Tai lieu trac nghiem hinh hoc lop 10 ban word full

Traộc nghieọm Hỡnh hoùc 10 CHNG I: VECT I VECT I.1 Xỏc nh vect r 1.Cho tam giỏc ABC, cú th xỏc nh bao nhiờu vect khỏc vect cú im u v im cui l nh A, B, C ? a) b) c) d) r 2.Cho t giỏc ABCD S cỏc vect khỏc cú im u v cui l nh ca t giỏc bng: a) b) c) d) 12 r 3.Cho lc giỏc u ABCDEF tõm O S cỏc vect khỏc cựng phng vi uuur OC cú im u v cui l nh ca lc giỏc l: a) b) c) d) uuur 4.Cho lc giỏc u ABCDEF tõm O S cỏc vect bng OC cú im u v cui l nh ca lc giỏc l: a) b) c) d) uuur uuur uuur r 5.Cho AB v mt im C, cú bao nhiờu im D tha món: AB = CD a) b) c) d) vụ s uuur uuur uuur r 6.Cho AB v mt im C, cú bao nhiờu im D tha món: AB = CD a) b) 7.iu kin no l iu kin cn v a) ABCD l hỡnh bỡnh hnh c) AD v BC cú cựng trung im c) d) vụ s uuur uuur AB = CD : b) ABDC l hỡnh bỡnh hnh d) AB = CD v AB // CD I.2 Tng hiu vect uuur 8.Cho hỡnh ch nht ABCD cú AB=3, BC=4 di ca AC l: a) b) c) d) 9.Cho ba im phõn bit A, B, C ng thc no ỳng? uuur uuur uuur uuur uuur uuur a) CA BA = BC b) AB + AC = BC uuur uuur uuur uuur uuur uuur c) AB + CA = CB d) AB BC = CA 10 Cho hai im A v B phõn bit iu kin I l trung im AB l: uur uur uur uur uur uur a) IA = IB b) IA = IB c) IA = IB d) AI = BI 11 Cho ABC cõn A, ng cao AH Cõu no sau õy sai: Traộc nghieọm Hỡnh hoùc 10 12 13 14 15 16 17 18 19 20 21 22 uuur uuur uuur uuur uuur uuur uuur uuur a) AB = AC b) HC = HB c) AB = AC d) AB = AC Cho ng trũn tõm O v hai tip tuyn song song vi tip xỳc vi (O) ti hai im A v B Cõu no sau õy ỳng: uuur uuur uuur uuur a) OA = OB b) AB = OB c) OA = OB d) AB = BA Cho ABC u , cnh a Cõu no sau õy ỳng: uuur uuur uuur uuur uuur a) AB = BC = CA b) CA = AB uuur uuur uuur uuur uuur c) AB = BC = CA = a d) CA = BC Cho .trũn tõm O , v hai tip tuyn MT, MT ' (T v T' l hai tip im) Cõu no sau õy ỳng: uuur uuuur a) MT = MT ' b) MT + MT ' = TT ' uuur uuuur c) MT = MT d) OT = OT ' Cho ABC, vi M l trung im ca BC Tỡm cõu ỳng: uuuur uuur uuur r uuur uuur uuur a) AM + MB + BA = b) MA + MB = AB uuur uuur uuuur uuur uuur uuuur c) MA + MB = MC d) AB + AC = AM Cho ABC vi M, N, P ln lt l trung im ca BC, CA, AB Tỡm cõu sai: uuur uuuur uuur r uuur uuur uuur r a) AB + BC + AC = b) AP + BM + CN = uuuur uuur uuuur r uuur uuuur uuur c) MN + NP + PM = d) PB + MC = MP Gi O l tõm ca hỡnh vuụng ABCD Vect no cỏc vect di õy uuur bng CA ? uuur uuur uuur uuur uuur uuur uuur uuur a) BC + AB b) OA + OC c) BA + DA d) DC CB iu kin no l iu kin cn v I l trung im ca on thng AB uur uur r uur uur r uur uur a) I A = I B b) IA + IB = c) IA IB = d) IA = IB Cho ba im ABC Trong cỏc mnh sau, tỡm mnh ỳng: uuur uuur uuur r a) AB + BC = AC b) AB + BC + CA = uuur uuur uuur uuur uuur uuur uuur c) AB = BC CA = BC d) AB CA = BC Cho bn im ABCD Trong cỏc mnh sau, tỡm mnh ỳng: uuur uuur uuur uuur uuur uuur uuur uuur a) AB + CD = AD + CB b) AB + BC + CD = DA uuur uuur uuur uuur uuur uuur uuur uuur c) AB + BC = CD + DA d) AB + AD = CD + CB Cho hỡnh vuụng ABCD, cỏc mnh sau, tỡm mnh ỳng ? uuur uuur uuur uuur uuur uuur uuur uuur a) AB = BC b) AB = CD c) AC = BD d) AD = CB uuur uuur uuuur r Cho ABC v mt im M tho iu kin MA MB + MC = Trong cỏc mnh sau tỡm sai : uuuur uuur uuur a) MABC l hỡnh bỡnh hnh b) AM + AB = AC uuur uuur uuuur uuur uuur c) BA + BC = BM d) MA = BC Traộc nghieọm Hỡnh hoùc 10 I.3 Tớch vect vi mt s 23 Cho ABC cú G l trng tõm, I l trung im BC ng thc no ỳng? uur uuur uur uur a) GA = 2GI b) IG = IA uuur uuur uur uuur uuur uuur c) GB + GC = 2GI d) GB + GC = GA 