CNG ễN TP HC K I NM 2013 2014 TRNG THPT PHC TH MễN: TON LP 10 I NI DUNG ễN TP i s - Cỏc phộp toỏn giao, hp, hiu ca hp y = ax + bx + c - Tỡm h s a,b,c parabol hay vit phng trỡnh parabol - Xột s bin thiờn v v hm s bc hai - Gii v bin lun h phng trỡnh bc nht n - Gii phng trỡnh quy v phng trỡnh bc nht, bc hai, gii h phng trỡnh gm mt phng bc nht hai n v mt phng trỡnh bc hai hai n - Gii phng trỡnh cha cn, cha giỏ tr tuyt i dng n gin Hỡnh hc - Chng minh ng thc vect - Tỡm ta trung im on thng, trng tõm ca tam giỏc v ta im tha yờu cu bi toỏn.Chng minh im thng hng v im khụng thng hng - Tớnh tớch vụ hng vect: Chng minh tam giỏc vuụng, cõn v tớnh chu vi v din tớch tam giỏc II BI TP Phn I S Bi 1: Tỡm xỏc nh ca cỏc hm s sau : y = 3x + x y= y= y = 5x 2 x x3 ( x 4) 2x + x + 3x + x+4 y = x + y = 3x + 3x y= y = x + 3x + 10 y= x x +3 y= 2x 3x 5x x + x2 11 y= x + x+2 Bi 2: Cho trc s: 12 y = x+3 x A = [4;9], B = ( 0; + ) , C = (;5] Xỏc nh cỏc hp sau v biu din trờn a A B, A C c A \ ( B C ); ( A \ B ) C b A \ B, B \ C d Ă \ B; Ă \ ( A B ) Bi 3: Cho Cho A = { x R : x 8} B = [ 2;7 ) Xỏc nh cỏc A B, A \ B; AB Bi 5: Cho hm s : f(x) = ax2 + bx + c a Xỏc nh hm s bit th hm s cú nh S(2; 1) v i qua im M(1; 0) b Kho sỏt v v th hm s va tỡm c Bi 6: Xỏc nh hm s bc hai : y = ax2 + bx bit rng th ca nú cú trc i xng l ng thng x= v i qua im A(1; 6) Bi 5: Xỏc nh a,c ca (P): y = ax x + c bit (P) i qua im P(2;1) v cú honh nh l V Parabol (P) vi a, c va tỡm c Bi 6: a) V th hm s: y = x2 + 2x b) Vit (P): y = ax2 + bx + bit (P) cú nh I(3;4) Bi 7: a) Kho sỏt v v th hm s: b) Tỡm (P) : y = ax + bx + y = x + x + bit (P) i qua A ( 1;6 ) , nh cú tung l Bi 8: Cho hm s y = ax2 + bx + a) Xỏc nh a, b ca hm s bit th hm s i qua A(1;0) v B(2;15) b) V th hm s va tỡm c cõu a) Bi 9: a/ Cho hai hp: A=[1; 4); B = { x R / A B, A \ B ? x 3} Hóy xỏc nh cỏc hp: b/ Tỡm hm s bc hai y = ax2 + bx +6 bit th ca nú cú nh I(2,2) Bi 10: Tỡm pt (P): y = ax2 + bx + c bit (P) qua im A(8 ;0) v cú nh I(6 ; 12) Bi 11 : Gii cỏc phng trỡnh sau : a x2 + x + = 2x b 3x = x ; c x 2x + = 2x d j e) x 3x + x 3x + = 10 k x + x = x + 3x + x + = + x x2 + x + = x n p -x + x + + x = i x + x + 11 = x l x + 3x = x + x + x + 10 = x + Bi 12: Gii phng trỡnh: 1) x = x2 2x 2) 3) x + x = 2x + = x 4) x 2x = Bi 13: Gii phng trỡnh sau: a 2x +1 = x ; d | x | = 3x2 x b |x2 2x| = |x2 5x + 6|; c |x + 3| = 2x + e | 2x 4| = x f |4x + 1| = 2x + Bi 14: Gii h phng trỡnh: a) x + y = 2 x + y xy = b) x + y xy = x + y = xy + x + y = c) x + y + x + y = d) x + y = 2 x + y + xy = 13 Bi 15: Gii h phng