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Kha hc Luyn thi i hc mn Ton thi tluyn s06

Hocmai.vnNgi trng chung ca hc tr Vit Tng i t vn: 1900 58-58-12 - Trang | 1 -

TLUYN THI THI HC S 06MN: TON

Thi gian lm bi: 180 pht

A. PHN CHUNG CHO TT C CC TH SINHCu I. (2 im)Cho h (Cm): y = x3 2mx2 + (2m2 1)x m(m2 1)1.Tm m hm st cc tr ti x1, x2 vi 1 2 1 2x x x x .

2.Tm m (Cm) ct Ox ti 3 im phn bit c honh dng.Cu II.(2 im)1. Gii phng trnh: 2011 9( 909) log ( 9) log ( 2011) 202x x x x

2. Tm m phng trnh cos3x cos2x + mcosx 1 = 0 c ng 8 nghim 5,2 2

Cu III. (1 im) Tnh tch phn 2

1

x 2

1

sinx+exI e x dx

Cu IV: (1 im)Cho hnh trc cc y l hai hnh trn tm O v O: OO = a. Gi A, B l hai im thuc ng trny tm O, im A thuc ng trn y tm O sao cho OA, OB vung gc vi nhau v AAl ngsinh ca hnh tr. Bit gc gia ng thng AO v mt phng (AAB) bng 300. Tnh th tch khi trtheo a.

Cu V.(1 im)

Cho x, y, z > 0 v x+2y+3z = 6. Tm gi tr ln nht ca biu thc S2 3

1 1 1

yx zx y z

B. PHN RINGChng trnh c bnCu VI.a. (2 im)1. Trong h ta trc chun Oxy, cho tam gic ABC cn ti nh A(2;2) ; ng thng (d) i qua trungim cc cnh AB, AC c phng trnh x + y 6 = 0. im D(2;4) nm trn ng cao i qua nh B catam gic ABC . Tm ta cc nh B v C.

2. Trong khng gian vi h trc Oxyz, cho ng thng (d):32 1

1 2 2

yx z

v hnh bnh hnh

ABCD c A(1;0;0), C(2;2;2), D (d). Cho din tch (ABCD) bng 3 2 ,tm ta D.Cu VIIa. (1 im)Tm nghim phc ca phng trnh z5 + 2z4 + 4z3 + 8z2 + 16z + 32 = 0Chng trnh nng caoCu VI.b. (2 im)1. Trong h ta trc chun Oxy, cho tam gic ABC cn ti nh A(2;2) ; ng thng (d) i qua trungim cc cnh AB, AC c phng trnh x + y 6 = 0. im D(2;4) nm trn ng cao i qua nh B catam gic ABC . Tm ta cc nh B v C.

2. Trong khng gian vi h trc Oxyz, cho ng thng (d):32 1

1 2 2

yx z

v hnh bnh hnh

ABCD c A(1;0;0), C(2;2;2), D (d). Cho din tch (ABCD) bng 3 2 ,tm ta DCu VII.b (1 im)Xt cc tam gic c 3 nh ly tcc nh ca agic u H c 12 cnh.1.C bao nhiu tam gic c ng mt cnh l ca H?2. C bao nhiu tam gic khng c cnh no ca H?

Gio vin: Trn Phng

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