1:Bi 1 : Cho hm s 222 5 33 1 + ( )x xy f xx x.Tnh khong cch gia hai im cc tr ca th hm s cho.Kt qu: 1 4184 , ABBi 2 :Tnh gn ng honh giao im ca hai th hm s : 3 212 3 1 ( ) : ( ) C y f x x x x v 3 2 3 322 2 3 1 + + ( ) : ( ) C y gx x x x.Kt qu: 11 6180 , x20 6180 , x30 5 , xBi 3Cho hai dy s( )nuv( )nvc : 1 1 1 11 2 22 15 17 12 1+ + ; ; ; ,( )n n n n n nu v u v u v v u n .a/ Tnh 5 10 15 18 5 10 15 18, , , , , , , u u u u v v v vb/ Lp quy trnh n phm.Kt qu: 5 10 15 185 10 5 5767 192547 47517071 1055662493526 135434 34219414 673575382 u u u uv v v vBi 4 Tm s t nhin th 2010 sau du phy khi chia 1 cho 23Kt qu: S thp phn th 2010 sau du phy l8Bi 5 : Cho hm s 3 22 3 3 18 8 + + ( ) ( ) y f x x a x ax . Tm a th hm s tip xc vi trc honh. Kt qu: 1 1 2963 8 8990 0 8990 a , , , a a aBi 6 : Ngi ta ct mt t giy hnhvung cnh bng 1 gp thnh mt hnh chp t gic u sao cho bn nh ca hnh vung dn li thnh nh ca hnh chp .Tnh cnh y ca khi chp th tch ln nht.Kt qu: Cnh y khi chp l : 0 5657 , xBi 7 : Mt ngi c lnh lng khi im l 700.000/thng. C ba nm anh ta li c tng lng thm 7%. Hi sau 36 nm lm vic anh ta c lnh tt c bao nhiu tin (Ly chnh xc n hng n v). Kt qu:450788972 2:Bi 1 . ( 5 im) Cho cc hm s 5 22008 3 2009 2007 0 + + ( ) , ( ) f x x x x x. Tnh cc gi tr sau:

1 2 2009 2008 2009 ( ) ; ( ) ; ( ) ; ( ) f f f fKt qu:Bi 2. ( 5 im)1) Tnh gn ng nghim ca phng trnh:2 27 8 2360 + x y .Kt qu:2) Tinh tng 1 2 99 1002 3 3 4 100 101 101 102 + + ... S . Ly nguyn kt qua hin trn man hinh.Kt qu:Bi 3. ( 5 im)Tm nghim gn ng (, pht, giy) ca phng trnh: 22 4 3 + + sin (sin cos ) x x xKt qu:Bi 4. ( 5 im)Cho 2 dy s { }nuva{ }nv vi : 1 + nu1 1111 222 1517 12++ ' ;n n nn n nu vu v uv v uvi n = 1, 2, 3, , k, ..1. Tnh 5 10 15 18 19 5 10 15 18 19, , , , ; , , , , u u u u u v v v v v2. Vit quy trnh n phm lin tc tnh v 1 + nvtheo nuv nv .Kt qu:Bi 5.( 5 im)1) Xc nh cc h s a, b, c ca hm s f(x) = ax3 + bx2 + cx 2007 bit rng f(x) chia cho (x 16) c s d l 29938 v chia cho (x2 10x + 21) c biu thc s d l 10873375016 x.2) Tinh chinh xac gia tricua biu thc s:P = 3 + 33 + 333 + ... +33.....33 13 ch s 3Kt qu:Bi 6. ( 5 im)1. Tm ch s tn cng ca s: 20082009.2. Tm UCLN ca 40096920, 9474372 v 51135438.Kt qu:Bi 7. ( 5 im)1) Tim s nguyn dng nho nht co ba ch s l abc sao cho 3 3 3 + + abc a b c. Co con s nguyn nao thoa man iu kin trn na khng ? Nu s lc cach tim.2) Cho day s co s hang tng quat : 2 2 2 2 sin( sin( sin( sin )nu(n ln chsin)Tim 0nvi moi 0 n nthi nugn nh khng thay i (ch xt n 10 ch s thp phn), cho bit gia tri0nu. Nu qui trnh bm phm.Kt qu:Bi 8.