39 tuyển chọn để thử sức học kỳ môn tóan nâng cao 10 bắc trung nam

510.76
T527C
PHAM TRONG THlT
Chuyen Nguyen Quang Dieu
-
Dong Thap)
uyen
chon
di thvc svcc hoc ky
I
FHAM
TRONG
THU
(GV
THPT
Chuyen
Nguyen
Quang Dieu - Dong
lhap)
uyen cnon
di
thic
sue hoc
ky
^^Wl
^^^^ w
MON TOAM
f
NANG
CAO
BAC-TRUNG-NAM^

Danh
chohocsinh
Idp 10
chuffng
trinh
ndng
cao
On
tap vd
nang
cao
ki
nojig
lam bai
•
HiJ V;EN 'um\
I
ffiG
NHA
XUAT BAN
fiAI
HOr OlinC GIA HA NOI
NHA
xufifT
BAN
Dfli
HOC
oud'c
Gin Ndl
16

Hdng
Chuoi - Hai Bd TrUng - Hd Npi
Dien
thoai
: Bien tap - Che ban: (04)
39714896;
Hdnh
chinh:
(04)
39714899;
Tong
bien
tap: (04)
39714897
Fox:
(04)
39714899
Chiu
trdch
nhi^m
xuat
ban
Gidm
doc - Tong
bien
tap : TS. PHAM TH!
TRAM
Biin
tdp THANH HOA
Che ban :

CONG
TY KHANG
VIET
Trinh bay bia
CONG
TY KHANG
VIET
Tong
phdt
hdnh
vd doi tdc
lien
ket
xuat
ban:
{
5
\G TV
TNHH
MTV
1 D!CH Vg VAN HOA KHANG VIET
f
Dja
Chi:
71
Oinh
Tien Hoang - P.Da Kao - Q.1 - TP.HCM ^
Dien
thoai:
08.

39115694
-
39105797
-
39111969
-
39111968
Fax:
08 3911
0880
Email:

\ Website: www.nhasachkhangviet.vn ^
SACH
LIEN KET
TUYEN
CHQN
39 DE THI
THLf
SL/C HQC KJ MON
TOAN
10
NANG
CAP
Ma so: 1L-113DH2013
In 2.000 cuon, kho 16x24 cm i' '
Tai:
Cty TNHH MTV IN AN MAI THjNH DL/C
Dia chi; 71, Kha Van Can, P. Hiep Binh Chanh, Q. Thu Dufc, TP. Ho Chi Minh
So xuat b^n: 420 - 201

3/CXB/03
- 58/DHQGHN ngay
03/04/201
3.
Quyet
dinh
xuat b^n so: 337LK-TN/QD-NXBDHQGHN, cap ngay 31/07/2013
In
xong
va nop JOu chieu quy IV nam 201 3
Md^i
iidi itdn
B6
sach
rfVE/V
CHON 39 DE
THLf
SL/C HOC KI MON TOAN I6p
1
0,
11 va 12
nang
cao dirac bien
soan
va tuycn chon diTa trcn noi dung chiTcIng
trinh
THPT
hicMi hiinh; bo
sach
toan niiy giup cac cm c6 dieu kicn lam qucn \6'\

cac
dang
dc thi hoc ki cf
muTc
do cao.
Ricng
cuon 12 co them phan phu luc giup
cac cm tif kiem tra, danh gia, bd
sung
kie'n thtfc ve toan
THPT
cho minh nham
tao ncn toan can ban vffng chitc cho cac cm
\i\S6c
khi chinh thtjTc
bU'dc
vao ki thi
Dai hoc, Cao
dang.
Hi
vong
bo
sach
sc gop phiin giiip cac em dat kct qua cao trong cac ki thi,
dong thcJi la mot
cong
cu hd trd cho cac bac phu huynh giiip cho con em hoc tap
tot
h(<n.
Trong qua

trinh
bien
soan,
d\x tac gia dfi cdgiing nhiTng cuon
sach
van co the
con
nhiJng
khiem khuyct
ngoai
y muo'n.
Chung
tdi
ni't
mong nhan di/dc sif gop y
chan
thanh ciia cac thiiy, co
giao,
cac em hoc sinh dc trong hln tai ban sau
sach
dUcJc
hoan
chinh hdn.
Tac gia
rii't
cam dn Nh;i xuii't ban Dai hoc
Qudc
gia Ha Noi,
Cong
ty TNHH

MTV DVVH
Khang
Vict da dong vicn, khuycn khich vii tao moi dieu kien de
cud^n
sach
nay st'lm den tay ban doc.
Website:
phamtronglhu.com.vn
Tac gia
PHAM
TRQNG
THLf
Kf
HIEU
DIJNG TRONG Bp SACH
Vectd phap luyen
VTPT
Vcctd chi ptiiTdng
VTCP
Dieu
phai chuTng minh
dpcm
Yeu
cau bai loan
YCBT
Mat phang
mp
[Jat dang thu-f
iJDT
fhUifng trinh

PT
HC'
phiftfng
Irinh
HPT
Hal
phiMng trinh
UPT
Ve
irai
VT
Ve
pha
i
VP
7 loi
khuySn
cho thi
sink
phuung
phdp
gidi
mQt
bcU
thi
Nhif
chung
ta da
bici mon Toan
la

mon hoc chic'm mot
vj
tri ra't quan trong
va
then
chot, rat
can
thiet
dc hoc cac
mon
khae
tif ticu
hoe cho
den
cac
Idp tren. Mon Toan
gitjp
cac em
nhan biet
cac
moi quan
he ve so
lifdng
va
hiiih
khong gian
cua the
gidi
hicn
Ihifc.

Niic)
do ma
ciic
em c6
phifdng phap nhan IhiJc mot
so
mat cua the' gidi xung
quanh
va
biet
each
boat dong
c6
hieu qua trong
dfli
song.
Mon Toan gop phan rat quan
trpng
trong
viee
rcn luyc'ii
phifinig
pliiip
suy
nghl, phifclng phap
suy
luan, phiTcIng phap
giai
quyct van
dc. No gop

piian phat
irien
tri thong
minh,
each
suy
nghl doc lap,
linh
boat,
sang
tao
va
vice
iilnh
thanh
cac
pham chat can thict cho
ngiTrti
lao dong nhiT can
cu,
can
than,
eo y chi
vifdt
kho khan, lam
vice
c6 kc
hoach,
eo ne
nep vii

liic
phong
khoa hoc.
Xua't phat tCf
vi
tri quan trpng ciia mon Toan, qua tlufe
te
giang
day
nhieu nam
d
cap THPT. Toi nhan lhay rang
de
hpc sinh hoe lot mon Toan thi ngoai
vice
cac
cm nam
vffng
kicn ihifc trong
sach
giiio khoa,
ky
niing
tinh
toan that tol ma con phai bie't phiTtJng
phap giai mot hai thi
nhif
liie
nao trong
lue

dang thi
dc eo
diem cao. Muon lam diWc
dieu nay tin' sinh can
phiii
tufin
thii
Iheo
cac
biTdc sau day:
1) That binh
tinh
trong luc lam bai thi.
2) Can
doe
that cham rai loan
bp de,
danh
gia
sc)
bp
dc)
de,
kho cija
cua cac
eau,
xem nhfrng can nao quen thupc,
la
vdi
minh.

3) Giai
ngay
lap tiJc
cac
eau ma ban thay de.
4) Mot vai eau can
thiel
den sir suy nghl sau h(<n, thi sinh can phai
doe ky eau
hoi,
gach
du'di eiic
gia
thiet
va yeu eau
ciia bai toan. Dinh hiTcfng
each
giai,
hinh
dung
do
phi'rc
tap ciia eiieh giai
dc c6
sir
lira
chpn diing dan.
5)
Trhih
bay bai giai thi sinh khong nen lam tat, moi biTdc ncn vic't mot dong

de de
kiem
tra,
vl
giam khao chain bai thi theo
ba
rem nen
eo
mot birdc nao do sai thi van con
diem
d
nhfrng
biftk-
bien doi diing
trifdc
do.
Cach
hay nha't
la
lam xong biTdc nao kiem
tra
bifiKc
ay de
phat hicn
ngay
cho sai.
6)
Trong qua
trinh
giai mot bai toan ne'u thi sinh

gap
kho khan giila ehiTng,
c6 the
chijfa
khoang trong trC-n giay thi
de bo
sung
sau va
nhanh chong ehuycn
sang
lam
cau
khae.
7) Khi
da
hoan ta't bai thi, neu con thCii gian thi sinh ncn doc lai bai giai
va ra
.scat
lai
cac
chi liet da
trnih
bay (thong
thirilng
cac
loi thi sinh hay
bo
sot bift'lc lam
la
tap

xac
dinh,
dieu kicn
c6
nghla ciia
can bac
ciian, ham
so
logarit, doi
can
khi dung phiTcfng
phap doi bien
de
tinh
tich
phan, loai
bo
ngiiiem ngoai
lai
trt)ng
phi/dng
trinh )
nham
hoan thicn bai thi tot h()n cho den het gid.
Nhieu
hpc tro toi
day ap
dung
7
l(1i khuyen tren

da
tn'f thanh
thii
khoa dai hpc
cua
nhieu
trirclng,
nhiTng thanh cong nha't
la
loi
ed
hoc tro
thii
khoa "kep" khoi
A va B
ciia
trirdng
Dai hpc Khoa hpc Tif nhien TP. HCM
va
Dai hpc
Y
DiTdc TP. HCM nam 2011.
Chuc
cac
thi sinh dat kel qua cao trong
cac
ki thi
PHAM
TRQNG THI/
Bp

BE
THfir
Sljrc
HQC KI MON
TOAN
LdfP
10
A. BO BE
THUf
sure HQC KI
I
MON
TOAN
LtfP
10
DE
SO 1
DE
THlIr
SllTC
HOC
KI
I
MON
TOAN
L6P
10
Thdi
gian
lam

bai:
90
phut
Cau
I. (1,0
diem)
Cho hai
tap
hdp
P =
|x
e K
I
|x
-
2|
< 3|,
Q =
|x
e II
x
+ 2
>4
1.
Viet
cac tap
hdp
P va Q
diTdti
dang

khoang,
doan,
ntj'a
khoang
hay
hctp
cija
cac
khoang,
doan,
nihi
khoang.
Bicu
dicn
cac tap
hdp
nay
tren
trijc
so.
2.
Chiang
minh
rang
Cj^CPnQ)
=
C^PuCj^Q.
Cau
11.(2,0
diem)

J
1.
Vcdothi
y =
-x~+4x-3.
2. Tim
m dc
phiTitng
trinh
x^ - 4 x + m = Oco it
nha't
ba
nghicm.
C-duUL(2,0diem)
1.
Cho
phifcfng
irinh
(m -
l)x~
-
2(m
+ l)x + m - 2 = 0 (1).
Tim
cac gia tn
nguycn
cua m dc
phiTcJng
Irinh
(1) c6 hai

nghicm
phsln
biet
x,,
X2sao
cho
tdng
X|
+
Xj
la
Ciic
so'
nguycn.
2.
Giai
va
bien
hian
phiTdng
trinh
-—— + ^ = 2
•
X
-2 X
tamG
,M
la
trung
diem

BC.
Di/dng
tron
ngoai
ticp
tam
giac
ABC cat
Cau IV.
(2,0
diem)
1.
Trong
mat
phang
Oxy cho tam
giac
ABC c6
A(-2;
1), B(l; 3),
trong
I
\
difclng
lhang
AM
lai E.
Tim
loa do
diem

E. V
1
Mu-
1 »r,^ ~
cosA
cosB
cosC
a ^
2.
Nhan
dang
tam
giac
ABC
thoa
man + + = — ( )•
a
b c be
Cau\.
(2,0
diem)
1.
Giai
phirong
irinh
X/4-3N/10-3T =
X
-2 . * i
^
, j

2. Tim
gia
tri nho
nha't
ciia
y = x +
—^— (voi
x >
3 ).
i
•'.•->
J,
X
-
3
•
Cfiu
VI.
(1,0
diem)
Cho tam giac ABC vuong tai A coAB = 3, AC = 4 va
Irung
tuycn AD. Tim
diem
E e AC sao cho BE 1
AD.
DAP
AN
THAM
KHAO

Cau
Dap an
I
(1,0
diem)
1. (0,5
diem)
Vie't cac tap hi/p P va Q
Axidi
dan^ khoang, doan
Taco x-2 <3c:>-3<x-2<3o-l<x<5. Vay P =
|-l;
5|.
Tifdng
tir
x
+ 2
>
4
<=>
X + 2 < -4
X + 2 > 4
Vay
Q =
(-a);-6)u(2;+<z5).
X < -6
x>2
-6
J.
P

Q
2,
(0,5diem)
Chxin^ minh rilns C^(PnQ) =
CjjPuCjjQ.
•
Taco PnQ =
(2;51
=>Cp,(PnQ) =
(-oo;2]u(5;+oo).
.Cg^P =
(-<x.;-l)u(5;+«);
C.^Q = !-6; 2]
=^C.:jPuC3^Q =
(-c»;2|u(5;+«).
Viiy
C.^(PnQ) = C5^PuCr.Q.
II
(2,0
diem
)
1. (1,0
diem)
Ve do thj y = -x^ + 4x -
3
(doc
giii
tif
giai).
2. (1,0

diem)
Tim m de phii'ofng trinh
1
/
-2 -l\
y
= 111 - 3/ \
/
•
'
-3
Ta
CO x~ -4
+
m = 0 o -x~ + 4
-3-m-3
PhiTitng
trinh
trcn
lii
PT hoaiih do giao diem
ciia
do thi
hiim
so
4
III
(2,0
diem)
y = -x^ + 4 x -3 va diTdng

thiing
y = m - 3.
+
Hiim
so y = -x^ + 4 x -3 la
hiim
so' chSn ncn do thi do'i
xifng
qua true tung. Khi x>0 thi ham so' trd thanh
y = -x^ + 4x -3. Do do do thj
ciia
ham so y = -x^ + 4 x - 3
bao gom
philn
do thj ham so y = -x~ + 4x -3 d ben phai true
tung
vii
phan do'i xiJng
ciia
no qua true tung.
-^^M.'-
;
V
\
Thco do thi, phiTdng
trinh
dii cho c6 it nhat ba nghiem khi v&
chi khi -3 < m - 3 <
1
<=> 0 < iTi< 4.

