1.Link zadatka Ako je [inline]\displaystyle z=\frac{1+i}{2}[/inline], [inline]i^2=-1[/inline], tada je vrednost izraza [inline]2^{1010}\cdot\left(z^{2022}-\overline z^{2022}\right)[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]-1[/inline]; [inline]\text{B)}[/inline] [inline]-i [/inline]; [inline]\text{C)}[/inline] [inline]i[/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]-1[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]-i [/inline]; [inline]\text{C)}[/inline] [inline]i[/inline]; [inline]\text{D)}[/inline] [inline]1[/inline]; [inline]\text{E)}[/inline] [inline]0[/inline]; [inline]\text{N)}[/inline] Ne znam.
2.Link zadatka Nakon prodaje [inline]20\%[/inline] ukupne količine brašna u jednoj prodavnici, brašno je poskupelo za [inline]30\%[/inline]. Preostala količina brašna je prodata (po novoj ceni) za [inline]13000[/inline] dinara. Da nije bilo poskupljenja, ukupna količina brašna bi bila prodata (u dinarima) za:
[inline]\text{A)}[/inline] [inline]12000[/inline]; [inline]\text{B)}[/inline] [inline]12200[/inline]; [inline]\text{C)}[/inline] [inline]12800[/inline]; [inline]\text{D)}[/inline] [inline]12500[/inline]; [inline]\text{E)}[/inline] [inline]13000[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]12000[/inline]; [inline]\text{B)}[/inline] [inline]12200[/inline]; [inline]\text{C)}[/inline] [inline]12800[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]12500[/inline]; [inline]\text{E)}[/inline] [inline]13000[/inline]; [inline]\text{N)}[/inline] Ne znam.
3.Link zadatka Za [inline]a>0[/inline], [inline]b>0[/inline] i [inline]a\ne b[/inline], izraz [inline]\displaystyle\left(\sqrt{ab}-\frac{ab}{a+\sqrt{ab}}\right):\frac{\left(\sqrt[4]a-\sqrt[4]b\right)\left(\sqrt[4]a+\sqrt[4]b\right)}{a-b}[/inline] identički je jednak izrazu:
[inline]\text{A)}[/inline] [inline]a\sqrt b[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a^2+b^2}{a+\sqrt{ab}}[/inline]; [inline]\text{C)}[/inline] [inline]a+\sqrt{ab}[/inline]; [inline]\text{D)}[/inline] [inline]b\sqrt a[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt a+\sqrt b[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]a\sqrt b[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{a^2+b^2}{a+\sqrt{ab}}[/inline]; [inline]\text{C)}[/inline] [inline]a+\sqrt{ab}[/inline]; [inline]\text{D)}[/inline] [inline]b\sqrt a[/inline]; [inline]\text{E)}[/inline] [inline]\sqrt a+\sqrt b[/inline]; [inline]\text{N)}[/inline] Ne znam.
4.Link zadatka Za funkcije [inline]\displaystyle f_1(x)=\frac{x+5}{\sqrt{(x+5)^2}}[/inline], [inline]f_2(x)=\sin^2x+\cos^2x[/inline], [inline]\displaystyle f_3(x)=\frac{\log_55^x}{x}[/inline] i [inline]\displaystyle f_4(x)=\frac{\sqrt[5]{x^5}}{x}[/inline], tačan je iskaz:
[inline]\text{A)}[/inline] [inline]f_1=f_2=f_3[/inline]; [inline]\text{B)}[/inline] [inline]f_1\ne f_3=f_4[/inline]; [inline]\text{C)}[/inline] [inline]f_2=f_3\ne f_4[/inline]; [inline]\text{D)}[/inline] [inline]f_2\ne f_3\ne f_4[/inline]; [inline]\text{E)}[/inline] [inline]f_1\ne f_2=f_4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]f_1=f_2=f_3[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]f_1\ne f_3=f_4[/inline]; [inline]\text{C)}[/inline] [inline]f_2=f_3\ne f_4[/inline]; [inline]\text{D)}[/inline] [inline]f_2\ne f_3\ne f_4[/inline]; [inline]\text{E)}[/inline] [inline]f_1\ne f_2=f_4[/inline]; [inline]\text{N)}[/inline] Ne znam.
