luyện giải đề trước kì thi vào lớp 10 ba miền bắc trung nam môn tóan

NGUYEN
DlICT/iN(Chubien)
NGUYEN
ANHHOANG-NGUYEN
DOANVU
NGUYEN
DlIC
HOA
-
DO
QUANG
THANH
-
NGUYEN
TH|
TRINH
UlYMGUIflilllllliCKiTHI
VAO LdP
10
BA MliN
B^c
-
Trung
-
Nam
1
NHA XUAT BAN TONG HOP
THANH
PHO HO
CHI
MINH

,
LUYEN GIAI
DE
TRl/dC
KY
THI VAO
L6P
10
BA MIEN BAC
-
TRUNG
-
NAM MON TOAN
NGUYIN
DCTCTAN
Chiu
trach nhi^m xua't
ban
NGUYEN
THI
THANH
Hl/ONG
Bicn
tap
Sura
ban in
Trinh
bay
Bia
QUOC

NHAN
HOANG NHLTT
Cong
ty
KHANG
VIET
Cong
ty
KHANG
VI^T
NHA XUAT BAN TONG HOP
TP.
HO CHf MINH
NHA SACH TONG H0P
62
Nguyen
Thj
Minh Khai,
Q.l
DT: 38225340
-
38296764
-
38247225
Fax:
84.8.38222726
Email:

Website:
www.nxbhcm.com.vn/

www.fidltour.com
Tong phat hdnh
CONG
TY
TNHH
MTV
D|CH
Vy VAN HOA
KHANG VI|T
Oja Chi:
71
Dinh Tien Hoang
- P.Oa Kao - Q.1 -
TP.HCM
Dien thoai:
08.
39115694
-
39105797
-
391 11969
-
39111968
Fax:
08.
3911 0880
Email: l<
Website: www.nhasachkhangviet.vn
In
Ian

thiJ
I, so
liiging 2.000 cuon,
kho
1
6x24cm.
Tai:
CONG
TY CO
PHAN
THL/ONG
MAI
NHAT
NAM
Dja chl:
006 L6 F,
KCN
Tan
Binh,
P.
Tay Thanh,
Q.
Tan Phu, Tp.
Ho
C*iJ
So DKKHXB:
1
55-1 3/CXB/44-24/THTPHCM ngay 31/01/2013.
*
Quyet dinh xuat

Wn so:
152/QD-THTPHCM-2013
do NXB Tor
Thanh Pho'
Ho Chi
Minh
cap
ngay 07/03/201
3
In xong va npp
ILAJ
chieu Ouv II nAm 201 3
tdi
N6I DAU
Quyen sach Luyen giai
de
trUdc
ky
thi
vdo Idp 10 ba
mien
Bac,
Trung,
Nam
mon Todn nham
gop vao
tu sach
cua ban doc mot tai Heu
toan thie't thiTc
va bo

ich
giup
cac em hoc
sinh
Idp
9
on
luyen
va
nang
cao
kien thtfc todn, chuan
hi tot
trong
cac ki
thi tuyen sinh
vao Idp 10.
Quyen sach
gom
2
phan
:
Phin
1 :
Cac
de
thi toan.
•
A. De
thi tuyen sinh

vao Idp 10 THPT.
\
• B.
De
thi tuyen sinh
vao idp 10
chuyen.
Bao
gom
de
thi
va
hiTdng
dan
giai diTdc tuyen chon
tif cac
de
thi
tuyen sinh
vao Iclip
10 cf mot so dia
phu^dng
(tCf nam
2010
den
2013).
Ph^n
2 :
Cac
de

toan
on
luyen.
•
A. De
toan
on
luyen thi
vao Idp 10 THPT.
• B.De
toan
on
luyen thi
vao Idp 10
chuyen.
Bao
gom
20 de
toan
va
hiTdng
dan
giai
do
chiing
toi
bien soan
vdi
nhieu
dang toan khac nhau nh^m

trd
giup
cac em
hoc
sinh ciing
co,
boi
di/dng nang
cao kien thufc toan.
Chung
toi
da co
gang
tim Idi
giai mdi,
hay
va
ngan
gon cho cac bai
loan
va
sau
Idi
giai cijfa
moi bai
toan
dcu
co
nhan
xet va

binh luan,
vdi
mong muon giup
cdc
em
hoc
sinh
nam
dUdc phUdng phap giai dang toan
do, tim
kiem
bai
toan
tU'dng tif,
b^i
toan mdi,
bai
toan tong quat nhSm
khdi
day
tiem nang tim
toi
sang
tao trong
hoc
toan
5
hoc
sinh.
Mac dil chung

toi da
co
gang
rat
nhieu trong bien soan, song
chac
han
quyen
sdch
van con
thicu
sot.
Raft mong nhan diTdc
cac
y
kien dong
gop
tijf
ban doc
de
cdc
Ian in sau
sach dU'dc hoan thien hdn.
;
Xin
tran
trong
cam dn
CAC
TAC GIA

Nha
sach
Khang Viet
xin
tran trong giai thieu
tai Quy doc gid vd xin
Idng
nghe
moi y kim
dong
gop, de
cuon
sach
ngdy cdng
hay
han,
ho ich han.
Thu
xin
gui
ve:
Cty
TNHH
Mpt
Thanh Vien
-
Dich
Vu Van Hoa
Khang Vi?t.
71,

Dinh Tien Hoang,
P.
Dakao. Quan 1,
TP. HCM
Tel: (08)
39115694
-
39111969
-
39111968
-
39105797
- Fax:
(08)
39110880
Hoac
Email:

PHAN
I. CAC DE THI TOAN
A.
Dfe
THI TUYEN SINH
vAO
L6F
10
THPT
m
so
1:

De thi
tuyen sinh vao Idp
10
THPT, Tp. Ho Chi Minh nSm 2012
-
2013
3
D6
so
2:
De thi
tuyen sinh vao Idp
10
THPT, Tp.
Ha
Npi nam 2012
-
2013
8
De s6'3:
De thi
tuyen sinh vao Idp 10 THPT, Tinh Dong Nai nam 2012
-
2013
13
De
so
4:
De thi
tuyen sinh vao Idp 10 THPT, Tp.

Da
Nang nam 2012
-
2013
16
so 5:
De thi
tuyen sinh vao Idp 10 THPT, Tinh Thi^a Thien Hue
nam hoc
2012-
2013
19
B6
SO
6: De thi
tuyen sinh vao Idp 10 THPT, Tp. Can Thd nSm 2012
-
2013
24
De
so
7:
De thi
tuyen sinh vao Idp 10 THPT, Tinh Hai Phong nam 2012
-
2013
28
D6
so
8:

De thi
tuyen sinh vao Idp 10 THPT, Tinh Nghe
An
nam 2012
-
2013
32
De
so
9:
De thi
tuyen .sinh vao Idp 10 THPT, Tinh Quang Ninh nam 2012- 2013
37
D6
so
10:
De thi
tuyen sinh vao Idp 10 THPT, Tinh Thanh Hda nSm 2012
-
2013
40
De s6'll:
De thi
tuyen sinh vao idp 10 THPT, Tinh Yen Bai nam 2012- 2013
44
D6
so
12:
De thi
tuyen sinh vao Idp 10 THPT, Tinh Ha Nam nam 2012- 2013

48
D6
so'
13:
De thi
tuyen sinh vao Idp 10 THPT, Tinh VTnh Phuc nam 2012
-
2013
51
De .so 14:
De thi
tuyen sinh vao Idp 10 THPT, Tinh Dak Lak nam 2012
-
2013
54
De
so
15:
De thi
tuyen sinh vao Idp
10
THPT, Tinh Tuyen Quang nam 2012
-
2013
58
D6
so
16:
De thi
tuyen sinh vao Idp 10 THPT, Tp.