24 Cho tam giỏc ABC cú trng tõm G v M l trung im BC Khng nh no sau õy l sai? uuur uuuur uuur uuur uuur a) AG = AM b) AB + AC = 3AG uuur uuur uuur uuur uuur uuuur c) GA = BG + CG d) GB + GC = GM 25 Cho hỡnh bỡnh hnh ABCD ng thc no ỳng? uuur uuur uuur uuur uuur uuur a) AC + BD = BC b) AC + BC = AB uuur uuur uuur uuur uuur uuur c) AC BD = 2CD d) AC AD = CD 26 Cho ABC vuụng ti A vi M l trung im ca BC Cõu no sau õy ỳng: uuuur uuur uuuur uuur uuuur a) AM = MB = MC b) MB = MC uuur uuuur BC uuur uuuur c) MB = MC d) AM = 27 Cho tam giac ABC Gi M v N ln lt l trung im ca AB v AC Trong cỏc mnh sau tỡm mnh sai : uuur uuur uuur uuur uuuur uuur uuuur uuur a) AB = AM b) AC = NC c) BC = 2MN d) CN = AC 28 Cho hỡnh vuụng ABCD cú tõm l O Trong cỏc mnh sau, tỡm mnh sai uuur uuur uuur uuur uuur uuur a) AB + AD = AO b) AD + DO = CA uuur uuur uuur uuur uuur uuur c) OA + OB = CB d) AC + DB = AB uuur uuur uuuur 29 Cho tam giỏc ABC, cú bao nhiờu im M tho : MA + MB + MC = a) b) c) d) vụ s 30 Cho hỡnh bỡnh hnh ABCD, cú M l giao im ca hai ng chộo Trong cỏc mnh sau, tỡm mnh sai: uuur uuur uuur uuur uuur uuur a) AB + BC = AC b) AB + AD = AC uuur uuur uuuur uuur uuur uuuur uuuur c) BA + BC = BM d) MA + MB = MC + MD 31 Cho G l trng tõm ca tam giỏc ABC Trong cỏc mnh sau, tỡm mnh ỳng : uuur uuur uuur uuur uuur uuur a) AB + AC = AG b) BA + BC = 3BG Traộc nghieọm Hỡnh hoùc 10 uuur uuur uuur uuur uuur uuur r c) CA + CB = CG d) AB + AC + BC = uur uur 32 Cho tam giỏc ABC im I tho: IA = IB Chn mnh ng: uuur uuur uuur uuur uur CA 2CB uur CA + 2CB a) CI = b) CI = 3 uuur uuur uur CA + 2CB uur uuur uuur c) CI = CA + 2CB d) CI = uuur uuur 33 Cho tam giỏc ABC u cú cnh bng a di ca AB + AC bng a a) 2a b) a c) a d) r uuur r uuur 34 Cho ABC t a = BC , b = AC Cỏc cp vect no sau cựng phng? r r rr r r r r r r r r r rr r a) 2a + b , a + 2b b) a 2b , 2a b c) 5a + b , 10a 2b d) a + b , a b Traộc nghieọm Hỡnh hoùc 10 II H TRC TO 1.Trong mpOxy cho hỡnh bỡnh hnh OABC, C Ox Khng nh no ỳng? uuur a) AB cú tung khỏc b) A v B cú tung khỏc c) C cú honh bng d) xA + xC xB = 2.Trong mp Oxy, cho hỡnh vuụng ABCD cú gc O l tõm hỡnh vuụng v cỏc cnh ca nú song song vi cỏc trc ta Khng nh no ỳng? uuur uuur uuur uuur uuur a) OA + OB = AB b) OA OB, DC cựng hng c) xA = xC, yA = yC d) xB = xC, yC = yB 3.Cho M(3;4) K MM1 Ox, MM2 Oy Khng nh no ỳng? a) OM = b) OM = uuuuur uuuuur uuuuur uuuuur c) OM OM cú ta (3;4) d) OM + OM cú ta (3;4) 4.Cho bn im A(5;2), B(5;3), C(3;3), D(3;2) Khng nh no ỳng? uuur uuur a) AB, CD cựng hng b) ABCD l hỡnh ch nht uuur uuur uuur c) I(1;1) l trung im AC d) OA + OB = OC r r 5.Cho u = (3;2), v = (1; 6) Khng nh no ỳng? r r r rr a) u + v , a = (4; 4) ngc hng b) u , v cựng phng r rr r rr c) u v , b = (6;24) cựng hng d) 2u + v , v cựng phng 6.Cho A(3;2), B(7;1), C(0;1), D(8;5) Khng nh no ỳng? uuur uuur uuur uuur a) AB, CD i b) AB, CD ngc hng uuur uuur c) AB, CD cựng hng d) A, B, C, D thng hng 7.Cho A(1;5), B(5;5), C(1;11) Khng nh no ỳng? uuur uuur a) A, B, C thng hng b) AB, AC cựng phng uuur uuur uuur uuur c) AB, AC khụng cựng phng d) AB, BC cựng phng 8.Cho bn im A(2, 1) ; B(2, 1) ; C(2, 3) ; D(2, 1) Xột mnh : (I) ABCD l hỡnh thoi (II) ABCD l hỡnh bỡnh hnh (III) AC ct BD ti M(0, 1) Tỡm mnh ỳng cỏc mnh sau : a) Ch (I) ỳng b) Ch (II) ỳng c) Ch (II) v (III) ỳng d) C u ỳng 9.Cho cỏc im A(1, 1) ; B(0, 2) ; C(3, 1) ; D(0, 2) Trong cỏc mnh sau, mnh no sai ? a) AB // DC b) AC = BD c) AD = BC d) AD // BC 10 Cho im A(1, 1) ; B(1, 3) ; C(2, 