Zadaci Za Pripremu Prijemnog Ispita

ZADACI ZA PRIPREMU

PRIJEMNOG ISPITA

Kragujevac, 2014. godine

VISOKA TEHNIKA KOLA STRUKOVNIH STUDIJA KRAGUJEVAC www.vts.edu.rs

Sadraj: Osnovne informacije

Zadaci iz Matematike .................. 1 str.

Zadaci iz Engleskog jezika ....... 15 str.

Potovani budui studenti,

Materijal koji smo pripemili pomoi e Vam da poloite prijemne ispite

iz Matematike i Engleskog jezika.

Kandidati koji ele da se upiu na studijski program "Informatika" polau

prijemni ispit iz predmeta Matematika i Engleski jezik.

Kandidati koji ele da se upiu na ostale studijske programe polau

prijemni ispit samo iz Matematike.

Visoka tehnika kola strukovnih studija u Kragujevcu svake godine, pre

prijemnog ispita organizuje BESPLATNU pripremnu nastavu iz matematike za

sve zainteresovane kandidate za polaganje. Termini za pripremnu nastavu bie

blagovremeno objavljeni na sajtu kole i na oglasnoj tabli kole.

S potovanjem,

Uprava Visoke kole

Zadaci iz Matematike VTS Kragujevac

Zadaci za pripremu prijemnog ispita izMATEMATIKE

1. Logaritmovati izraz a3 6pa3 b5.

2. Izracunati zbir prvih 12 clanova niza 2;4;8;16. . .

3. Dokazati identitet tg2 x+1=1

cos2 x.

4. Resiti trigonometrijsku jednacinu sin2x cosx= 0.5. Napisati jednacinu prave koja prolazi kroz presek pravih 4x 3y 8 = 0 i

x+2y13= 0, i normalna je na pravoj 3x+ y8= 0.6. Napisati jednacinu tangente konstruisane iz tacke A(0;2) na elipsu

2x2+3y2 = 6.

7. Jednakostranicni trougao povrsine 36p3cm2, upisan je u krug. Kolika je

povrsina tog kruga?

8. Ako se stranice jednog kvadrata povecaju za 2cm, tada se njegova povrsinapoveca za 24cm2. Kolika je stranica tog kvadrata?

9. Resiti sistem jednacina,

2x y+3z = 20x2y+2z = 73x+2y z = 1 :

10. Skratiti razlomakx222x+40x25x+6 .

11. Odrediti x iz jednacine logx= 5loga+2logb4logc2logd.12. Odrediti cetiri broja koja obrazuju geometrijsku progresiju, u kojoj je zbir

krajnjih clanova 56, a proizvod srednjih clanova 108.

13. Dokazati identitet (1+ tgx)2+(1 tgx)2 = 2cos2 x

.

14. Resiti trigonometrijsku jednacinu tg2 x tgx= 2.15. Temena jednog cetvorougla su A(3;4);B(2;0);C(2;1) i D(2;2). Odre-

diti presek njegovih dijagonala.

16. Napisati jednacinu hiperbole kojoj pripadaju tackeM(813 ;4) i N(13;715).

17. Naci povrsinu i zapreminu pravilne prave cetvorostrane zarubljene piramidecije su osnovne ivice 10cm i 4cm, a visina

p7cm.

1


18. Resiti jednacinu tg2 x+13ctg2 x14= 0.19. Resiti sistem jednacina,

x+ y = 30y+ z = 0z+u = 3xu = 2 :

20. Pravilni sestougao stranice a rotira oko duze dijagonale. Izracunati povrsinui zapreminu nastalog obrtnog tela.

21. Napisati jednacinu prave kroz tacku A(2;3) koja sa osom Ox gradi dva putaveci ugao od ugla koji sa osom Oy zaklapa prava 2y x= 3.

22. Ispitati polozaj prave 2x y3= 0 i kruznice x23x+2y3= 0.23. Resiti jednacinu 3tg2 x+3ctg2 x9= 1.24. Resiti sistem jednacina,

2x+4y+ z = 13x y+2z = 65x+3y z = 1 :

25. U krugu ciji je precnik AB = 25dm, data je tetiva AC = 20dm. Izracunatipovrsinu koja nastaje rotacijom AC oko AB.

26. U elipsux2

49+

y2

24= 1 je upisan pravougaonik tako da njegove dve paralelne

stranice prolaze kroz zize elipse. Odrediti koordinate temena pravougaonika.