Ho
Chi Minh nam 2011
-
2012
61
De
so
17:
De
thi tuyen sinh Idp 10 THPT, tinh Quang Nam nam 2011
-
2012
66
De
so
18:
De thi
tuyen sinh vao Idp 10 THPT. tinh Daklak nam 2011
-
2012
69
De
so
19:
De
thi tuyen sinh vao Idp 10 THPT, tinh Ninh Thuan nam 2011
-
2012
72
D6

so
20:
Dc thi
tuyen .sinh vao Idp 10 THPT, tinh Ha Tinh nam 2011
-
2012
75
De
so
21:
De thi
tuyen sinh idp 10 THPT, tinh Thanh Hda
nam
2011
-
2012
79
De
so
22:
Dc
thi tuyen sinh vao Idp
10
THPT, tinh Kicn Giang nam 2011
-
2012
82
De
so
23:

De thi
tuyen sinh vao Idp 10 THPT, tinh Khanh Hoa nam 2011
-
2012
85
D6
so
24:
De thi
tuyen sinh Idp
10
THPT, tinh Binh Dmh nam 2011
-
2012
88
D^
so
25:
De thi
tuyen sinh Idp 10 THPT, tinh Quang Ngai nam 2011
-
2012
92
D^'
s6'26:
De thi
tuyen sinh vao Idp
10
THPT, Tp.
Da

Nang nam 2011
-
2012
96
f)c
.so 27:
Dc thi
tuyen sinh vao idp 10 THPT, Tp.
Ha
Noi
nam
2011
-
2012
99
D^
so
28:
De thi
tuyen .sinh vao Idp
10
THPT, tinh Quang Tri nam 2011
-
2012
103
De
so
29:
Dc
thi tuyen sinh vao Idp 10 THPT. tinh Nghp

An nam
2011
-
2012
106
De s6'30:
De thi
tuyen sinh Idp 10 THPT, tinh Ninh Binh nam 2011
-
2012
110
D6
SO
31:
De
thi tuyen sinh Idp 10 THPT, tinh Hai DiTdng nam 2011
-
2012
114
D6 .so 32:
Dc thi
tuyen sinh Idp
10
THPT, tinh Lang Sdn nam 2011
-
2012
118
Dd so'33:
D^ thi
tuycn sinh Idp 10 THPT, Tp.HCM, nam 2010

-
2011
121
Dc
so
34:
De thi
tuycn sinh vao Idp
10
THPT, tinh Bac Lieu nam 2010
-
2011
127
De
so
35:
De thi
tuycn sinh vao Idp
10
THPT, tinh
Ba Ria -
Vung Tau nam
hoc
2010-
2011
129
B.
Dfe
THI TUY^N SINH VAO
L6P

lO
CHUYftN
De
so'
36:
De thi
tuyen sinh
vao Idp 10
chuyen Toan,
Tp. Ho Chi
Minh
nSm hoc
2012-
2013
132
D^
s6'
37:
De thi
tuyen sinh
vao Idp
10 chuyen TriTdng
Dai Hoc
SuT
Pham, Tp.
Ho Chi
Minh nam
hoc
2012
-

2013
135
D^
so'
38:
De thi
tuyen sinh
vao
Idp 10 chuyen Toan Trifdng
Dai
Hoc
Sif
Pham, Tp.
Ho
Chi Minh nam hoc 2012
-
2013
141
D^'
so'39:
De thi
tuyen sinh
vao Idp
10 chuyen TriTdng
phd
thong Nang khie'u, DHQG
Tp.Ho Chi Minh nam
hoc
2012
-

2013
146
so'40:
De thi
tuyen sinh
vao Idp
10 chuyen TriTdng
phd
thong Nang khie'u, DHQG
Tp.Ho
Chi
Minh nam hoc 2012
-
2013
151
B6
S6'41:
DC
thi
tuyen sinh vao Idp 10 Chuyen TriTdng THPT Dai Hoc Sir Pham
Ha Noi
nam
hoc
2012
-
2013
156
De
s(")'42:
Dc thi

tuyen sinh vao Idp 10 Chuyen TriTdng THPT Dai Hoc
SuT
Pham
Ha Noi
nam hoc 2012-2013
161
Bi
so
43:
De thi
tuyen sinh
vao Idp 10
Chuyen TriTcfng THPT Chuyen Khoa
Hoc
TiT
Nhien, Dai Hoc Qudc Gia
Ha
Npi nam hoc 2012
-
2013
165
D^
so' 44:
De thi
tuycn sinh
vao Idp 10
Chuyen Trrfdng THPT Chuyen Khoa
Hoc
TiT
Nhien, Dai Hoc Qudc

Gia Ha
Npi nam hoc 2012
-
2013
170
so'45:
De thi
tuyen sinh vao Idp 10 chuyen, Tinh Dong Nai nam
hoc
2012-
2013
173
so'46:
De
thi tuyen sinh vao Idp 10 chuyen, Tinh Dong Nai nam
hoc
2012-
2013
177
s6'
47:
De thi
tuyen sinh
vao Idp 10
THPT Chuyen Toan, Tp.Can
Thd nam hoc
2012-
2013
181
Bi so'48:

De thi
tuyen sinh vao Idp 10 THPT Chuyen Toan, Tinh Quang Ngai n3m
hoc
2012-
2013
186
De so'49:
De thi
tuyen sinh
vao Idp
10 THPT Chuyen Todn, Tinh Hu^g
Yen nam hoc
2012-2013
190
D6
SO'
50:
De thi
tuyen sinh
vao Idp
10 THPT Chuyen Toan, Trifdng THPT, Tinh
Hai
Du'dng nam hoc 2012
-
2013
196
Dl .so' 51:
Dc thi
tuyen sinh
vao Idp 10

THPT Chuyen, Tinh
Hoa
Binh
nam hoc
2012-
2013
200
DC
,s6'
52:
De thi
tuyen sinh
vao Idp
10 THPT Chuyen Todn THPT, Chuyen Phan
Bpi
Chau, Tinh Nghe
An
nam hoc 2012
-
2013
204
t)6
s6'53:
De thi
tuyen sinh
vao Idp
10 THPT Chuyen
Lam
Sdn, Tinh Thanh
Hda nam

hoc 2012- 2013
209
D^
.s6'
54:
De thi
tuye'n sinh
vao Idp
10 THPT Chuyen Toan, Tinh
Ba Ria -
Vung
Tau
nam hoc 2012- 2013
213
Dd s6' 55:
Dc thi
tuyen sinh
vao Idp 10
THPT Chuyen Toan, TriTdng THPT Chuyen
Phan Boi Chau, Tinh
Ba Rja -
Vung Tau nam hoc 2012
-
2013
218
s6'
56:
De thi
tuyen sinh vao Idp 10 chuyen, tru'dng Dai
hoc

