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Đề Thi toán HKII Lớp 11
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1
s 1
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
I. Phn chung cho c hai ban Bi 1. Tm cc gii hn sau:
1) x
x x
x
2
1
2lim
1
2) x
x x4lim 2 3 12
+ 3)x
x
x3
7 1lim
3+
4) x
x
x23
1 2lim
9+
Bi 2. 1) Xt tnh lin tc ca hm s sau trn tp xc nh ca n:
x xkhi xf x x
x khi x
2 5 63( ) 3
2 1 3
+ >
=
+
2) Chng minh rng phng trnh sau c t nht hai nghim : x x x3 22 5 1 0 + + = . Bi 3. 1) Tm o hm ca cc hm s sau: a) y x x2 1= + b) y
x 23
(2 5)=
+
2) Cho hm s xyx
11
=
+ .
a) Vit phng trnh tip tuyn ca th hm s ti im c honh x = 2. b) Vit phng trnh tip tuyn ca th hm s bit tip tuyn song song vi d: xy 2
2
= .
Bi 4. Cho hnh chp S.ABCD c y ABCD l hnh vung cnh a, SA vung gc vi y, SA = a 2 . 1) Chng minh rng cc mt bn hnh chp l nhng tam gic vung. 2) Chng minh rng: (SAC) (SBD) . 3) Tnh gc gia SC v mp (SAB) . 4) Tnh gc gia hai mt phng (SBD) v (ABCD) .
II . Phn t chn. 1 . Theo chng trnh chun.
Bi 5a. Tnh x
x
x x
3
22
8lim
11 18+
+ +.
Bi 6a. Cho y x x x3 21 2 6 83
= . Gii bt phng trnh y / 0 .
2. Theo chng trnh nng cao.
Bi 5b. Tnh x
x x
x x21
2 1lim
12 11
+.
Bi 6b. Cho x xyx
2 3 31
+=
. Gii bt phng trnh y / 0> .
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 2
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
I . Phn chung cho c hai ban. Bi 1. Tm cc gii hn sau:
1) x
x x x
x
2 1 3lim
2 7 +
+ 2)
xx x3lim ( 2 5 1)
+ + 3)
x
x
x5
2 11lim
5+
4) x
x
x x
3
20
1 1lim
+
+.
Bi 2 .
1) Cho hm s f(x) = x
khi xf x xm khi x
3 11( ) 1
2 1 1
=
+ =
. Xc nh m hm s lin tc trn R..
2) Chng minh rng phng trnh: m x x2 5(1 ) 3 1 0 = lun c nghim vi mi m. Bi 3. 1) Tm o hm ca cc hm s:
a) x xyx
2
22 2
1
+=
b) y x1 2 tan= + .
2) Cho hm s y x x4 2 3= + (C). Vit phng trnh tip tuyn ca (C): a) Ti im c tung bng 3 . b) Vung gc vi d: x y2 3 0+ = . Bi 4. Cho t din OABC c OA, OB, OC, i mt vung gc v OA = OB = OC = a, I l trung im BC
1) Chng minh rng: (OAI) (ABC). 2) Chng minh rng: BC (AOI). 3) Tnh gc gia AB v mt phng (AOI). 4) Tnh gc gia cc ng thng AI v OB . II . Phn t chn. 1 . Theo chng trnh chun .
Bi 5a. Tnh nn n n2 2 21 2 1
lim( .... )1 1 1
+ + ++ + +
.
Bi 6a. Cho y x xsin2 2 cos= . Gii phng trnh y / = 0 . 2 . Theo chng trnh nng cao . Bi 5b. Cho y x x22= . Chng minh rng: y y3 / /. 1 0+ = .
Bi 6b . Cho f( x ) = f x xxx3
64 60( ) 3 16= + . Gii phng trnh f x( ) 0 = .
