1.Link zadatka Vrednost izraza [inline]2014^3-2013\cdot2014\cdot2015[/inline] jednaka je:
[inline]\text{(A)}\;1[/inline] [inline]\text{(B)}\;2013[/inline] [inline]\text{(C)}\;2014[/inline] [inline]\text{(D)}\;2015[/inline] [inline]\text{(E)}\;-1[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;1[/inline] [inline]\text{(B)}\;2013[/inline] [inline]\enclose{box}{\text{(C)}\;2014}[/inline] [inline]\text{(D)}\;2015[/inline] [inline]\text{(E)}\;-1[/inline] [inline]\text{(N)}[/inline] Ne znam
2.Link zadatka Pojeftinjenje neke robe najpre za [inline]10\%[/inline], a zatim za [inline]20\%[/inline], jednako je pojeftinjenju iste robe za:
[inline]\text{(A)}\;30\%[/inline] [inline]\text{(B)}\;25\%[/inline] [inline]\text{(C)}\;32\%[/inline] [inline]\text{(D)}\;28\%[/inline] [inline]\text{(E)}\;19\%[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;30\%[/inline] [inline]\text{(B)}\;25\%[/inline] [inline]\text{(C)}\;32\%[/inline] [inline]\enclose{box}{\text{(D)}\;28\%}[/inline] [inline]\text{(E)}\;19\%[/inline] [inline]\text{(N)}[/inline] Ne znam
3.Link zadatka Ako realni brojevi [inline]x[/inline] i [inline]y[/inline] zadovoljavaju jednakost [inline]\displaystyle\frac{2x+i}{y+i}=\frac{1+i\sin\alpha}{1-i\sin3\alpha}[/inline], [inline]\displaystyle\left(\alpha\ne k\pi,\;\alpha\ne\frac{\pi}{2}+k\pi,\;k\in\mathbb{Z},\;i^2=-1\right)[/inline], tada je količnik [inline]\displaystyle\frac{y}{x}[/inline] jednak:
[inline]\text{(A)}\;-4+2\cos2\alpha[/inline] [inline]\text{(B)}\;4+2\cos2\alpha[/inline] [inline]\text{(C)}\;2-4\cos2\alpha[/inline] [inline]\text{(D)}\;-2-4\cos2\alpha[/inline] [inline]\text{(E)}\;2-2\sin2\alpha[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;-4+2\cos2\alpha[/inline] [inline]\text{(B)}\;4+2\cos2\alpha[/inline] [inline]\text{(C)}\;2-4\cos2\alpha[/inline] [inline]\enclose{box}{\text{(D)}\;-2-4\cos2\alpha}[/inline] [inline]\text{(E)}\;2-2\sin2\alpha[/inline] [inline]\text{(N)}[/inline] Ne znam
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4.Link zadatka Izraz [inline]5^{\frac{3-\log_{10}5}{\log_{10}25}}[/inline] je jednak izrazu:
[inline]\text{(A)}\;10\sqrt2[/inline] [inline]\text{(B)}\;5[/inline] [inline]\text{(C)}\;\displaystyle\frac{5}{\sqrt2}[/inline] [inline]\text{(D)}\;\displaystyle\frac{10}{\sqrt2}[/inline] [inline]\text{(E)}\;5^{\frac{1}{5}}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}\;10\sqrt2}[/inline] [inline]\text{(B)}\;5[/inline] [inline]\text{(C)}\;\displaystyle\frac{5}{\sqrt2}[/inline] [inline]\text{(D)}\;\displaystyle\frac{10}{\sqrt2}[/inline] [inline]\text{(E)}\;5^{\frac{1}{5}}[/inline] [inline]\text{(N)}[/inline] Ne znam
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5.Link zadatka Ako je [inline]\displaystyle x+\left|x\right|=\frac{x}{\left|x\right|}[/inline], [inline]\left(x\in\mathbb{R}\setminus\left\{0\right\}\right)[/inline], tada [inline]x[/inline] pripada skupu:
[inline]\text{(A)}\;\left(0,1\right)[/inline] [inline]\text{(B)}\;\left(-1,0\right)[/inline] [inline]\text{(C)}\;\left(1,3\right)[/inline] [inline]\text{(D)}\;\left(2,+\infty\right)[/inline] [inline]\text{(E)}\;\left(-\infty,0\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}\;\left(0,1\right)}[/inline] [inline]\text{(B)}\;\left(-1,0\right)[/inline] [inline]\text{(C)}\;\left(1,3\right)[/inline] [inline]\text{(D)}\;\left(2,+\infty\right)[/inline] [inline]\text{(E)}\;\left(-\infty,0\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
6.Link zadatka Ako je [inline]\displaystyle f\left(\frac{1-x}{1+x}\right)=x[/inline] [inline]\left(x\in\mathbb{R}\setminus\left\{-1,0,1\right\}\right)[/inline], tada je [inline]f\bigl(f\left(x\right)\bigr)[/inline] jednako:
[inline]\text{(A)}\;x[/inline] [inline]\text{(B)}\;\displaystyle\frac{1-x}{1+x}[/inline] [inline]\text{(C)}\;\displaystyle\frac{1}{x}[/inline] [inline]\text{(D)}\;\displaystyle\frac{1+x}{1-x}[/inline] [inline]\text{(E)}\;2x[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}\;x}[/inline] [inline]\text{(B)}\;\displaystyle\frac{1-x}{1+x}[/inline] [inline]\text{(C)}\;\displaystyle\frac{1}{x}[/inline] [inline]\text{(D)}\;\displaystyle\frac{1+x}{1-x}[/inline] [inline]\text{(E)}\;2x[/inline] [inline]\text{(N)}[/inline] Ne znam
7.Link zadatka Ako je [inline]a=-0,3[/inline] koja od sledećih relacija je tačna?