27. Za funkcije y = x2mx+m 1 i y = x2 2x+m, odrediti m tako danjihove ekstremne vrednosti budu jednake.

28. Odrediti zbir svih trocifrenih brojeva deljivih sa trinaest.

29. Resiti jednacinu 8log100x8log10x+8logx = 456.30. Odrediti strane jednakokrakog trougla cija je visina 8cm, a obim 32cm.


2x+4y+ z = 13x y+2z = 65x+3y z = 1 :

32. Resiti jednacinu 2asin2 x+2bcos2 x= (b+a)sin2x+(ba)cos2x.

2


33. Date su koordinate dva temena trougla A(6;2);B(2;2) i ortocentarH(1;2). Odrediti koordinate treceg temena.

34. Napisati jednacinu elipse cije su tangente x+ y5= 0 i x4y10= 0.35. Izracunati povrsinu i zapreminu prave zarubljene kupe ako je visinaH = 4cm,

izvodnica s= 5cm i omotac M = 85pcm2.

36. Resiti jednacinu 5cos2x+3sin2 x= 3cos2 x.

37. Dokazati identitettg2(45+ x)1tg2(45+ x)+1

= sin2x.

38. Resiti jednacinu 6sin2 x+3sinxcosx5cos2 x= 2.39. Odrediti aritmeticku progresiju ciji je zbir tri uzastopna clana jednak 18, a

zbir kvadrata ta tri clana 126.


x2+ x+1y2+ y+1

= 3

x+ y = 6 :

41. Odrediti x, ako je logx=35log(a+b) 4

7log(ab).

42. U funkciji y = (m+ 2)x2 + (1+m)x+m, odrediti parametar m tako dafunkcija ima maksimalnu vrednost za x= 2.

43. Izracunati vrednost izrazaz2

z3+1ako je z= 52i.

44. Zbir tri broja koji cine geometrijsku progresiju iznosi 21, a zbir njihovih re-

ciprocnih vrednosti je712

. Koji su to brojevi?

45. Dokazati identitet2sinxcosx sin(x y)cos(x y)2sinxsiny = tg(x+ y).

46. Resiti jednacinu tgx+ tg2x= tg3x.

47. Dva temena paralelograma su A(3;5) i B(3;1), a presek dijagonala jeS(2;1). Odrediti ostala temena tog paralelograma.

48. Napisati jednacinu zajednickih tangenti krivih 3x24y2= 12 i 2x2+2y2= 1.49. Napisati jednacinu kruznice ciji je centar u tacki C(4;2) i koja dodiruje

pravu 3x+4y16= 0.50. Resiti nejednacinu log2(x

23x+4)< 1.

3


51. Izracunatii zapreminu lopte opisane oko pravilne sestostrane zarubljene pi-ramide cije su osnovne ivice 6cm i 3cm, a bocna ivica 5cm.

52. Osnovica prizme je paralelogram cije su stranice 9cm i 10cm, a dijagonala17cm. Izracunati zapreminu prizme ako njena povrsina iznosi 334cm2.

53. Visina trapeza je h, a osnovice su mu a i b. Izracunati povrsinu trougla kojise dobija produzenjem krakova tog trapeza.

54. Resiti jednacinu cos2xp2sinx+ sin2x= 0.55. Napisati jednacinu kruga kome pripadaju tacke A(4;2);B(1;3) iC(5;1).56. Resiti jednacinu log5x log16= log(21x8)1.

57. Resiti jednacinu2x

x+b xb x =

b2

4(x2b2) .

58. Resiti jednacinulog(35 x3)log(5 x) = 3.

59. Izracunati zapreminu piramide cija je osnova pravougaonik sa dimenzijama6cm i 15cm, i ako je njen omotac povrsine 126cm2.

60. Resiti jednacinu 2sin2 x+4sinx cosx4cos2 x1= 0.61. Odrediti stranicu romba ako je odnos njegovih dijagonala m : n i povrsina P.

62. Resiti jednacinux+3x3

x+1x1 = 3

13.

63. Ispitati medusobni polozaj dve kruznice, x2 + y2 2x 6y + 6 = 0 ix2+ y210x8y+40= 0.

64. Visina zarubljene piramide je 15cm, njena zapremina 475cm3, a odnos povr-sina njenih osnova je 4 : 9. Izracunati povrsine tih osnova.

65. Resiti jednacinu log2(x+14)+ log2(x+2) = 6.

66. Odrediti jednacinu kruznice ciji je centar tacka C(5;4) i koja spolja dodirujekruznicu x2+ y24x5= 0.

67. Resiti jednacinu2y+ay

2yy+a

= 2.