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 3
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
Bi 1. Tnh cc gii hn sau:
1) x
x x x3 2lim ( 1)
+ + 2) x
x
x1
3 2lim
1+
+ 3)
x
x
x2
2 2lim
7 3+
+
4) x
x x x
x x x
3 2
3 23
2 5 2 3lim4 13 4 3
+ 5) lim
n n
n n
4 5
2 3.5
+
Bi 2. Cho hm s: x
khi x >2 xf x
ax khi x 2
3 3 2 22( )14
+
= +
. Xc nh a hm s lin tc ti im x = 2.
Bi 3. Chng minh rng phng trnh x x x5 43 5 2 0 + = c t nht ba nghim phn bit trong khong (2; 5).
Bi 4. Tm o hm cc hm s sau:
1) xyx x25 3
1
=
+ + 2) y x x x2( 1) 1= + + + 3) y x1 2 tan= + 4) y xsin(sin )=
Bi 5. Cho hnh chp S.ABC c ABC vung ti A, gc B = 600 , AB = a; hai mt bn (SAB) v (SBC) vung gc vi y; SB = a. H BH SA (H SA); BK SC (K SC).
1) Chng minh: SB (ABC) 2) Chng minh: mp(BHK) SC. 3) Chng minh: BHK vung . 4) Tnh cosin ca gc to bi SA v (BHK).
Bi 6. Cho hm s x xf xx
2 3 2( )
1 +
=
+ (1). Vit phng trnh tip tuyn ca th hm s (1), bit tip
tuyn song song vi ng thng d: y x5 2= .
Bi 7. Cho hm s y x2cos 2= . 1) Tnh y y, . 2) Tnh gi tr ca biu thc: A y y y16 16 8 = + + .
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 4
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
Bi 1. Tnh cc gii hn sau:
1) x xx
3 2lim ( 5 2 3) +
2) x
x
x1
3 2lim
1++
+ 3)
x
x
x2
2lim
7 3
+
4) x
x
x
3
0
( 3) 27lim
+ 5)
n n
n n
3 4 1lim
2.4 2
+
+
Bi 2. Cho hm s: x
khi xf x x
ax khi x
11( ) 1
3 1
>=
. Xc nh a hm s lin tc ti im x = 1.
Bi 3. Chng minh rng phng trnh sau c t nht mt nghim m: x x3 1000 0,1 0+ + =
Bi 4. Tm o hm cc hm s sau:
1) x xyx
22 6 52 4
+=
+ 2) x xy
x
2 2 32 1
+=
+ 3) x xy
x x
sin cossin cos
+=
4) y xsin(cos )=
Bi 5. Cho hnh chp S.ABCD c y ABCD l hnh vung cnh a, SA (ABCD) v SA = 2a. 1) Chng minh SAC SBD( ) ( ) ; SCD SAD( ) ( ) 2) Tnh gc gia SD v (ABCD); SB v (SAD) ; SB v (SAC). 3) Tnh d(A, (SCD)); d(B,(SAC))
Bi 6. Vit phng trnh tip tuyn ca th hm s y x x3 23 2= + : 1) Ti im M ( 1; 2) 2) Vung gc vi ng thng d: y x1 2
9= + .
Bi 7. Cho hm s: x xy2 2 22
+ += . Chng minh rng: y y y 22 . 1 = .
Ht H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 5
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
A. PHN CHUNG: Bi 1: Tm cc gii hn sau:
a) n nn
3
32 2 3
lim1 4
+
b) x
x
x21
3 2lim
1+
Bi 2: Xt tnh lin tc ca hm s sau trn tp xc nh ca n:
x x khi xf x x
khi x
2 3 22( ) 2
3 2
+ + = +
=
Bi 3: Tnh o hm ca cc hm s sau: a) y x x x2sin cos tan= + b) y xsin(3 1)= + c) y xcos(2 1)= + d) y x1 2 tan4= +
Bi 4: Cho hnh chp S. ABCD c y ABCD l hnh thoi cnh a, BAD 060= v SA = SB = SD = a. a) Chng minh (SAC) vung gc vi (ABCD). b) Chng minh tam gic SAC vung. c) Tnh khong cch t S n (ABCD).