1. (1,0
diem)
Txm cac gia trj nguyen cua m
Phu'dng
trinh
da cho co hai nghiem phan biet khi va chi khi
m
^ !
](*)•
m
-
1
;t 0
A'
= 5m-1 >0
m
> -
5
Ta
CO X| + X, =
2(m
+ l)
m-1
=
2
+
-
m-l
De tong X| +
X2

la so
nguyen
thi
dieu
kien
can vii dii la m-1
lii
iTc'k-
ciia
4. Co cac
Iri/cJng
hdp:
«
m-1
=::±1.
m-1 =
±2.
m-1 ^±4.
•
Giiii
ciic
triTdng
hdp
tren
vii
ket hdp
dieu
kien
ta
difde

me
{2;
3; s}.
2. (1,0
diem)
Giai
va
hiC'n
luan phif(/ng trinh
Dieu
kiC-n
<
X ^ 2
X ^0'
VcTi
dieu kien do PT da cho
tiTdng
diTdng (m
+1
)x = 6 (*)
»Vdi
m = -1 thi (*)
VP
nghiem nen PT da cho v6 nghiem.
6
m
+
1
iWvri'-V'J'
'

Vdi
m ^ -1 thi
CO
nghiem x =
PhUdng
irinh
da cho c6 nghiem treno
^2 • " ^
6
m
+1
^0
Ket
luiin:
m
= -1 hay m = 2
:
PhU'Ong
trinh
dii
cho v6 nghiem.
m
^ -1 va m 2: PhMng
Irinh
da cho c6 nghicm x =
m
+1
IV
(2,0
diem)

1.
(1,0 diem) 'Vim to a do diem E.
G lii Irong lam cua lam
giac
ABC ncn
Xj
=3X(, -(x^
+X3)
= 3.^-(-2 +
l)==2
yc=3yG-(yA+yB)=3J-(i+3)=-3
•C(2; -3).
(3 '
( 7 ^
f
3 1
-; 0
U
;
, MA = —; 1 . ME =
XE-:^;
yE
V
/
-; 0
U
;
XE-:^;
yE
V

/
• Ta CO M
7 21 • • 1-2 37
MA.ME
= —x +y,. +— va MB.MC = —BC =
2 4 4 4
, . , fMA.ME = MB.MC
Mai
khac
\
[MA
cung phi/dng ME
7
2
7 21 37
Xc + Vc + =
E
-' E 4 A
''E
3
2
_
7
2
209
—
h
53
37
yE

53
<=>
\
1
Vay E
7 58 ^
-2^E
+
yE+y=o
2xp +
7yp=3
209 37'
^53' 53
J
2. (7,0 diem) Nhan dan^ tarn
giac
Ta
CO
(*)«
bccosA
+
accosB
+
abcosC
= (**)
Tir a- - b- + c^ -
2bccosA
^
bccosA
= ^(b^ + c^ - ) (1)

TiTdng liT:
accosB
- ^(a- + c^ - b") (2);
abcosC
= ^(a^ + b" - c") (3)
The (1), (2) va (3) vao (**) va nil gon la diTdc:
b" + c" = a"
c::>
AABC vuong lai A.
6
V
1.
(1,0 diem) Giai
phtfc/nj?
trinh
(2,0
diem)
PhiTclng
irinh
da cho liTOng diTdng
74 10
— <x< —
27 3
0,5
4-3V 10-3x =(x-
74 10
— <x< —
27 3
74 10
— <x< —

27 3
• » «f
3Vl()-3x
=4x
-)
- X'
<=>
74 10
— <x < —
27 3
<=>'
9(10~3x)
= (4x
74 10
— <x < —
27 3
-x^r
0,25
x-^-SxVlfix
2
+
27x-90
= 0
o
<
74 10
— <x < —
27 3
(x-3)(x
+ 2)(x^ -7x + i5)-0 ("=)

Vc'Ji
74 10 .
— <x <— va
27 3
X- -7x + 15-
( 7^
X — +
—>0,VxeR.
4
0,25
Nc-n
(*)<=>
X = 3 . Vay phirong
trinh
c6 mol nghicm x =
3.
2. (1,0 diem) Tim jjia
tr
j nho
nha't
ciia
Ta CO y = X - 3 + -
X
1
-+3.
3
0,25
Ap
dung BDT
Co-si

ta c6: y > 2 j(x - 3)
•
—+ 3 = 5.
V x-3
0,5
Vay miny = y(4) = 5
0,25
VI
'llni
diem K
(1,0
diem)
• Ta
CO
AD.BE = -
'•
•(
AB
+AC)(AE
-AB)
i*J <i •
(1,0
diem)
2
1
2
f
• . -2
AB.AE-AB
+ AC.AE-AC.AB

0,5
Ma
ABl
AE
ABIAC
AB.AE-O
AB.AC = 0
0,25
Ncn
AD.BE
= ^(AE.AC-AB^).
.
Ma AD 1 BE
AD.BE
= 0 o AE.AC = AB^ => AE = - •
4
0,25
DE SO 2
DE
THCT
SOC HOC Ki I MON TOAN LdP 10
Thdi
gian lam bai: 90 phut
Caul.
f7,tf^/t'//ijCho lap
help
S -
{l;
2; 3; 4; 5; 6}. j
1.

Tim lap hop con A, B ciia S sao cho A u B
|l;
2; 3; 4|, A n B =
|l;
2 •
2. Tim cac lap C sao cho Cu(AnB) = AuB.
CSu
II.
(2,0
diem)
1.
Ve do ihj y = 3x + 4.
2. Xac djnh a, c dc do ihi ham so y = ax- -4x + c di qua hai diem
A(l;-3),
B(2;5).
3. Xac dinh
giao
diem cua hai do ihi
Ircn.
Cau
III. (2,0
diem)
1.
Giiii
phifiJng Irinh yjl-x' +x\J\ 5 = ^3 - 2x - x
2.
Giiii
va bicn luan phifdng Irinh m^x - m~ - 4 = 4m(x - 1).
Cau
IV. (2,0

diem).
Trong
mill
phdng
Oxy, Um diem M biel:
1.
MNPQ la hinh binh
hanh
vdi N(2; 3), P(-6; -3), Q(l; 8).
1
2. M
ihuoc
inic
hoanh
va gck giiJa hai
vecld
MA, MB la 135" vdi cac Ipa
do ciia
diem
A(4; - 3), B(3; 1).
Cau
V. (2,0
diem)
1.
Giai he phiTdng Irinh
x^y(l
+ y) + x-y-(2 + y) + xy^ -30 = 0
x"y+
x(l + y+ y") + y-l
1

= 0.
1
1
2. Cho a, b la hai so
dUdng.
Chiang
minh a" + b~ + - + - > 2(\/a + >Jb).
a b
C'Au\l.
(1,0
diem)
Cho lam giiic ABC c6 A = 120", AB.AC =-6 va AM.BC =-16 (vdi M la
irung diem ciia BC). Tinh do dai cac
canh
AB va AC.
8
DAP
AN THAM KHAO
Cau
Dap an
Diem
I
(1,0
diem)
1. (0,5
diem)
Tini tap hop con A, B ciia S sao
cho
Tir
AuB = |i; 2; 3; 4| suy ra hai ph;1n liV 3 vii 4 phai Ihuoc

mpl
vii chi mol
irong
hai lap A va B. Do do c6 bon kel qua
sau:
A
=
{1;
2; 3|
A
=
{1;
2; 4}
A
=
{l;
2; 3; 4}
A
= jU 2)
B
=
{l;
2; 4)'
B
=
{l;
2; 3) '
B
= {,;2| •
B

=
{l;
2; 3; 4
2.
(0,5diem)
Tm cac tap C sao cho Cu{AnB) = AuB.
ViCu(AnB)
= AuB ma AuB =
jl;
2; 3; 4},AnB =
{l;
2}
ncn 3, 4 € C. Do do cac lap C Ihoa man yeu cau bai
loan
la:
{3;
4}, {l; 3; 4}, {2; 3; 4},
{l;
2; 3; 4}.
0,5
II
(2,0
diem)
1. (0,5
diem)
Ve do thj y = 3x + 4 (doc gia liT
giiii).
2. (0,5
diem)
Xac

dinh
a, c de do thj ham so'
Vi
do Ihi da cho di qua hai
diem
A(l: -3), B(2; 5) ncn
-3 = a-4 + c a + c = l [a = 4
5 = 4a-8 + c 4a + c = i3 [c = -3
3. (1,0
diem)
Xac djnh jjiao
diem
ciia hai do thj
tren
Toa do
giao
diem ciia hai do ihj IrC-n la
nghiem
ciia he
jy
= 4x 4x-3^l3x + 4 =
4x~-4x-3
y
= 3x + 4 [y = 3x + 4
X
=•
4x -7x-7 =
{)
y
= 3x + 4

X = •
7 + N/I6T
8
y
= 3x + 4
7 +
>/l6i
X
=
X
=
OS
y
=
-
53
+
3V16T
hoac
y
=
•
7-V16I
8
53-37161
9
Vay
giao
diem
ciia

hai do
Ihj ircn lii
[7
+
7I6I
53 +
3V16I
]
[7-Vl61_
53-3VI6I
8 ' 8 ' 8 ' 8
0,25
Ill
(2,0
diem)
1. (1,0 diem)
Giai
phiidnn
trinh
Ill
(2,0
diem)
Die
11 kiC-n
<
3
- 2x -
x^
> 0
7-X2+XN/X

+ 5>0 (1)
x
+ 5>0
0,25
Ill
(2,0
diem)
Khi
do PT da cho tn^
lhanh
7-x- + x\/x +
5=3-2x-x-
<=>
xVx
+ 5
=-4-2x
0,25
Ill
(2,0
diem)
<=>
<
x(-4-2x)>0 [-2<x<0
x-(x
+ 5) =
(-4-2x)- [x-^
+ x-
-16x-16
= 0
0,25

Ill
(2,0
diem)
<=>
1
Vaj
-2<x
<0
^
<=>
X
-I
(ihoa
man (1)).
(x
+
i)(x 16)
= 0
/
phifdng trinh
da cho c6
nghiem
x -1.
0,25
Ill
(2,0
diem)
2.
(1,0 diem)
Giai

va
bien
luan
phUc/ng
trinh

Ill
(2,0
diem)
Ta
CO
nr^x - - 4 =
4ni(x
- 1)
<=>
m(m -
2)(m
+ 2)x =
(m
-
2)"^
0,25
Ill
(2,0
diem)
•
m ±2 va m ^0 ihi PT da
cho
c6
nghic

m
x = —•
m(m
+ 2)
0,25
Ill
(2,0
diem)
•
Vc'ii
m = -2 hoac m = 0 ihi PT da cho v6
nghicm.
0,25
Ill
(2,0
diem)
•
Vdi m = 2
Ihi
PT da cho c6
nghicMii
liiy
y.
0,25
IV
(2,0
diem)
1. (1,0 diem) T\m
toa
do

diem
M
IV
(2,0
diem)
Goi
M(x;y)e{Oxy).Tac6
PN =
(8;
6), PQ = (7; 11) la hai
vccld
khong ciing phifdng
iiC-n
ba
diem
N, P, Q
khong
lhang
hang.
0,25
IV
(2,0
diem)
MNPQ
la
hinh binh
hanh
<=>
NM = PQ
0,5

