110^\circ[/inline] [inline]\text{B)}[/inline] [inline]90^\circ[/inline] [inline]\text{C)}[/inline] [inline]80^\circ[/inline] [inline]\text{D)}[/inline] [inline]70^\circ[/inline] [inline]\text{E)}[/inline] [inline]50^\circ[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]110^\circ[/inline] [inline]\enclose{circle}{\text{B)}}[/inline] [inline]90^\circ[/inline] [inline]\text{C)}[/inline] [inline]80^\circ[/inline] [inline]\text{D)}[/inline] [inline]70^\circ[/inline] [inline]\text{E)}[/inline] [inline]50^\circ[/inline] [inline]\text{N)}[/inline] ne znam
18.Link zadatka Ako su [inline]a[/inline] i [inline]b[/inline] realni brojevi takvi da je ostatak pri deljenju polinoma [inline]x^{2022}+ax+b[/inline] sa [inline]x^2-1[/inline] jednak [inline]2bx+a[/inline], onda je [inline]ab[/inline] jednako:
[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]4[/inline] [inline]\text{E)}[/inline] [inline]6[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]0[/inline] [inline]\text{B)}[/inline] [inline]1[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]2[/inline] [inline]\text{D)}[/inline] [inline]4[/inline] [inline]\text{E)}[/inline] [inline]6[/inline] [inline]\text{N)}[/inline] ne znam
19.Link zadatka Broj celobrojnih vrednosti parametra [inline]a[/inline] za koje jednačina [inline]\left|x^2-22x+21\right|=a[/inline] ima najveći mogući broj rešenja je:
[inline]\text{A)}[/inline] [inline]231[/inline] [inline]\text{B)}[/inline] [inline]100[/inline] [inline]\text{C)}[/inline] [inline]99[/inline] [inline]\text{D)}[/inline] [inline]22[/inline] [inline]\text{E)}[/inline] [inline]21[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]231[/inline] [inline]\text{B)}[/inline] [inline]100[/inline] [inline]\enclose{circle}{\text{C)}}[/inline] [inline]99[/inline] [inline]\text{D)}[/inline] [inline]22[/inline] [inline]\text{E)}[/inline] [inline]21[/inline] [inline]\text{N)}[/inline] ne znam
20.Link zadatka Koji od brojeva [inline]1223[/inline], [inline]1309[/inline], [inline]1989[/inline], [inline]2431[/inline] i [inline]2717[/inline] je proizvod tri uzastopna prosta broja?
[inline]\text{A)}[/inline] [inline]1223[/inline] [inline]\text{B)}[/inline] [inline]1309[/inline] [inline]\text{C)}[/inline] [inline]1989[/inline] [inline]\text{D)}[/inline] [inline]2431[/inline] [inline]\text{E)}[/inline] [inline]2717[/inline] [inline]\text{N)}[/inline] ne znam[inline]\text{A)}[/inline] [inline]1223[/inline] [inline]\text{B)}[/inline] [inline]1309[/inline] [inline]\text{C)}[/inline] [inline]1989[/inline] [inline]\enclose{circle}{\text{D)}}[/inline] [inline]2431[/inline] [inline]\text{E)}[/inline] [inline]2717[/inline] [inline]\text{N)}[/inline] ne znam
Izvor: LINK
Postupci: https://upis.matf.bg.ac.rs/wp-content/uploads/2022/06/resenjePrijemni2022.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.