B. PHN T CHN: 1. Theo chng trnh chun Bi 5a: Cho hm s y f x x x3( ) 2 6 1= = + (1) a) Tnh f '( 5) . b) Vit phng trnh tip tuyn ca th hm s (1) ti im Mo(0; 1) c) Chng minh phng trnh f x( ) 0= c t nht mt nghim nm trong khong (1; 1).
2. Theo chng trnh Nng cao
Bi 5b: Cho x xf x x xsin3 cos3( ) cos 3 sin3 3
= + +
.
Gii phng trnh f x'( ) 0= .
Bi 6b: Cho hm s f x x x3( ) 2 2 3= + (C). a) Vit phng trnh tip tuyn ca (C) bit tip tuyn song song vi ng thng d: y x22 2011= +
b) Vit phng trnh tip tuyn ca (C) bit tip tuyn vung gc ng thng : y x1 20114
= +
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 6
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
A. PHN CHUNG Cu 1: Tm cc gii hn sau:
a) x xx x
23 4 1lim1 1
+
b) x
x x
2 9lim3 3
+ c) x
x x
2lim2 7 3
+ d) x x
x x
2 2 3lim2 1
+
+
Cu 2: Cho hm s x x
khi xf x x
m khi x
2 2 2( ) 2
2
=
=
.
a) Xt tnh lin tc ca hm s khi m = 3 b) Vi gi tr no ca m th f(x) lin tc ti x = 2 ?
Cu 3: Chng minh rng phng trnh x x x5 43 5 2 0 + = c t nht ba nghim phn bit trong khong (2; 5)
Cu 4: Tnh o hm ca cc hm s sau:
b) y x x2 3( 1)( 2)= + c) yx2 21
( 1)=
+ d) y x x2 2= + e) xy
x
42
22 1
3
+=
B.PHN T CHN: 1. Theo chng trnh chun Cu 5a: Cho tam gic ABC vung cn ti B, AB = BC= a 2 , I l trung im cnh AC, AM l ng
cao ca SAB. Trn ng thng Ix vung gc vi mp(ABC) ti I, ly im S sao cho IS = a. a) Chng minh AC SB, SB (AMC). b) Xc nh gc gia ng thng SB v mp(ABC). c) Xc nh gc gia ng thng SC v mp(AMC).
2. Theo chng trnh nng cao Cu 5b: Cho hnh chp u S.ABCD c cnh y bng a v cnh bn bng 2a. Gi O l tm ca y
ABCD. a) Chng minh rng (SAC) (SBD), (SBD) (ABCD). b) Tnh khong cch t im S n mp(ABCD) v t im O n mp(SBC). c) Dng ng vung gc chung v tnh khong cch gia hai ng thng cho nhau BD v SC.
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 7
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
I. PHN BT BUC: Cu 1: Tnh cc gii hn sau:
a) ( )x
x x2lim 5+
+ b)x
x
x23
3lim
9+
Cu 2 (1 im): Cho hm s x
khi xx xf x
A khi x
22 1 1
22 3 1( )12
+ + +=
=
Xt tnh lin tc ca hm s ti x 12
=
Cu 3 (1 im): Chng minh rng phng trnh sau c t nht mt nghim trn [0; 1]: x x3 5 3 0+ = . Cu 4 (1,5 im): Tnh o hm ca cc hm s sau:
a) y x x( 1)(2 3)= + b) xy 21 cos2
= +
Cu 5 (2,5 im) : Cho hnh chp S.ABCD c y ABCD l hnh thoi tm O cnh a, BAD 060= , ng cao SO = a.
a) Gi K l hnh chiu ca O ln BC. Chng minh rng: BC (SOK) b) Tnh gc gia SK v mp(ABCD). c) Tnh khong cch gia AD v SB. II. PHN T CHN 1. Theo chng trnh chun Cu 6a (1,5 im): Cho hm s: y x x32 7 1= + (C). a) Vit phng trnh tip tuyn ca th (C) ti im c honh x = 2. b) Vit phng trnh tip tuyn ca th (C) c h s gc k = 1. Cu 7a (1,5 im): Cho hnh chp tam gic S.ABC c y ABC l tam gic u, SA (ABC), SA= a. M
l mt im trn cnh AB, ACM = , h SH CM. a) Tm qu tch im H khi M di ng trn on AB. b) H AK SH. Tnh SK v AH theo a v . 2. Theo chng trnh nng cao
Cu 6b (1,5 im): Cho cc th (P): xy x2
12
= + v (C): x xy x2 3
12 6
= + .