5.Link zadatka Ako je [inline]\displaystyle a=\frac{\sqrt{3.63:3}+\sqrt{0.3\cdot2.7}}{\sqrt{0.8+0.64}-\sqrt{1-0.96}}[/inline] i [inline]\displaystyle b=\sqrt{(1-5/4)^2}-\sqrt{(1+5/4)^2}[/inline], onda je vrednost izraza [inline]a+|b|[/inline] jednaka:
[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]-2[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]-4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]2[/inline]; [inline]\text{C)}[/inline] [inline]-2[/inline]; [inline]\text{D)}[/inline] [inline]0[/inline]; [inline]\text{E)}[/inline] [inline]-4[/inline]; [inline]\text{N)}[/inline] Ne znam.
6.Link zadatka Proizvod svih vrednosti realnog parametra [inline]m[/inline] za koje parabola [inline]y=4x^2-4mx+4m+5[/inline] dodiruje [inline]x[/inline]-osu jednak je:
[inline]\text{A)}[/inline] [inline]-4[/inline]; [inline]\text{B)}[/inline] [inline]-6[/inline]; [inline]\text{C)}[/inline] [inline]-5[/inline]; [inline]\text{D)}[/inline] [inline]6[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]-4[/inline]; [inline]\text{B)}[/inline] [inline]-6[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]-5[/inline]; [inline]\text{D)}[/inline] [inline]6[/inline]; [inline]\text{E)}[/inline] [inline]5[/inline]; [inline]\text{N)}[/inline] Ne znam.
7.Link zadatka Broj svih rešenja jednačine [inline]2\cdot3^{x-\sqrt{x^2-1}}+3\cdot9^{x-\sqrt{x^2-1}}=1[/inline] 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]3[/inline]; [inline]\text{E)}[/inline] [inline]0[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]1[/inline]; [inline]\text{C)}[/inline] [inline]2[/inline]; [inline]\text{D)}[/inline] [inline]3[/inline]; [inline]\text{E)}[/inline] [inline]0[/inline]; [inline]\text{N)}[/inline] Ne znam.
8.Link zadatka Neka je [inline]a_1,a_2,a_3,\ldots[/inline] rastući aritmetički niz takav da važi [inline]a_2=2a_1^2[/inline] i [inline]a_3=3a_1^3[/inline]. Vrednost izraza [inline]a_1+a_2^2+a_3^3+a_4^4[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]356[/inline]; [inline]\text{B)}[/inline] [inline]288[/inline]; [inline]\text{C)}[/inline] [inline]324[/inline]; [inline]\text{D)}[/inline] [inline]264[/inline]; [inline]\text{E)}[/inline] [inline]312[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]356[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]288[/inline]; [inline]\text{C)}[/inline] [inline]324[/inline]; [inline]\text{D)}[/inline] [inline]264[/inline]; [inline]\text{E)}[/inline] [inline]312[/inline]; [inline]\text{N)}[/inline] Ne znam.
9.Link zadatka Ako je [inline]\log_225=a[/inline], onda je [inline]\displaystyle6\log_\frac{1}{2}\frac{1}{5}+\log_{1+\sqrt5}\left(6+2\sqrt5\right)[/inline] jednako:
[inline]\text{A)}[/inline] [inline]3a+2[/inline]; [inline]\text{B)}[/inline] [inline]2a-3[/inline]; [inline]\text{C)}[/inline] [inline]2a+3[/inline]; [inline]\text{D)}[/inline] [inline]2a[/inline]; [inline]\text{E)}[/inline] [inline]3a-2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]3a+2[/inline]; [inline]\text{B)}[/inline] [inline]2a-3[/inline]; [inline]\text{C)}[/inline] [inline]2a+3[/inline]; [inline]\text{D)}[/inline] [inline]2a[/inline]; [inline]\text{E)}[/inline] [inline]3a-2[/inline]; [inline]\text{N)}[/inline] Ne znam.
10.Link zadatka Broj svih celobrojnih rešenja jednačine [inline]\sqrt{9-6\log_3(x+3)+\log_3^2(x+3)}=3-\log_3(x+3)[/inline] je:
[inline]\text{A)}[/inline] [inline]28[/inline]; [inline]\text{B)}[/inline] [inline]25[/inline]; [inline]\text{C)}[/inline] [inline]26[/inline]; [inline]\text{D)}[/inline] [inline]27[/inline]; [inline]\text{E)}[/inline] [inline]24[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]28[/inline]; [inline]\text{B)}[/inline] [inline]25[/inline]; [inline]\text{C)}[/inline] [inline]26[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]27[/inline]; [inline]\text{E)}[/inline] [inline]24[/inline]; [inline]\text{N)}[/inline] Ne znam.