68. Izracunati povrsinu trapeza cije su osnovice 6cm i 20cm, a kraci su 13cm i15cm.

69. Resiti jednacinu 2sinx cosx+ cosx+2sinx+1= 0.

4



14x+2y6z = 94x+ y+9z = 36x4y+3z = 4 :

71. Izracunati3an1 b1n

4c2n d1+n:3an1 bn1

5c1n d2+n.

72. U jednacini 3x2 8x+ q = 0 odrediti parametar q tako da jedno njenoresenje bude tri puta vece od drugog.

73. Resiti jednacinu log4(2x3)2= 0.

74. Dokazati identitetsinx+ sin3xcosx+ cos3x

= tg2x.

75. Resiti jednacinu cos3x+ sin3x= cosx+ sinx.

76. Uprostiti izrazx

x1 3x1x2 +

2x+1x23x+2.

77. Pod kojim uglom se seku krive x2+ y2 = 16 i x2+ y210x= 0.78. Odrediti povrsinu i zapreminu pravilne petostrane piramide cija je bocna ivica

b= 5cm, a ugao nagiba bocne ivice prema osnovi iznosip6.

79. Dokazati identitet1

1+ sinx+

11 sinx =

2cos2 x

.

80. Resiti trigonometrijsku jednacinu 2cos2 x5cosx3= 0.81. Temena trougla su A(1;2);B(1;1);C(2;3). Kako glase jednacine pravih

koje sadrze visine tog trougla?

82. Srediste kruznice koja dodiruje obe koordinatne ose, pripada pravoj3x5y+15= 0. Kako glasi jednacina te kruznice?

83. Izracunati povrsinu romba cija je jedna dijagonala 12cm i stranica 10cm.

84. Kci je 22 godine mlada od majke, a pre 5 godina bila je od majke mlada triputa. Koliko godina ima majka a koliko kcerka?

85. Izvrsiti naznacene operacije i uprostiti izraza2+b2

ab a

2

abb2 +b2

a2ab .

86. Resiti i diskutovati sistem jednacina,

a2x y = abb3x+ay = b2 :

5


87. Resiti jednacinu sinx+ cos2 x= 1.

88. Osnova piramide je romb stranice 15cm. Bocne strane su nagnute premaosnovi pod uglom od

p4. Izracunati zapreminu piramide ako je povrsina

omotaca 4dm2.

89. Uprostiti izraza2a6a24

a12a 2.

90. Odrediti stranice i uglove pravouglog trougla, ako je njegov obim 24cm, apoluprecnik upisane kruznice 2cm.

91. Izracunati zapreminu pravilne sestostrane zarubljene piramide, ako su osnov-ne ivice 2m i 1m, a bocna ivica 2m.

92. U jednacini x2+ px+9= 0 odrediti p pod uslovom da je1x1+

1x2

=109.

93. Napisati jednacinu prave koja prolazi kroz tacku A(1;3) i normalna je napravu cija je jednacina x y+3= 0.

94. U jednacini x2 2mx + 2 = 0 odrediti parametar m tako da bude(3x11)(3x21) = 10, gde su x1 i x2 resenja jednacine.

95. Odrediti duzine dijagonala i povrsinu jednakokrakog trapeza cije su osnove9cm i 3cm, a ugao nagiba kraka prema duzoj osnovi

p3.


x+ y+ z = 3ax2y+ z = a+2bx+ y z = a :

97. Odrediti realan parametar a, tako da jednacina

(a1)x22(a+1)x+a2= 0 ;ima jednaka resenja.

98. Resiti jednacinu sinx cosx sin2 x= cosx sinx.

99. Izracunati tgx ako je7sinx5cosx3sinx+4cosx

= 2.

100. Logaritmovati jednakost x=a2 b2 3

pab2

cd2 4pc2 d3

.

101. Za koje vrednosti realnog parametra m jednacina (m+ 2)x2+ 4x 1 = 0ima dva resenja?

6



3x2y+5z = 86x+4y+ z = 2

3x2y+3z = 6 :


2x+ y+2z = 23x6y4z = 2x+5y+4z = 1 :

104. Uprostiti izrazx2

y2

+yx

: xy2 1

y+

1x

:(x y)2+4xy

1+yx

.

105. U jednacini (5k 1)x2 (5k+ 2)x+ 3k 2 = 0 odrediti parametar k daresenja budu jednaka.

106. Dokazati logb a loga b= 1.

107. Dokazati identitetsin(x+ y)+ sin(x y)sin(x+ y) sin(x y) =

tgxtgy

.