Su pham Tp.
Ho Chi
Minh nam hoc 2011
-
2012
223
De so' 57:
De thi
tuyen sinh vao Idp 10 chuyen toan, trifdng
Dai hoc
Sir pham Tp.
Ho
Chi Minh nam hoc 2011
-
2012
227
De so'58:
De thi
tuyen sinh vao Idp 10 chuyen toan, THPT chuyen, Tp.
Ho Chi
Minh
nam hoc 2011
-
2012
232
D6 so'59:
De thi
tuyen sinh vao Idp 10 chuyen, tru-dng THPT chuyen, Dai hoc Sir pham
Ha Noi nam hoc 2011
-

2012
237
D6 so' 60:
De thi
tuyen sinh vao Idp 10 chuyen toan, triTdng THPT chuyen Dai hoc
Sir
pham Ha Noi nam hoc 2011
-
2012
242
Dc s6' 61:
De thi
tuyen sinh
vao Idp 10
chuyen toan, THPT tinh Binh Dinh
nam hoc
2011
-
2012
245
De so'62:
De thi
tuyen sinh vao Idp 10 chuyen, trirdng pho thong nang khie'u,
Dai hoc
Quoc gia, Tp.HCM nam hoc 2011
-
2012
250
so'63:
De

thi tuyen sinh vao Idp 10 chuyen toan, trU'dng pho thong nang khie'u,
Dai
hoc Quoc gia, Tp.HCM ndm hoc 2011
-
2012
255
D(1 so'64:
De
thi tuyen sinh vao Idp 10 chuyen, triTdng THPT chuyen KHTN, DHKHTN,
HiQG
Ha
Noi nam hoc 2011
-
2012
260
l.e .d' 65:
De thi
tuyen sinh
vao Idp 10
chuyen toan, triTdng THPT chuyen KHTN,
DHKHTN, DHQG Ha Npi nam hoc 2011
-
2012
264
D6
so
66:
De thi
tuyen sinh vao Idp 10 chuyen toan, THPT chuyen, Tp.
Ho

Chi Minh
nam hoc 2010- 2011
269
D6 so' 67:
De thi
tuyen sinh vao Idp 10 chuyen, trifdng THPT Quoc hoc Hue
nam hoc
2010- 2011
273
so'
68:
De thi
tuyen sinh
vao
Idp 10 chuyen toan, thanh pho
Ha
Noi,
nam hoc
2010- 2011
279
s6'69:
De thi
tuyen sinh vao Idp 10 chuyen, trirdng pho thong nang khie'u,
Dai hoc
Quoc gia, Tp.HCM nam hoc 2010
-
2011
284
D^' s6' 70:
De thi

tuyen sinh vao Idp 10 chuyen, triTdng pho thong nang khie'u, Dai
hoc
Quoc gia, Tp.HCM nam hoc 2010
-
2011
289
PHAN
II. CAC DE
TOAN
ON
LUY|N
A. De toan
on
luyen thi vao Idp 10 THPT
295
B.
De toan
on
luyen thi vao Idp 10 chuyen
315
i';;"
-it'//
Cty
TNHH MTV DWH
Khang
Viet
Plian
I.
CAC
DE THI

TOAlV
A.
Di
Tfli rmifi swfl
yko
i6? lo
run
D]fe
so 1
DE
THI TUYEN SINH VAO L(3P 10 THPT, TP.Hd CHf MINH
^-
' NAM HQC 2012 - 2013
Bai
1:
(2 diem) Giai cac phiTctng trinh va he phiTdng trinh sau
:
'2x-3y
=
7
a) 2x^-x-3
= 0 ,j , , b)
3x
+ 2y = 4
c)xVx'-12
=
0
y ^ d)
x^-2V2X-7
= 0

Bai
2:
(1,5 diem)
, ,
a)
Ve do thj (P)
cija
ham so y = ^x^ va
di/dng thang (D):
y = ~
+
2
tren
cting mot he triic toa do.
b) Tim toa do cac giao diem cua (P) va (D)
d
cau tren b^ng phep tinh.
Bai
3:
(1,5 diem) Thu gon cac bieu thiJc sau
:
1
2V^ 1 '
a)
A = ^ + —
vdi
X >
0;
X ^
1

,
x
+ Vx x-1 x-V^ lot-,
b)
B =
(2
-
V3)726TT5^
-
(2
+
^/3)^/26
-
15^3
Bai
4: (1,5 diem) Cho phiTcJng trinh:
x^
-
2mx
+m
-
2
=
0
(x
la an
so)
a) ChtJng minh rhng phtTdng trinh luon c6 nghiem phan biet vdi moi
m.
b) Goi

X,,
X2
la
cac nghiem ciia phiTdng trinh.
. ,
Tim m de bieu thiJc M
= —
dat gia tri nho nha't.
X|
+ X2 - 6X|X2
Bai
5:
(3,5 diem) Cho du-dng Iron (O)
c6
tam
O va
diem
M
n^m ngoai diTdng
tron (O). Dirdng thang MO c^t (O) tai
E
va
F
(ME < MF).
Ve
cat tuyen MAB
va
tiep tuyen MC cija (O)
(C la
tiep diem,

A
nam giffa hai diem
M va
B.
A
va
C
nKm khac phia doi vdi dirdng thing MO).
a) ChiJng minh r5ng: MA.MB
=
ME . MF
'
b)
Goi H la
binh chieu vuong
goc
ciia diem
C len
difdng thing MO. ChiJng
minh tiJ giac AHOB noi tiep.
c) Tren nijfa mat phing
bd
OM
c6
chi^a diem A,
ve
nuTa du-dng tron diTcJng kinh
MF;
nufa diTdng tr6n nay cat tiep tuyen tai
E

cua (O)
d
K. Goi
S la
giao diem
cua
hai
dudng thang
CO va
KF. Chtfng minh r^ng diTdng thing MS vuong
goc
vdi
dufcfng thing KC.
Chi?ng minh r^ng diTcfng thing MS vuong g6c vdi di/c(ng thing KC.
Luygn
giai
66
truOc
kl
thi v^o Idp 10 ba mign
BSc.
Trung,
Nam
mOn
ToAn
_ Nguyin
DiJfc
Ta'n
d)
Goi P va Q Ian

Itfdt
la
tam diTdng tron ngoai tiep cac
tam
giac EFS
va ABS
va
T la
trung diem cua KS. ChiJug minh ba diem P, Q,
T
thang hang.
Hl/dNG DAN GIAI
Bai
1.
a)
a-b-c
= 2-(-l)
+ (-3)
=
0
Phu'dng trinh c6 hai nghiem phan biet
Xi
=
-1,
=
-c
3
2
b)
2x

- 3y = 4
<=>
i
3x
+ 2y = 4
X = 2
9.2+
6y = 12
4x
-6y = 14
13x
= 26
9x
+ 6y = 12
9x
+ 6y - 12
X = 2 fx = 2
i'K'
"' [9.2 + 6y = 12 [6y =-6 [y =-1
He phiTdng trinh c6 nghiem (x; y)
la
(2;
-1)
c) Dat y = x^(y
>
0). PhiTdng trinh trd thanh: y^ + y
-
12 =
0
A =