IV
(2,0
diem)
fx
-9
«(x-2;
y-3)-(7;
1
Do^ • Vay
M(9;
14).
[y
= 14
0,25
IV
(2,0
diem)
2.
(1,0 diem) Tim toa do
diem
M
IV
(2,0
diem)
Taco
MA-(4-x;
-3),
MB
=
(3-x;

1)
0,5
Theogia
lhietcosl35" =cos(MA, MB)
=
MA.MB
MA
MB
(4-x)(3-x)-3
-
V(4-x)-+(-3)-V(3-x)2+l2
•
n
''if
o 2(-x-'
+ 7x - 9) =
yj2(\-
- 8x +
25)(x-^
- 6x + 10) (*)
DieiikiC-n
- x" + 7x-9 > 0 (I)
(='^)c:>x"^ -14x-^+
51x-~22x-88
= 0
•o
(X -
4)(x
+
l)(x-

-
11X
+ 22) - 0
<=>
X
=
4,
X = -1
1
1±
V33-
X
=
So
dic3u kien
(1)
chon
x = 4, x =
-N/33
Vay M,(4;
0), M,
V
(2,0
diem)
1. (1,0 diem)
Giai
he
phiTc/ns
trinh
He phifting

liinh
da cho
tiftJng
dufcJng
xy(x
+
y)"' +x"y"(x
+ y) = 3()
xy(x
+ y) + xy + X + y
1
1
<=>
i
xy(x
+
y)(x
+ y +
xy)
= 30
xy(x
+
y)
+ xy + x + y = ll
X
+ y = 11 . T
Dal
<!
,
dieu kien

u" > 4v, HPT
Iren
lai
thanh
xy
= v
iivdi
+
V)
= 30
<=>
i
uv(ll-iiv)
= 30 (1)
uv
+ 11 + v =
11
uv + 11 + V =
11
(2)
.Tir(l):
uv
= 5
uv
= 6
•
Vdi uv = 5 u +
V
= 6.
Giai trifttng hrtp

nay HPT dii cho c6
,
,
f5-V2l
5
+
N/2TV5
+
N/2T
nghicni
(x; y) =
•
Vdi uv = 6 => u +
V
=
5.Giai Irifctng
hdp nay HPT da cho c6
nghiem (x;y)
=
(l;
2),(2; 1).
Vay HPT da cho c6
nghiem
(x; y)
la
(1;
2),(2;
1),
5-y[2\ + V2T
5

+ V2T 5-x/2T'
11
2. (1,0 diem)
Chrfn};
minh
Ap
dung BDT Co-si ta c6:
a-+l>2l 1=27:^(1),
h'-^'->2.\^-=24^(2)
a V a b V b
Cong (1) va (2) thco vc
siiy
ra Jpcm.
Diing
lliifc
xay ra khi va chi' khi a = b = 1.
0,5
0,25
0,25
VI
(1,0
diem)
Tinh
do dai cac canh Ali va AC.
•AB.AC
= -6 => AB.AC.cos 120" - -6
AB.AC.
1
=
-6=i>

AB.AC
= 12
(I)
•AM.BC
= -16
-(AB+AC).(AB
- AC) = -16
=^ AB"
-
AC"
= -32 =>
AB-
-
AC"
- -32 (2)
TCrd).
(2)
siiy
ra AB'^ +
32AB-
- 144 = 0 => AB" =4
i=>
AB = 2 va AC = 6.
0,25
0,25
0,5
DE
SO 3
DE
THLT

SCrC
HOC KI I MON TOAN L6P 10
Thdi
gian lam bai: 90 phut
CSu
I. (1,0 diem). Cho lap hc.tp A = {x e /J |x| < s}, B = jx e Z19 < <
26}.
Xac
dinh
cac lap help A n B, A w B, A \, B \.
CSu II.
(2,0 diem)
1.
Xac dinh cac he so'
ciia
parabol y = ax- + bx
-3bicl
rang parabol di qua
diem
A(5; - S) va c6 Iruc do'i xiJng x = 2. Vc parabol tim dU'dc.
2.
Cho parabol (P): y = x"^-4x + 3. Xac dinh m dc (P) va diTdng th^ng
d:
y = mx - m^ + 12 cal nhaii tai 2 diem c6
hoiinh
do
trai
dau.
Cau III.
(2,0 diem)

1. Giiii
phu'dng
Irinh
V3x^
+X-1=2
^7 ^
—
X
1
4 + (m + 2)x
2. Giiii
va bien luan phiTdng
trinh
= ni - 1.
3-2x
Cau
IV. (2,0 diem).
Trong
mal phring Oxy cho tam giac ABC c6
A(2;
1), B(l; 3), C (-
1.
Tim loa do Irong lam G
ciia
lam giac ABC.
2.
Tim loa do
Irirc
lam H
ciia

lam giac ABC.
CSu
V. (2,0 diem)
0).
1. Giiii
he phifctng
Irinh
x"
+ y- + xy = 7
x-+y-+x
+ y= 8
2.
Cho cac so' difdng x, y, /. Ihoa man x + y + / = 1. Chifng minh:
^2x"
+ xy + 2y- + ^2y- + y/ +
2/.~
+ ^2/~ + /x + 2x- > 75. , ,,.
Cau VI.
(1,0 diem) Cho hinh binh hanh
ABCD.
Goi M la diem
liiy
y.
Chu-ngminh
MA.MC
-
MB.MD
=
BA.BC.
Ml

DAP AN THAM KHAO
•V
;
Cau Dap
an
Diem
I
(1,0
diem)
Xac
djnh cac tap h(/p
I
(1,0
diem)
Ta
CO x < 5 -5 < x < 5.
Vi
X nguycn nen
A-|-4;
-3; -2; -1; 0; 1; 2; 3; 4}.
0,25
I
(1,0
diem)
Ta
CO 9 < x" < 26 o 3 < X <
N/26. Vi
x nguycn nen
B-j-5;
-4; -3; 3; 4; s}.

0,25
I
(1,0
diem)
AnB
= {-4; -3; 3; 4}.
AuB
= |-5; -4; -3; -2; -1; 0; 1; 2; 3; 4; 5J.
0,25
I
(1,0
diem)
A\
=
j-2;
-1; 0; 1; 2J.
B\
= {-5; 5}.
0,25
II
(2,0
diem
)
1. (1,0 diem) Xac djnh cac he .so'ciia parabol
II
(2,0
diem
)
Vi
do ihi da cho di qua diem A(5; -8) nen

-8 = 25a + 5b-3 o 25a + 5b = -5 (I)
Mat
khac
(P) c6 true doi
xifng
x = 2 nC-n -— = 2(2) ' '
2a
0,25
II
(2,0
diem
)
Tir
(1) va (2) suy ra a =
-1;
b = 4.
0,25
II
(2,0
diem
)
Ve
y = -x- +4x-3(docgia tif
giiii).
0,5
2.
(1,0 diem)
Xac dinh
m de
(P)

va
di/tfns
thang
Phifdng innh hoiinh
do
giao
diem
cua
(P)
va
6\i(1ng thilng
d la
X-
-4x +
3 =
mx-m^
+12<=>x^
-(4 +
m)x
+
m^
-9 = 0.
0,5
Parabol
(P)
vii during
thang
d cat
nhau
tai 2

diem
c6
hoanh
do
mi
i
da'u
ichi
vii chi khi
-
9 <
0
<=>
-3
<
m< 3.
0,5
Ill
1.
(1,0 diem)
Giai
phU"(/njj trinh
(2,0
diem
)
Bicn
doi phi/dng
Irinh
vc
dang

73x^ + x -
1
=
7
-
3x^
- x
(1)
0,25
(2,0
diem
)
Diit
u =
VJX"
+
X
-1.
Khi
do u > 0
vii
3x^
+ x =
u~
+
1
Phu-dng
trinh (1) tnl
ihiinh
u~

+
ii
-
6
=
0.
0,25
Phirdng trinh Iron
c6
nghicm
u =
2 (thoa man)
vii
u =
-3 (loai).
0,25
Vc1i
u =
2tac6
\/3x^+x-l
=
2<=>3x^+x-5
= 0
-l±76i
<=>
x =
6
-l±76i
<=>
x =

6
0,25
^
f-l-^/6T
-\
^l6\
Vay
phifcJng trmh
co tap
ngnicm
S-< ;
[6
6 J
2.
(1,0 diem)
Giai
va
bien
luan
phifc/ng
trinh

Vc'Ji
X
^
phifdng trinh
da cho
Ird lhanh 3mx
=
3m

-
7.
0,25
•
Vc'Ji m ^ 0 ihi
x =
—^
•
Nghicm
thoa
man dieu kicn khi
3m
3
3m-7 3 ^ „ 14
X
9^-<=>
^-o6m-14?t9mc:>m^
2
3m 2 3
0,25
•
Vdi m
= 0
thi Ox
=
-7:
Phi/dng trinh
v6
nghicm.
0,25

Kc't
luan:
14
•
Vdi
ni
—— vii m
5^0
thi phifdng trinh
da cho c6
nghicm
,
,
3m
-
7
duy
nhat
x =
3m
0,25
14
•
V(1fi m
=
hoiic
ill
- 0
thi phifdng trinh
da cho v6

nghicm.
1/1
IV
(2,0
diem)
1.
(0,5 diem)
Tini
toa do
tnin;; tam
G
ciia tam
giac
ABC.
Toa
do
Irong
tam
G
ciia tam
giac
ABC
lii
Xr:
=
XA,
+
X|j
+
Xp

_
2 +
1
-1 _ 2
3
~ 3 ~ 3
YA+yti+yc
_' + 3 + 0 4
•Viiy
G
2
4
3'
3
0,5
3 3
2. (1,5 diem)
Tim
toa do
diem
trifc tam
H
cua tam
giac
ABC
Goi
H(x; y)e(Oxy)
AH
=
(x-2;y-l),

BC
=
{-2;
-3)
BH=(x-I;y-3),
AC
=
(-3; -1).
H
la
triTc tam ciia tam
giac
ABC
ncn la c6:
AH
J_BC
BHIAC
AH.BC
=
()
BH.AC
= 0
<=>
i
-2(x-2)-3(y-l)
=
() [2x
+
3y
= 7

<=>
i
-3(x-l)-l(y-3)
= 0
[3x
+ y = 6
1
1
7
9
y
=
-
7
(2,0
diem)
Vay;
H
n
9
I
7 ' 7;
1.
(1,25 diem)
Giai
hy
phififng
trinh
^
S = X + y

T
Dat
<^
vdiS' >4P(*)
P = xy
He phiTcfng trinh
da cho
tret thiinh
-
P = 7
(1)
S 2P + S = 8
(2)
Tir
(1)
va
(2)
suy ra S" -
S
- 6 = 0 S =
3
hoac
S =
-2.
•
Vdi
S = 3 P = 2
(thoa man (*)).
Liic
do ta cd

X
+y
=3
X
= [
a
cd
<!
o
<^
hoiic <^
lxy
=
2
y
=
2
x
= 2
y
= l •
Vdi
S = -2 P = -3
(thoa man (*)).
X
+ y =
-2
J
X
= 1

Liic
do ta cd
a
CO
<
[xy
=
-3
<=>
y
=
-3
hoac
•
x
=
-3
y
= l
.q
!("(>
Vily
he da
cho
cd
bo'n nghicm (x;
y)
lii
(1;
2), (2; 1),

(1;
-3),
(-3;
1).
0,5
0,25
0,5
0,25
0,25
0,25
0,25
0,25
0,25
15
TnTGn
Chon UH
IIIU
KUL'
liyi
M
MIUII
lUdll
inp 'n i-j,ing - l
IHIIIT
riTng-
VI
diem)
2.
(«,75
<fi^'/n>

Chufng niinh
Ta CO 4(2x- + xy + 2y') = 5(x + y)" +3(x -yr >5(x + y)^
Do
CO
X, y > Oncn
yj2x~
+\y + 2y'^ > —(x + y) (1)
TiTdngtir
72y' + + 2z" > ^(y + z) (2)
72z' +zx + 2x- >-^(z + x) (3)
Cong (1), (2), (3) theo ve' va ket
help
x + y + z =
1
suy ra
dpcm.
Dang
Ihu'c
xay ra khi vii chi khi x = y = z = ^
•
0,25
0,25
0,25
Chiing
niinh
Goi O la
tarn
cua
hinh
binh

hanh, ta c6:
M
A.MC = (OA - OM)(OC - OM)
-OA.OC-(OA + OC)OM + OM^ =OM2-OA^ (1)
TiTdng tir MB.MD^OM- - OB'
(2)
Tir(l)va (2)suy ra:
MA.MC
-
MB.N4D
= OB^ - OA" = (oB +
OA)(OB
- OA)
= CB.AB = BA.BC
(dpcm).
0,5
0,25
0,25
DE SO 4
DE
THlIr sCrC
HOC Ki I MON TOAN LOP 10
Thdi
gian
lam bai: 90
phut
Cfiu
I. (1,0
diem).
Cho so ihiTc m.