108. Resiti jednacinu sinx+ sin2x+ sin3x+ sin4x= 0.

109. Ako su tacke A(1;2) i B(6;4 15) krajevi duzi, odrediti koordinate tacaka A1,A2, A3 i A4 koje dele tu duz na pet jednakih delova.

110. Odrediti jednacinu tangente krive x29y2 = 9, ako je odnos njenih odsecakana koordinatnim osama 3 : 7.

111. Kvadrat ABCD rotira oko prave kojoj teme C pripada i paralelna je sa BD.Kolika je povrsina i zapremina tog rotacionog tela?

112. Uprostiti izraza2+axa2x x3

a xax+ x2

2xa2 x2 +

3a+ x

.

113. Zbir dve stranice trougla je 15cm, a visine koje njima odgovaraju su 4cm i6cm. Izracunati povrsinu trougla.


cos2 x= (1+ tgx)2+(1 tgx)2.


2x2y+ z = 3abx+2y z = 4b

2x+ y+3z = 5a :

7


116. Na elipsix2

100 y

2

36= 1 naci tacku cije je rastojanje od desne zize (fokusa)

cetiri puta vece od njegovog rastojanja od leve zize.

117. Na hiperboli 9x28y2 = 72 odrediti tacku u kojoj je dodiruje prava koja saosom Ox obrazuje ugao p=3.

118. Nad duzi a = 12cm opisan je polukrug i pravougaonik, cije su tri stranicetangente polukruga. Izracunati povrsinu izmedju pravougaonika i polukruga.

119. Trougao cije su stranice a = 4cm, b = 6cm i c = 8cm, rotira oko stranice c.Izracunati zapreminu nastalog tela.

120. U jednacini x2 (m2 1)x+m2 2 = 0, odrediti m tako da jedno resenjebude dva puta vece od drugog.

121. Resiti jednacinupa25x :

pax+4 =

pa.

122. Izracunatia216a+4

a2+4a21a2+9a+14

:a4a+2

.


2x+ y+2z = a3x y3z = 2ax+3y+ z = 3a :


cos2 x= tg2 x+1.

125. Osnovice trapeza su 142cm i 89cm, a dijagonale su 120cm i 153cm. Odre-diti povrsinu trapeza.

126. Odrediti koordinate tacke koja predstavlja projekciju tacke A(3;5) na pravux+2y+2= 0.

127. Odrediti jednacine zajednickih tangenti krivih 4x2 + 5y2 = 20 i5x2+4y2 = 20.

128. Odrediti paralelene stranice trapeza cija je povrsina 128cm2, odnos osnovica3 : 5 i visina 8cm.

129. Izracunati zapreminu prave pravilne trostrane zarubljene piramide cije su os-novne ivice 8cm i 2cm, a povrsina 47

p3cm2.

130. Resiti nejednacinu x(x2)+3> x23x.131. Resiti jednacinu 7 3x+15x+2 = 3x+45x+3.

8



2x+ y z = 2a+2bx+ y+ z = a2b

3x+2y5z = 7b :

133. Odrediti modul kompleksnog broja z=(2+ i)2

2+4i.

134. Resiti nejednacinu32x2+3x

> 2.

135. Izracunati zapreminu pravilne cetvorostrane zarubljene piramide, ako su os-novne ivice 7m i 5m, a bocna ivica 2m.

136. Odrediti jednacinu tangente krive 4x2 + 9y2 = 9 ako se zna da su njeniodsecci na koordinatnim osama u odnosu 3 : 7.

137. Obim jednakokrakog tr ougla je 72cm, a razlika kraka i osnovice je 6cm.Odrediti povrsinu trougla.

138. Kolika je ivica kocke kojoj zapremina poraste za 128cm3, kada se njene ivicepovecaju za 2cm?

139. Resiti jednacinu 3t22(3a1)t4a= 0.140. Resiti jednacinu 4 logx= 3plogx.

141. Izracunati5x

5x2+ x 315x

25x210x+1 10x(5x4)125x2 .

142. Jednakokraki trapez osnovica 8cm i 2cm, opisan je oko kruznice. Izracunatipovrsinu trapeza.

143. Ispitati prirodu resenja jednacine x22(m+4)x+m29= 0, za razne vred-nosti parametra m.

144. Izracunaj povrsinu paralelograma cije su dijagonale 26cm i 30cm, i jednastranica 14cm.

145. Izracunati zapreminu pravilne cetvorostrane zarubljene piramide, ako su povrsineosnova 50cm2 i 8cm2, a povrsina dijagonalnog preseka 28cm2.