1
+ 48 =
49;
N/A = 7
y,
= ^ii^ =
3
(thich hdp);
yj = ^^y^ = -4
(khong thich hdp)
y,
= 3. Ta CO
x^
= 3 o X = ±73
Phifdng trinh c6 hai nghiem phan biet:
x,
d)
A' = 2 + 7 = 9; yfA' =3
PhiTdng trinh c6 hai nghiem phan biet
'
1 1
Nhan xet:
1)
Neu
phi/dng trinh ax^
+ bx + c = 0 c6 a - b + c = 0 thi
phiTdng trinh
c6 hai
—c
nghiem

Xi
=
-1;
X2
=
—
a
2)
Ban
doc
hay
giai
he
phi/dng trinh
bKng
phiTdng phdp the.
3)
PhiTdng trinh dang ax"
+
bx^
+ c = 0,
dat
y =
x^
ta
diTdc phiTdng trinh bac
hai
ay^ + by +
c
= 0. Giai tim y roi tim

x.
Bai
2. a)Ve
(P),
(D)
Bang gia
tri
X
-4 -2 0 2 4
4 1 0 1 4
X
0 4
X
y 2
2 0
Cty
TNHH
MTV DWH Khang V
b) PhiTdng trinh hoanh do giao diem cua (P) va
(D)
1
X 11
-x^ = — +
2
o -x^
+-X-
2
= 00
x^+2x-
8 = 0

4
2 4 2
A'=1+8 = 9,
>/A'=3
-1
+ 3 ^ -1-3
x,
= = 2 ; X2 = = -4
1
1
1
2 1 .2
x, = 2thi
y, =-x( = 2^ =1
x,
= -4 thi y, =
-X?
=
-(-4)^
=4 ^
Vay (P)
va
(D)
c^t
nhau tai hai diem phan biet A(2; 1)
va
B(-4;
4)
Nhan xet:
De tim tpa do

giao diem ciia
(D) va (P)
bang phep tinh
ta lap
1
~x
phiTdng trinh hoanh do giao diem cua (D)
va
(P):
-x^ = —
+
2
4
2
Nghiem cua phu^dng trinh
la
hoanh dp cua cac giao diem.
*'
Bai
3.
A =
_L^.2V^
1
X +
>/x
X -
1
X - N/X
1
2V^

Vx(Vx
+ i)
(Vx+i)(V^-i) V^(V^-i)
V^-l
+
2x-V^-l
2x-2
2(V^
+
l)(V^-l,
v^(v^ + i)(v^ -1) v^(v^ + i)(v^ -1) vr(V5r + i)(vi -1)
Luygn
giSi
dg
truflc
ki thi vao I6p 10 ba
mign
BSc,
Trung,
Nam man
ToAn
_
Nguygn
Pile
Tgn
B
= (2 - V3)V26 + I5V3 - (2 + S)yj26 - 1572
= ^2(2 - V3) (26 +
15N/3)
- y(2 + ^/3) (26 - I5V2)

= ^(7 - 4V3)(26 + I5V3) - ^(7 + 4V3)(26 - 15V2~
= Vl82 + 105>/3 -
IO4V3
- 180 - Vl82 -
10573
+ 104^3 - 180
72 72 ^ ^
73 + 1)
-J(>/3-l)
+ + i 2
72 72 72
Nhan
xet jt
1) Nhan ra rang
x
+
7x=7x(7x
+
ij,
x-i = ^7x + i)(Vx -
ij,
X - 7x =
7x|7x
-
ij.
Tijf
do de CO difdc Idi giai cua bai toan.
2) Ta CO (2 -
73)V26
+ 1573 - (2 +

73)(26
- 1572) '
= ^(2 - 73) (26 + 1572) - ^(2 + 73) (26 - 1572)
= = V2 + 73 - V2 - 73 , giup den B = 72
Bai
4. a) A' = - m + 2 = - m — + — =
4 4
m
+ — > 0, vdi moi m.
4
Vay phU"dng
trinh
c6 hai nghiem phan biet vdi mpi m.
b)
Theo
he
thiJc
Vi-et ta c6: x, +
XT
= 2m,
X|X2
= m - 2
-24
-24
Do do M =
X|+X2-6x,X2
(X1+X2)
-2X,X2-6X|X2
-24
-24 -6

(X|
+
Xj)^-8x,X2
(2m)^-8(m-2) m^ - 2m + 4
-6
-6
(m^
-2m + l) + 3 (m - 1)^ + 3
> -2 , vdi moi m
Vi(m-
I)^ + 3>3o
< 2 o
-6
> -2
(m - 1)' + 3 (m - 1)" + 3
M
> -2. Dau "=" xay ra o (m -
1
)^ = 0 o m = 1
Vay M dat gia
tri
nho nhat bang-2, khi m = 1.
'»'
^
X,
Nhan
xet: Day la bai toan van dung he thuTc Vi-et va can lUu y them la:
(m-
1)^ + 3 >3 o
< -(= 2)

(m - + 3
de CO du-dc M >-2
Bai
5.
a) Xet AMEA va AMBF cd EMA (chung).
3 (m - 1)^ + 3
> -2
MEA = MBF (Ttf giac AEFB noi tiep).
Do do AMEA ^ AMBF => — = (g.g)
MB
Vay MAMB = ME.MF
b) Xet AMCA va AMBC cd
CMA (chung)
MCA = MBC (He qua
gdc tao bdi tia tiep tuyen
va day cung)
Do do AMCAAMBC (g.g)
MC MA ^_2
x.AA^o
=> = => MC = MA.MB .
MB
MC
MC 1 OC (Vi MC la tiep tuyen cua (O))
AMCO vuong tai C; CH la diTdng cao => MC^ = MH.MO
Ta cd MA.MB = MH.MO (= MC^)
•i
Pi-
xel AMHA va AMBO cd HMA (chung),
— = MA
(VI

MA.MB = MH.MO). Do do AMHA
MB
MO
AMBO
(c.g.c)
o MHA = MBO
Vay
tu"
giac AHOB noi tiep.
c) Ta cd MKF = 90" (Gdc noi tiep ch^n nuTa difdng
tron,
AMKF vuong tai K,
KE
la
dirdng
cao => MK^ = ME.MF
Ta cd MC^ = MA.MB = ME.MF = MK^ ^ MC = MK
Xet AKMS (MKS = 90") va ACMS (MCS = 90") cd: •
MK = MC, MS (canh chung)
Do dd AKMS = ACMS (canh huycn - canh gdc vuong)
^j^,,,
=> MS la dudng
trung
trifc
cua KC.
Vay MSI KC.
d) • Goi I la giao diem cua MS va KC
fij?
/((.ff ;
;;

Tacd SIK = 90" i
-f>^-'-
• ^ • ' ' '
Luyjn
giai 66
truflc
k1
thi
vAo
I6p 10
ba mign BJc,
Trung,
Nam mOn
ToAn
_
NguySn
Pile
TSn
AISK
vuong tai
I, IT la
diTdng trung tuyen => TS
= TI
AMSC
vuong
tai C, CI la
diTdng
cao => MC^
=
MI.MS

