Cac BT Ham Phan Thuc

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Cac BT Ham Phan Thuc

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THI TH I HC CAO NG 2012

LUYN THI I HC Cu I (2 im)A.Hm hu t:Cu 1: Cho hm s .

1. Kho st s bin thin v v th (C) ca hm s cho.

2. Vit phng trnh tip tuyn ca th (C), bit h s gc ca tip tuyn bng 5.Cu 2. Cho hm s c th l (C)

1. Kho st s bin thin v v th ca hm s

2. Chng minh ng thng d: y = x + m lun lun ct th (C) ti hai im phn bit A, B. Tm m on AB c di nh nht.Cu 3:(2 im):

1. Kho st v v th (C) ca hm s: . Tm cc im thuc (C) cch u 2 tim cn.

2. Tm cc gi tr ca m phng trnh sau c 2 nghim trn on [0, 2/3].

sin6x + cos6x = m (sin4x + cos4x)Cu 4:

1. Kho st v v th (C) ca hm s y =

2. Tm trn (C) hai im i xng nhau qua ng thng MN bit M(3; 0) v N(1; 1)Cu 5:(2.0 im) Cho hm s (C)

1. Kho st s bin thin v v th hm s (C)

2. Vit phng trnh tip tuyn vi th (C), bit rng khong cch t tm i xng ca th (C) n tip tuyn l ln nht.Cu 6: (2,0 im) Cho hm s , c th l (C)

1. Kho st v v (C)

2. Vit phng trnh tip tuyn ca (C), bit tip tuyn i qua im A(6; 5)Cu 7: (2 im): Cho hm s y = c th l (C)

1. Kho st s bin thin v v th (C) ca hm s trn.

2. Tm trn (C) nhng im M sao cho tip tuyn ti M ca (C) ct 2 tim cn ca (C) ti A, B sao cho AB ngn nht.

Cu 8: (2 im): Cho hm s (C)

1. Kho st s bin thin v v th (C) ca hm s.

2. Tm m ng thng d: y = x + m ct (C) ti hai im phn bit A, B sao cho OAB vung ti O.Cu 9: (2 im) Cho hm s c th (C).

1. Kho st s bin thin v v th hm s.

2. Vi im M bt k thuc th (C) tip tuyn ti M ct 2 tim cn ti A v B. Gi I l giao hai tim cn, tm v tr ca M chu vi tam gic IAB t gi tr nh nht.Cu 10: (2 im) Cho hm s (C)

1. Kho st s bin thin v v th (C) ca hm s.

2. Cho M l im bt k trn (C). Tip tuyn ca (C) ti M ct cc ng tim cn ti A v B. Gi I l giao im ca cc ng tim cn. Tm im M sao cho ng trn ngoi tip IAB c din tch nh nht.Cu 11: (2 im) Cho hm s y =

1. Kho st s bin thin v v th (C) ca hm s cho.

2. Cho im Mo(xo; yo) thuc th (C). Tip tuyn ca (C) ti Mo ct cc tim cn ca (C) ti cc im A v B. Chng minh Mo l trung im ca on thng AB.Cu 12: Cho hm s (C)

1. Kho st s bin thin v v th (C) ca hm s cho

2. Vit phng trnh tip tuyn vi th (C), bit rng khong cch t tm i xng ca (C) n tip tuyn l ln nht.Cu 13: (2,0 im) Cho hm s (C)

1. Kho st s bin thin v v th (C) ca hm s cho

2. Tm trn th (C) nhng im c tng khong cch n hai tim cn ca (C) nh nht.Cu 14: Cho hm s (C)

1.Kho st v v th hm s cho.

2. Tm trn (C) cc cp im i xng nhau qua ng thng y=-2x+7.

Cu 15: Cho hm s (C)

1.Kho st v v th hm s cho.

2.Gi I l giao im hai tim cn ca (C). Tm trn (C) im M sao cho tip tuyn ca (C) ti M ct hai ng tim cn ti J,K sao cho ng trn ngoi tip tam gic IJK c din tch nh nht. B. Hm a thc bc ba:Cu 16: Cho hm s y = 4x3 + mx2 3x.