146. Resiti jednacinu sinx+3sinx+ sin5x= 0.

147. Dokazati da jetgx tgytgx+ tgy

=sin(x y)sin(x+ y)

.

148. Odrediti parametar a tako da prava (a+2)x+(a2+9)y+3a28a+5 = 0prolazi kroz koordinatni pocetak.

9


149. Dijagonale romba, duzine 8cm i 6cm, pripadaju koordinatnim osama. Napisatijednacine pravih koje sadrze stranice tog romba.


12x2+5y2 = 3453x2+7y2 = 138 :


ax+ y = 18x+ay = 2 :

152. Resiti jednacinu 3x+1+12 3x = 13.

153. Uprostiti izraza2+a2an+13an

(a+2)2a24a24

3a2a

.

154. Osnova prizme je jednokraki trougao cija je osnovica 1m, a visina jednakavisini prizme. Ako je zapremina prizme 720dm3, naci njenu povrsinu.

155. Visina trostrane zarubljene piramide je 10cm. Osnovne ivice jedne osnove su27m, 29m i 52m, a obim druge osnove je 72m. Odrediti zapreminu zarubljenepiramide.

156. Dokazati trigonometrijski identitet1+ sinx1+ cosx

=

1+

tgx2

22

.

157. Resiti jednacinu (1+ cos2x) tgx cos2x tg2x= 0.158. Odrediti ugao izmedju pravih cije su jednacine 2x + y 5 = 0 i

x+3y3= 0.159. Odrediti rastojanje izmedu dve paralelne prave 3x 4y + 10 = 0 i

6x8y+15= 0.160. Pravilna cetvorostrana prizma ima omotac 8m2 i dijagonalu 3m. Izracunati

njenu zapreminu.

161. Kosa trostrana prizma ima osnovne ivice 5m, 6m i 9m, a donju ivicu 10m.Izracunati zapreminu prizme ako njena bocna ivica obrazuje sa osnovom ugaood 450.

162. Resiti nejednacinu 22x2x6> 0.163. U jednacini 3x27x+m2m = 0, odrediti m tako da zbir kvadrata njenih

resenja bude379.

164. Odrediti povrsinu jednakokrakog trapeza cija dijagonala d = 2cm obrazuje saosnovicom ugao od p=4.

10


165. Odrediti tacku u kojoj funkcija y = x2 2(a+ 2)x 2a 5 ima ekstremnuvrednost.

166. Resiti jednacinu tg2 x3ctg2 x= 2.

167. Dokazati trigonometrijski identitetsinx+ sin3x+ sin5xcosx+ cos3x+ cos5x

= tg3x.

168. Odrediti najkrace rastojanje parabole y2 = 64x od prave 4x+3y+36= 0.

169. Iz tackeM(6;2) povuci prave tako da sa osom Ox obrazuju jednakostranicnitrougao.

170. Putnik vidi brdo pod uglom odp6, a kada mu se priblizi na udaljenost od

730m, vidi ga pod uglom odp4. Kolika je visina brda?

171. Naci jednacinu kruznice ciji je centar tacka C(5;2) i kojoj pripada tackaA(1;5).

172. Resiti nejednacinu log10x4x+1

< 1.

173. Za koje vrednosti parametra m prava y =52x + m dodiruje hiperbolu

4x2 y2 = 36.174. Osnova pravog paralelopipeda je romb cija je povrsina 1m2, a povrsine dija-

gonalnih preseka su 3m2 i 6m2. Izracunati zapreminu paralelopipeda.

175. Uprostiti izraz xx2+ xy

2x+ y

+y

x2+ xy

:xy2+ y

x

.

176. Ispitati znak funkcije y= x24x+3.

177. Izracunati 6r

ax 5ra

x

2: 3pax2.

178. Stranice trougla su 25cm, 24cm i 7cm. Izracunati poluprecnike upisane iopisane kruznice.

179. Bazen oblika pravouglog paralelopipeda ima dimenzije 4m, 4:5m i 2:5m.Za koje vreme ce bazen biti pun, ako se u njega uliva 5 litara vode svakesekunde?


mx+ny = m2+n2

mxny = m2n2 :

181. Naci rastojanje tacke A(2;1) od prave cija je jednacina 4x+3y+10= 0.

11


182. U pravom valjku poluprecnika r i visine h, upisana je pravilna cetvorostranaprizma. Kolika je svaka bocna strana prizme?