0) Trong cỏc mnh sau, tỡm mnh sai : uuur uuur a) AB = AC b) A, B, C thng hng Traộc nghieọm Hỡnh hoùc 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 uuur uuur uuur uuur r c) BA = BC d) BA + 2CA = Khng nh no ỳng? r r a) a = (5; 0), b = (4; 0) cựng hng r r b) c = (7; 3) l vect i ca d = (7; 3) r r c) u = (4; 2), v = (8; 3) cựng phng r r d) a = (6; 3), b = (2; 1) ngc hng r r r r Trong h trc (O; i , j ), ta ca i + j l: a) (0; 1) b) (1; 1) c) (1; 0) d) (1; 1) r r r r Cho a = (3;4), b = (1; 2) Ta ca a + b l: a) (4; 6) b) (2;2) c) (4;6) d) (3;8) r r r r Cho a = (1; 2), b = (5;7) Ta ca a b l: a) (6;9) b) (4;5) c) (6; 9) d) (5;14) r r r r Cho a = (5; 0), b = (4; x) Hai vect a , b cựng phng nu x l: a) b) c) d) r r r r r r Cho a = (x; 2), b = (5; 1), c = (x; 7) Vect c = a + b nu: a) x = 15 b) x = c) x = 15 d) x = r r Cho hai vect : a = ( , ) v b = ( , ) Tỡm ta ca vect : r r r u = 2a b r r r r a) u = ( , ) b) u = ( , 11 ) c) u = ( , ) d) u = ( , ) uuur uuur Cho ba im A ( 1; 3) ; B ( 1; 2) C( 2; 1) To ca vect AB AC l : a) ( 5; 3) b) ( 1; 1) c) ( 1;2) d) (4; 0) uuur Trong mp Oxy cho A(5;2), B(10;8) Ta ca AB l: a) (15; 10) b) (2; 4) c) (5; 6) d) (50; 16) Cho A(2, 1), B(0, 3), C(3, 1) Tỡm im D ABCD l hỡnh bỡnh hnh a) (5, 5) b) (5, 2) c) (5, 4) d) ( 1, 4) Cho ba im A(1, 1) ; B(3, 2) ; C(6, 5) Tỡm ta im D cho ABCD l hỡnh bỡnh hnh: a) D(4, 3) b) D(3, 4) c) D(4, 4) d) D(8, 6) Cho A(2;3), B(4;7) Ta trung im I ca on thng AB l: a) (6; 4) b) (2; 10) c) (3; 2) d) (8;21) uuuur uuur Cho im M, N, P tho MN = k MP Tỡm k N l trung im ca MP ? a) b) c) d) 2 Cho tam giỏc ABC cú B(9;7), C(11;1), M v N ln lt l trung im ca uuuur AB, AC Ta ca MN l: a) (2;8) b) (1;4) c) (10; 6) d) (5; 3) Traộc nghieọm Hỡnh hoùc 10 25 Cỏc im M(2;3), N(0;4), P(1;6) ln lt l trung im cỏc cnh BC, CA, AB ca tam giỏc ABC Ta nh A l: a) (1; 5) b) (3;1) c) (2;7) d) (1;10) 26 Cho tam giỏc ABC cú A(3;5), B(1;2), C(5;2) Trng tõm ca ABC l: a) G1(3; 4) b) G2(4; 0) c) G3( ; 3) d) G4(3; 3) 27 Tam giỏc ABC cú A(6;1); B(3;5) Trng tõm ca tam giỏc l G(1;1) To nh C l: a) C(6;3) b) C(6;3) c) C(6;3) d) C(3;6) 28 Cho A(1;1), B(2;2), C(7;7) Khng nh no ỳng? a) G(2;2) l trng tõm tam giỏc ABC b) B gia hai im A v C uuur uuur c) A gia hai im B v C d) AB, AC cựng hng 29 Cho ABC cú trng tõm l gc ta O, hai nh A(2;2) v B(3;5) Ta nh C l: a) (1;7) b) (2;2) c) (3;5) d) (1; 7) 30 Cho bn im A(1;1), B(2;1), C(4;3), D(3;5) Chn mnh ỳng: a) T giỏc ABCD l hbh b) G(2; 5/3) l trng tõm BCD uuur uuur uuur uuur c) AB = CD d) AC , AD cựng phng uur uur r 31 Cho A (1; 2) ; B(2; 3) Tỡm to ca im I cho IA + IB = ? a) ( 1; 2) b) ( 1; ) c) ( 1; ) d) ( 2; 2) uuur uuur uuur 32 Cho A(2;5); B(1;1); C(3;3) To im E tho AE = AB AC l: a) E(3;3) b) E(3;3) c) E(3;3) d) E(2;3) Traộc nghieọm Hỡnh hoùc 10 CHNG II: TCH Vễ HNG CA HAI VECT V NG DNG I GI TR LNG GIC CA MT GểC BT Kè ( 00 1800 ) 1.Giỏ tr ca sin 600 + cos300 bng bao nhiờu? 3 a) b) c) d) 2.Giỏ tr ca tan 300 + cot 300 bng bao nhiờu? 