trỡnh: a) x = y y = x b) x = 5x+y y = y +x Bi 16: Cho h phng trỡnh c) x y = x + y = m d) y2 + y = x2 x = x + y2 a) Gii h m =10 b) Gii x = 3x+2y y = y +2x v bin lun Bi 17: Gii v bin lun h phng trỡnh: mx + y = m + 1) x + my = x + my = 2) mx 3my = 2m + (m 1) x + (m + 1) y = m 3) (3 m) x + y = Phn2.Hỡnh Hc: Bi 1: Cho iờm bõt ki M,N,P,Q Chng minh cac ng thc sau: a) c) uuur uuur uuuur uuuur PQ + NP + MN = MQ ; uuuur uuur uuuur uuur MN + PQ = MQ + PN ; b) uuur uuuur uuur uuuur NP + MN = QP + MQ ; Bi 2: Cho im phõn bit A, B, C, D, E, F chng minh : uuur uuur uuur uuur uuur uuur uuur uur a ) AB + DC = AC + DB uuur uuur uuur uuur b) AB + ED = AD + EB uuur uuur uuur uur uuur uuur uuur uuur uur d ) AD + CE + DC = AB EB uuur c) AB CD = AC BD uuur e) AC+ DE - DC - CE + CB = AB uuur uuur uuur uuur uuur uuur uuur uuur uuur f ) AD + BE + CF = AE + BF + CD = AF + BD + CE Bai 3: Cho hinh binh hanh ABCD, co tõm O CMR: uuur uuur uuur uuur r OA + OB + OC + OD = Bai 4: Cho t giauucur ABCD Goi I, J lõn lt la trung iờm AC va BD Goi E la trung uuur uuur uuur r iờm I J CMR: EA + EB + EC + ED = Bai 5: Cho tam giac ABC vi M, N, P la trung iờm AB, BC, CA CMR: uuur uuur uuuur r =0; uuuur uuur uuur r c) AM + BN + CP = a) AN + BP + CM uuur uuuur uuur b) AN = AM + AP ; Bai 6: Cho hỡnh bỡnh hnh ABCD tõm O Goi I, J lõn lt la trung iờm BC va CD CMR: uuur uuur uuur uuur AB + AC + AD = AC uuur uuuur uuur uuuur MA + MC = MB + MD uuur uur uur uuur uuur AB + AI + JA + DA = 3DB ( ) Bi 7: Cho tam giỏc MNP cú MQ l trung tuyn ca tam giỏc Gi R L trung im ca MQ Cmr : uuur uuur uur r a ) RM + RN + RP = uuur uuur uuur uuur b) ON + 2OM + OP = 4OR , O c) Dng im S cho t giỏc MNPS l hỡnh bỡnh hnh Chng t rng uuur uuur uuur uuur MS + MN PM = MP d)Vi im O tựy ý, hóy chng minh rng uuur uuuur uuur uuur uur uuur uuur uuuur uuur ON + OS = OM + OP ; ON + OM + OP + OS = 4OI Bi 8:.Cho im bt kỡ A,B,C,D v M,N ln lt l trung im ca on thng AB,CD.Chng minh rng: uuur uuur uuur uuur uuuur a) CA + DB = CB + DA = 2MN b) uuur uuur uuur uuur uuuur AD + BD + AC + BC = 4MN uuur uur uuur uuur uuur c) Gi I l trung im ca BC.Chng minh rng: 2( AB + AI + NA + DA) = 3DB Bi 9: Cho tam giỏc MNP cú MQ ,NS,PI ln lt l trung tuyn ca tam giỏc Chng minh rng: uuur uuur uur r a ) MQ + NS + PI = b) Chng minh rng hai tam giỏc MNP v tam giỏc SQI cú cựng trng tõm c) Gi M L im i xng vi M qua N , N L im i xng vi N qua P , P L im i xng vi P qua M Chng minh rng vi mi im O bt kỡ ta luụn cú: uuuur uuuur uuur uuur uuur uuur ON + OM + OP = ON ' + OM ' + OP ' G ln lt l trng uuur uuur