183. Resiti nejednacinu 32x10 3x+9 0.184. Odrediti jednacine pravih kojima pripadaju stranice trougla ABC, kome je

teme A(3;4), a jednacine pravih koje sadrze visine kroz druga dva njegovatemena su 7x2y1= 0 i 2x7y6= 0.

185. Koji broj treba dodati brojiocu i imeniocu razlomka25da bismo dobili razlo-

mak57?


3x+ y+ z = 2x2y+3z = 3x+ y+ z = 6 :

187. Za koje vrednosti realnog parametra m jednacina x2+mx+36= 0 ima dvos-truki koren?

188. Odrediti x iz jednacine log3181

= x.

189. Resiti nejednacinu5x1

4 3x13

10>

5x+13

.

190. Uprosti izraz 3xx+ y

+x

x y 2xy3

:

4xyx2 y2 .

191. Resiti sistem nejednacina,

2(2x+1) > 3 1+ x5

x39

> 1+2x7

2:

192. Ispitati prirodu resenja jednacine x2(2m+1)x+m21= 0, za razne vred-nosti parametra m.

193. Odrediti realan i imaginarni deo kompleksnog broja z=3+ i

(2 i)2 .

194. Osnovna ivica pravilne sestostrane prizme iznosi 3m, a dijagonala bocnestrane 6m. Izracunati njenu zapreminu.

195. Resiti jednacinu 3x+1+3x1+3x2 = 5x+5x1+5x2.

196. Uprostiti izrazx41a3+a

ax3+ x2+ x+1

2a2+2

x22x+1.

12


197. Izracunati y= z2+2z3 za z= 2 i.198. Resiti jednacinu log3 x+ log3(x+2) = 1+ log3(3x4).199. Resiti nejednacinu (x3)(x23x+2)< 0 .

200. Uprostiti izraz3a24b3

3:9a2b

4

1 b712a11

.

201. Odrediti p i q u funkciji y = x2+ px+ q, tako da za x = 2 funkcija imaminimum 1.

202. Resiti jednacinu 23x223x323x4 = 0.203. Resiti nejednacinu log3 x+ log3(x+1)< log3(2x+6).

204. Naci tacku S koja je simetricna tacki A(2;3) u odnosu na pravu koja prolazikroz tacke B(1;3) i C(6;4).

205. Uprostiti izraz((12)8)2 754 (4)9

(25)2 186 108 .

206. Sin je mladi od oca 22 godine, a pre 5 godina je bio mladi 3 puta. Kolikogodina ima otac a koliko sin?

207. Za koju vrednost parametra m jednacina x2+2(3m)x+2m3= 0 nemaresenja?

208. Resiti jednacinu 4x+313 4x+1 = 23x123x3.209. Naci tacku S simetricnu tackiM(8;9) u odnosu na pravu koja prolazi kroz

tacke A(3;4) i B(1;2).

210. Resiti jednacinu logx log 1x+1

log2= log(2x+3).

211. Izvrsiti naznacene operacije i uprostiti izraz2x

x13x2+2x+1

x31 +x+1

x2+ x+1.

212. Izracunati

10

rab4

c2

3:

5

ra2b3

c4

2.


a2x+ y = 18x+ay = 2 :

214. Resiti jednacinu 152x3 = 3x 53x6.215. Za koje vrednosti parametra m je funkcija y= (m+1)x22(m+3)x+m3

negativna za svako x?

13


216. Resiti jednacinu 7sin2 x3cos2 x= 2.217. Stranice trougla su 13cm;14cm i 15cm. Prava paralelna najvecoj stranici

trougla odseca trapez obima 39cm. Naci povrsinu trapeza.

218. Izvrsiti naznacene operacije i uprostiti izraz16x x2x24 +

3+2x2 x

23xx+2

.

219. Resiti nejednacinux1x+2

3.


(a+2)x+(a2)y = 162x+4y = a2 :

221. Dokazati identitet1+ sinx cosx1+ sinx+ cosx

= tgx2.

222. Izracunati povrsinu jednakokrakog trapeza opisanog oko kruznice, cije su os-novice 8cm i 2cm.

223. Napisati jednacinu prave kroz tacku A(1;3) koja je normalna na pravux y+3= 0.

14

Engleski jezik - priprema za test Visoka tehnika kola strukovnih studija Kragujevac

15

ENGLISH LANGUAGE GRAMMAR TEST

CHOOSE THE CORRECT ANSWER:

Na svako pitanje zaokruiti odgovor A), B) ili C).