a) Chng minh rng (P) tip xc vi (C). b) Vit phng trnh tip tuyn chung ca (P) v (C) ti tip im. Cu 7b (1,5 im): Cho hnh chp S.ABCD c y ABCD l hnh vung tm O, cnh a; SA = SB = SC
= SD = 52a
. Gi I v J ln lt l trung im BC v AD.
a) Chng minh rng: SO (ABCD). b) Chng minh rng: (SIJ) (ABCD). Xc nh gc gia (SIJ) v (SBC). c) Tnh khong cch t O n (SBC).
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 8
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
A. PHN BT BUC Cu 1: Tnh cc gii hn sau:
a)x
x x
x x
2
22 3 4
lim4 2 1+
+
+ + b)
x
x x
x
2
21
3 2lim
1 +
c) x
x
x
2
2
5 3lim
2+
Cu 2: Cho hm s x khi xf xax khi x21 1
( )4 1 +
= >
. nh a hm s lin tc ti x = 1
Cu 3: Chng minh rng phng trnh x x32 6 1 0 + = c 3 nghim trn [2; 2].
Cu 4: Tnh o hm ca cc hm s sau:
a) xyx
3 52 1
+=
+ b) y x xsin .cos3=
Cu 5: Cho hnh chp S.ABCD c y ABCD l hnh vung cnh a, hai mt bn (SAB), (SBC) vung gc vi y, SB = a.
a) Gi I l trung im SC. Chng minh rng: (BID) (SCD). b) Chng minh rng cc mt bn ca hnh chp l cc tam gic vung. c) Tnh gc ca mp(SAD) v mp(SCD). B. PHN T CHN 1. Theo chng trnh chun
Cu 6a: Cho hyperbol (H): yx
1= . Vit phng trnh tip tuyn ca (H):
a) Ti im c honh x0 1= .
b) Tip tuyn song song vi ng thng d: y x14
= .
Cu 7a: Cho lng tr tam gic ABC.ABC. Gi I, J, K ln lt l trng tm ca cc tam gic ABC, ABC, ACC. Chng minh rng:
a) (IJK) // (BBCC) b) (AJK) // (AIB) 2. Theo chng trnh nng cao Cu 6b: Gii v bin lun phng trnh f x( ) 0 = , bit f x x m x mx( ) sin2 2(1 2 )cos 2= + .
Cu 7b: Cho hnh chp S.ABCD c y ABCD l hnh thang vung, AD // BC, AB = a, BC = a, ADC 045= . Hai mt bn SAB, SAD cng vung gc vi y, SA = a 2 .
a) Tnh gc gia BC v mp(SAB) b) Tnh gc gia mp(SBC) v mp(ABCD) c) Tnh khong cch gia AD v SC
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 9
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
Bi 1: 1) Tnh cc gii hn sau: a) + +
+
4
2
2 2lim
1n n
n b)
3
2
8lim
2xx
x c)
+
+
+13 2
lim1x
x
x.
2) Cho y f x x x3 2( ) 3 2= = + . Chng minh rng phng trnh f(x) = 0 c 3 nghim phn bit.
3) Cho x x
khi xf x x
a x khi x
2 22( ) 2
5 3 2
=
=
. Tm a hm s lin tc ti x = 2.
Bi 2: Cho y x2 1= . Gii bt phng trnh: y y x2. 2 1 < .
Bi 3: Cho t din OABC c OA = OB = OC = a, AOB AOC BOC0 060 , 90= = = . a) Chng minh rng ABC l tam gic vung. b) Chng minh OA vung gc BC. c) Gi I, J l trung im OA v BC. Chng minh IJ l on vung gc chung OA v BC.