11.Link zadatka Oko kruga poluprečnika [inline]4\text{ cm}[/inline] opisan je jednakokraki trapez. Ako je krak trapeza dužine [inline]10\text{ cm}[/inline], onda je dijagonala tog trapeza dužine:
[inline]\text{A)}[/inline] [inline]3\sqrt{17}\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]12\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]13\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{25}{2}\text{ cm}[/inline]; [inline]\text{E)}[/inline] [inline]2\sqrt{41}\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3\sqrt{17}\text{ cm}[/inline]; [inline]\text{B)}[/inline] [inline]12\text{ cm}[/inline]; [inline]\text{C)}[/inline] [inline]13\text{ cm}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{25}{2}\text{ cm}[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]2\sqrt{41}\text{ cm}[/inline]; [inline]\text{N)}[/inline] Ne znam.
12.Link zadatka Ostatak koji se dobija pri deljenju polinoma [inline]P(x)=(x-1)^{2022}+x^4-1[/inline] polinomom [inline]Q(x)=x^3-2x^2+2x[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]3x^2-6x[/inline]; [inline]\text{B)}[/inline] [inline]2x^2-4x[/inline]; [inline]\text{C)}[/inline] [inline]3x^2+6[/inline]; [inline]\text{D)}[/inline] [inline]x^2+2x[/inline]; [inline]\text{E)}[/inline] [inline]2x^2+4[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]3x^2-6x[/inline]; [inline]\text{B)}[/inline] [inline]2x^2-4x[/inline]; [inline]\text{C)}[/inline] [inline]3x^2+6[/inline]; [inline]\text{D)}[/inline] [inline]x^2+2x[/inline]; [inline]\text{E)}[/inline] [inline]2x^2+4[/inline]; [inline]\text{N)}[/inline] Ne znam.
13.Link zadatka Zbir svih rešenja jednačine [inline]\sin x\cdot\sin2x=\cos x[/inline] na intervalu [inline](0,2\pi)[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]3\pi[/inline]; [inline]\text{B)}[/inline] [inline]2\pi[/inline]; [inline]\text{C)}[/inline] [inline]4\pi[/inline]; [inline]\text{D)}[/inline] [inline]6\pi[/inline]; [inline]\text{E)}[/inline] [inline]5\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]3\pi[/inline]; [inline]\text{B)}[/inline] [inline]2\pi[/inline]; [inline]\text{C)}[/inline] [inline]4\pi[/inline]; [inline]\enclose{circle}{\text{D)}}[/inline] [inline]6\pi[/inline]; [inline]\text{E)}[/inline] [inline]5\pi[/inline]; [inline]\text{N)}[/inline] Ne znam.
14.Link zadatka Vrednost izraza [inline]\displaystyle\frac{\cos10^\circ-\sin20^\circ}{\sin10^\circ+\sin70^\circ}[/inline] jednaka je:
[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt2}{\sqrt3}[/inline]; [inline]\text{C)}[/inline] [inline]\displaystyle\frac{1}{\sqrt3}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]\displaystyle\frac{2}{3}[/inline]; [inline]\text{B)}[/inline] [inline]\displaystyle\frac{\sqrt2}{\sqrt3}[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]\displaystyle\frac{1}{\sqrt3}[/inline]; [inline]\text{D)}[/inline] [inline]\displaystyle\frac{1}{2}[/inline]; [inline]\text{E)}[/inline] [inline]\displaystyle\frac{1}{\sqrt2}[/inline]; [inline]\text{N)}[/inline] Ne znam.
15.Link zadatka Zbir svih celobrojnih rešenja nejednačine [inline]\displaystyle\sqrt{x^2-3x-10}\ge\sqrt{14+5x-x^2}[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]9[/inline]; [inline]\text{B)}[/inline] [inline]11[/inline]; [inline]\text{C)}[/inline] [inline]13[/inline]; [inline]\text{D)}[/inline] [inline]18[/inline]; [inline]\text{E)}[/inline] [inline]16[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]11[/inline]; [inline]\text{C)}[/inline] [inline]13[/inline]; [inline]\text{D)}[/inline] [inline]18[/inline]; [inline]\text{E)}[/inline] [inline]16[/inline]; [inline]\text{N)}[/inline] Ne znam.