Ta
CO
MI.MS
=
MC^
=
MA.MB.
Xet AMAI va AMSB c6 AMI
(chung),
—
=
^
(vi MI.MS
=
MA.MB)
MB
MS
Do do AMAI
^
AMSB (c.g.c) MIA
=
MBS =>
Tu"
giac ABSI noi tiep.
Ta c6n
CO
MI.MS
=
ME.MF (= MA.MB)
/! A

ME
MI
Xet AMEI va AMSF c6 EMI (chung),
=
(MI.MS
=
ME.MF)
MS
MF
Do do AMEI AMSF (c.g.c) => MEI
=
MSF =>
TuT
giac EFSI noi tiep.
Hai dirdng tron (ABSI) va (EFSI) cat nhau tai S va I c6 tarn Ian lifdt la Q,
P
=> PQ
la
du-dng trung triTc cua doan thang SI.
Ma
T
thuoc diTdng trung tri/c
cua doan thang SI (Vi TS = TI) nen
T
e
PQ
Vay P, Q,
T
th^ng hang.
Nhan xet

Cau a), b) quen thupc, cau c) ne'u nhan ra
MC^
=
MA.MB
=
ME.MF
=
MK' => MC
=
MF giijp den vdi Idi giai. Cau
d)
kho,
chi ve cac tam P, Q khong nen ve cac du'dng tron (P), (Q)
se
rac roi tren
hinh ve.
De
dang thay PQ
la
du'dng trung triTc cua doan thang SI, tim each
chiJng minh TS = TI.
KY
THI TUYEN
SINH
VAO LdP
10
THPT, TP.HA NOI
NAM
HQC
2012

-
2013
Bai
1.
(2,5 diem)
1) Cho bieu thiJc
A = ^ ^
. Tinh gia tri cua A khi
x =
36
Vx
+
2
2) Rut gpn bieu thufc
B
'
^ ^
:4il^(vdix>0;x^I6)
Vx
+ 2
\Ix
+ 4 N/X -
4^
3) Vdi cdc cua bieu thiJc
A v^ B
n6i tren, hay tim cdc gia tri cua
x
nguyen
de
gia tri cua bieu thuTc B(A

-
I) la
so nguyen.
Bai
2.
(2,0 diem). Giai b^i toan sau bang each lap
phiTcJng
tnnh hoSc he phiTcfng tiinh:
12
Hai ngifdi cilng lam chung mot cong viec trong
—
gid thi
xong. Neu
moi
ngirdi
lam mot
minh
thi
ngiTdi thuf nhat hoan thanh cong viec trong
it
hcfn
ngirdi thu" hai
la 2
gict. Hoi neu lam mot minh thi moi ngiTdi phai lam trong
bao nhieu thcfi gian de xong cong vi^c?
Cty
TNHH MTV DWH
Khang Vigt
Bai 3. (1,5 diem)
1) Giai he phu'Png trinh

X
y
X
y
2) Cho phi/Png trinh: x^
-
(4m
-
l)x +
3m^
-
2m
= 0
(an x). Tim
m de
phiTdng
trinh c6 hai ngiem phan biet
Xi,
X2
thoa man dieu kien:
+
xj
=1
Bai 4. (3,5 diem)
Cho dircfng tron (O; R)
c6
du-cfng kinh AB. Ban kinh CO vuong g6c vdi AB,
M
la
mot diem

bat ki
tren cung nho AC (M khac
A,
C): BM
cat
AC
tai H.
Gpi K la hinh chie'u cua H tren AB.
1) Chu-ng minh CBKH
la
tuT
giac noi tiep
2) Chu-ng minh ACM
=
ACK
3) Tren doan thang BM
lay
diem
E
sao cho BE
=
AM. Chitng minh tam gidc
ECM
la
tam giac vuong can tai C.
4) Gpi
d la
tiep tuyen cua (O) tai diem A; cho
P la
diem nam tren

d
sao cho hai
diem
P, C
nam
trong cdng
mot
nu-a
mat
phang
bd
AB
va
"^^'^^
= R
.
MA
ChiJng minh du-dng thang PB di qua trung diem cua doan thang HK.
Bai 5. (0,5 diem). Vdi x,
y la
cac so du-dng thoa man dieu kien
x >
2y, tim gia
tri
„2
2
nho nha't cua bieu ihuTc:
M
= i-
.

xy
Hl/dfNG
DAN
GIAI
'
Bail,
'
/36+4
6 + 4
10 5 r :
8
'
4 1
1) Gia
tri
cua
A
khi
x =
36
la:
5
4
2)
B
=
N/36
+2
6 +
2

X
+
16
_
>/x
-
4)
+
(N/^
+
4)
,Vx+4
Vx-4j"Vx+2
(7x+4)(Vx+4)
_ X-4V2+4Vx+16 Vx+2
x +
16Vx
+ 2
Vx+2
X
+
16
V5^
+
2
3) B(A- 1)
=
X
-
16

V^
+
2'
X
+
16
X -16
Vx+4
R
+ 2
-1
x
-
16
X
+
16
X -
16
Vx+2
2 _ 2
x-16 Vx+2
x-16
De B(A
-
1)
la
so'
nguyen thi x
-

16 la iTdc cua
2.
Tacdx- 16
=
l;-l;2;-2ox
=
17; 15; 18;
14
Vi x>0,
x,t 16.
Luygn
dS
trudc
ki thi vao I6p 10 ba
mjgn
B&c.
Trung. Mam mSn Toan , Mguygn
Difc
Tan
Do
vay x = 14; 15; 17; 18 la cac gia tri nguyen cua x can tim.
Nhan xet: Day la cac bai toan de, quen thuoc
Bai
2. Goi
thdi
gian
ngiTdi
thuT
nhat
lam mot minh xong cong viec la x (gicJ)

12
(Dieu
kien x > — )
Thdi
gian
ngiTcfi
thiJ hai lam mot minh xong cong viec la x + 2 (gid)
1
"
Trong 1 gid,
ngiTdi
thiJ
nhat
lam diTdc: 1 : x = - (cong viec)
Trong
1 gid,
ngiTdi
thiJ hai lam diTdc: 1 : (x + 2) = (cong viec)
X
~i~
^
(4
H
Trong 1 gid, hai
ngiTdi
lam chung diTdc:
-
+
—i—
(cong vice) hay 1 : — = — (cong viec)

X X + 2 5 12
Ta CO phiTdng
trinh
—
+ —^-—
X X + 2
_5_
12
«
12(x + 2)+ 12x = 5x (x + 2)
o 12x + 24 + 12x = 5x^ + lOx o 5x^ - 14x - 24 = 0
A'
=49+ 120= 169, VA' = 13
X,
= = 4 (thich hdp), Xj = ^—^ = ^ (khong thich hdp)
5 5 5
h Vay
thdi
gian
ngiTdi
thiJ
nhat
lam mot minh xong cong viec la 4 gid
Thdi
gian
ngiTdi
thi? hai lam mot minh xong cong viec la: 4 + 2 = 6 (gid)
Nhan xet: Day la
dang
bai:

Giai
bai toan
bang
each
lap phtfdng
trinh,
bai
tocin
ve cong vice, rat qucn thuoc vdi moi hoc sinh.
Bai
3.
flO
1)
<=>
<
X y
X y
'x
= 2
6 _ 2 ^ J o
2 v
—
+
—
= 4
X y
X y
X = 2
y
=