X6t
cac tap h(;p A = (3m-1; 3m + 7) va B = (-1; 1).
l.Timmdc Be A. 2. Tim m dc AnB = 0.
Cfiu
II. (2,0
diem)
1.
Xac
djnh
cac he so a, b, c cua parabol y = ax^ + bx + cbiet rang parabol di
qua
ba diem A(0; 1), B(-2; 1), C(3; 2).
2. Ve do ihi parabol (P) iJng vdi cac gia trj a, b, c vilfa tim diTctc.
Cfiu
III. (2,0 ^i/w)
1.
Giai phi/dng
Irinh
3x^ -2x-l
= X -X.
2.
Giiii
phiTdng
trinh
2x'* + - 16x^ + 3x + 2 = 0.
Cfiu
IV. (2,0
diem).
Trong mat phang Oxy cho lam
giac

ABC c6 A(2; 6),
B(-3; -4),
C(3;()).
.•
1.
Tim toa do D la chan cua dutfng phan
giac
trong cua goc A. tfy >
2. Tim Ipa do lam cua
diTdng
tron
noi tiep lam
giac
ABC.
C&u\.(2,0di^'m) h*.;
, . [x^ -y = 2x +
1
(1)
1.
Giai
he
phufdng
trinh < ^ , -
[y- -x = 2y + l (2) 'V'/ I
2.
Cho
X,
y, / lii ciic so
IhiTc
du'dng. ChiJng

minh
rang:
2^f^ l^y 2V7 ^ 1 _i_ _i_
Cau
VI. (1,0
diem)
Tim dac diem cua lam
giac
ABC thoa S^g^^ = bcsin BcosC.
DAP AN THAM KHAO
Cau
Dap an
Diem
I
(1,0
diem)
1.(0,5
diem)
Tim m
I
(1,0
diem)
Ta CO B c A <=> 3m -1 < -1 <
1
< 3m + 7
0,25
I
(1,0
diem)
lm<0

o
<^
o -2 < m < 0.
m
>-2
0,25
I
(1,0
diem)
2. (0,5
diem)
Tim m
I
(1,0
diem)
De A n B = 0 thi la c6 hai tru'(1ng hdp:
g
• 3m + 7<-lom<
3
0,25
I
(1,0
diem)
•
1
<3m - I <=> m >-•
3
8 2
Vay A n B = 0 khi m < — hoac m > -
•

3-3
0,25
II
(2,0
diem)
I.
(1,0
diem)
Xac dinh cac he S(Ya, b. c cua parabol
II
(2,0
diem)
Vi
do thi (P) di qua diem A(0; I) nen c = 1, do do phifdng
trinh
parabol (P) c6 dang y = ax^ + bx + 1.
0,25
II
(2,0
diem)
I'4a-2b
+ l = l
Vi
(P) qua B(-2; 1), C(3; 2) nen la co he
<^
[9a + 3b +
1
= 2
0,5
17

Giiii
he phiTdng
Irinh
Ircn
ta diTdc '^^JJ
^^^^J^'
0,25
2. (1,0 diem) Ve do thi (P) vlnn vtVi cac gia tri a, h, c viTa tim dtftfc.
1
-> 2
Vc y = —x~ + —X +
1
(doc gia nr giai).
^15 15 • ^
III
(2,0
diem)
1. (1,0 diem) Giai phif(/n^
trinh
18
Ta CO
3x-
-2x-l
= X~ - X <=> <
x'
- X >0
3x"
-2x -
1
= X" - X

3x"
-2x-l = -x~ +x
<=> <
x
< 0 hoac X > 1
2x-
-x-I=0 »
4x-
-3x-l=()
X
<() hoac X > 1
X
=
1
hoac X = — „
2 <^
X
-
1
hoilc X = - —
4
" 2
x
= l •
X = —
4
Vay phi/dng
trinh
da cho c6 ha nghicm x = x = 1; x =
2.

(1,0 diem) Giai phtf(Jnn trinh
Ta lhay phiTdng
trinh
da cho khong c6 nghicm x = 0 ncn la chia
hai
vc ciia phifdng
Irinh
dii cho x", la di/tfc
2 X- + —
X + —
X- + — + 3
X + —
-16
= 0 (1)
Dal
I = X + -,
X
2 1 2 ' T
>2=>r=x+ — + 2=>x+ —= r- 2
x^
x
1
PT (1) trO
lhanh
2(r - 2) + 3t - 16 = 0 hay 2l^+3l-20 = 0
<=> I = -4 hoiic I = — (ihoa man
dicu
kicn).
2
Vdi

l = -4, tc. CO X + - = -4 hay x + 4x +
1
= 0
X
Giai
phifdng
Irinh
nay la difdc
X,
=-2-N/3
X. =-2 + N/3
•
Vdil
= -,lac6 x + - = - hay 2x'- 5x + 2 = 0
2 X 2
Giai
phifdng
Irinh
nay la di/dc X3 = 2; x^ = ^.
0,25
0,5
0,25
0,25
0,25
0,25
0,25
Cty
TNHH
MTV DWH
Khang

Vi^t
Vay PT da cho c6 bon nghicm x = 2; " = ^; x = -2 ± >/3.
IV
(2,0
diem)
1. (1,0 diem)
Tini
toa do D la chan cua 6\iHnn phan giac trong
IV
(2,0
diem)
A . ^ ,
Hinh
mo la , y „
B
D C
IV
(2,0
diem)
Goi D(xu; yo)
Thco
linh
cha'l diTdng phan giac Irong, la c6:
DB_
AB_ yl(-5f+(-l{)f /125 5
0,25
IV
(2,0
diem)
DC AC

^3'+(-(,f
V45 3
c^3DB =
-5DC(*)
0,25
IV
(2,0
diem)
Tac6 3DB = 3(-3-x^; -4-y^\C
=-5(5-x^;
-y^,)
0,25
^ • ^ f-9-3xu =-25 + 5xi.
Dodo ^ ^c^-
[-12-3y,,=5yp
=2
3
0,25
Vay 0^2;
/
0,25
2. (1,0 diem) Tim toa do tarn
ciia
dxiiin^ tron noi tiep
Tam I ciia dilTlng Iron noi licp lam giac ABC
chinh
la chan
ciia
phan giac Irong g()c B Irong lam giac ABC. Goi I(x,; y,)
Thco

linh
cha'l diTttng phan giac, la c6:
|,25
lA BA 7l25 2
0,25
f
Taco
21D = 2
V
2-x,;
-^-y,j,
-IA = -(2-x,; 6-y,)
0,25
Dodo
(**)<=>•
'4-2x,=-2 + x, Jx|=2
-3-2y|=-6 + y| [y|=l
0,25
Vay 1(2; 1).
0,25
Tuyg'n
chgn 39 de
thif sifc
hqc ki mfln ToanTflp 10 Nflng cao - Phjm Trgng Thu~
(2,0
diem)
1. (1,0
diem)
Giai phifi/na trinh
Lay (1)

trCf
(2) ve
theo
vc la difdc:
X-
-y- -(x-y) = Oo(x-y)(x + y-l) = 0<=>
y
= x
y
= I -X.
Thay
vao(l)
.y
= x=>x"-3x-l = 0<=>x = .
•
y = I- x=>x-x-2=()<=>x =
-l
hoac
x = 2.
Vay he phiTcIng Irinh da cho c6
nghicm
(x; y) la
3_^ 3->/[3l f3 + ^/I3 3 + VT3^
(-1;
2), (2; -1).
2. (1,0
diem)
Chrfng minh
Ta CO <
•

3
2
x'
+y
-i
i<-l-
X
y ~ 2
A2
(1)
Tifdng lir
yU/.2
1
1
(2),
_2£_
//+x^
<1
1
1
V /
x /
(3)
Cong
vc vdi vc cua (1), (2) va (3) la c6 dicu
phai
chifng minh.
VI
(1,0
diem)

Tim
dac
diem
cua tam jjiac ABC
thoa

Ta
CO
S^y(, =
bcsin
BcosC
a be ,
o — = be.
b
a^+b^-c^
4R 2R 2ab
<=>
a^ = a^ + b" - c^
<=>
b = c.
Vay lam
giac
ABC can lai A.
DE
SO 5
DE
THLT SQC HOC KI I MON TOAN L6P 10
Thdi
gian lam bar. 90 phut
Cflu

I. (1,0
diem).
Tim tap xac djnh ciia cac hiim .so':
V4X
+ 8
x +
1
^/x
+ I X -
C&uU. (2,0
diem)
Cho hai difcfng
lhang
d|:y = mx-4va d-,:y = -mx-4.
1.
Chtfng minh
rang
vdti moi m, d, vii d^luon ciCl
nhau
lai mot diem co djnh
tren
true
lung.
2. Tim m dc lam
giac
tao thiinh bdi d,, dj va
true
hoanh
c6 dien
lich

la 8.
CSu III.
(2,0
diem)
,
1.
Cho phiTdng lrinh(m - l)x*^ + 2(m - l)x + m + 3 = 0 (1). Tim m de phiTdng
trinh
(I)
CO
hai nghicm
phan
biel x,, x,
thoa
main x^ + x^
+3X|X2
=1.
2. Giai phifcing trinh 7x + 3 =
72x"-8
+ Vv-x. ' '
CSu
IV. (2,0
diem).
Trong mat
phang
Oxy cho lam
giac
ABC c6
A(l;
-I),

B(5;
-3) va C e Oy, Irong lam G ciia tam
giac
nkm trcn Ox. ' ;
1.
Tinh loa do cac diem C, G.
2. Tinh chu vi ciia lam
giac
ABC.
Cau
V. (2,0
diem)
1.
Giai he phi/dng trinh -j " x + y-
[xy
+ x - y = -1
2. Cho a, b, c> 0 vii a + b + e = 4.Chii'ng minh
rang:
ab be ca
•
+ + < 1.
a + b + 2e 2a + b + c a + 2b + e
CauWl.
(1,0
diem)
Diem M va N
liin
lu-dt la Irong tam ciia lam
giac
ABC va A'B'C.

ChiJiigminh MN =
^(AA'+
BB'+ CC).
DAP
AN THAM KHAO
Cdu
Dap an
Diem
1. (0,5
diem)
Tim tap xac djnh ciia ham so
(1,0
diem)
—4x 4-
1
I
Ham so y - . - V3x - 5
du'dc
xac dinh khi -
Vx + 1
x + I >0
3x-5>0
<=>
{
5
3
'
([r.h
>
lift'

Vily
lap
Xiic
dinh ciia hiim so'
lii
D =
5
3
0,25
0,25
21
2.
(0,5
diem)
Tim tap xac
dinh
ciia
ham
so'
dUctc
xac
dinh
khi<
4x
+ 8>0
x-1
- x +
1
9^0
0,25

1
111
III ."^VJ
y —
x-1
-
x
+
1
dUctc
xac
dinh
khi<
4x
+ 8>0
x-1
- x +
1
9^0
0,25
[x>-2
<=>
o
x-1
^ X +
1
Vay
tap xac
dinh
ci'u

x>-2
<
•
I ham so la
D==[-2; 0)u(0;
+oo).
0,25
II
(2,0
diem)
1.
(1,0
diem)
Chitrij;
minh
ranjj
vdfi
moi m
II
(2,0
diem)
Vdi
d,: y - mx - 4 ,
khi
x = 0
ihi
y = -4.
Vdi
d,: y = -mx -4,
khi

x = 0
ihi
y = -4.
0,5
II
(2,0
diem)
Vay d|
va
djiuon
c;tt
nhau
tai
diem
A(0;
-4)nam
tren
Oy.
0,5
II
(2,0
diem)
2.
(1,0
diem)
Tim m de tam
j»iac
tao
thanh
b<lfi