1. While John was playing the piano, his sister............her homework.

A) does B) was doing C) has done

2. We'll wait for her until she..........

A) returns B) will return C) will have returned

3. They................football since lunch, and they are still playing.

A) are playing B) are being playing C) have been playing

4. Don't worry, the water we are drinking....................

A) has been boiled B) boils C) being boiled

5. Not one of the students....................

A) invited B) has invited C) has been invited

6. The champion had high hopes.......................the medal.

A) win B) to winning C) of winning

7. She.....................to be a popular singer.

A) is said B) says C) said

8. He is used to...........................on a computer, but I am not.

A) working B) worked C) work

9. I finally managed to get the engine.................., and we continued our trip.

A) start B) starts C) started

10. I enjoy....................these things for you.

A) doing B) to have done C) in doing


16

11. She can't make him................it.

A) do B) to do C) doing

12. The boy wasn't.....................to lift the package by himself.

A) so strong B) strong enough C) enough strong

13. It was...................interesting book that I read it several times.

A) so B) such C) such an

14. Could you give her....................milk, please?

A) few B) a little C) a few

15. We were sure that hardly.................would agree with us.

A) nobody B) anybody C) someone

16. I'm sure John will succeed if he tries..................

A) hardly B) hardest C) harder

17. Do you know...................sweater it is?

A) whose B) which C) whom

18. She sings very well,.................?

A) can't she B) doesn't she C) isn't she

19. Can you multiply 27...................30?

A) with B) by C) and

20. Why did you let him go without.........................coat?

A) a B) the C) /

21. She chose Kevin's painting, not..................

A) Times B) Tim's C) Tims'

22. How many......................do you have?

A) sisters-in-law B) sister-in-laws C) sisters-in-laws

23. You always sit in that same seat,..........................?

A) dont you B) do you C) are you


17

24. She repaired the computer by.........................

A) her B) she C) herself

25. He is the pilot..........................flies for JAT.

A) which B) whose C) who

26. There...................somebody else in this room.

A) is B) are C) were

27. How much money is..................in the cash box?

A) their B) there C) it

28. The boys divided the pizza among...............

A) they B) them C) their

29. The hen laid................egg.

A) the B) / C) an

30. People speak French in.....................Canada, too.

A) a B) the C) /

31. This smells great, but it................funny.

A) tastes B) tasted C) is tasting

32. I wish they................strong enough to help us.

A) are B) were C) was

33. If Rose were at this concert, it..................more fun.

A) will be B) would be C) would have been

34. She.................for Greece next week.

A) left B) would leave C) will leave

35. The show................when we arrived.

A) begin B) had already begun C) has begun

36. Mike...............poor work recently.

A) did B) does C) has done


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37. I wondered if she...................him.

A) invites B) would invite C) will invite

38. We used to.............in New York.

A) live B) living C) lived

39. The bus should.............here by now.

A) been B) have been C) has been

40. Howard denied............the book.

A) to lose B) lost C) losing

41. Would you like to go...........a ride.

A) with B) on C) for

42. They were here, but they've gone back to............apartment.

A) theirs B) his C) their

43. There isn't.............food in the house.

A) none B) some C) any

44. I could have done better if I...........more time.

A) had had B) have had C) had

45. He............move the piano in.

A) helped ourselves B) helped us C) helped in to

46. The assassination attempt..........millions, because the speech was on television.

A) was seen by B) to be able to C) was saw by

47. Real wealth is.............avoid doing what one would rather not.

A) being able as to B) to be able to C) /

48. Despite her broken leg, Alana can walk..............get around.

A) good enough to B) well enough to C) fine enough to

49. When we get our tickets,............be marked "first class".

A) it will B) they will C) it is to


19

50. ................of us are staying at home.

A) Some B) A little C) Less

51. The thief was caught just as he.............into the car.

A) has got B) was got C) was getting

52. Whenever she saw Bill, he...........the same book.

A) was writing B) writes C) has written

53. ..............when you came home?