5
X y
X = 2
y
= 1
Vay
he phiTdng
trinh
c6 nghiem (x; y) la (2; 1)
2)
A = (4m -1)^-4 (3m^ - 2m) = 16m^ - 8m + 1 - 12m^ + 8m
=
4m^ + 1 > 0, vdi moi m
Vay
phiTdng
trinh
c6 hai nghiem phan biet, vdi moi m.
Theo he thiJc
Vi-et,
ta c6 •
X, + X2 = 4m - 1
Xj.Xj = 3m^ - 2m
Do
do xf +
X2
= 7
<=>
(X|
+
Xj)^

- 2X|X2 = 7
«
(4m
-
1)'
-
2(3m2
-
2m)
= 7 o
16m^
- 8m + 1
<=>
lOm^ - 4m - 6 = 0 o 5m^ - 2m - 3 = 0
Ta CO a + b + c = 5 + (-2) + (-3) = 0
c 3
mi
= 1, m-, =
—
= —
Cty
TIMHH
MTV
\liang
Vi$t
6m
+ 4m = 7
.
(I:s;'
'A,-

Vay
m = 1, m = thi x^ + X2 = 7
Nhan xet:
1)
Bai toan nay de, quen thuoc ' Is
2)
Tufhethu'cVi-etc6xi+X2
=
4m-l,x,X2
= 3m^-2m
Ta
c6:xf
+ xj = (4m - 1)^ - 2(3m^ - 2m) = lOm^ - 4m + 1, giup den difdc
m
= 1; m = -—
Bai
4.
1)
ACB = 90" (goc noi tiep chan nuTa
du-cJng
Iron)
Ti?
giacCBKH c6
HCB
+ HKB = 90" + 90" = 180".
Do
do ti? giac
CBKH
noi tiep
2)

Ta CO ACM = ABM (Hai gdc noi tiep
ciing
chan cung AM)
ABM
= ACK
(Tu"
giac
CBKH
noi tiep)
Do
do ACM = ACK
3)
Ta CO CO 1 AB (gt) => AC = BC =^ AC = BC
Xet ACM A
va ACEB ta c6:
AM
= BE (gt);
CAM
=
CBE
(hai goc noi tiep
cilng
ch^n cung
MC), AC
= BC.
Do do
ACMA
=
ACEB
(c.g.c)

=>CM = CE,
MCA
= ECB
Ta CO MCE = MCA + ACE = ECB + ACE = 90"
AECM
vuong
tai C (MCE = 90") c6 CM = CE
Do
vay tarn giac
ECM
vuong can tai C . •
4)
Goi N la giao diem cua PB va HK
•{X
Xet
ABKH
va
ABMA
c6 KBH (chung), BKH = BMA (= 90") /g^
Dod6ABKH-ABMA(g.g)=^-l^
=
lJi=>:^
=
— (1)
MA
MB MA KH
Luyjn
giai
6i
frUSc ki thi vSo lOp 10 ba mi6n Ba.

Nam
mfln ToAn
_
Nguyjn DCfc Ta'n
Ta CO PA ±
AB,
NK ± AB => PA // NK
APAB
CO
NK // PA =>
(2)
AP
BA
BABK
R _
BK
^
AP
"
NK
^
AP
~
2NK
"
^
" '
AP.MB
„ ^ , MB R
Ma

= R (gt) => =
— (3)
MA
MA AP • ' •
Tir
(1), (2), va (3)
CO
KH = 2NK. Do do N la trung diem cua HK
. ,
Vay
du'cing lhang PB di qua Irung diem ciia
doan
thang HK
Nhan xet: Day la bai loan rat
quen
ihuoc doi vdi moi hoc sinh Idp 9.
Bai
5.
VI
X, y > 0 v^ X
>
2y
Ta
CO
— > 2 va ap dung bai
dang
ihiJc Co-si cho hai so du'dng, ta c6
y
x^
+ 4y^ >

lyjx^Ay^
<=> x^ + 4y^ > 4xy
x^+y^
4x^+4y^
3x^
x^ + 4y^
Do
vay M
=
— = — =
+ — ;
xy
4xy 4xy 4xy
4
y 4xy 4 2 2
Dau "=" xay ra
o
x = 2y
Vay
gia tri nho nhaft cua bieu
thiifc
M la
^.
Nhan xet:
Tijr
dieu kien rang
buoc
x > 2y, cho ta dif
doan
rang M dat gia tri

nho
nhat
khi x = 2y.
Tir
do, giup dieu chinh he so thich hdp "x^" va "4y^" roi van dung ba't
dang
thiJc Co-si cho hai so du'dng de giai
nhiT
tren.
x^
+ y^ 4x^ + 4y^
Thao tac "bien"
—
thanh — giup c6 Idi giai dep.
xy
4xy
Tir
Idi giai nay cung cho ta Idi giai khdng van dung ba't d^ng thuTc Co-si cho
hai so du'dng
nhu"
sau:
x^
+ y^ 4x^ + 4y^ 3x^ + (x^
-
4xy + 4y^) + 4xy
M
=
xy
4xy 4xy
4

y 4xy 4 2
NhU'vay
M >
^ .
Cty
TNHH MTV DVVH Khang Vi^t
at
SO
3
KY
THI TUYEN
SINH
VAO L(3P
10
THPT, TINH D5NG NAI
NAM
HOC
2012
-
2013
CSu 1.(1,5 diem)
^ h-
1)
Giai phu'dng
trinh:
7x^
-
8x
-
9 = 0

;(,:;;!•
,
•3x + 2y =
l
_4x + 5y-6
. " ,1
2)
Giai he phu'cfng
trinh:
Cfiu
2. (2,0 diem)
1)
Rut gon cac bieu thUc: M
=
;=— ; N =
—1=
'
V3 ^-l
2)
Cho
Xi;
X2
la hai nghiem ciia phUcfng
trinh:
x^
-
x
-
1 = 0
Tinh:

— + —
X,
X2
Cfiu
3. (1,5 diem) Trong mat
phang
vdi he true toa do Oxy cho cac ham so:
y
= 3x2
^j^.
(p). y = 2x
-
3 c6 do thi la (d); y = kx -1- n c6 do thi la (d,)
vdi
k va n la nhiJng so thifc
1)
Vedo thi (P).
2)
Tim k va n biet (d,) di qua diem
T(l;
2) va (d,) // (d).
Cfiu
4. (1,5 diem) Mot thuTa dat hinh
chff
nhat
c6 chu vi
bang
198m, dien
tich
bang