Bi 4: Cho y f x x x3 2( ) 3 2= = + . Vit phng trnh tip tuyn ca th hm s f(x) bit tip tuyn song song vi d: y = 9x + 2011.
Bi 5: Cho xf xx
2 1( )
= . Tnh nf x( ) ( ) , vi n 2.
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 10
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
A. PHN BT BUC: Cu 1: Tnh cc gii hn sau:
a) x
x
x x23
3lim
2 3+
+ b)
x
x
x
3
0
( 1) 1lim
+ c)
x
x
x
2
2
5 3lim
2+
+
Cu 2: a) Chng minh rng phng trnh sau c t nht 2 nghim: x x32 10 7 0 =
b) Xt tnh lin tc ca hm s x
xf x x
x
3, 1( ) 1
2 , 1
+
=
=
trn tp xc nh .
Cu 3: a) Vit phng trnh tip tuyn ca thi hm s y x3= ti im c honh x0 1= . b) Tnh o hm ca cc hm s sau: y x x y x x x x2 21 (2 )cos 2 sin = + = + Cu 4: Cho hnh chp S.ABCD c SA (ABCD) v ABCD l hnh thang vung ti A, B . AB = BC = a, ADC SA a045 , 2= = .
a) Chng minh cc mt bn ca hnh chp l cc tam gic vung. b) Tnh gc gia (SBC) v (ABCD). c) Tnh khong cch gia AD v SC. B. PHN T CHN: 1. Theo chng trnh chun
Cu 5a: a) Tnh x xx22
1 1lim
24+
b) Cho hm s f xx
8( ) = . Chng minh: f f( 2) (2) =
Cu 6a: Cho y x x3 23 2= + . Gii bt phng trnh: y 3 < . Cu 7a: Cho hnh hp ABCD.EFGH c AB a AD b AE c, ,= = =
. Gi I l trung im ca on BG. Hy
biu th vect AI
qua ba vect a b c, ,
.
2. Theo chng trnh nng cao Cu 5b: a) Tnh gn ng gi tr ca 4,04 b) Tnh vi phn ca hm s y x x2.cot=
Cu 6b: Tnh x
x x
x
2
3
3 1lim
3+ +
Cu 7b 3: Cho t din u cnh a. Tnh khong cch gia hai cnh i ca t din .
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 11
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
II. Phn bt buc Cu 1: 1) Tnh cc gii hn sau: a)
x
x
x x21 2
lim2 3+
+ b)
x
x x x
x x
3 2
32
3 9 2lim
6+
c) ( )x
x x x2lim 3
+ +
2) Chng minh phng trnh x x3 3 1 0 + = c 3 nghim phn bit .
Cu 2: 1) Tnh o hm ca cc hm s sau: a) ( )y x x
x
23 1
= +
b) y x xsin= + c) x xyx
2 21
=
2) Tnh o hm cp hai ca hm s = tany x 3) Tnh vi phn ca ham s y = sinx.cosx Cu 3: Cho hnh chp S.ABCD c y ABCD l hnh vung cnh a, ( )SA ABCD v = 6SA a . 1) Chng minh : BD SC SBD SAC, ( ) ( ) . 2) Tnh khong cch t A n mt phng (SBD). 3) Tnh gc gia SC v (ABCD)
II. Phn t chn 1. Theo chng trnh chun Cu 4a: Vit phng trnh tip tuyn ca th hm s = 1y x
x ti giao im ca n vi trc honh .
Cu 5a: Cho hm s = + +360 64
( ) 3 5f x xx x
. Gii phng trnh f x( ) 0 = .
Cu 6a: Cho hnh lp phng ABCD.EFGH c cnh bng a . Tnh .AB EG .
2. Theo chng trnh nng cao Cu 4b: Tnh vi phn v o hm cp hai ca hm s y x xsin2 .cos2= .
Cu 5b: Cho = + 3 2
23 2x x
y x . Vi gi tr no ca x th y x( ) 2 = .