1+ a) b) c) d) 3 3.Trong cỏc ng thc sau õy, ng thc no ỳng? 3 a) sin1500 = b) cos1500 = 2 c) tan 150 = d) cot1500 = 3 4.Cho v l hai gúc khỏc v bự nhau, cỏc ng thc sau õy ng thc no sai? a) sin = sin b) cos = cos c) tan = tan d) cot = cot 5.Trong cỏc ng thc sau õy, ng thc no sai? a) sin(1800 ) = sin b) cos(180 ) = cos c) tan(1800 ) = tan d) cot(1800 ) = cot 6.Trong cỏc ng thc sau õy, ng thc no sai? a) sin 00 + cos 00 = b) sin 900 + cos900 = +1 c) sin1800 + cos1800 = d) sin 600 + cos 600 = 7.Cho gúc tự iu khng nh no sau õy l ỳng? a) sin < b) cos > c) tan > d) cot < 8.Trong cỏc khng nh sau, khng nh no sai? a) cos 600 = sin 300 b) cos 600 = sin1200 c) cos300 = sin1200 d) sin 600 = cos1200 9.ng thc no sau õy sai : a) sin450 + sin450 = b) sin300 + cos600 = c) sin600 + cos1500 = d) sin1200 + cos300 = 10 Cho hai gúc nhn v ( < ) Khng nh no sau õy l sai? Traộc nghieọm Hỡnh hoùc 10 a) cos < cos b) sin < sin c)tan + tan > d) cot > cot 11 Cho ABC vuụng ti A, gúc B bng 300 Khng nh no sau õy l sai? 1 a) cos B = b) sin C = c) cos C = d) sin B = 2 12 iu khng nh no sau õy l ỳng? a) sin = sin(1800 ) b) cos = cos(1800 ) 13 14 15 16 17 18 19 20 c) tan = tan(1800 ) d) cot = cot(1800 ) Tỡm khng nh sai cỏc khng nh sau: a) cos 750 > cos500 b) sin 800 > sin 500 c) tan 450 < tan 600 d) cos300 = sin 600 Bt ng thc no di õy l ỳng? a) sin 900 < sin1000 b) cos950 > cos1000 c) tan 850 < tan1250 d) cos145 > cos1250 Hai gúc nhn v ph nhau, h thc no sau õy l sai? a) sin = cos b) tan = cot c) cot = d) cos = sin cot Trong cỏc h thc sau h thc no ỳng? a) sin + cos = b) sin + cos = c) sin + cos = d) sin 2 + cos 2 = Cho bit sin + cos = a Giỏ tr ca sin cos bng bao nhiờu? a) sin cos = a b) sin cos = 2a a a 11 c) sin cos = d) sin cos = 2 cot + 3tan Cho bit cos = Tớnh giỏ tr ca biu thc E = ? 2cot + tan 19 19 25 25 a) b) c) d) 13 13 13 13 Cho bit cot = Tớnh giỏ tr ca E = 2cos + 5sin cos + ? 10 100 50 101 a) b) c) d) 26 26 26 26 ng thc no sau õy l sai? a) (cos x + sin x) + (cos x sin x) = 2, x b) tan x sin x = tan x sin x, x 900 c) sin x + cos x = 2sin x cos x, x Traộc nghieọm Hỡnh hoùc 10 10 d) sin x cos x = 3sin x cos x, x 21 ng thc no sau õy l sai? cos x sin x = ( x 00 , x 1800 ) a) sin x + cos x ( x 00 ,900 ,1800 ) b) tan x + cot x = sin x cos x 2 ( x 00 ,900 ,1800 ) c) tan x + cot x = 2 sin x cos x d) sin 2 x + cos 2 x = II TCH Vễ HNG CA HAI VECT Traộc nghieọm Hỡnh hoùc 10 14 uuur uuur 41 Cho cỏc im A(1, 1); B(2, 4); C(10, 2) Tớnh tớch vụ hng BA AC : a) 30 b) 10 c) 10 d) 30 42 Cho im A(1, 4) ; B(3, 2) ; C(5, 4) Chu vi tam giỏc ABC bng bao nhiờu ? a) + 2 b) + c) + d) + 2 43 Gi G l trng tõm tam giỏc u ABC cú cnh bng a Trong cỏc mnh sau, tỡm mnh sai ? uuur uuur uuur uuur a) AB AC = a b) AC.CB = a 2 uuur uuur uuur uuur a c) GA.GB = d) AB AG = a rr r r r r r 44 Trong h trc ta ( O, i , j ) cho cỏc vect sau: a = 4i j , b = j Trong cỏc mnh sau tỡm mnh sai : r r r r a) a = ( , ) b) b = ( , ) c) | a | = d) | b | = III H THC LNG TRONG TAM GIC GII TAM GIC Traộc nghieọm Hỡnh hoùc 10 15 Cho tam giỏc ABC tho h thc b + c = 2a Trong cỏc mnh sau, mnh no ỳng ? a) cosB + cosC = 2cosA b) sinB + sinC = 2sinA c) sinB + sinC = sin A d) sinB + cosC = 2sinA 2 Cho tam giỏc ABC tha h thc b + c = 2a Trong cỏc mnh sau, mnh no ỳng ? a) cosB + cosC = 2cosA b) sin B + sin C = sin A c) sin B + sin C = sin A d) sin B + cos C = sin A Cho tam giỏc ABC ng thc no sai: B+C A = sin a) sin ( A+ B 2C ) = sin 3C b) cos 2 A + B + 2C C = sin c) sin( A+ B) = sinC d) cos 2 Gi S = ma2 + mb2 + mc2 l tng bỡnh phng di ba trung tuyn ca tam giỏc ABC Trong cỏc mnh sau mnh no ỳng ? a) S = (a2 + b2 + c2) b) S = a2 + b2 + c2 c) S = (a2 + b2 + c2) d) S = 3(a2 + b2 + c2) di trung tuyn mc ng vi cnh c ca ABC bng biu thc no sau õy a) b) b2 + a2 c2 + 2 ( 2b + a ) c d) b + a c Tam giỏc ABC cú cosB bng biu thc no sau õy? b2 + c2 a a + c2 b2 a) b) sin B c) cos( A + C) d) 2bc 2ac Cho tam giỏc ABC cú a2 + b2 c2 > Khi ú : a) Gúc C > 900 b) Gúc C < 900 c) Gúc C = 900 d) Khụng th kt lun c gỡ v gúc C Chn ỏp ỏn sai : Mt tam giỏc gii c nu bit : a) di cnh b) di cnh v gúc bt k c) S o gúc d) di cnh v gúc bt k = 640 Cnh b bng bao nhiờu ? Cho ABC vi a = 17,4; B = 44 33 ' ; C a) 16,5 b) 12,9 c) 15,6 d) 22,1 c) b2 + a c2 Traộc nghieọm Hỡnh hoùc 10 16 = 340 44 ', A B = 117 Tớnh AC ? 