[inline]\text{(A)}\;a<a^2<a^3[/inline] [inline]\text{(B)}\;a<a^3<a^2[/inline] [inline]\text{(C)}\;a^2<a<a^3[/inline] [inline]\text{(D)}\;a^2<a^3<a[/inline] [inline]\text{(E)}\;a^3<a<a^2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;a<a^2<a^3[/inline] [inline]\enclose{box}{\text{(B)}\;a<a^3<a^2}[/inline] [inline]\text{(C)}\;a^2<a<a^3[/inline] [inline]\text{(D)}\;a^2<a^3<a[/inline] [inline]\text{(E)}\;a^3<a<a^2[/inline] [inline]\text{(N)}[/inline] Ne znam
8.Link zadatka Odnos binomnih koeficijenata uz stepen [inline]x^{1007}[/inline], [inline]\bigl(x\in\left(0,+\infty\right)\bigr)[/inline] u razvojima binoma [inline]\left(1+x\right)^{2014}[/inline] i [inline]\left(1+x\right)^{2013}[/inline] redom, iznosi:
[inline]\text{(A)}\;\displaystyle\frac{1007}{1006}[/inline] [inline]\text{(B)}\;2[/inline] [inline]\text{(C)}\;\displaystyle\frac{3}{2}[/inline] [inline]\text{(D)}\;\displaystyle\frac{1}{2014}[/inline] [inline]\text{(E)}\;\displaystyle\frac{1}{2015}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;\displaystyle\frac{1007}{1006}[/inline] [inline]\enclose{box}{\text{(B)}\;2}[/inline] [inline]\text{(C)}\;\displaystyle\frac{3}{2}[/inline] [inline]\text{(D)}\;\displaystyle\frac{1}{2014}[/inline] [inline]\text{(E)}\;\displaystyle\frac{1}{2015}[/inline] [inline]\text{(N)}[/inline] Ne znam
9.Link zadatka Data je kvadratna funkcija [inline]f\left(x\right)=x^2+bx+c[/inline] [inline]\left(b,c\in\mathbb{R}\right)[/inline] takva da je [inline]f\bigl(f\left(1\right)\bigr)=f\bigl(f\left(2\right)\bigr)=0[/inline], pri čemu je [inline]f\left(1\right)\ne f\left(2\right)[/inline]. Vrednost [inline]f\left(0\right)[/inline] jednaka je:
[inline]\text{(A)}\;-6[/inline] [inline]\text{(B)}\;\displaystyle-\frac{2}{3}[/inline] [inline]\text{(C)}\;\displaystyle-\frac{3}{2}[/inline] [inline]\text{(D)}\;\displaystyle\frac{1}{4}[/inline] [inline]\text{(E)}\;-2[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;-6[/inline] [inline]\text{(B)}\;\displaystyle-\frac{2}{3}[/inline] [inline]\enclose{box}{\text{(C)}\;\displaystyle-\frac{3}{2}}[/inline] [inline]\text{(D)}\;\displaystyle\frac{1}{4}[/inline] [inline]\text{(E)}\;-2[/inline] [inline]\text{(N)}[/inline] Ne znam
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10.Link zadatka Neka je [inline]s=1+q+q^2+\cdots[/inline] [inline]\left(\left|q\right|<1\right)[/inline] i [inline]S=1+Q+Q^2+\cdots[/inline] [inline]\left(\left|Q\right|<1\right)[/inline], gde su [inline]s[/inline] i [inline]S[/inline] dati brojevi. Tada je zbir [inline]1+qQ+q^2Q^2+q^3Q^3+\cdots[/inline] jednak:
[inline]\text{(A)}\;\displaystyle\frac{s\cdot S}{s+S-1}[/inline] [inline]\text{(B)}\;\displaystyle\frac{s\cdot S}{2\cdot s\cdot S-s-S+1}[/inline] [inline]\text{(C)}\;\displaystyle\frac{s\cdot S}{s\cdot S+s+S-2}[/inline] [inline]\text{(D)}\;\displaystyle\frac{2s\cdot S-1}{s+S-1}[/inline] [inline]\text{(E)}\;s\cdot S[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}\;\displaystyle\frac{s\cdot S}{s+S-1}}[/inline] [inline]\text{(B)}\;\displaystyle\frac{s\cdot S}{2\cdot s\cdot S-s-S+1}[/inline] [inline]\text{(C)}\;\displaystyle\frac{s\cdot S}{s\cdot S+s+S-2}[/inline] [inline]\text{(D)}\;\displaystyle\frac{2s\cdot S-1}{s+S-1}[/inline] [inline]\text{(E)}\;s\cdot S[/inline] [inline]\text{(N)}[/inline] Ne znam