Cu 6b: Cho hnh lp phng ABCD.ABCD c cnh bng a. Xc nh ng vung gc chung v tnh khong cch ca hai ng thng cho nhau BD v BC.
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 12
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
Bi 1: Tnh cc gii hn sau:
a) n n
n
1
13 4
lim4 3
+
+ b)
x
x
x23
1 2lim
9+
Bi 2: Chng minh phng trnh x x3 3 1 0 + = c 3 nghim thuc ( )2;2 .
Bi 3: Chng minh hm s sau khng c o hm ti x 3=
x khi xf x x
khi x =
2 93( ) 3
1 3
= +
Bi 4: Tnh o hm cc hm s sau: a) y x x x2(2 1) 2= + b) y x x2.cos=
Bi 5: Cho hm s xyx
11
+=
c th (H). a) Vit phng trnh tip tuyn ca (H) ti A(2; 3). b) Vit phng trnh tip tuyn ca (H) bit tip tuyn song song vi ng thng y x1 5
8= + .
Bi 6: Cho hnh chp S.ABCD c y ABCD l hnh vung cnh a, SA = a, SA vung gc vi (ABCD). Gi I, K l hnh chiu vung gc ca A ln SB, SD.
a) Chng minh cc mt bn hnh chp l cc tam gic vung. b) Chng minh: (SAC) vung gc (AIK). c) Tnh gc gia SC v (SAB). d) Tnh khong cch t A n (SBD).
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
HUYNH CH HAORectangle
1
s 13
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
Bi 1: Tnh cc gii hn sau:
a) x
x x
x
2
21
2 3 5lim
1+
b) x
x x
x
3
1
1lim
1++ +
Bi 2: Chng minh rng phng trnh x mx x m3 22 0 + = lun c nghim vi mi m.
Bi 3: Tm a hm s lin tc ti x = 1.
x x x khi x 1f x x a
x a khi x = 1
3 2 2 2( ) 3
3
+
= + +
Bi 4: Tnh o hm ca cc hm s:
a) y xx x x2 42 3 1
3 1= + + + b) x xyx x
cossin
= +
Bi 5: Cho ng cong (C): y x x3 23 2= + . Vit phng trnh tip tuyn ca (C): a) Ti im c honh bng 2. b) Bit tip tuyn vung gc ng thng y x1 1
3= + .
Bi 6: Cho hnh chp S.ABCD c y ABCD l hnh thoi tm O cnh a, aOB 33
= , SO ABCD( ) ,
SB a= . a) Chng minh: SAC vung v SC vung gc vi BD. b) Chng minh: SAD SAB SCB SCD( ) ( ), ( ) ( ). c) Tnh khong cch gia SA v BD.
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .
1
s 14
N TP HC K 2 Nm hc 2013-2014 Mn TON Lp 11
Thi gian lm bi 90 pht
Bi 1: Tnh cc gii hn sau:
a) ( )x
x x x2lim 3 2
+ b) ( )x
x x x2lim 4 1 2+
+ +
Bi 2: Chng minh rng phng trnh x x32 10 7 0 = c t nht hai nghim.
Bi 3: Tm m hm s sau lin tc ti x = 1
x khi xf x x
mx khi x
2 11( ) 1
2 1
<
= + +
Bi 4: Tnh o hm ca cc hm s sau:
a) xyx
3 2
2 5
=
+ b) y x x x2( 3 1).sin= +
Bi 5: Vit phng trnh tip tuyn ca th hm s yx
1= :
a) Ti im c tung bng 12
.
b) Bit tip tuyn song song vi ng thng y x4 3= + .
Bi 6: Cho t din S.ABC c ABC u cnh a, SA ABC SA a3( ),2
= . Gi I l trung im BC.
a) Chng minh: (SBC) vung gc (SAI). b) Tnh khong cch t A n (SBC). c) Tnh gc gia (SBC) v (ABC).
--------------------Ht------------------- H v tn th sinh: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SBD :. . . . . . . . . .