10 Tam giỏc ABC cú àA = 680 12 ', B a) 68 b) 168 c) 118 d) 200 11 Cho tam giỏc ABC, bit a = 13, b = 14, c = 15 Tớnh gúc B ? a) 590 49 ' b) 530 ' c) 590 29 ' d) 620 22 ' 12 Cho tam giỏc ABC, bit a = 24; b = 13; c = 15 Tớnh gúc A ? a) 330 34 ' b) 1170 49 ' c) 280 37 ' d) 580 24 ' = 60 di cnh b bng bao nhiờu ? 13 Tam giỏc ABC cú a = 8, c = 3, B a) 49 b) 97 c) d) 61 0 à 14 Tam giỏc ABC cú a = 16,8; B = 56 13 ' ; C = 71 Cnh c bng bao nhiờu? a) 29,9 b) 14,1 c) 17,5 d) 19,9 15 Cho tam giỏc ABC tho : b2 + c2 a2 = 3bc Khi ú : a) A = 300 b) A= 450 c) A = 600 d) A = 750 uuur uuur 16 Cho tam giỏc u ABC vi trng tõm G Gúc gia hai vect GA v GB l: a) 300 b) 600 c) 900 d) 1200 17 Mt tam giỏc cú ba cnh l 13, 14, 15 Din tớch tam giỏc bng bao nhiờu ? a) 84 b) 84 c) 42 d) 168 18 Cho tam giỏc ABC cú a = 4; b = 6; c = Khi ú din tớch ca tam giỏc l: 15 a) 15 b) 15 c) 105 d) 19 Mt tam giỏc cú ba cnh l 26, 28, 30 Bỏn kớnh ng trũn ni tip l: a) 16 b) c) d) 20 Mt tam giỏc cú ba cnh l 52, 56, 60 Bỏn kớnh ng trũn ngoi tip l: 65 65 a) b) 40 c) 32,5 d) 21 Tam giỏc vi ba cnh l 5; 12, 13 cú bỏn kớnh ng trũn ngoi tip l ? 13 11 a) b) c) d) 2 22 Tam giỏc vi ba cnh l 6; 8; 10 cú din tớch l bao nhiờu ? a) 24 b) 20 c) 48 d) 30 23 Tam giỏc vi ba cnh l 3; 4; cú bỏn kớnh ng trũn ni tip tam giỏc ú bng bao nhiờu ? a) b) c) d) 24 Tam giỏc vi ba cnh l 5; 12; 13 cú bỏn kớnh ng trũn ni tip tam giỏc ú bng bao nhiờu ? a) b) 2 c) d) 25 Tam giỏc vi ba cnh l 6; 8; 10 cú bỏn kớnh ng trũn ngoi tip bng bao nhiờu ? Traộc nghieọm Hỡnh hoùc 10 17 26 27 a) b) c)5 d) Tam giỏc ABC cú a = 6; b = ; c = M l im trờn cnh BC cho BM = di on AM bng bao nhiờu ? 108 a) b) c) d) r uuur r uuur Cho ABC, bit a = AB = (a1; a2) v b = AC = (b1; b2) tớnh din tớch S ca ABC Mt hc sinh lm nh sau: rr a.b (I) Tớnh cosA = r r a.b r ( ar.b ) 2 (II) Tớnh sinA = cos A = r2 r2 a b 1 r r ( r r) (III) S = AB.AC.sinA = a b a.b 2 ( a12 + a22 ) ( b12 + b22 ) ( a1b1 + a2b2 ) (IV) S = S= ( a1b2 + a2b1 ) 2 S = (a1b2 a2b1) Hc sinh ú ó lm sai bt u t bc no? a) (I) b) (II) c) (III) d) (IV) ã Cho cỏc im A(1, 1); B(2, 4); C(10, 2) Gúc BAC bng bao nhiờu? a) 900 b) 600 c) 450 d) 300 Cho cỏc im A(1; 2), B(2; 3), C(0; 4) Din tớch ABC bng bao nhiờu ? 13 13 a) b) 13 c) 26 d) Cho tam giỏc ABC cú A( 1; 1) ; B( 3; 3) ; C( 6; 0) Din tớch ABC l a) 12 b) c) d) r r r r Cho a = ( 2; 3) v b = ( 5; m ) Giỏ tr ca m a v b cựng phng l: 13 15 a) b) c) 12 d) 2 Cõu no sau õy l phng tớch ca im M ( 1; 2) i vi ng trũn (C) tõm I ( 2; 1) , bỏn kớnh R = 2: a) b) c) d) ( 28 29 30 31 32 ) Traộc nghieọm Hỡnh hoùc 10 18 33 Cho ng trũn (C) ng kớnh AB vi A( 1; 2) ; B( 2; 1) Kt qu no sau õy l phng tớch ca im M ( 1; 2) i vi ng trũn (C) a) b) c) d) 34 Khong cỏch t A n B khụng th o trc c vỡ phi qua mt m ly Ngi ta xỏc nh c mt im C m t ú cú th nhỡn c A v B di mt gúc 780 24 ' Bit CA = 250m, CB = 120m Khong cỏch AB bng bao nhiờu ? a) 266m b) 255m c) 166m d) 298m 35 Hai chic tu thu cựng xut phỏt t v trớ A, i thng theo hai hng to vi mt gúc 600 Tu th nht chy vi tc 30km/h, tu th hai chy vi tc 40km/h Hi sau gi hai tu cỏch bao nhiờu km? a) 13 b) 15 13 c) 10 13 d) 15 36 T mt nh thỏp chiu cao CD = 80m, ngi ta nhỡn hai im A v B trờn