uuuur uuuur AA + BB + CC = 3GG Bi 10*: Gi G v Chng minh rng tõm ca tam giỏc ABC v tam giỏc ABC Bi 11*: Cho tam giỏc ABC , gi M l trung im ca AB, N l mt im trờn AC cho NC=2NA, gi K l trung im ca MN uuur uuur uuur a ) CMR: AK= AB + AC uuur uuuur uuur b) Gọi D trung điểm BC, chứng minh : KD= AB + AC Bi 12*: a) Cho MK v NQ l trungr tuyn ca tam giỏc MNP.Hóy phõn tớch cỏc vộct uuur uuur uuur uuur r uuuur MN , NP, PM theo hai vộct u = MK , v = NQ uuur uur b) Trờn ng thng NP ca tam giỏcr MNP ly mt im S cho SN = 3SP Hóy uuur uuuur r uuur phõn tớch vộct MS theo hai vộct u = MN , v = MP c) Gi G l trng tõm ca tam giỏc MNP Gi I l trung im ca on thng MG v H l im trờn cnh MN cho MH = MN Hóy phõn tớch cỏc vộct uur uuuur uur uuur MI , MH , PI , PH r uuuur theo hai vộct u = PM , uuur r r uuur r r uuur r r Bi 14: Cho : OA = i j , OB = 5i j , OC = 3i + j a) Tỡm ta trng tõm, trung im cnh AC ca tam giỏc ABC b) Tỡm to ca cỏc vect r c) Xột a = (2; y ) Tỡm y ngc hng r a uuur AB r uuur uuur u = AB 3BC uuur phng vi AB v cựng Khi ú r a v uuur AB cựng hng hay Bi 15: Cho im A(3;2), B(1;3), C(1;6) a) Chng minh rng A,B, C l nh ca tam giỏc Chng minh rng tam giỏc ABC vuụng ti A Tớnh chu vi v din tớch tam giỏc b) Tớnh cỏc gúc ca tam giỏc Bi 16: Cho im A ( 3; 1) , B ( 2; ) , C ( 5;3) a) Tỡm D cho t giỏc ABCD l hỡnh bỡnh hnh b) Tỡm M cho C l trng tõm tam giỏc ABM c) Tỡm N cho tam giỏc ABN vuụng cõn ti N d) Tớnh gúc B Bi 17: Cho im A ( 1; 1) , B ( 1; ) , C ( 3; ) a) Cmr ba im A, B, C lp thnh mt tam giỏc b) Tớnh di cnh ca tam giỏc ABC c) CM ABC vuụng Tớnh chu vi v din tớch ABC d) Tớnh AB AC v cos A Bi 18: Cho im A(2; 5), B(1; 1), C(3; 3) a Tỡm to im D cho AD = AB AC b Tỡm to im E cho ABCE l hỡnh bỡnh hnh Tỡm to tõm hỡnh hỡnh hnh ú? c Tớnh chu vi tam giỏc ABC d Tớnh uuur uuur uuur uuur uuur uuur uuur AB.BC ; AC.BC ; AB + BC AC ( ) Bi 19: Cho A(3;2), B(4;3) a) Tỡm M Ox cho tam giỏc MAB vuụng ti M b) Tớnh din tớch tam giỏc MAB c) Tỡm D cho t giỏc MABD l hỡnh bỡnh hnh Bi 20: Trong mp Oxy cho A(1; 4); B(1; 1); C( 4; 2) a.Chng minh ba im A, B, C to thnh mt tam giỏc b.Tớnh uuur uuuur uuur uuur uuur AB AC ; AB.( AC + BC ) c Tỡm im D cho ABCD l hỡnh bỡnh hnh d Tỡm im E(x; 6) cho A, B, E thng hng Bi 21 Cho ba im A( 1; 1), B(5; 2), C(2 ; 7) a) Tỡm ta trung im I ca on BC b) Chminh ABC cõn ti nh A, tớnh chu vi, din tớch ca ABC c) Tỡm ta im K cho KA+ KB = Bi 22 Cho A(2:3),B(1;1),C(3;3) a) CMR tam giỏc ABC cõn b/Tớnh din tớch tam giỏc ABC Bi 23 Cho tam giỏc ABC cú A(4;1),B(2;4),C(2;2) a) CMR tam giỏc ABC cõn b) Tớnh din tớch ABC