( 5 im)Cho tam gic ABC vung ti nh A(-1; 3) c nh, cn cc nh B v C di chuyn trn ng thng i qua 2 im M(-3 ; -1), N(4 ; 1). Bit rng gc 030 ABC. Hy tnh ta nh B.Kt qu:Bi 9. ( 5 im)Cho hnh ng gic u ni tip trong ng tron (O) cobn knh R = 3,65 cm. Tinh din tich (co t mau) gii han bi na ng tron ngkinh AB la canh cua ngu giac u vang tron (O) (hinh ve).Kt qu:Bi 10. ( 5 im)Cho tam gic ABC co cac inh 9 3 ( ; ) A, 3 17 7 _ ,; Bva( ) 1 7 ; C .1) Vit phng trinh ng tron ngoai tip tam giac ABC. 2) Vit phng trinh tip tuyn cua ng tron, bit tip tuyn i qua imKt qu: 3:Cu 1: Cho a thc f(x) bc 3 vi h s ca x3 l k, k nguyn dng tha mn:f(2009) = 2010; f(2010) = 2011Chng minh rng: f(2011) f(2008) l s l.Kt qu: f(2011) f(2008) = 3(2k + 1) l s l vi mi k nguyn dngCu 2: Tm a2009 bit 110112 3+ + ' + + +( )( ) ; *( )( )n nan na a n Nn nKt qu: 20092008 401920100.aCu 3: Tnh chnh xc CLN v BCNN ca hai s a = 24614205, b = 10719433Kt qu: CLN(24614205, 10719433) = 21311 v BCNN(24614205, 10719433) =12380945115Cu 4: Tm tt c cc s c 6 ch s tha mn hai tnh cht sau:1) S to thnh bi ba ch s cui ln hn s to thnh bi ba ch s u 1 n v.2) L s chnh phng.Kt qu: 183184, 328329, 528529, 715716Cu 5: Tnh din tch phn gch cho(c gii hn trong 4 cung trn nh hnh v), bit ABCD l hnh vung cnh 5,35 cm; M, N, P, Q ln lt l trung im ca AB, BC, CD, DA.Kt qu: 6,14cm2Cu 6: Cho 30 3 0 0 32 2 _ _ < < < < , ,sin , ; cos , x x y yTnh gn ng gi tr ca biu thc sau5 2 2 5 2 27 72 2 + + + +tan ( ) cot ( )sin ( ) cos ( )x y x yPx y x yKt qu: 978,7071 4:Bi 1: (3 im) Tnh gn ng cc nghim (, pht, giy) ca phng trnh 3 5 2 + (sin cos ) sin cos x x x x A NBPC QDMKt qu: 0 0127 26 32 75 360 + ' , " x k0 0262 33 27 25 360 + ' , " x k0 0351 1 14 2 360 + ' , " x k0 04141 1 14 2 360 + ' , " x kBi 2: (3 im) Tnh gn ng gi tr ca a v b nu ng thng + y ax b i qua im 5 2 ( ; ) A v l tip tuyn ca Elip 2 2116 9+ x yKt qu: 112 4490710 24533 ' ,,ab

220 226843 13422 ',,abBi 3: (3 im) Cho bit tanx = tan350.tan360.tan370 .tan520.tan530v 00 0. Tnh a10 v tng S10 ca 10 s hng u tin.Kt qu:a) a10 0,63548 b) S10 14,63371Bi 6: (5 im) Tnh gn ng gi tr ca a v b nu ng thng y = ax + b l tip tuyn ca th hm s1 2 412+ ++x xxyti tip im c honh 2 1+ xKt qu:a-0,04604 vb 0,74360 Bi 7: (5 im) Tm 11 s t nhin lin tip c tng cc bnh phng ca chng l mt s chnh phng nh hn 10000.Kt qu:u1 = 18,u2 = 19,u3 =20, u4 = 21,u5 = 22,u6 =23, u7 =24, u8 = 25,u9 =26, u10 = 27, u11 = 28.Bi 8: (5 im) a thc P(x) = ax4 + bx3 + cx2 + dx + e c gi tr bng 5, 4, 3, 1, -2 ln lc ti cc gi tr x bng 1, 2, 3, 4, 5. Tnh gi tr ca a, b, c, d, e v tnh gn ng cc nghim ca a thc . Kt qu:1 7 59 59, , , , 824 22 24 12a b c d e v x1 4, 36150 ; x2 8, 22722 Bi 9: (5 im) Tm hai ch s tn cng ca sa) A = 2999.b) B = 3999.Kt qu: a) 88 b)67Bi 10: (5 im) Tnh gn ng di dy cung chung ca hai ng trn c phng trnh:x2 + y2 2x 6y 6 = 0 v x2 + y2 2x + 3y 2 = 0Tnh gn ng di dy cung chung ca hai ng trn .Kt qu:' )94( 44444 , 003367 , 3hay yx v ' 44444 , 003367 , 1yx AB = 4, 06734 19:1. Cho a thc P(x)= x5+ax4+bx3+cx2+dx+e, bit P(1)=-4; P(2)=3; P(3)=14; P(4)= 239; P(5)=1224a) Vit li gii tm a thc P(x)b) Tm s nguyn dng nh nht sao cho P(x) -1814 l mt s chnh phngKt qu:a. P(x)=x5-x4-20x3+57x2-40x-1b. x=122. Gi S v p ln lt