mt t di cỏc gúc nhỡn l 720 12' v 340 26' Ba im A, B, D thng hng Tớnh khong cỏch AB ? a) 71m b) 91m c) 79m d) 40m 37 Khong cỏch t A n B khụng th o trc tip c vỡ phi qua mt m ly Ngi ta xỏc nh c mt im C m t ú cú th nhỡn c A v B di mt gúc 560 16 ' Bit CA = 200m, CB = 180m Khong cỏch AB bng bao nhiờu ? a) 163m b) 224m c) 112m d) 168m CHNG III: PHNG PHP TO TRONG MT PHNG 19 Traộc nghieọm Hỡnh hoùc 10 I PHNG TRèNH NG THNG Cho tam giỏc ABC cú A(2;0); B(0;3); C(3;1) ng thng i qua B v song song vi AC cú phng trỡnh l: a) 5xy+3=0 b) 5x+y3=0 c) x+5y15=0 d) x5y+15=0 Cho ng thng (d): 2x+y2=0 v im A(6;5) im A i xng vi A qua (d) cú to l: a) (6;5) b) (5;6) c) (6;1) d) (5;6) Trong cỏc im sau õy, im no thuc ng thng (): 4x3y=0 a) A(1;1) b) B(0;1) c) C(1;1) d) D( ;0) Trong cỏc mnh sau õy mnh no ỳng? a) ng thng song song vi trc Oy cú phng trỡnh : x = m (m 0) b) ng thng cú phng trỡnh x = m21 song song vi trc Ox x y =1 c) ng thng i qua hai im M(2;0) v N(0;3) cú ph.trỡnh : + H s gúc ca ng thng () : x y+4=0 l: a) b) c) d) 3 x = t .thng i qua im A(4;3) v song song vi .thng (): l: y = 3t a) 3xy+9=0 b) 3xy+9=0 c) x3y+3=0 x = + t Cho ng thng (): Trong cỏc mnh sau, mnh no sai? y = 3t a) im A(2;0) thuc () b) im B(3;3) khụng thuc (); c) im C(3;3) thuc () x2 y = d) Phng trỡnh : l phng trỡnh chớnh tc ca () Phng trỡnh no l phng trỡnh tham s ca ng thng xy+2=0 l: x = t x = x = + t x = t a) b) c) d) y = + t y = t y =1+ t y = 3t Cỏc phng trỡnh sau, phng trỡnh no l phng trỡnh ca ng thng : Traộc nghieọm Hỡnh hoùc 10 20 x = m a) m vi m R y = b) xy=1 c) x2 + y + = d) 1 + =4 x y 10 Cho A(5;3); B(2;1) ng thng cú phng trỡnh no sau õy i qua A;B: a) 2x2y+11=0 b) 7x2y+3=0 c) 2x+7y5=0 11 Cỏc cp ng thng no sau õy vuụng gúc vi nhau? x = 2t a) (d1): v (d2): 2x+y1=0 y = + t d) .thng khỏc x = b) (d1): x2=0 v (d2): y = t c) (d1): y=2x+3 v (d2): 2y=x+1 d) (d1): 2xy+3=0 v (d2): x+2y1=0 12 ng thng no qua A(2;1) v song song vi ng thng : 2x+3y2=0? a) xy+3=0 b)2x+3y7=0 c) 3x2y4=0 d) 4x+6y11=0 x = + 2k 13 Cho phng trỡnh tham s ca ng thng (d): (k R) Phng y =1 k trỡnh no sau õy l phng trỡnhg tng quỏt ca (d): a) x+2y5=0 b) x+2y+1=0 c) x2y1=0 d) x2y+5=0 r 14 Ph.trỡnh tham s ca .thng (d) i qua M(2;3) v cú VTCP u =(1;4) l: x = + 3t x = 3t x = 2t x = 2t a) b) c) d) y = + 4t y = + 4t y = + 3t y = + t 15 To im i xng ca im A(3;5) qua ng thng y = x l: a) (3;5) b) (5;3) c) (5;3) d) (5;3) 16 Ph.trỡnh tng quỏt ca ng thng (d) i qua hai im M(1;2) v N(3;4) l: a) x+y+1=0 b) x+y1=0 c) xy1=0 d) .thng khỏc 17 Vect phỏp tuyn ca ng thng i qua hai im A(1;2);B(5;6) l: r r r r a) n = (4;4) b) n = (1;1) c) n = (4;2) d) n = (1;1) x = + 3t l hai ng thng : y = 2t a) Ct b) Song song c) Trựng 19 H ng thng (dm): (m2)x +(m+1)y3=0 luụn i qua mt im c nh ú l im cú to no cỏc im sau? a) A(1;1) b) B(0;1) c) C(1;0) d) D(1;1) 18 Hai ng thng (d1) : x+3y 3=0 v(d2) : Traộc nghieọm Hỡnh hoùc 10 21 20 Phng trỡnh ng trung trc ca AB vi A(1;3) v B(5;1) l: x = + 3t x = + 3t x+2 y2 = b) c) d) y =1+ t y = + 2t Cho im A(1;2); B(3;2) v ng thng (): 2xy+3=0 im C trờn ng thng () cho ABC l tam giỏc cõn ti C cú to l: a) C(2;1) b) C(0;0) c) C(1;1) d) C(0;3) Cho ng thng (d): y=2 v hai im A(1;2);C(0;3) im B trờn ng thng (d) cho tam giỏc ABC cõn ti C cú to l: a) B(5;2) b) B(4;2) c) B(1;2) d) B(2;2) Cho ba im A(1;2); B(0;4);C(5;3) im D mt phng to cho ABCD l hỡnh bỡnh hnh cú to l: a) D(1;2) b) D(4;5) c) D(3;2) d) D(0;3) Cho hai im A(0;1) v im B(4;5) To tt c cỏc im C trờn trc Oy cho tam giỏc ABC l