1. Kho st v v th (C) hm s khi m = 0.

2. Tm m hm s c hai cc tr ti x1 v x2 tha x1 = 4x2.Cu 17. Cho hm s y = f(x) = mx3 + 3mx2 (m 1)x 1, m l tham s

1. Kho st s bin thin v v th ca hm s trn khi m = 1.

2. Xc nh cc gi tr ca m hm s y = f(x) khng c cc tr.Cu 18: Cho hm s y = x3 + 2mx2 + (m + 3)x + 4 c th l (Cm).

1. Kho st s bin thin v v th (C1) ca hm s trn khi m = 1.

2. Cho ng thng (d): y = x + 4 v im K(1; 3). Tm cc gi tr ca tham s m sao cho (d) ct (Cm) ti ba im phn bit A(0; 4), B, C sao cho tam gic KBC c din tch bng .

Cu 19: (2,0 im) Cho hm s (1)

1. Kho st s bin thin v v th hm s (1) khi m = 2.2. Tm cc gi tr ca tham s m hm s (1) ng bin trn tp xc nh ca n.Cu 20. Cho hm s y = x3 3(m + 1)x2 + 9x + m 2 (1) c th l (Cm)

1. Kho st v v th hm s (1) vi m = 1.

2. Xc nh m (Cm) c cc i, cc tiu v hai im cc tr i xng vi nhau qua ng thng

y = x/2.Cu 21. Cho hm s y = x3 + mx + 2 (1)

1. Kho st s bin thin v v th ca hm s (1) khi m = 3.

2. Tm m th hm s (1) ct trc honh ti mt im duy nht.Cu 22. Cho hm s

1. Kho st v v th hm s khi m = 1.

2. Xc nh m th hm s c cc i, cc tiu i xng nhau qua t y = xCu 23: Cho hm s y = x3 + 3x2 + mx + 1 c th (Cm).

1. Kho st v v th khi m = 3.

2. Xc nh m (Cm) ct ng thng y = 1 ti 3 im phn bit C(0, 1), D, E sao cho cc tip tuyn ca (Cm) ti D v E vung gc vi nhau.

Cu 24: (2 im) Cho hm s y = x3 3x2 9x + m, trong l tham s thc.

1. Kho st s bin thin v v th ca hm s cho khi m = 0.

2. Tm tt c cc gi tr ca tham s th hm s cho ct trc honh ti 3 im phn bit c honh lp thnh cp s cng.Cu 25. (2 im) Cho hm s y = ( x3 ( 3x2 + mx + 4, trong m l tham s thc.

1. Kho st s bin thin v v th ca hm s cho, vi m = 0.

2. Tm tt c cc gi tr ca tham s m hm s cho nghch bin trn khong (0; +).Cu 26: (2 im) Cho hm s y = x3 3x2 + 4

1. Kho st s bin thin v v th (C) ca hm s.

2. Gi d l ng thng i qua im A(3; 4) v c h s gc l m. Tm m d ct (C) ti 3 im phn bit A, M, N sao cho hai tip tuyn ca (C) ti M v N vung gc vi nhau.

Cu 27. (2,0 im) Cho hm s y = x3 3(m + 1)x2 + 9x m, vi l tham s thc.

1. Kho st s bin thin v v th ca hm s cho ng vi m = 1.

2. Xc nh m hm s cho t cc tr ti x1, x2 sao cho .Cu 28: (2 im) Cho hm s y = x3 3(m + 1)x2 + 9x m

1. Kho st s bin thin v v th ca hm s khi m = 1.

2. Xc nh cc gi tr m hm s nghch bin trn mt khong c di bng 2.Cu 29: (2 im) Cho hm s y = x3 + 2mx2 + (m + 3)x + 4 c th l (Cm).

1.Kho st s bin thin v v th (C1) ca hm s trn khi m = 1.