II
(2,0
diem)
Ncum==:()
Ihi d|Va d-,la hai
diTclng thdng
trung
nhau,
ncn
Ox, d|
va
dTkhong
lao
lhanh
tam
giac (khong ihoa
man
YCBT).
0,25
II
(2,0
diem)
Do
do m 0 ,
giii
stir
d, cat Ox lai B
iij
cat Ox tai C
fl;

ol
vm
J
0
,
m ,
0,25
II
(2,0
diem)
DicMi
tich
lam
giac
la
S =
-OA.BC
=
4.
2
2
0
thanh:
^
8
m
16
m
0,25
II

(2,0
diem)
Thco
giii
Ihict
S = 8
<=>
—
m
-
-
8
o m = ±2. Vay m = ±2.
0,25
III
1.(1,0 diem)
Tim ni de
phifc/n}^
trinh
(1) c6 hai
nshieni
(2,0
diem)
Phu'ctng
trinh
(1) c6 hai
nghicm phan
bicl
khi
va chi

khi
m
^
1
o m <
1
(*).
A'
=
-4(m-l)>()
0,25
(2,0
diem)
Thco
dinh
li
Vi-el
la c6 x, + x^ =
-2,
XiX, = ^ •
m
-1
0,25
(2,0
diem)
Taco
xj +x^ +3X|X2 = lo(x, +X2)^ +^\^2
<z>
4 +
iH-tl

=
1
<=>
5m
-
1
=
m
-
1
<=>
m = 0
(Ihoa
man
(*))
m
-
1
0,25
Vay
m = 0.
0,25
2. (1,0
diem) Giai phifi/ng
trinh

Dicu
kicMi
<
x

+ 3>()
•
'
••.
i / 11, /
2x-8>()»4<x
<7. , ;
7-x>()
?
0,25
V('^i
dicu
kicn
trcn,
phifdng
trinh
da cho
tiTdng diTdng
x
+ 3 =
2x-8
+ 7- x +
27(2x
-8)(7-x)
o ^{2x
-8)(7-x)
=
2
0,25
o (2x -8)(7 - X) = 4 <» x- -

11X
+ 30 = 0
<=>
X = 5
hoac
x = 6.
0,25
Vay phi/(tng
trinh
da cho c6 hai
nghicm
la x = 5; x = 6.
0,25
IV
(2,0
diem)
1.
(1,0
diem) Tinh
toa do cac
diem
C, G.
IV
(2,0
diem)
Vi
G e Ox va C e Oy
ncn
toa do G{x; 0) va C(0; y).
0,25

IV
(2,0
diem)
Goi
I la
trung
diem ciia
AB:
<
X^ + Xg _ ^
^ =>I(3;
-2).
0,25
IV
(2,0
diem)
Do
linh
chii't
Irong
lam
ciia
lam
giac
ABC la
difdc
IC = 3IG
(*)
f3x-9
= -3 fx-2

(*)«(-3;
y + 2) =
3(x-3;
2)« c^^
[y
+ 2 = 6 [y = 4
0,25
IV
(2,0
diem)
Vay
G(2;()) vii C((); 4).
0,25
IV
(2,0
diem)
2. (1,0
diem) Tinh
chu vi
ciia
tam
giac ABC.
IV
(2,0
diem)
AB
=
(4; -2)^ AB
=
N/16

+ 4 =2V5.
0,25
IV
(2,0
diem)
BC
= (-5; 7) =^ BC =
V25
+ 49 = V74.
0,25
IV
(2,0
diem)
CA
=
(1; -5)=>BC
=
N/1
+ 25=V26.
0,25
IV
(2,0
diem)
Chu
vi tam
giac
ABC la AB + BC + CA = 2Vs + ^ + V26.
0,25
V
(2,0

diS'm)
1.
(1.0
diem)
Giiii
he
Dhif(/ni!
trinh
V
(2,0
diS'm)
Day
la he
chu'a
doi
xu'ng,
de
difdc
he doi
xiiTng
la dal l = -x vii
f
'*
I" + v~ + I + V = '
diTcIc
he
nhiTsau:
<^ ^ (*)
[ly
+ t + y =

1
[S
= t + y . -^^^ '
Dal
^S->4P.
•
[P-ly '
f
.
S- - 2P + S =
2
(1) •
He phifdng
trinh
trd
thanh
<
S + P = l (2)
0,25
23
Tir
(2) => P =
1
- S (3). The (3) vao (1) la
diTilc:
S-
-
2(1
- S) + S = 2
<=>

S- + 3S - 4 = 0
<=>
S = i
hoac
S = -4.
0,25
.Vc'Ji
S =
1
=> P = 0
(Ihoa
man > 4P). Luc do ta c6 he:
I
+
V
=
1
ly
= 0
t
= 0
7x
= 0
y
= l
—>
y
= l
I
=

1
x
=
-l
•
y
= 0
y
= ()
.
Vdi S = -4 => P = 5 .
Tru'dng
hdp nay vo
nghiem
vi
khong
Ihoa
man S" > 4P. Vay HPT
dii
cho c6 hai
nghiem
(x; y) la
((0; 1).(-1;
0).
2.
(1,0
diem) Chtfn^
niinh
Goi
A =

ah
he
ca
a
+
h
+ 2c 2a +
h
+ c a +
2h
+ c
Sii-dimg
BDT
_^<1
X
4-
y 4
I
X y)
,
Vx, y > 0
(doc
giti
liT chrfng minh).
^
, ah ah
Ta
CO
1
—

< —
a
+
h
+ 2c (a + c) + (c + h) 4
ah
ah
•
+ •
a
+ c c + h
(1)
Tu'cJng
lif:
he
1
<
—
2a
+
h
+ c 4
he
he
^
+
a + e
ac
a
+

2h
+ e 4
ac
ac
•
+ •
Ui
+ h
h
+ e
y
(2)
(3)
Cong
(I). (2) va (3)
iheo
ve, ta
du'ac
A < 1.
Diing
thiJc xiiy
ra
khi
va ehi
khi
a = h = c =
—
•
0,25
0,25

0,5
0,25
0,25
VI
(1,0
diem)
Chrfrij; niinh
Giii
si'r
O la
diem
bat
ki,
ta c6:
OM
= ^(OA + OB + GO, ON = ^(OA' +
OB'
+ OC)
Suy
ra ON - OM = -(OA' - OA +
OB'
-
OB
+ OC - OC)
Hay
MN = -(AA' +
BB'
+
CC').
0,5

0,25
0,25
"XtynTWFn5rrviivvFrKit3n5~vi?T~'
DE SO 6
THLT
SVSC
HOC Ki I MON
TOAN
L6P 10
Thdi
gian
lam bai: 90
phut
CSu I.
(1,0
diem)
Tim tap xac
djnh
ciia
cac
hiim
so:
1.
y = —
2. y =
-
\^
-5\ 2
x^-3x
+ 2 (-2x + 5)V^ '±^\''±:± ^

CSu II.
(2,0
diem)
I [
Xet
tinh
chan,
le
ciia
ham so y =
r(x)tiong
moi
trU'ctng
hdp
sau:
j
2.
y^
x-3
+
x
+ 3
X
1.
y =
-3x-
+2x.
Cfiu
III.
(2,0

diem)
1.
Giai
va
bien luan phifttng
trinh
m(x - 1)' + 5 = x(mx + 1).
2. Giai phu'(tng
trinh
73 + x +
Vfi
- x = 7(xT3K6 xT +
3.
,|,\ f : >
C&u
IV.
(2,0diem). Trong
mill
phang
Oxy cho A(2; 4), B(l;
1).Tinh
toa do cua
C,
D
bicl
ABCD
lii
hinh
vuong.
• .

Cau
V. (2,0
diem)
(X"+x
+
l)(y^+y
+ l) = 3_
(l-x)(l-y)
= 6
1.
Giai
he
phu'cing
trinh
1
1 2
2.
Cho ah >
1. Chiang minh
+ >
l
+
a^
1
+ b- l +
i'^^
cau
VI. (l,OdiSm)
Cho
lam

giac
ABC. Goi M lii
trung
diem
cua AB vii N
lii diem Iren canh
AC
thoa
miin
AN = AC. Goi K
lii
trung
diem ciia
MN.
Chu-ngminh
AK = -AB + -AC.
4
6
DAP AN THAM KHAO
Cdu
Dap
an
f>iem
I
(1.0
diem)
1.
(0,5
diem)
Tm\p xac

dinh
ciia
hiim
s6'
I
(1.0
diem)
H;im
so y - • —^—
du'dc
xac
dinh
khi
<
x2-3x + 2
\-\>0
X- -3x + 2^0
0,25
lUyBII
L'lHIII
jy ge
inu
sue not kl mn loAn I6p 10 N5ng cao -
Phjm
Trgng-Thu
<=>
i
X >1
X ^
1

<=>
x^2
X>1
x^2
Vay tap
Xiic
dinh
cua ham so'la
D =
(l;
2)u(2;
+00).
2.
(0,5
diem)
Tini
tap xac djnh
ciia
ham s(Y
Ha
111
so y =
x-^
-5x
+ 2
(-2x
+
5)\/x
+ 4
diWc Xiic

dinh
khi
-2x
+
5;^0
x
+
4>0
5
X ^
—
1
X >-4
Vay lap
xac
dinh
ciia ham
so la D =
5^
f5
1
-
;
-
u
—;
+00
V
2y
II

(2,0
diem)
1. C//> diem) Xet tinh ch^n, li;
ciia
ham s(Y
Tap Xiic
djnh
D = R.
Vc'ti
moi
X e D
=:>
-X e D . Ta c6
!(
-x) = -3(
-xr^
+2( -x) =
3x-^
-2x =
-(-3x-''
+2x) =
-f(x).
Vily
y -
~3x'^
+ 2x la
hiim
so Ic.
2.
(1,0

diem) Xet tinh chan, It;
ciia
ham so
Tilp
Xiic
djnh
D =
K\{0}.
Vc'ti
mpi
X e D => -X e D . Ta c6
R-x)-
-x-3
+
-x
+ 3 X + 3
+
x-3
-X
X
= l"(x).
X-3
+ X + 3
Vi)y
y =
lii ham
so
chSn.
Ill
(2,0

diem)
I.
(1,0
diem) Giai
va
hiyn luan phiTdn^
trinh
Ta
CO
ni(x
-
j)-
+5
x(mx
+
!)<=> m(x- -2x
+ l) +
5
=
x(mx
+ 1)
<=>(2m
+ l)x = m + 5.
• V('<i
111
?e
-
J-
ihi
PT

dil cho
c6
njihiC'm
x = ^ ^ •
2 2m+
1
1
9
•
Vi'ti
m = -—
ihi
Ox =
— ncn
PT
dii
cho v6
nghiem.
2.
(1,0
diem) Giai phtf<fnK
trinh
Dicu
kicn
-
3
< x < 6.
Dal
al
u =

N/3
+
X
+
V6-X
(u >
0) ihi u"
= 9 + 2^x +
3)(6-\)
u'
-9 2
Fhififng
irinh
dii cho
mil
ihiinh
ii = —-— + 3
<=>
-
2ii
- 3 = 0
=^ii
= 3.
u
=
3 Ihi
\fJ+ X + = 3o
X = -3
x=6
•

-3
< X < 6
V(3 +
x)(6-x)
=0
Viiy
phiTdng
Irinh
dii cho
c6
hai nghiem
la x =
-3;
x = 6.
IV
(2,0
diem)
Tinh
toa
do
ciia
C,
I)
GpiC(x;y).Tac6
BA =
(i;
3); BC = (x
-1;
y -1)
ABCD lii

hinh
vuong:
BA.BC
= 0
BA- =BC^
l(x-l)
+
3(y-I)
= 0 fx =
4-3y
[(x-l)-
+(y-l)-
-10
l(3-3y)- +{y-l)-
=10
<=>
i
X 4 -
3y
x
= 4
I0y 20y
= 0 [y = 0
hoiic
<
x
= -2
y
= 2 •
7VMV>«A'

I'(/P I- C(4; 0)
Taco
AB =
DCo(-l;
-3) =
(4-Xi5;
-y^)
<=> \
4-Xij=-l
. Viiy D(5;
3).
Tn((fnii lufp
2. C( -
2;
2)
Taco
AB =
DCo(-U
-3) =
(-2-X[j;
o {
Viiy
D(-l;5).
<=>
{
XD
=-1
yu-5
•
V

(2,0
diem)
1.
(1,0
diem) Giai
hy
phif(/n^
trinh
He phifcfng
Irinh
da
cho lifcing
difitng
x'^y"
+x- +y-
+xy(x
+ y) + xy + x +
y-2
= 0
l-(x
+ y) +
xy
= 6
I
}
1
<
MtP =
''"^S^^4P.
•

lP = xy
ie phU'dng trinh
(*)
Ird
lhanh
P-+ S 2P + PS
+ P + S
-
2
= 0 (1)
P
=
S + 5
(2)
"he
(2)
vao (1)
va
rut gon
lai ta
du-clc
35" +
15S
+ 18
= 0
_S
= -2
0,25
<
Vdi S