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11.Link zadatka Proizvod svih realnih rešenja jednačine [inline]\displaystyle\frac{2013x}{2014}=2013^{\log_x2014}[/inline] pripada skupu:
[inline]\text{(A)}\;\left(0,1\right][/inline] [inline]\text{(B)}\;\left(1,2\right][/inline] [inline]\text{(C)}\;\left(2,3\right][/inline] [inline]\text{(D)}\;\left(3,4\right][/inline] [inline]\text{(E)}\;\left(4,+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;\left(0,1\right][/inline] [inline]\enclose{box}{\text{(B)}\;\left(1,2\right]}[/inline] [inline]\text{(C)}\;\left(2,3\right][/inline] [inline]\text{(D)}\;\left(3,4\right][/inline] [inline]\text{(E)}\;\left(4,+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
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12.Link zadatka Krug sadrži tri tačke čije su koordinate [inline]\left(0,6\right)[/inline], [inline]\left(0,10\right)[/inline] i [inline]\left(8,0\right)[/inline]. Apscisa druge tačke u kojoj dati krug seče [inline]x[/inline]-osu, jednaka je:
[inline]\text{(A)}\;7[/inline] [inline]\text{(B)}\;7,25[/inline] [inline]\text{(C)}\;7,5[/inline] [inline]\text{(D)}\;7,75[/inline] [inline]\text{(E)}\;9[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;7[/inline] [inline]\text{(B)}\;7,25[/inline] [inline]\enclose{box}{\text{(C)}\;7,5}[/inline] [inline]\text{(D)}\;7,75[/inline] [inline]\text{(E)}\;9[/inline] [inline]\text{(N)}[/inline] Ne znam
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13.Link zadatka Sva realna rešenja iracionalne jednačine [inline]\displaystyle\frac{1}{\sqrt x+\sqrt{x-2}}+\frac{1}{\sqrt{x+2}+\sqrt x}=\frac{1}{4}[/inline] pripadaju skupu:
[inline]\text{(A)}\;\left[2,6\right)[/inline] [inline]\text{(B)}\;\left[6,10\right)[/inline] [inline]\text{(C)}\;\left[10,14\right)[/inline] [inline]\text{(D)}\;\left[14,18\right)[/inline] [inline]\text{(E)}\;\left[18,+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;\left[2,6\right)[/inline] [inline]\text{(B)}\;\left[6,10\right)[/inline] [inline]\text{(C)}\;\left[10,14\right)[/inline] [inline]\enclose{box}{\text{(D)}\;\left[14,18\right)}[/inline] [inline]\text{(E)}\;\left[18,+\infty\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
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14.Link zadatka Dat je trougao [inline]ABC[/inline] sa stranicama [inline]AB=\sqrt2\text{ cm}[/inline] i [inline]AC=\sqrt3\text{ cm}[/inline]. Neka je tačka [inline]D[/inline] na stranici [inline]BC[/inline] tako da je [inline]\angle BAD=30^\circ[/inline] i [inline]\angle CAD=45^\circ[/inline]. Dužina duži [inline]AD[/inline] iznosi (u [inline]\text{cm}[/inline]):