2430m^.
Tinh
chieu dai va chieu rong cua thuTa da't hinh
chff
nhat
da cho.
Cfiu
5. (3,5 diem) Cho hinh vuong
ABCD.
Lay diem E
thuoc
canh
BC, vdi
E
khong trung B va E khong trung C. Ve EF vuong goc vdi AE, vdi F
thuoc
CD.
Dirdng thdng AF c^t diTdng thing BC tai G. Ve diTdng thing
a
di qua
diem A va vuong gdc vdi AE, di/dng thing a cit diTdng thing DE tai diem H.
i\ • u AE
CD
1)
Chffngminh
= .
AF
DE
2)
Chffng minh rang tff

giac
AEGH
la ti?
giac
noi tiep diTdng tron.
3)
Goi b la tiep tuye'n cua du'dng tron ngoai tie'p tam
giac
AHE tai E, bie't b cat
du'dng trung
trffc
cua
doan
thang EG tai diem K. Chffng minh rang KG la tiep
tuye'n cua du'dng tron ngoai tiep tam
giac
AHE.
Hl/OfNG
DAN
GIAI
Cfiul.
l)7x^-8x-9
= 0
A' = 16 + 63 = 79; VA^
=
V79
PhiTdng
trinh
c6 hai nghiem
phan

biet x,
= ^ ,
Xj
=
-—z-^
|3x.2y
= l ^
4x
+ 5y = 6
X
= -1
2)
15x
+
lOy
= 5
<=>
<=>
8.(-l)
+ lOy = 12
o
<=> <
7x
= -7
8x
+
lOy
= 12
X
= -1

y
= 2
8x
+
lOy
= 12
fx
=
-l
^lOy
= 20
He phiTdng trinh
c6
nghiem
(x;
y) la (-1; 2)
Nhan
xet:
Bai
toan
bay de va
quen
thupc
doi vdi mpi
hpc
sinh
Idp
9.
C&u2.
^

Vl2j^
^ _ 2^^
V3
73 V3 V3
N
= ^-^^ = 2 -
2V2
+
1
^ (^-Q =
V2
-
1
72-1
72-1 72-1
2)
a=:
1
>0, c =
-l
<0.
PhiTPng
trinh
c6 hai
nghiem
phan
biet
Xi, X2 (xi, X2
khac
0).

Theo
he
thuTc
Vi-et
ta c6 xi +
X2
= 1,
X|X2
= -1
1) M
Do
do — + —
X2
+ X,
X,X2
-1
=
-1
Nhan
xet: Day
cQng
la bai
toan
de,
thi
sinh
co the
sijf
dung
A=l+4

= 5>0
de chiirng
to
phu'dng
trinh
co hai
nghiem
phan
biet.
X
1
-1
0
1
1
2 2
y
=
3x^
3
3
0
1
3
4
4
2)
(d,)//(d)o
k
= 2

n
^ -3
.
Ta CO k = 2
CtyTNHH MTV DVVH
Khang
Vi$t
T (1;
2) e (d,) ^ 2 =
2.1
+ n
=>
n = 0
(ihich
hdp)
Vay
k = 2; n = 0
Nhan
xet: Day la bai
toan
do thj ham so
ciing raft
quen
thupc.
Cau 4.
NiJfa
chu vi
ciia ihiira
difl
la: 198 : 2 = 99 (m)

99
Gpi
chieu
rpng
ciia thijfa
dal
la: x(m) (Dicu kien
x < —)
si
OX
• t
Chieu
dai cua
thiJa
dat la 99 - x (m)
Dien tich ciia thiira
dat la
x(99
- x)
(m')
hay
2430nr.
Ta co
phu^dng
trinh
x(99
-
X)
=
2430

X' - 99x +
2430
= 0
A
=
99^
-
4.1.2430
=
9801
-
9720
= 81
7A
= 9
99
+ 9 99-9
X|
= —:— = 54
(loai);
Xj = —z— = 45
(nhan)
2
- • . 2
Vay
chieu
rpng
ciia
thufa
dal la 45m ' '

Chieu
dai cua
thij-a
dat
la:
99 - 45 = 54 (m)
Nhan
xet: Day la bai
toan
giai
bai
loan
bang
each
lap
phu^Png
trinh, loai
toan
hinh
hpc ra't de va
quen
thupc.
cau
5.
1)
Tu" giiic AEFD
co
AEF
+
ADF

= 90" +
90"
= I8O"
=> Tu"
giac
AEFD
npi
liep
=> EAF
= EDF
Xet AEAF vii ACDE
co AEF = DCE (=
90")
DodoAEAF'^ ACDE (gt)
'
AE
AF AE CD
•
Vay
CD
DE
AF
DE
2)
Taco
EAF
+
HAG
=
90",

'
CDE
+
HEG
- 90"
(ACDE
vuong
tai C).
EAF
= CDE
(chu-ng
minh trcn).
, ji
Suy
ra
HAG
=
FIEG
.
Vay tiiTgiac AEGH npi
tiep
3) Gpi
O la
trung
diem ciia
HE.
Ta
CO O la
tarn
du'dng

Iron
ngoai
tiep
tu"
giac
AEGH
cQng
la
dU'cJng
tron
ngoai
tiep
tarn
giac
AHE.
XetAOEKva AOGK
c6 OE = OG (=
R), OK
(canh
chung),
^
KE
=
KG
(K
thupc
dirdng
trung
trifc
cua

EG.
. i;*
Do
do
AOEK
=
AOGK
(c.c.c)
^ OEK -
OGK
1 s
'i^'
Luyjn giSi di tri/flc ki thi vao Iflp 10 ba miSn B^c. Trung, Nam mOn To^n _ Nguygn Difc Ta'n
Ma
OEK = 90" (b la
ticp tuycn
cua
(O))
ncn OGK = 90"
KG
± OG va G
thuoc dudng tron
(O) (Vi tur
giac
AEH noi
tiep difdng
tron (O)).
Do do KG la
tiep tuye'n
cua

difdng tron
(O)
TiJc
la KG la
tiep tuyen
cua
du'dng tron ngoai tiep tarn giac
AHE.
Nhan
xet: Bai
todn hinh
hoc
cung quen thupc,
de
chtfng minh
KG la
tiep
tuye'n
cua
dufcJng tron
(O), ne'u da den
diTdc
KG 1 OG can
chiJng minh them
G thuoc diTdng tron
(O).
2) Giai
he
phu'dng trinh:
D6S64

f,, DE THI
TUYEN
SINK
VAO LdP 10
THPT, TP.OA
NANG
NAM
HOC
2012 - 2013
Bai
1.
(2,0
diem)
1) Giai phu'dng trinh:
(x + l)(x +
2)
=
0
2x + y -1
"x-2y
= 7
Bai
2.
(1,0
diem)
Rut
gon
bieu ihiJc
A = (VlO -
72)^3+