= -3=>
X +
y
=
-3
<=>
xy
=2
P
= 2 . LiJC do
X
=-1
<
hoac
[y =
-2 •
ta CO
he
phUcIng trinh
x =
-2
y=-r
0,25
.
Vdi S = -2=*P = 3.
Tril'dng
hcip
nay v6
nghicm
vi

khong
thoa
man
>4P.
Vay
HPT
da cho
c6
hai nghicm
(x; y) la
(-1; -2), (-2;
-1).
0,25
2.
(1,0 diem) Chtfng minh
BDT
da cho tiTdng diTdng
^
>
^—
l
+ a- +
b-+a^b2
1
+ ab
0,25
<=>
a- + b- -
2ab
-

ab(a-
+
b"
-
2ab) <
0
<=>(a-
+b-
-2ab)(l-ab)<()
0,5
<:5>(a-b)-(l
-ab)<()
(
dung do
(a-b)^
>()
va
ab>l)
Suy ra
BDT
diTdc chilng
minh.
0,25
VI
(1,0
diem)
Chii"ns minh VI
(1,0
diem)
Ta

CO
AK
=
^(AM
+
AN)
(vi
K
la
trung diem cua
MN)
0,5
VI
(1,0
diem)
_
1
2
-AB+-AC
2 3 J
= -AB + -AC.
4 6
0,5
28
DE
SO 7
DE
THCT
SLTC
HOC

Ki I MON
TOAN
LCJP
10
Thdi
gian
lam
bai:
90
phut
Cfiu I. (1,0 diem).
1.
Cho
cac tap hdp so
A = (-4; 5], B = ^-V2;
+ooj. Hay xac
djnh
cac tap
hdp sau va bicu dien tren true so A u
B;
A n
B;
A
\; B \.
2.
Hay tim tat
ca
cac lap con cua tap hdp
X =
|1;

2; 3|. ^, i
CSu II. (2,0 diem) Cho parabol
(P):
y = -x^ + 2x
+
3.
*
':.
1.
Lap bang bien thien va ve parabol
(P).
«• «
2.
DuTcJng thang
d:
y = 2x -1 citt
(P)
tai hai diem
A va
B. Tmi toa do A, B
va
tinh do dai doan AB.
s. '"
CliU III. (2,0 diem)
*;
1.
Cho phu^dng trinh (m
-
l)x^ + 2(m
-

4)x + m
-
5
=
0.
Tim
m de
phiTdng Irinh
CO
hai nghiC-m phan biet
x,,
X2
thoa man he ihufc
-i-
+
=
3.
xr
X2 ;
2.
Giai phiTdng trinh
x^
- 5x-13
=
X" + X + 1.
C&ul\. (2,0 diem). Trong mat phang Oxy cho A(-2;
1), B(4;
3)
va
C(-l;y)

1.
Xac dinh gia tri y de tam giac ABC vuong tai C.
2.
Xac dinh gia trj y de tam giac ABC co trong tam
G
Cfiu
\
(2,0 diem)
mx + y =
-2
2x + y = -m
. Tim
m
de
he
phu'dng trinh c6 nghicm
1.
Cho he phm^ng trinh
duy
nhat thoa man y^ =
x.
2.
Chiang minh a) (sina + cosa)" + (sina
-
cosa)^
=2.
b)
CO.S20"
+COS40"
+COS60" +

+
COS160''
+cosl8()°
=-1.
Cfiu VI. (1,0 diem)
Cho tam giac ABC. Goi A', B',
C
Ian lifdt
la
trung diem cac canh BC, CA,
AB.
ChiJ-ng minh rang AA'
+ BB' +
CC' =
0.
%
- , ' :
ffil
••••
<(it''
•
•
•
29
DAP AN
THAM KHAO
Cdu
Dap an
Diem
I

(1,0
diem)
1.
(0,5 diem) Hay xac dinh cac tslp h(/p sau
AuB = (-4; +CO); AnB =
(-N/2;
5|;A\B-(-4;
-N/2];
B\ = (5; +CO).
Doc
giii
Ui* vc hinh hicii dicn Ircn
true
so.
0,25
0,25
2. (0,5 diem) Hay
tini
tat ca cac tap con ciia tap h(/p
0,|i},{2t,{3l,{.;
2!,{2;3|.{.;
3}, {l; 2; 3
0,5
H
(2,0
diem)
1.
(1,0 diem) Lap ban^ hien thien va vc paraboi (P).
Doc
giii

tif giai.
2. (1,0 diem) Tim toa do A, B va
tinh
do dai
doan
AB.
Toa do
giao
diem A va B eua (P) va d la nghiem ciia he
-X" + 2x + 3 = 2x -
1
y = 2x -
1
X- -4 fx = +2 fx = 2 fx = -2
o
•<
c:>
<
<=>
<
hoac
y = 2x-i fy = 2x-i [y = 3
Siiyra
A(2;3);
B(-2;-5)
y = -5
Do dai AB =
J(-4)'
+(-8)"
- N/SO = 4%/?.

0,25
0,5
0,25
III
(2,0
diem)
1.(1,0
diem) Tim m de phifc/n^
trinh
co hai nghiem phan bi^L
PT da eho eo hai nghiem phan biel x,, X2 va X|X-, ^ 0
<=> <
m
-
1
;t 0
A' = -2m + 11 > 0 o
m
- 5
m
- I
•^0
m<j {*)
m
* 5
Ta c6: — += 3 o x^ + Xj =
3x^X2
X- X2
ci>{x.
+x,)^

-2x,x,
=3(x.x-,)^
'
2(m-4)^'
m-1
-2
m-5
m-1
= 3
m-5
m
-
1
o 4(m' - 8m + 16) - 2(m -5)(m - 1) = 3(m^ - 10m + 25)
<=> nr - lOm+21 = 0 <=> m = 3 (nhan)
hoac
m=7(loai).
0,25
0,25
0,25
Vay gia
iri
m can tim la m = 3.
0,25
2. (1,0 diem) Giai phif(fng
trinh

Vi
X" + X +
1

1
X + —
2
+
- > 0, Vx G R.
4
Ncn
X-
-5X-13
= X" + X +
1
o
1 ")
x~
-5x-13
= x~ + X + I
X'
-5x-13
= -(x- + X + 1)
<=>
6x = -14
2x-
-4x-12
= 0
<=>
7
X = —
3
= 1±V7
Vay phifdng

Irinh
da cho c6 ba nghicm x x =
1
±
0,25
0,25
0.25
0,25
IV
(2,0
diem)
1.
(1,25 diem) Xac dinh gia
tri
y de tam
giac
ABC vuong tai C.
Ta CO CA = (-1; 1-y); CB = (5; 3-y)
Dc tam
giac
ABC vuong tai C thi CA.CB = 0
« ( - 1).5 + (1 - y)(3 - y) = 0
<=>
y^ - 4y - 2 = 0
<:=> y = 2 ± N/6.
0,5
0,25
0,25
0,25
2. (0,75 diem) Xac djnh gia

tri
y de tam
giac
ABC c6 trung
tfim
Do G la trong lam cua AABC ncn
XA+XB+XC
yc
_yA+yB+yc
l
= -2 + 4-l
o-i =>y =
1
15 = l + 3 + y
0,25
0,5
V
(2,0
diim)
1.
(1,0 diem) Tim m de h^ phiff/ng trinh c6 nghicm
Ta CO
mx + y = -2 [(m-2)x = m-2
2x + y = -m [y = -m-2x
(*)
He (*) CO nghiem duy nhal<=> m ?t 2.
Khi
do he c6 nghicm
|x = l
[y

= -m-2
0,25
0,25
luyen
engn
jy
BB
Iw
'•Ale
hoc.
ki
man
luail \fi]}
lU NJliy lJU ^ nijiii iiyiig iiiu-
T
m + 2 = 1
Mill
kluic, y-=
X
<=>(-m -2)-=
1
»
Lm+2
= -l
'm
=
-l
(Ihoa man).
m
= -3

Vay
CO
hai gia
lii
cua m la m = -1
hoac
m = -3.
2. (1,0
diem)
ChiynK
niinh
a) Ta CO
VT
^ siira +
2sinacosa
+
cos'cx
+
sura
-
Zsinacosa
+
cos'a
=
2(sin"a +
cos~a)
= 2.
b) Vi cos2()" = cos( 180^' - 160^') = -cosl60"
cos4()"
-cosdSO"

- 140") =-cosl40"
cos6()" = cos(
1KO"
- 120") = -cosl 20"
cosSO"
-cos(180"
-100") = -cosl00"
Siiy
ra VT = cosl8()" =-1
VI
(1,0
diem)
ChUnn
minh
Ta CO 2AA' = AB + AC; 2BB' = BC + BA; 2CC' = CA + CB
Tif
do siiy ra
2(AA''
+
BB'
+ CC
AB
+ BA
=
0
+
0
+
0 = 0.
AC

+ CA) + (BC + CB
DE
SOS
OE THCT
SOC HOC KI I MON TOAN L6P 10
Thdi gian lam bai: 90 phut
Cau
I. (1,0
diem).
Cho hai lap hi.tp A = jn e Nl n <
II j,
B = jx e
xl
x - i
1.
Tim lap hdp A n
B.
Vicl
kcl qua
difc'li
dang
licl
kc.
2. Tim lal ca cac lap hdp C sao cho C c A va C c B. Bai loan c6 tat ca bao
nhieu nghicm?
Cfiu
U. (2,0
diem)
1.
Tim parabol (P); y =ax- + bx + 2,bict parabol c6 dinh 1(2; -2).

2. Lap
bang
bicn Ihicn va \ do thj ciia ham so' paiabol (P)
vi'Ji
a, b vCra lim.
Cau
III. (2,0
diem)
1.
Cho phift^ng
Irinh
(m - I)x" - 2(ni + l)x + m - 2 = 0.Tim m dc phiMng
Irinh
CO
nghicm phaii
bicl
x,, x-, Ihoa man he
Ihifc
— + —
x,
x^
=
5.
2. Giai phiftJng
lilnh
x" + — -4
X"
2
X
+ —

X
+
7 = 0.
Cfiu
IV. (2,0
diem).
Trong mat
phang
Oxy cho lam
giac
ABC c6 cac diem
M(l;
4), N(3; 0). P(-1; 1)
liin
lu-i.n
la
Iriing
diem cac
canh
AB, AC, BC. •
1.
Tim Ipa do cac dinh cua lam
giac
ABC.
2. Tinh do dai liung luyen AP ciia lam
giac
ABC.
Cfiu
V. (2,0
diem)

1. Giiii
he phu'dng trinh
2x-' +
3
= 5y
2y^ +
3
= 5x'
m
2. Cho sin x +
cosx
= - Tinh sinx.cosx va .sin' x + cos x.
3
Cau\l. (1,0
diem).
Cho
= 5N/2,
b =6, Ci, b) = 135". Tinh (a - 2b)(b - 2a),
DAP AN THAM KHAO
Cdu
Dap an
Diem
I
(1,0
diem)
1. (0,5
diem)
Tim tap h(/p A n
B.
Viet ket qua

dxiiii
danj;
liC't
ke.
I
(1,0
diem)
Taco
A =
{0;
1; 2; 10}
Malkhcic
x-l <2o-2<x-l<2o-l<x<3.
Siiy
ra
B=(-I;
3).
0,25
I
(1,0
diem)
Dodo AnB =
{0;
1; 2}.
0,25
I
(1,0
diem)
2. (0,5
diem)

Tim ta't cii cac tap h(/p C sao cho
I
(1,0
diem)
Ta CO C
c:
A va C c B
=>
C c A n B.
0,25
I
(1,0
diem)
Tird6C
= 0, jo}, [ij, {2}, {O;
1},
{O; 2}, {l; 2}, {O; 1; 2}.
Biii
loan c6 lal ca 8 nghicm.
0,25
II
(2,0
diem
)
1. (1,0
diem)
Tim parabol
II
(2,0
diem

)
Ta CO
- —
= 2
<=>
4a + b = 0.
2a
0,25
33
Thay toa do dinh 1(2; - 2) vao (P): y = ax^ + bx + 2 ta
diMc:
-2 = 4a + 2b + 2
<=>
4a + 2b = -4.
0,25
f4a
+ b = 0 [a = l
Giai
he <
<=>
•
•
4a + 2b = -4 [b = -4
0,25
Vay
parabol can lim la y = x~ - 4x + 2.
0,25
2.
(IJ) diem) Lap bang bien thien va ve d<1
thj

(doc gia ti/ giai)
Ill
(2,0
diem)
\.(1,0
diem) Tim m de phUc/ng trinh c6 hai nghi^m phan
bi^L
Ill
(2,0
diem)
PT(
la
cho
CO
hai nghi(
A'
= 5m -
1
> 0 «
•
m-1
jmphanbiCl
x,, Xj va
XjXj
0
m
^
1
m
>-^(*)

0,25
Ill
(2,0
diem)
r,,, , , 2(m + l) m — 2
Theo dinh li
Vi-cl
la co x, + x, = , x.x, =
'
2 m-1 ' ^ m-1
0,25
Ill
(2,0
diem)
„ 1 1 x,+X2 2(m + l)
Suy ra — + — =
—'
=
———— •
X|
Xj X|X2 m-2
0,25
Ill
(2,0
diem)
Do
do —
+
— =
5

o ^''^ =
5
o 2m
+ 2
= 5m -
10 <=>
m = 4
X|
Xj m-2
(thoa man dicu kien (*))
Vay
gia in m can
lim
la m
=
4.
0,25
Ill
(2,0
diem)
2.
(1,0 diem)
Giai
phifc/ng trinh
Ill
(2,0
diem)
Dicu
kicn
\.