[inline]\text{(A)}\;\displaystyle\frac{\sqrt6}{2}[/inline] [inline]\text{(B)}\;\displaystyle\frac{1}{\sqrt{2+\sqrt6}}[/inline] [inline]\text{(C)}\;\displaystyle\sqrt{\frac{5}{2}}[/inline] [inline]\text{(D)}\;\displaystyle\frac{\sqrt6+1}{\sqrt{2+\sqrt6}}[/inline] [inline]\text{(E)}\;\displaystyle\frac{1}{2}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\enclose{box}{\text{(A)}\;\displaystyle\frac{\sqrt6}{2}}[/inline] [inline]\text{(B)}\;\displaystyle\frac{1}{\sqrt{2+\sqrt6}}[/inline] [inline]\text{(C)}\;\displaystyle\sqrt{\frac{5}{2}}[/inline] [inline]\text{(D)}\;\displaystyle\frac{\sqrt6+1}{\sqrt{2+\sqrt6}}[/inline] [inline]\text{(E)}\;\displaystyle\frac{1}{2}[/inline] [inline]\text{(N)}[/inline] Ne znam
15.Link zadatka Dat je polinom [inline]P\left(x\right)=a_0x^4+a_1x^3+a_2x^2+a_3x+a_4[/inline] [inline]\left(a_0,a_1,a_2,a_3,a_4\in\mathbb{R},\;a_0\ne0\right)[/inline], takav da je [inline]P\left(0\right)=P\left(1\right)=P\left(2\right)=P\left(-1\right)=0[/inline] i [inline]P\left(-2\right)=12[/inline]. Tada je [inline]P\left(3\right)[/inline] jednako:
[inline]\text{(A)}\;\displaystyle\frac{1}{3}[/inline] [inline]\text{(B)}\;\displaystyle-\frac{1}{2}[/inline] [inline]\text{(C)}\;1[/inline] [inline]\text{(D)}\;2[/inline] [inline]\text{(E)}\;12[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;\displaystyle\frac{1}{3}[/inline] [inline]\text{(B)}\;\displaystyle-\frac{1}{2}[/inline] [inline]\text{(C)}\;1[/inline] [inline]\text{(D)}\;2[/inline] [inline]\enclose{box}{\text{(E)}\;12}[/inline] [inline]\text{(N)}[/inline] Ne znam
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16.Link zadatka Bočne strane trostrane piramide su pravougli trouglovi sa temenom pravog ugla u vrhu piramide. Površine tih bočnih strana su [inline]6\text{ cm}^2[/inline], [inline]8\text{ cm}^2[/inline] i [inline]12\text{ cm}^2[/inline]. Zapermina piramide je:
[inline]\text{(A)}\;6\text{ cm}^3[/inline] [inline]\text{(B)}\;8\sqrt2\text{ cm}^3[/inline] [inline]\text{(C)}\;8\text{ cm}^3[/inline] [inline]\text{(D)}\;6\sqrt2\text{ cm}^3[/inline] [inline]\text{(E)}\;12\text{ cm}^3[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;6\text{ cm}^3[/inline] [inline]\enclose{box}{\text{(B)}\;8\sqrt2\text{ cm}^3}[/inline] [inline]\text{(C)}\;8\text{ cm}^3[/inline] [inline]\text{(D)}\;6\sqrt2\text{ cm}^3[/inline] [inline]\text{(E)}\;12\text{ cm}^3[/inline] [inline]\text{(N)}[/inline] Ne znam
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17.Link zadatka Ako je uređen par [inline]\left(x,y\right)[/inline] [inline]\left(x,y\in\mathbb{R},\;x,y>0,\;x\ne1\right)[/inline], rešenje sistema jednačina [inline]x^y=y^x[/inline], [inline]x^p=y^q[/inline] [inline]\left(p,q\in\mathbb{R}\setminus\left\{0\right\},\;p\ne q\right)[/inline], tada je proizvod [inline]x\cdot y[/inline] jednak:
[inline]\text{(A)}\;\displaystyle\frac{p-q}{2}[/inline] [inline]\text{(B)}\;\displaystyle\frac{2}{p-q}[/inline] [inline]\text{(C)}\;1[/inline] [inline]\text{(D)}\;\displaystyle\left(\frac{p}{q}\right)^{\frac{p+q}{p-q}}[/inline] [inline]\text{(E)}\;\displaystyle\left(\frac{q}{p}\right)^{\frac{p+q}{p-q}}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;\displaystyle\frac{p-q}{2}[/inline] [inline]\text{(B)}\;\displaystyle\frac{2}{p-q}[/inline] [inline]\text{(C)}\;1[/inline] [inline]\enclose{box}{\text{(D)}\;\displaystyle\left(\frac{p}{q}\right)^{\frac{p+q}{p-q}}}[/inline] [inline]\text{(E)}\;\displaystyle\left(\frac{q}{p}\right)^{\frac{p+q}{p-q}}[/inline] [inline]\text{(N)}[/inline] Ne znam