tam giỏc vuụng l: a) (0;1) b) (0;1); (0; ) c)(0;1);(0; ); 0;2 + ; 0;2 d) 0;2 + ; 0; a) xy+1=0 21 22 23 24 ( ( )( ) ( ) ) 25 Vi giỏ tr no ca m thỡ hai ng thng sau song song vi nhau: 26 27 28 29 30 (d1): (m1)xy+3=0 v (d2): 2mxy2=0 ? a) m=0 b) m= c) m=a (a l mt hng s) d) m=2 .thng i qua im M(1; 2) v song song vi .thng (d): 4x + 2y + = cú phng trỡnh tng quỏt l: a) 4x + 2y + = b) 2x + y + = c) 2x + y = d) x 2y + = Tớnh khong cỏch t im M (2; 2) n ng thng : 5x 12y 10 = a) 24/13 b) 44/13 c) 44/169 d) 14/169 Tớnh khong cỏch t im M(0; 3) n ung thng : x cos + y sin + 3( sin ) = a) b) c) sin d) sin + cos Tỡm ta im M' i xng vi im M (1; 4) qua .thng d: x 2y + = a) M'(0; 3) b) M'(2; 2) c) M'(4; 4) d) M' (3; 0) Tớnh gúc nhn gia hai ng thng: d1: x + 2y + = 0; d2: x 3y + = a) 300 b) 450 c) 600 d) 23012' Traộc nghieọm Hỡnh hoùc 10 22 x = + t y = 2t Trong cỏc phng trỡnh sau õy, ph.trỡnh no l ph.trỡnh tng quỏt ca (d)? a) 2x + y = b) 2x + y + = c) x + 2y + = d) x + 2y = Cho hai .thng: d1: 4x my + m = ; d2: (2m + 6)x + y 2m = Vi giỏ tr no ca m thỡ d1 song song vi d2 a) m = b) m = c) m = d) m = v m = Tỡm ta hỡnh chiu vuụng gúc H ca im M(1; 4) xung ng thng d: x 2y + = a) H(3;0) b) H(0; 3) c) H(2; 2) d) H(2; 2) Trong cỏc ng thng sau õy, ng thng no vuụng gúc vi ng thng d: x + 2y = v hp vi trc ta thnh mt tam giỏc cú din tớch bng 1? a) 2x + y + = b) 2x y = c) x 2y + = d) 2x y + = Tinh goc gia hai thng 1: x + y + 11 = v 2: x + y + = a) 450 b) 300 c) 88057 '52 '' d) 1013 ' '' Cho ng thng d cú phng trỡnh tng quỏt: 3x + 5y + 2003 = Trong cỏc mnh sau, tỡm mnh sai: r r a) d cú vect phỏp tuyn n = (3; 5) b) d cú vect ch phng u = (5; 3) c) d cú h s gúc k = 5/3 d) d song song vi .thng 3x + 4y = Lp phng trỡnh ca ng thng i qua giao im ca hai ng thng: d1 : x + 3y = 0; d2 : x 3y = v vuụng gúc vi ng thng: d3 : 2x y + = a) 3x + 6y = b) 6x + 12y 5= c) 6x +12y+10= d) x + 2y + 10=0 Cho tam giỏc ABC cú ta cỏc nh l A(1; 2), B(3; 1), C(5; 4) Phng trỡnh ng cao v t A l: a) 2x + 3y = b) 3x 2y = c) 5x 6y + = d) 3x 2y + = r ng thng i qua im M (1; 2) v vuụng gúc vi vect n = (2; 3) cú phng trỡnh chớnh tc l: x y x y x +1 y + x +1 y + = = = = a) b) c) d) 3 2 3 ng thng i qua im N (2; 1) v cú h s gúc k = 2/3 cú phng trỡnh tng quỏt l: a) 2x 3y + = b) 2x 3y = c) 2x + 3y + = d) 3x 2y + = 31 Cho phng trỡnh tham s ca ng thng (d): 32 33 34 35 36 37 38 39 40 23 Traộc nghieọm Hỡnh hoùc 10 II PHNG TRèNH NG TRềN Cho A(2;1); B(3;2) Tp hp nhng im M(x;y) cho MA 2+MB2=30 l mt ng trũn cú phng trỡnh: a) x2+y210x2y12=0 b) x2+y25x+y6=0 c) x2+y2+5xy6=0 d) x2+y25x+y6=0 Cho hai ng trũn cú phng trỡnh: (C1): x2+y26x+4y+9=0 (C2): x2+y2=9 Tỡm cõu tr li ỳng : a) (C1) v (C2) tip xỳc b) (C1) v (C2) nm ngoi c) (C1) v (C2) ct d) (C1) v (C2) cú tip tuyn chung Cho ng trũn (C) v ng thng (d) cú phng trỡnh : (C) : x2+y2+6x2y15=0 (d) :x+3y+2=0 Hai tip tuyn ca (C) song song vi ng thng (d) cú phng trỡnh l: a) x+3y+5=0 v x+3y5=0 b) x+3y10=0 v x+3y+10=0 c) x+3y8=0 v x+3y+8=0 d) x+3y12=0 v x+3y+12=0 Phng trỡnh ng thng no sau õy l phng trỡnh tip tuyn ca ng trũn (C): x2+y24=0 a) x+y2=0 b) x + y4=0 c) 2x+3y5=0 d) 4xy+6=0 2 Phng trỡnh : x +y +2mx+2(m1)y+2m =0 l phng trỡnh ng trũn m tho iu kin : 1 a) m< b) m c) m=1 d) Mt giỏ tr khỏc 2 ng thng (d): 2x+3y5=0 v ng trũn (C) : x 2+y2+2x4y+1=0 cú bao nhiờu giao im: a) b) c) d) Hai ng trũn sau õy cú bao nhiờu tip tuyn chung: (C1) : x2+y24x+6y3=0 v (C2) : x2+y2+2x4y+1=0 a) b) c) d) e) Cho h ng trũn cú phng trỡnh: (Cm): x2+y2+2(m+1)x4(m2)y4m1=0 