2 -) 4 1
Dal
u =
X
+ —• Suy ra x" + —= u" -4.
0,25
Ill
(2,0
diem)
Phu'dng
irinh
da cho Ird lhanh -4u + 3 = 0
<=>
" ' •
[u
= 3
0,25
Ill
(2,0
diem)
•
Vdi u =
1
ihi
X
+ - =
1
CO
x~ -
X

+ 2 = 0. PhiTdng
trinh
nay v6
X
nghicm.
0,25
Ill
(2,0
diem)
.
Vdiu-3lhix
+ 3ox 3x + 2 = 0«
X
[x = 2
Vay
phiWng
Irinh
da cho c6 hai nghicm x =
1;
x = 2.
0,25
IV
(2,0
diem)
1. (1,5 diem) Tim tga do cac dinh cua tam giac
ABC.
Ti?
giac
AMPN
la hinh binh hanh ncn ta c6 MA = PN (*)

Ma MA =
(XA-l;yA-4);
PN = (4; -1).
fxA
-1 = 4 X,
Nen
(*)<=>-I
<=>
=
5
|_y^-4 =
-l
[yA=3
•A(5;
3). -x:
M
la Irung diem canh
AB,
la c6:
XB
=2XM
-XA
=2-5 = -3
yB=2yM-yA
=8-3 = 5
B(-3;
5).
N
la trung diem canh
AC,

la c6:
XQ
=
2x[si
-
XA
=6-5 =
1
yc
=2yN
-yA =0-3
= -3
C(l;
-3).
Vay
loa do ba dinh cua tam giac
ABC
la:
A(5;
3), B(-3; 5),C(1; -3).
2.
(0,5 diem)
Tinh
do dai trung tuyen
AP
cua tam giac
ABC.
Taco
AP
= (-6; -2).

Suy ra
AP
= ^{-6f
+(-2)^
= 2V1O.
V
(2,0
diim)
1. (1,0 diem)
Giai
h^ phifi/ng trinh
Xel
2x-^
+
3
= 5y (1)
2y''+3 = 5x (2)
Lay
(1)
IrCr
(2) ve iheo
ve"
la diTdc:
2(x-' -y"')
= 5(y -
X) <i>
2(x -
y)(x^ +
xy
+ y^) +

5(x - y) = 0
c:>(x-y)(2x"-
+2xy+ 2y" +5) = 0
0 (X - y)^x- + y"
+
(X
+ y)- +
5J = 0 <=> X = y (3)
1
VI X- + y- +(x
+ y)'' + 5
>0, Vx, yj.
1^
Thay (3) viio (1) la diTdc: 2x-^ + 3 = 5x <=> 2y? - 5x + 3 = 0
<=>(x-l)(2x- +2x-3) = 0
X -
1
= 0
2x- +2x-3 = ()
<=>
X =
X =
Vay he phiTcJng
Irinh
da cho c6 ba nghiem (x; y) la
(1;
1).
0,25
0,25
2. (1,0 diem)

Ti'nh
TiT
sinx +
COSX
=> sin" x + cos- x +
2sinxcosx
=-
3 9
=>
1
+
zsinxcosx
= — =>
sinxcosx
9 18
SUV
x +
COS-
X = (sinx +
cosx)'
- 3sinxcosx(sinx +
cosx)
27
-3
18
2 _ 22
3 ~ 27
0,5
0,5
VI

(1,0
diem)
Chufn^ minh
Ta c6:
a.b =
cos(a,b)
=
5V2.6.(
-
cos45")
= -30.
•
(a - 2b)(b - 2a) = 5a.b - 2a- - 2b^ =
-150-100
- 72 = -322.
0,5
0,5
Di
so 9
DE
THCT
SOC HOC Ki I MON
TOAN
L6P 10
Thdi gian lam bai: 90 phut
C&uh
(1,0 diem)
1.
Lap
mcMih

dc
phii
dinh
ciia cac mcnh dc chiJa bicn sau:
a) Bx G x, x" -5x >().
b) Vxe X, X- >4x-4.
2. Vict cac lap hdp sau bhng
each
liet
ke c^c phan luT cua no:
a) A = {xeNI2<x<9}.
b) B = jxe xl (x + 2)(x-3)(x 4) = oj.
Cflu
II.
(2,0 diem)
1.
Tim parabol (P): y = ax" + bx + c biel rang (P) dal gia Iri \(1n nhal y = 9 khi
X = 2 va nhan gia Iri y = 5 lai x = 4.
2. Lap bang bicn
Ihicn
va vc do ihi ciia (P) vdi a, b, c viTa lim.
C&uUl.
(2,0 diem) |
1.
Tim m dc phu'dng
Irinh
(m - 1)" x = m + x c6 nghiem duy nha't. •
2.
Giiii
phiftJng

Irlnh
x" + 6x - 2 x + 3 + 9 = 0. \
3.
Giiii
phifcing
Irinh
^?>x- -4x -2 = V2x + 7.
CSu IV. (2,0 diem). Trong mal phang Oxy cho diem A( - 2; 1). ^ |
1.
Tmi toa dp ciia diem B doi xufng
vdti
diem A qua goc tpa dp O, tim tpa dp
cua diem B' doi xi^ng vdi diem A qua true hoanh.
2. Gpi C la mot diem c6 lung dp bang 2 vii lam
giac
ABC vuong cf C. Tim
tpa
dp ciia diem C.
C&uW. (2,0 diem) ^
1. Giiii
he phifPng trinh
y + 2 =x-2
4x-y = 16
2. Chij'ng
minh
sin'^x +
cos'^x
=
1
-4sin'^xcos-x

+
2sin"*xcos'^x.
Cfiu
VI. (1,0 diem). Cho lam giiic ABC dp dai 3 ciinh la AB = 12, AC = 9,
BC = i5.
Tinh
AB.AC, AB.BC.
DAP AN
THAM
KHAO
Cau
Dap
an
Diem
I
(1,0
diem)
1.
(0,5
diem)
Lap mOnh de
phii
djnh ciia cac ni^nh de
I
(1,0
diem)
a) Vx 6 S. x^ -5\<().
0,25
I
(1,0

diem)
b) 3x G X, x" <4x -4.
0,25
I
(1,0
diem)
2. (O.S diem)
Viet cac tap h(/p sau bhne
each
liet ke
I
(1,0
diem)
a) A = {2; 3; 4; 5; 6; 7; 8}.
0,25
I
(1,0
diem)
b) Ti CO (X + 2)(x - 3)(x- - 4) = 0 o
Vi>y
B-{-2;2;3|.
x+2=0 r
x-±2
x-3=0 o ^ •
x2-4 = 0 -
0,25
37
II
(2,0
diem)

1. (1,0 diem) T\m paraboL
II
(2,0
diem)
Taco
a<0 r .
a
<0
^ =2 b + 4a-0
2a
. 12a + 2b = -4
4a + 2b + c = 9
wH*(V^.
^ 16a + 4b + c = 5
16a
+ 4b + c = 5
0,5
II
(2,0
diem)
Giai
he
Iron
•
a
=
-l
b
= 4 •
c

= 5
0,25
II
(2,0
diem)
Vay parabol can tim la y = -x^ + 4x + 5.
0,25
II
(2,0
diem)
2.
(1,0 diem) Lap
bang
bien thien va ve do
thi
(doc
jjia
ti/
^iai)
III
(2,0
diem)
1. (0,5 diem) Tim m de
iphiitin^
trinh c6 nghi^m duy nha't
III
(2,0
diem)
Ta CO (m - l)^x = m + X
<=>

|(ni - 1)~ -
1
jx
= m
<=> m(m -2)x = m.
0,25
III
(2,0
diem)
PhiTctng
trinh
da cho to nghicm duy
nha'l
khi va chi khi
m
0 va m 2.
0,25
III
(2,0
diem)
2.
(1,0 diem) Giai
phmn^
trinh
III
(2,0
diem)
Ta CO X- + 6x - 2 X +
3
+ 9 = 0 o (X + 3)^ - 2 X + 3 = 0

x
+ 3(x +
3
-2) = ()
0,25
III
(2,0
diem)
• Xct >
t
+ 3 =
()<=>x
= -3.
0,25
III
(2,0
diem)
• Xct x + 3=
2<=>x
+ 3 =
±2<=>x
= -5
hoac
x =
-1.
0,25
III
(2,0
diem)
Vay phi/cJng

Irinh
c6 ba nghicm la x = -5, x = -3, x =
-1.
0,25
III
(2,0
diem)
3.
(0,5 diem) Giai phi^(/n^ trinh
III
(2,0
diem)
Tai
<=>
, L •> 1 2x + 7>0
:6
V3x- -4x-2 = V2x + 7
<=>
<^
.
3x'
-4x-2 = 2x + 7
x Z
2
3x-
-6x-9 = 0
0,25
III
(2,0
diem)

<=>
X = -1
hoac
X = 3.
Vay phiTiJng
Irinh
da cho c6 hai nghicm x = -1; x = 3.
0,25
38
IV
(2,0
diem)
1. (1,0 diem) Tvm to
a
do cua diem B doi xtfng \6\m A .
Ta bict
riing
hai diem doi xi^ng vc'Ji
nhau
qua go'c tpa do thi
cac tpa dp tU"(1ng u'ng ciia chung doi
nhau.
Do do ncu A(-2;
1)
thi
B(2; -1). ' "
>
''
*
Ta bie't

rllng
hai did'm doi
xii"ng
vc'Ji
nhau
qua true hoanh c6
hoanh
dp bllng
nhau
va
tung
dp doi
nhau.
d/
J/
:
Do do ncu A(-2;
l)thi
B'(-2; -1).
2.
(1,0 diem) Tim toa dp cua diem C.
Gpi
C(x;
2)e{Oxy).
Taco
BC = (x-2; 3), AC = (x + 2; I).
Tarn
giac
ABC vuong
tiii

C khi va chi khi
BC.AC
= 0
<=>(x~2)(x
+ 2) + 3.1 =
Oc:>x^
- 4 + 3==0ox = ±l.
Vay C(l: 2) hoacC(-l; 2).
V
(2,0
diem)
1. (1,0 diem) Giai he phifc/n^
trinh
Neil v > -2 : He da cho In*
thanh
y+2=x-2
4x-y = 16
x-y = 4 fx =4
<=>
<!
<=>
-
4x-y = 16 y=0>-2.
Ncu
v < -2 : He da cho
Iril
thanh
•
-y-2=x-2
4x-y = 16

fx
+ y = 0
4x-y= 16
x
=
]6
5
y
= <-2.
Vay he phifdng
Irinh
da cho co hai nghicm (x; y) la (4; 0),
'16.
\(A
. 3 ' 5
2.
(1,0 diem) Chrfny
niinh
Dal
a = sin'x va b =
cos-x
=> a + b = 1.
0,25
VT
=
a-*
+
b'*
=
(a^

+
b^
)^
- laW = ((a +
b)^
-
2ab)^
-
lii^h^
0,25
= (1 - 2ab)- - 2a-b' =
1
-4ab + 4a^b^ - 2a^b^ =
1
-4ab + 2a^b^
0,25
=
1
- 4sin^xcos^x + 2sin^xcos^x
(dpem).
0,25
39
VI
Ti'nh
ABAC, AB.BC.
(1,0
diem)
Tinh
ABAC
Ta

CO
BC- = BC^ =(AC-AB)'
=>
BC-= AC-+ AB 2AC.AB
0,5
=>
2AC.AB = AC' + AB- - BC' = 81 + 144 - 225 = 0
=>
AC.AB = ().
Tinh
AB.BC
Ta
CO
AB.BC =
AB(
AC - AB) = AB.AC - AB^
=0-144
- -144.
0,5
DE
SO 10
DE
THlIr
SL/C HOC
Kl I
MON
TOAN
L6P
10
Thai

gian
lam bar. 90 phut
CSu
I. (1,0
diem).
Tim tap xac dinh ciia cac hiim so:
2013 1 , 1
1.
y =
^4^
2. y =
x~
-3x + 2
+
X-
-1
Cau
II. (2,0
diem)
Tim gia tri
Ic'in
nha't,
nho nhal (ncu co) cua cac ham so:
1.
y = x- -4x v('Ji 0<x <3. 2. y = -x- -4x + 3v('Ji 0<x <5.
Cau
\U. (2,0
diem)
, ™ , , . (2m + l)x + 5 (2m + 3)x + m-4 ,
1.