16.Link zadatka Broj svih celobrojnih rešenja nejednačine [inline]\displaystyle\frac{x^2+7x-18}{(x-1)|x+3|}\ge6[/inline] jednak je:
[inline]\text{A)}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\enclose{circle}{\text{A)}}[/inline] [inline]4[/inline]; [inline]\text{B)}[/inline] [inline]3[/inline]; [inline]\text{C)}[/inline] [inline]1[/inline]; [inline]\text{D)}[/inline] [inline]5[/inline]; [inline]\text{E)}[/inline] [inline]2[/inline]; [inline]\text{N)}[/inline] Ne znam.
17.Link zadatka Asimptote hiperbole [inline]9x^2-4y^2=36[/inline] i prava [inline]9x+2y-24=0[/inline] obrazuju trougao [inline]ABC[/inline] čija je površina jednaka:
[inline]\text{A)}[/inline] [inline]14[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]10[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\text{E)}[/inline] [inline]12[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]14[/inline]; [inline]\text{B)}[/inline] [inline]8[/inline]; [inline]\text{C)}[/inline] [inline]10[/inline]; [inline]\text{D)}[/inline] [inline]9[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]12[/inline]; [inline]\text{N)}[/inline] Ne znam.
18.Link zadatka Broj svih celobrojnih rešenja jednačine [inline]x\cdot y\cdot z=700[/inline] je:
[inline]\text{A)}[/inline] [inline]648[/inline]; [inline]\text{B)}[/inline] [inline]324[/inline]; [inline]\text{C)}[/inline] [inline]432[/inline]; [inline]\text{D)}[/inline] [inline]216[/inline]; [inline]\text{E)}[/inline] [inline]540[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]648[/inline]; [inline]\text{B)}[/inline] [inline]324[/inline]; [inline]\enclose{circle}{\text{C)}}[/inline] [inline]432[/inline]; [inline]\text{D)}[/inline] [inline]216[/inline]; [inline]\text{E)}[/inline] [inline]540[/inline]; [inline]\text{N)}[/inline] Ne znam.
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19.Link zadatka Ako je zbir binomnih koeficijenata razvoja [inline]\left(\sqrt[3]5+\sqrt{10}\right)^n[/inline] jednak [inline]2048[/inline], tada je broj iracionalnih članova tog razvoja jednak:
[inline]\text{A)}[/inline] [inline]9[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]8[/inline]; [inline]\text{D)}[/inline] [inline]11[/inline]; [inline]\text{E)}[/inline] [inline]10[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]9[/inline]; [inline]\text{B)}[/inline] [inline]6[/inline]; [inline]\text{C)}[/inline] [inline]8[/inline]; [inline]\text{D)}[/inline] [inline]11[/inline]; [inline]\enclose{circle}{\text{E)}}[/inline] [inline]10[/inline]; [inline]\text{N)}[/inline] Ne znam.
20.Link zadatka Ako je odnos dužina izvodnice i poluprečnika osnove prave kružne kupe [inline]3:1[/inline], onda je odnos zapremina date kupe i lopte upisane u tu kupu jednak:
[inline]\text{A)}[/inline] [inline]9:4[/inline]; [inline]\text{B)}[/inline] [inline]2:1[/inline]; [inline]\text{C)}[/inline] [inline]27:8[/inline]; [inline]\text{D)}[/inline] [inline]3:1[/inline]; [inline]\text{E)}[/inline] [inline]3:2[/inline]; [inline]\text{N)}[/inline] Ne znam.[inline]\text{A)}[/inline] [inline]9:4[/inline]; [inline]\enclose{circle}{\text{B)}}[/inline] [inline]2:1[/inline]; [inline]\text{C)}[/inline] [inline]27:8[/inline]; [inline]\text{D)}[/inline] [inline]3:1[/inline]; [inline]\text{E)}[/inline] [inline]3:2[/inline]; [inline]\text{N)}[/inline] Ne znam.
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