Vi giỏ tr no ca m thỡ ng trũn cú bỏn kớnh nh nht? a) m=0 b) m=1 c) m=2 d)m=3 Cho hai ng trũn cú phng trỡnh: (C1) : x2+y24x+6y3=0 v (C2) : x2+y2+2x4y+1=0 Cỏc ng thng tip xỳc vi c hai ng trũn trờn l: 49 a) x=3 b) y= c) y= x+ d) y= x+3 3 Traộc nghieọm Hỡnh hoùc 10 24 49 x+ g) y= x+ v y= x+3 12 3 49 h/ y= x+ v y= x+3 v y= x+ 3 12 10 ng thng no cú phng trỡnh sau õy tip xỳc vi ng trũn (C): x2+y24x+6y3=0? a) x2y+7=0 b) x 15 y 14 + 15 = e) y= 11 12 13 14 15 16 17 18 x = + 3t x+2 y2 = c) d) y = + t Cho hai ng trũn: (C1): x2 + y2 + x y + = v (C2): x2 + y2 x + y = Trong cỏc mnh sau, tỡm mnh ỳng? a) (C1) ct (C2) b) (C1) khụng cú im chung vi (C2) c) (C1) tip xỳc vi (C2) d) (C1) tip xỳc ngoi vi (C2) Cho im A(1; 1), B(7; 5) Phng trỡnh ng trũn ng kớnh AB l: a) x2 + y2 + x + y + 12 = b) x2 + y2 x y + 12 = 2 c) x + y x y 12 = d) x2 + y2 + x + y 12 = Cho ba im A(3; 5), B(2; 3), C(6; 2) ng trũn ngoi tip tam giỏc ABC cú phng trỡnh l: a) x2 + y2 25 x 19 y + 68 = b) x2 + y2 + 25 x + 19 y 68 = 25 19 68 25 19 68 c) x2 + y2 x y+ =0 d) x2 + y2 + x+ y+ =0 3 3 3 Lp phng trỡnh tip tuyn ti im M(3; 4) vi ng trũn : (C): x2 + y2 x y = a) x + y = b) x + y + = c) x y = d) x + y = ng trũn i qua im A(2; 4), B(5; 5), C(6; 2) cú phng trỡnh l: a) x2 + y2 + x + y + 20 = b) x2 + y2 x y + 10 = c) x2 + y2 x y + 20 = d) x2 + y2 x y 20 = Tớnh bỏn kớnh ca ng trũn tõm I (1; 2) v tip xỳc vi ng thng : 3x 4y 26 = a) 12 b) c) d) Tỡm tip im ca ng thng d: x + 2y = vi ng trũn (C): ( x 4)2 + ( y 3)2 = a) (3; 1) b) (6; 4) c) (5; 0) d) (1; 20) Phng trỡnh no sau õy l phng trỡnh ng trũn: a) x2 + y2 x y + = b) x2 + y2 10 x y = 2 c) x + y x y + 20 = d) x2 + y2 x + y 12 = 25 Traộc nghieọm Hỡnh hoùc 10 III PHNG TRèNH NG ELIP c = cú phng trỡnh chớnh tc l: a x2 y x2 y x2 y x2 y a) b) c) d) + =1 + =1 + =1 + =1 25 25 16 25 16 25 ng trũn v elip cú phng trỡnh sau õy cú bao nhiờu giao im: x2 y (C) : x2+y29=0 (E) : + =1 a) b) c) d) e) 2 x y Cho elip ( E ) : + = v cho cỏc mnh : 25 (I) (E) cú tiờu im F1 ( 4; 0) v F2(4; 0) (II) (E) cú t s c/a = 4/5 (III) (E) cú nh A1(5; 0) (IV) (E) cú di trc nh bng Trong cỏc mnh trờn, mnh no sai ? a) I v II b) II v III c) I v III d) IV v I Mt elip cú trc ln bng 26, t s c/a = 12/13 Trc nh ca elip bng bao nhiờu ? a) b) 10 c) 12 d) 24 2 x y Dõy cung ca elip ( E ) : + = (0 < b < a) vuụng gúc vi trc ln ti a b tiờu im cú di l : 2c 2b 2a a2 a) b) c) d) a a c c Lp phng trỡnh chớnh tc ca elip cú nh l (3; 0), (3; 0) v hai tiờu im l (1; 0), (1; 0) ta c : x2 y x2 y x2 y x2 y a) b) c) d) + =1 + =1 + =1 + =1 9 9 Cho elip ( E ) : x2 + 4y2 v cho cỏc mnh : (I) (E) cú trc ln bng (II) (E) cú trc nh bng (III) (E) cú tiờu im F1 ( ; ) (IV) (E) cú tiờu c bng Trong cỏc mnh trờn, tỡm mnh ỳng ? Elip cú tiờu c bng ; t s Traộc nghieọm Hỡnh hoùc 10 a) (I) b) (II) v (IV) 26 c) (I) v (III) d) (IV) 27 Traộc nghieọm Hỡnh hoùc 10 Traộc nghieọm Hỡnh hoùc 10 28 ... 2C ) = sin 3C b) cos 2 A + B + 2C C = sin c) sin( A+ B) = sinC d) cos 2 Gi S = ma2 + mb2 + mc2 l tng bỡnh phng di ba trung tuyn ca tam giỏc ABC Trong cỏc mnh sau mnh no ỳng ? a) S = (a2 + b2... + 2k 13 Cho phng trỡnh tham s ca ng thng (d): (k R) Phng y =1 k trỡnh no sau õy l phng trỡnhg tng quỏt ca (d): a) x+2y5=0 b) x+2y+1=0 c) x2y1=0 d) x2y+5=0 r 14 Ph.trỡnh tham s ca .thng (d) i... To im i xng ca im A(3;5) qua ng thng y = x l: a) (3;5) b) (5;3) c) (5;3) d) (5;3) 16 Ph.trỡnh tng quỏt ca ng thng (d) i qua hai im M(1;2) v N(3;4) l: a) x+y+1=0 b) x+y1=0 c) xy1=0 d) .thng khỏc