Tim m dc phiTc^ng tiinh . — = , co nghicm.
Vy-x-
s/y-x^
2.
Giiii
phiTdng Irinh x'* - 5 - x(-4x- +2x + 3) = x(4x^ -3).
3.
Giiii
phifdng tiinh x~ -
1
=
N/X
+ 1.
Cau
IV. (2,0
diem).
Trong mat phiing Oxy cho diem A(l; 3), B((); 2), C(4; 5).
1.
Tim toa do ciia diem E ihoa man CE = 3AB - 4AC.
2. Tim toa do ciia diem A' doi xiVng vdi diem A qua B.
Cau
V. (2,0
diem)
1.
Giai he phifdng trlnh ftx + y)" + x + y = 2(9 + xy).
[xy(x
+ l)(y + l) = 72
2. Tinh
cosu,
sina,

cotu hiel
tana
= -2 va 90" < a < 180".
40
CfiU
VI. (1,0
diem).
Cho tarn
giac
ABC co AB = 24cm, AC = 32cm, BC = 40cm.
1.
Chijrng minh tarn giiic ABC viiong lai A.
2. Tinh do dai dift-fng
tiling
tuycn BM ciia tarn
giac
ABC.
DAP
AN
THAM KHAO
(1,0
diem)
Dap an
Diem
1. (0,5
diem)
Tim tap xac djnh ciia ham s(Y
Ham so y =
2013 1
3-2x>0

-t-
—
du'dc
xac dinh khi <;
4-x- >0
>/3^
2x<3
x~
< 4
<=>
<
~>
o -2 < X <-•
1
-2<x<2
Vay tap xac dinh ciia ham so la D =
0,25
0,25
2. (0,5
diem)
Tim tap xac djnh ciia ham
.so
Ham so v =
x-
-3x + 2 + X- -1 ^0.
x~
- jx + 2
+
\- -\
diTik-

xiic dinh khi
Xel
x-
-3x + 2
x~
-
=
0o^
X-
-3x + 2 = 0
x l
= 0
o
X
= 1.
Viiy
tap
Xiic
dinh ciia hiim so la D = x \1|
X
-
-1
x = ±l
0,25
0,25
II
(2,0
diem)
1. (1,0
diem)

Tim ^ia trj Win
nha't,
nho nhtYt (neu co) ciia ham so'.
y
= x~ -4x CO a = i > OnC-n be lom hifdng
ICMI.
b
4
Hoanh
do dinh x, = - — = - = 2 e
|0;31
Vay miny = l"(2) = -4, maxy =
max{r(()),
l(3)j = 1(0) = 0.
0,25
0,25
0,5
2. (1,0
diem)
Tim
y^ia
tri Win
nha't,
nho
nha't
(neu co) ciia ham s(Y
y
=
-X"
-4x +

3CO
a = -1 < OnC-n be lom hUdng xiiong.
Hoanh
do dinh == ^ =-2i[0;5]
Vay miny = r(5) = -42, maxy = 1(0) = 3.
0,25
0,25
0,5
41
lu^uii
unfit
Jg ug
iiiu
JUL
lu
iiaiiu
Lau
- I
iigiii iigiig
iiig-
III
(2,0
diem)
1.
(0,5 diem) Tim ni de
phifc/ng trinh
c6
nghiC'm
III
(2,0

diem)
,
(2m + l)x + 5 (2m + 3)x + m-4
f-3<x<3
Ta
CO , — = , <=> •
79-x=
V9_,2
l2x =
9-m
0,25
III
(2,0
diem)
9-m
PhU'dng
Irinh
da cho c6
nghicm
khi va chi khi -3 <
—-—
< 3
<=>-6
< 9 - m < 6
<=>
3 < m < 15.
0,25
III
(2,0
diem)

2.
(0,5 diem)
Giai
phififn^
trinh

III
(2,0
diem)
Ta
Da
L-6
x"*
-
5-x(-4x^
+2x + 3) =
x(4x^
-3) o
x"*
-2x^ -5 = 0
I
u = x^ (u > 0) la
CO
phirong
irinh
- 2u - 5 = 0
u
=
1
+

N/6
u
=
1
-
N/6
(loai)
0,25
III
(2,0
diem)
Vdi
11 =
1
+
V6
=>
x^ =
1
+
N/6
X =
±7l
+
>/6.
Vay phi/iing
Irinh
da cho c6 hai
nghicm
x = ±Vl + \/6.

0,25
III
(2,0
diem)
3.
(1,0diem)
Giai
phifi/ng
trinh

III
(2,0
diem)
T
' 2 , 1—r |x i>o
Ta
CO X -
1
=
V
x
+
1
«
<
[(x^-1)'
=x + l
0,25
III
(2,0

diem)
<=>
<
X
> i
[1"
- '
o
<
x"*-2x-+
l = x + l
[x(x-^-2x-l)
= ()
0,25
III
(2,0
diem)
X
>
1
x(x
+
l)(x- -x-l)
= 0
0,25
III
(2,0
diem)
<=>
Va>

"x
= -1
1
+ V5
X
=
2
phifdng trinh
da cho c6
nghicm
x =
-1;
x =
*
•
0,25
IV
(2,0
diem)
1.
(1,0 diem) Tim toa do
ciia
diem
E
thoa
man
IV
(2,0
diem)
Taco

AB =
(-I;
-l)^3AB-(-3;
-3).
0,25
IV
(2,0
diem)
AC
=
(3; 2)^-4AC
= (-12
-8).
0,25
IV
(2,0
diem)
Dodo CE-3AB-4AC o(x,
-4
;
y,,-5)
= (-15; -11)
0,5
X,,
- 4 = -15
<=>
<i
<=>
y, 5
=

-ll
X,;
=-11
y,,=-6
•Vay
E(-l 1; -6).
2.
(1,0 diem) Tim toa do
ciia
diem
A'
d(Yi
xvtnp^
diem
A qua B.
Vi
A" doi
xiJng vc'Hi
A qua B, ncn B la
irung dicm ciia
AA'
2
yA+yA'
X
=2Xj X.
=2.()-l = -l
<=>^
^ " ^ -Vay
A'(-l;
1).

ixhH
yA'
=
2yB-yA=2.2-3
= i
V
(2,0
diem)
1.
(1,0 diem)
Giai
hC' phi/oTnK trinh
He phiTcJng
irinh
da cho
lu'iJng diTdng
X(X
+
l)
+
y(y
+ 1)= 18'
(*)
x(x
+
1). y(y+ 1)
= 72
u
=
x(x

+ 1) ., u +
V
= 18
Dal
{ . He (*) lai
lhanh
[V
= y(y + 1)
u
v = 72
u
= l2 ^
<=> •!
hoac i
v=6
u
= 6
v
= 12
. Vi'Ji
u
= 12
v=6
x^
+ x-12 = 0
y"
+ y - 6 = 0
x
= 3
X

= -4
y
= 2 •
,y
= -3
Vdi
u=6
v
= 12
+
x-6 =
()
y-
+y-12 =
()
x
= 2
x
= -3
y
= 3 •
y
= -4
Vay
he
phiTdng
Irinh
da cho c6
nghicm
(x; y) la (3; 2), (2; 3),

(3;-3),
(-3; 3), (-4; 2), (2; -4), (-4; -3), (-3; -4).
2.
(1,0 diem)
Tinh.
Tinh
cosa:
1
+
lan^a
= '
cos^a
l
+
(-2)^=-^
cos^a
2 ' '
=>
cos a =
—
=>
cosa
=
—7=
5 V5
(do 90"
<a<18()").
43
(
\

Tinli
sinu: sinix lanci
cosa
= ( - 2)
•
=—j=-
0,25
Tiiih
colu: cola =—!—
tanu
2
0,25
VI
(1,0
diem)
1. Chilfnj» minh tain
giac
AHC
viiong
tai A.
VI
(1,0
diem)
Taco
BC- =40-
=1600
(cm").
AB-
+ AC- = 24- + 32- = 1600 (cm").
0,25

VI
(1,0
diem)
BC-
= AC- + AB- => AABC vuong lai A.
0,25
VI
(1,0
diem)
2. Tmh do dai
difi/ng
trung
tuyen
BM ciia tarn
giac
ABC.
VI
(1,0
diem)
^
, ^ a-+c- b- BC-+AB- AC"
1
a CO in: = =
''
2 4 2 4
0,25
VI
(1,0
diem)
BC-+AB-

AC- 40-+24- 32"
2 4 2 4
Siiy
ra = s/Hi (cm).
0,25
DE
SO 11
DE
THCT
S\iC HOC Ki I MON
TOAN
L6P 10
That
gian
lam bar. 90
phut
Cau
I. (1,0
diem)
. Tim lap xac dinh ciia cac ham so':
2013x- 7x
y=
I— +—
i
Vx-l
X X-6
2. y =
-
x
+ 2

Cau
11.(2,0
diem)
1.
Tim
parabol
(!'): y =ax- +bx + c,bicl
parabol
c6 Iruc do'i
xi'riig
x = -lva
qua hai diem A( ~ 2; 6), B(2; -10).
2. Lap
bang
bicn thien va ve do
liij
ciia ham so' bac hai tren
vc'ifi
a, b, e vifa
tim.
Cau III. (2,0
diem)
1.
Tim m dc phiWng
Irinh
m-(x -2) + 7m =(6- m)(x + m)-2 v6
so'nghiem.
2.
Giiii
phu'dng

irinh
X-
+8x-l
=
2x + 6
3.
Giiii
phiftlng
Irinh
\l5x~
+2x-7S
= 2x + 3.
cau IV. (2,0
diem).
Trong mal
phang
Oxy cho diem A( 1; 0), B(3; 0), C((); 4).
Goi
M, N, P Ian kfcn la trung diem cac
canh
BC, CA, AB.
44
1.
Tinh
giii
iri ciia bieu ihi'rc AM.BC + BN.CA + CP.AB.
2. Tinh cos
A,
cosB,
cosC.

Cau
V. (2,0
diem)
fx
+ V + xy =
1 1
: •
1.
Giiii
he phu"(<ng
Irinh
j , ' ,
>,Aii.;
Si!
i
x" + y- + 3(x + y) = 28 ' .
^
2.
Riit
goii
A
= (1
-cos-x)lan-x
+
1
~ uurx. B = (colx - lanx)" -(colx + lanx)-
Cflu
VI. (1,0
diem).
Cho lam

giac
ABC c6 BC = a, AC = h. AB = c Ihoa man
fi
+ c = 2a.Chi'fng minh ning: • - |
1.
sin B +
sinC
= 2 sin A.
2.A
=
i_,.i
ha S K
DAP
AN THAM
KHAO
Can
Dap an
Diem
I
(1,0
die in)
1. (0,5
diem)
Tim tap xac djnh ciia ham .s<Y
2013x- 7x
V
=
•
X"
-X -6

-
diAJc
Xiic
dinh khi
x-1
>0
X"
-x-6;t0
X
>]
X
?i
-2 o
<^
x*3
X
>
1
x^3'
Vay lap
Xiic
dinh ciia ham so la D =
(l;
3)u(3; +oo).
2. (0,5
diem)
Tini
tap xac djnh ciia ham so
Hiim
so y = ^-^^—-—^difdc xiic dinh khi

^
x + 2 •
X
>0
X
>0
c^i
<=> X > 0.
x^-2
Vily
lilp
Xiic
djnh ciia
hiim
so'
lii
D = [0; + «).
II
(2,0
diem)
1. (1,0
diem)
Tmi parahol (P)
Vi
(P)
CO
iriic
doi xii'ng x = -1 vii (P) qua hai diem A( - 2; 6),
b
B(2;

-10)nC-n
-1
2a
6 =
4a-2b
+ c
-10 = 4a + 2b + c
0,25
0,25
0,25
0,25
0,5
4S