l din tch v chu vi ca n- gic u ni tip ng trn(O; 2,34567), S v C l din tch hnh trnv chu vi ng trn. a)Tm n0,0111 S-S 0,0114b) Tm n nh nht 0,025 C-p 0,028Kt qu:a) n=100b)n= 223. Chohnh10cnhuA1A2A10nitip ng trn (O; R), trn cc on OAily cc im Misao cho 1iiOM Ri+.Tnh S=M1M2+M2M3++M9M10 + M10M1, bit R=20cm.Kt qu:107,96878324.Cho a thc P = 2x3+3x2y+5xy2-4y3Vit quy trnh bm phm lin tc tnh gi tr ca P ti(x=1, y=1,1) (x=2; y=2,01); (x=3; y=3,001); (x=4; y=4,0001) (x=5; y=5,00005) Kt qu:t tnh 5. Gii phng trnh x2+y2+z2=xyz, trong x, y , z l cc s nguyn tKt qu:6. Trong mt phng to Oxy cho parabol (P): y =x2+ 3x+2 v ng thng d: 3x-y+5=0. Quayng thng (d) quanh im I(-1; 2) ta c ng thng (d). Gi A, B, C, D l cc giao im ca (d) v (d) vi (P).Tnh din tch t gic li c bn nh l cc im trn.Kt qu:6,049181151( vdt)7. Cho hm s f(x)=-5x9+3x7 a) Tnh f(1); f(2)(1); f7(1)b) f(1)+f2(2) +f3(3)++f(7)(7)c) Vit quy trnh bm phm tnh f1(1)+f2(1,1) +f3(1,01)++f9(1,001), phn bin s s hng th n c n-1 ch s thp phn, trong n-2 s 0 v cui cng l ch s 1. Kt qu: a. f(1) = -24f2(1) = -234 f(7)(1)=-892080b. -173876082c. P=-3.077.049,8978. a)Tm ch s hng trm ca s 3275131b) Tm ch s hng nghn ca s 12341001Kt qu:a. Ch s hng trm ca s 3275131 l 4b. Ch s hng n v ca 12341001 l 1 9. Cho hm s f(x) = 4cos2x -5cosx a) Tnh f(12) (250)b) Tnh f(1)(10)+f(2)(20)+f(3)(30)+f(4)(40)+f(5)(50)+f(6)(60) ( s o ca bin s tnh bng )Kt qu:a. 7693,037911b. -1120,78588810. Mt dy c nhiu hn 10 nh trn mt ng ph, tng ca cc s nh ca dy l 1334. Tm dy .Kt qu:18, 20, .,74 hay 36, 38, , 80 20:Cu 1:Tnh gi tr gn ng ca a v b nu ng thng y = ax + b l tip tuyn ca th hm s 224 2 51x xyx+ ++ ti tip im c honh x = 1-5 Kt qu: 0,606264 av1,91213278 bCu 2: Tnh gn ng gi tr ln nht v gi tr nh nht ca hm s: ( )3 3sin os sin2 f x xc x x + +Kt qu: -1,439709873 GTNNv1,707106781 GTLNCu 3: th hm s sin +1cos +ca xyb xi qua cc im A10;3 _ , ,B31;5 _ , ,C( ) 2;1 .Tnh gn ng gi tr ca a , b , cKt qu: a 0,617827635 b 1,015580365 c 1,984419635Cu 4: Tnh gn ng khong cch gia im cc i v im cc tiu ca th hm s:

3 21 5 712 6 3y x x x +Kt qu: 5,776752478 dCu 5: Tm gi tr gn ng vi 5 ch s thp phn ca im ti hn ca th hm s: [ ]4 4sin ostrn0;2 y xc x +Kt qu: 1 2 9 9 im t i hn 0, ,....., 2 6,283194c x x xCu 6: Cho hai ng trn c phng trnh : ( )( )2 212 22: 10 6 1 0: 6 8 12 0c x y x yc x y x y+ + + + + a.Vit phng trnh ng thng i qua tm ca hai ng trnb.Tm to cc giao im ca ng trn trnvi( )1cKt qu:. 2 11 0 ax y ( ) ( ) .10,13809; 0,430953484 N -0,13809;-5,569046516 b MCu 7: Tm mt nghim gn ng ca phng trnh: a. 21 0 x tgx b. sinx sinx2 4 1 + Kt qu:. 0,583248467 a x .0,767366089 bCu 8:Mt ngi gi ngn hng mt s tin bng nhau l 63530 ng vi li sut 0.6%/thng. Hi sau 15 thng th nhn v c vn ln li l bao nhiu?Kt qu:999998 ngCu 9: Cho dy s 1 2 1 1144 ;u 233;...v i mi2n n nu u u u n+ + . Tnh37 38 39,vu u uKt qu: 37 38 394807526976 7778742049 12586269025 u u us.