A) Had it still snowed B) Did it still snow C) Was it still snowing

54. I told him I.............from his parents.

A) haven't heard B) wasn't heard C) hadn't heard

55. The young man...........for hours when the fishermen found him.

A) has been swimming B) had been swimming C) had to be swimming

56. I..............very late when I was in London.

A) have got up B) get up C) used to get up

57. He ought............for his fine performance.

A) to be congratulating B) to be congratulated C) be congratulated

58. A surgeon ................. on Jims knee last night.

A) operated B) was operated C) operates

59. They've been marred...............ten years.

A) ago B) since C) for

60. I shan't go out until it............raining.

A) stops B) will stop C) will have stopped

61. She looks after the boy as if he..............her own little brother.

A) is B) were C) was

62. The girls couldn't help..................

A) crying B) to cry C) cry


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63. He hasn't got any sisters. John hasn't got any............

A) either B) neither C) too

64. Everybody took part...........the play.

A) at B) on C) in

65. ................John come to the party if Sue invited him?

A) Will B) Did C) Would

66. They don't want..............to eat.

A) no more B) anything more C) nothing more

67. The situation is so bad that we can do................about it.

A) little B) few C) a little

68. Don't pay any attention to him.............he says.

A) why B) whatever C) how

69. .............Welsh live in a mountainous country.

A) A B) - C) The

70. John can lie in............sun for hours.

A) the B) a C) -

71. Every time we..........Mary, she says something nice to my wife.

A) saw B) are seeing C) see

72. She doesn't feel so well. She.............down all afternoon.

A) has laid B) has been lying C) has lied

73. She couldn't do it all by herself,............she?

A) can B) was C) could

74. John looked at the TV set and asked..............fixed.

A) whether it had been B) was it C) whether it has been

75. Sunglasses must..............when the sun is so bright.

A) to be worn B) be worn C) be wearing


21

76. They expected the game...............before ten o'clock.

A) finish B) to be finished C) be finished

77. If................the bus, we'd have taken the train.

A) we'd missed B) we'd miss C) we miss

78. He wants me to have this............by noon.

A) done B) to do C) being done

79. Could you give me.............sugar, please?

A) few B) a little C) a few

80. Does Peter have............different subjects at school as we do?

A) so little B) as much C) as many

81. When shall we see each other again? Any time you wish. I am on holiday and I'll

fit.......your plans.

A) in with B) down with C) in for

82. He behaved.............he had been drinking.

A) so that B) for C) as if

83. Her room always smells.............perfume.

A) of B) on C) in

84. The windows need painting, and so...............

A) of B) on C) in

85. Five years ago at this time of year I............in India.

A) have lived B) was living C) have been living

86. They decided to leave early, ...........was better for everybody.

A) what B) that C) which

87. What did you do when the fire broke...........?

A) away B) off C) out

88. She found the parcel.............to the wrong address.


22

A) had been sent B) had to sent C) had sent

89. Unfortunately, we.............Jim since last year.

A) haven't seen B) didn't see C) weren't seen

90. Everything is closed and locked. They............be on holiday.

A) outgoing to B) have to C) must

91. When she goes shopping, she usually...........the most expensive things.

A) chooses B) is choosing C) is chosen

92. He turned on the TV set, the moment I............the room.

A) had left B) have left C) leave

93. I hope you were not.............at my lecture.

A) boring B) bored C) been bored

94. If I were you........... some money, not waste it.

A) I'll save B) I'd save C) I saved

95. Theres a very good thriller on TV tonight. I hope we'll get home...........to see it.

A) enough early B) so early C) early enough

96. It's surprising how much she..............her mother.

A) is resembling B) is resembled C) resembles

97. Mary...........to London several times in 1995.

A) has been B) went C) was going

98. He must............the prize. He deserves it.

A) be given B) to be given C) be giving

99. I wish Tom...........us on our excursion last week.

A) could join B) has joined C) could have joined

100. When we saw John, he..........planting some flowers.

A) will be B) has been C) was

101. The students wanted to know how much more time........before the examination.


23

A) there was B) was there C) was it

102. The old woman enjoyed...........that evening.

A) hers B) herself C) she herself

103. ...........when you come home?

A) has it still rained B) did it still rain C) was it still raining

104. As soon as the sun..........out, Peter and Mary can go to the park.

A) comes B) will be coming C) will come

105. I asked Ann how long ago..........left Paris.

A) had she B) she has C) she had

106. All of them insisted............staying for dinner.

A) should he B) that he should C) on his

107. ...........them next week or do you have some other plans?

A) are you meeting B) have you met C) have they met

108. The machine...........to cut down trees.

A) use B) was used C) has used

109. I'll come to the party,...........you come too.

A) since B) unless C) provided

110. Im sure Mr Brown doesn't think very..........of her work.

A) high B) highly C) highest

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