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18.Link zadatka Neka je [inline]S[/inline] skup svih realnih rešenja nejednačine [inline]\text{tg }x\left(1-\text{tg}^2x\right)\left(1-3\text{tg}^2x\right)\left(1+\text{tg }2x\cdot\text{tg }3x\right)>0[/inline] i neka je [inline]S_1\subset S[/inline]. Tada skup [inline]S_1[/inline] može biti:
[inline]\text{(A)}\;\displaystyle\left(-\frac{\pi}{2},\frac{\pi}{2}\right)[/inline] [inline]\text{(B)}\;\displaystyle\left(\frac{\pi}{3},\frac{\pi}{2}\right)[/inline] [inline]\text{(C)}\;\displaystyle\left(\frac{3\pi}{4},\pi\right)[/inline] [inline]\text{(D)}\;\displaystyle\left(\frac{7\pi}{6},\frac{3\pi}{2}\right)[/inline] [inline]\text{(E)}\;\displaystyle\left(\frac{\pi}{2},\frac{5\pi}{6}\right)[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;\displaystyle\left(-\frac{\pi}{2},\frac{\pi}{2}\right)[/inline] [inline]\enclose{box}{\text{(B)}\;\displaystyle\left(\frac{\pi}{3},\frac{\pi}{2}\right)}[/inline] [inline]\text{(C)}\;\displaystyle\left(\frac{3\pi}{4},\pi\right)[/inline] [inline]\text{(D)}\;\displaystyle\left(\frac{7\pi}{6},\frac{3\pi}{2}\right)[/inline] [inline]\text{(E)}\;\displaystyle\left(\frac{\pi}{2},\frac{5\pi}{6}\right)[/inline] [inline]\text{(N)}[/inline] Ne znam
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19.Link zadatka Od lista hartije kružnog oblika izrezan je kružni isečak od koga je napravljen konusni levak najveće zapremine. Centralni ugao tog kružnog isečka u radijanima je:
[inline]\text{(A)}\;\displaystyle\frac{\pi}{3}[/inline] [inline]\text{(B)}\;\displaystyle\frac{2\pi}{3}\sqrt6[/inline] [inline]\text{(C)}\;\displaystyle\frac{2\pi}{3}[/inline] [inline]\text{(D)}\;\displaystyle\frac{2\pi}{\sqrt3}[/inline] [inline]\text{(E)}\;\displaystyle\frac{\pi\sqrt6}{2}[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;\displaystyle\frac{\pi}{3}[/inline] [inline]\enclose{box}{\text{(B)}\;\displaystyle\frac{2\pi}{3}\sqrt6}[/inline] [inline]\text{(C)}\;\displaystyle\frac{2\pi}{3}[/inline] [inline]\text{(D)}\;\displaystyle\frac{2\pi}{\sqrt3}[/inline] [inline]\text{(E)}\;\displaystyle\frac{\pi\sqrt6}{2}[/inline] [inline]\text{(N)}[/inline] Ne znam
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20.Link zadatka Iz skupa od [inline]10[/inline] studenata, među kojima su samo jedan student elektrotehnike i samo jedan student matematike, biramo komisiju od [inline]6[/inline] članova, ali tako da ako je u komisiji student elektrotehnike mora u toj komisiji biti i student matematike. Koliko se takvih komisija može obrazovati?
[inline]\text{(A)}\;210[/inline] [inline]\text{(B)}\;98[/inline] [inline]\text{(C)}\;126[/inline] [inline]\text{(D)}\;154[/inline] [inline]\text{(E)}\;165[/inline] [inline]\text{(N)}[/inline] Ne znam[inline]\text{(A)}\;210[/inline] [inline]\text{(B)}\;98[/inline] [inline]\text{(C)}\;126[/inline] [inline]\enclose{box}{\text{(D)}\;154}[/inline] [inline]\text{(E)}\;165[/inline] [inline]\text{(N)}[/inline] Ne znam
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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.