2. Cho (d) l ng thng c phng trnh y = x + 4 v im K(1; 3). Tm cc gi tr ca tham s m sao cho (d) ct (Cm) ti ba im phn bit A(0; 4), B, C sao cho tam gic KBC c din tch bng .Cu 30: (2 im): Gi (Cm) l th ca hm s y = x3 + (2m + 1)x2 (m + 1)

1. Kho st s bin thin v v th khi m = 1.

2. Tm m th (Cm) tip xc vi ng thng y = 2mx (m + 1)Cu 31: (2 im)

Cho hm s y = x3 + (1 2m)x2 + (2 m)x + m + 2 (m l tham s) (1)

1. Kho st s bin thin v v th ca hm s (1) khi m = 2

2. Tm cc gi tr ca m th hm s (1) c im cc i, im cc tiu, ng thi honh ca im cc tiu nh hn 1.

Cu 32: (2 im)

Cho hm s y = (1/3)x3 mx2 +(m2 1)x + 1 c th (Cm)

1. Kho st s bin thin v v th (C2) khi m = 2.

2. Tm m, hm s (Cm) c cc i, cc tiu v yC + yCT > 2.

Cu 33: (2,0 im)

1. Kho st s bin thin v v th (C) ca hm s: y = x3 3x2 + 2

2. Bin lun theo m s nghim ca phng trnh:

Cu 34: (2,0 im)

1. Kho st s bin thin v v th (C) ca hm s

2. Vit phng trnh tip tuyn ca th (C), bit tip tuyn ny i qua gc ta O.Cu 35. Cho hm s y = (x m)3 3x (1)

1. Xc nh m hm s (1) t cc tiu ti im c honh x = 0.

2. Kho st s bin thin v v th (C) ca hm s (1) khi m = 1.Cu 36. (2 im) Cho hm s y = x3 + 3x2 + mx 2 (1), m l tham s thc.

1. Kho st s bin thin v v th hm s khi m = 0.

2. Tm cc gi tr ca m hm s (1) nghch bin trn khong (0; 2).Cu 37. Cho hm s y = x3 + (1 2m)x2 + (2 m)x + m + 2 (1) m l tham s.

1. Kho st s bin thin v v th (C) ca hm s (1) vi m = 2.

2. Tm tham s m th ca hm s (1) c tip tuyn to vi ng thng d: x + y + 7 = 0 gc sao cho .Cu 38: (2 im) Cho hm s y = 2x3 3(2m + 1)x2 + 6m(m + 1)x +1 c th (Cm).

1. Kho st s bin thin v v th ca hm s khi m = 0.

2. Tm m hm s ng bin trn khong (2; +).C. Hm a thc bc 4 trng phng:

Cu 39. Cho hm s y = f(x) = x4 2x2.

1. Kho st v v th (C) ca hm s.

2. Trn (C) ly hai im phn bit A v B c honh ln lt l a v b. Tm iu kin i vi a v b hai tip tuyn ca (C) ti A v B song song vi nhau.

Cu 40: Cho hm s y = x4 + mx3 2x2 3mx + 1 (1)1. Kho st s bin thin v v th (C) ca hm s (1) khi m = 0.

2. nh m hm s (1) c hai cc tiu.

Cu 41. Cho hm s y = 8x4 9x2 + 1.

1. Kho st s bin thin v v th (C) ca hm s.

2. Da vo th (C) hy bin lun theo m s nghim ca phng trnh

8cos4x 9cos2x + m = 0 vi x ( [0; ].Cu 42: (2 im)

1. Kho st v v th hm s y = x4 4x2 + 3

2. Tm m phng trnh c ng 4 nghim.

Cu 43: (2 im) Cho hm s y = x4 4x2 + m (C)

1. Kho st hm s vi m = 3.

2. Gi s th (C) ct trc honh ti 4 im phn bit. Tm m hnh phng gii hn bi th (C) v trc honh c din tch phn pha trn v phn pha di trc honh bng nhau.

Cu 44. (2 im) Cho hm s y = x4 2mx2 + m 1 (1), vi l tham s thc.

1. Kho st s bin thin v v th hm s (1) khi m = 1.

2. Xc nh hm s (1) c ba im cc tr, ng thi cc im cc tr ca th to thnh mt tam gic c bn knh ng trn ngoi tip bng .

Cu 45: (2 im) Cho hm s y = x4 (2m + 1)x2 + 2m.

1. Kho st s bin thin v v th (C) ca hm s khi m = 2.

2. Tm tt c cc gi tr ca m th hm s ct trc Ox ti 4 im phn bit cch u nhau.

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