N/5
Bai 3. (1,5 diem) Bie't rang du'cfng
cong trong hinh
ve ben la mot
parabol
y = ax^.
1)
Tim he so a. ' " ' ^"
2)
Goi M va N la cac
giao
diem
cua
du'dng thang
\
y
=
X
+
4 vdi
parabol.
Tim
toa do cua cAc
diem
M va N.
Bai
4.
(2,0
diem)
Cho

phiTdng trinh x^
-
2x
-
3m^
=
0,
vdi m la
tham
so.
1) Giai phifdng trinh
khi m = 1.
2)
Tim tat ca cac gia tri cua m de
phiTdng trinh
c6 hai
nghiem
Xi,
X2
khdc
0
va thoa dieu kien
^ - ^ = -
Bai
5. (3,5
diem)
Cho hai
du'dng tron
(O) va (O')
tie'p

xuc
ngoai
tai A. Ke
tie'p
tuyen chung ngoai
BC, B e (O), C e
(O'). DiTcfng thang
BO c^t (O) tai
diem
thtf hai
la D.
1) ChiJng minh
r^ng
tur gidc CO'OB 1^
mot
hinh thang vuong.
'
Cty
TNHH
MTV DWH Khang
Vi$t
2) Chitng minh rang
ba
diem
A, C, D
th^ng hang.
3)
Tir D ke
ticp tuyen
DE vdi

diTcJng tron
(O') (E la
tiep diem). Chu-ng minh
rang
DB = DE.
Hi/^ng dSn giai
- ' ^ '
Bai
1. l)(x+ l)(x + 2) = 0o
X +
1
= 0
x
+ 2 = 0
<=>
x
= -1
X - -2
Phu'dng trinh
c6 hai
nghiem phan biet:
x, =
-1;
X2
= -2
[5x
= 5
X - 2y - 7
j2x
+ y = -l [4x + 2y = -2 5x = 5

x
- 2y = 7
<=>
i
X - 1
1
- 2y = 7
X -2y = 7
x
= i rx = i
-2y
= 6 [y = -3
He phu'dng trinh
c6
nghiem (x;
y) duy
nhat
la
(1;
-3).
Nhan xet:
Day la bai
toan
qua de
Ba:
2. A = (VlO -
V2)V3
+ V5 = (V5 -
l)^^^/3
+

Vs
=
(VF-l)V^T2Vf
=
(V5-l)^(V5
+ lf
=
(>/5 - l)(V5 + l) = 5 -
1
= 4
Nhan xet:
Bai nay qua de.
Bai 3. 1) parabol
y =
ax^
di qua
diem
(2;
2)
o
2
=
a.2^
oa = — oa = -
,x),
00
I.
Vay
a = -
2

2)
(P): y = -x\y = x + 4
2
PhiTdng trinh hoanh
do
giao diem
cua (d) va
(P):
-x^ = x + 4
2
Ta
CO
^x^ = x + 4c^x^ =2x +
8<:=>x^-2x-8
=
0
A'=l+8
= 9,
VA^
= 3
x,=l^
= -2
X, =
1
'1
1
.2 „ . 1
X,
= 4 thi y, = 4^ = 8 ;
X2

= -2 thi y-^ =
-(-2)2
= 2
Vay M(4;
8)
vaJ^(;:2L2)Jioac M(-2;
2) va
M(4;
8)
Luy$n
giai
dg
trudc
kl thi v^o Idp 10 ba mjgn BJc.
Trung,
Nam mOn ToAn _ Nguygn 0(!c IJn
Nhan
xet: Day la bai loan ve ham so va do thi, dang toan nay cung
ra'l
quen
thuoc va de.
Bai 4. 1) m = 1, phiTc-fng trinh tret thanh - 2x - 3 = 0
a-b + c=l-(-2)-3 = 0 ' ' ^'
Phu'dng
Ifmh c6 hai nghiem phan bict:
Xi
=
-1;
X2
= — = 3 i , ^!

a
2) PhiTcfng trinh c6 hai nghiem
Xi,
X2
khac
0
()2 - 2.0 - 3m^ ^ 0
A'
=
1
+ 3m^ > 0
Dieu
kien m 0
m
^ 0
m
e
C:>
m ^ 0
Theo
he
thuTc
Vi-ct,
la c6 •
X|
+ Xj = 2
XjXj
= -3m'
Vi
x, + X2 = 2 > 0; X|X2 = -3m' < 0 (vi m ^ 0);

2^ _ ^ = > 0 nen X2 > 0 > X,
X-,
X, 3
Ma
(x, - X2)^ = 4 + 12m^ nen X2 - x, = 2^1 + 3m^
.
. « -2 2
Ta
CO
8
3
IT
O XI — XT
-A
= _ -! ^ =
.2 A, J X,X2 3
(X,
+X2)(x,
-Xj) 8 -2.2Vr+W_
X,X
1^2
=
- <=>
3
-3m^
<=> Vl + 3m^ = 2 o
1
+ 3m^ = 4 o m = ±1 i
m
= 1 (thich hdp), m = -1 (ihich hcJp)

Nhan
xet: Day la bai loan ve phiTdng trinh bac hai va uTng diing cua he
thiJc
Vi-et,
phat hicn
X2
> 0 >
X|
giup c6 di/dc Idi giai cua bai toan.
Bai5. a)BC la tiep tuyen chung
ngoai cua (O). (O'). Do do BC 1
OB,
BC 1 O'C =i> O'C // OB
TiJ giac
CO'OB
la hinh thang. Ma
OBC = 90" (BC 1 OB). Do do tuf
giac
CO'OB
la hinh thang vuong
2) (O) va (O') tiep xuc ngoai tai A (gt)
=>0, O', A thang hang.
Ta
CO
DOA = AO^ (so le Irong va OB // O'C)
Cty
TNHH MTV DWH Khang
Vi$t
AOAD
=

CO
OA ^ OD (= R) =>
AO
AD
can tai O.
Ma
0'A = 0'C(=r)=>AO'ACcanlaiO'.
Do vay
AOAD
^ AO'AC => OAD = 0\^C
SJ*
'
Ta
CO
OAD + OAC = O^ + OAC = 180" => Hai tia AD, AC doi
nhau.
Vay
ba diem A, C, D
ihiing
hang.
3) Ta
CO
BAD ^ 90" (goc noi tiep ch^n
niJa
diTdng
tron)
ABDC
vuong tai B, BA la du-dng cao => DB^ = DA.DC
Xet
ADEA

va ADCE c6 EDA (chung), DEA = DCE (He qua goc tao bdi tia
tiep tuyen va day cung). Do do
ADEA
^ ADCE (g.g) ,
^
,
^^
= ^=^DE^=DA.DC.
DC
DE
Ta
CO
DB^ = DE^ (=
DA.DC).
Vay DB = DE.
Nhan xet: Day la bai toan hinh hoc de v^
quen
thuoc.
D6
SO 5
DE THI
TUYEN
SINH
VAO L(3P 10
THPT,
TJNH
THL/A
THIEN
HUE
NAM HOC 2012 - 2013

Bai
1. (2,0 diem)
a)
Cho bid'u thiJc: C = ^^^^ + - (V5 + 3) . ChiJng to C = V3
b) Giai phu^c^ng trinh: 3Vx - 2 - Vx^ - 4 =0
Bai
2. (2,0 diem) Cho ham so y = x^ c6 do thj (P) va dKdng lhang (d) di qua
diem
M(
1;
2) c6 he so goc k^O.
a) Chijrng minh r3ng vdi moi gia tri k ^ 0. Du-clng
thang
(d) luon cat (P) tai hai
diem
phan
biet A va B.
b)
Goi
XA
va
XB
la
hoanh
6o cua hai diem A va B. Chij-ng minh
rang
XA
+ Xu -
XA.XB
- 2 = 0

Bai
3. (2, 0 diem)
<

a) Mot xe lura di tir ga A den ga B. Sau do 1 gid 40 phut, mot xe lu-a
khac
di tiT
ga B den ga A vdi van toe I6n hiln van toe cua xe lura thi? nha'l la 5km/h. hai
xe lura gap
nhau
tai mot ga
each
ga B 300km. Tim van toe cua moi xe, biet
r^ng
quang
diTcJng
s^t
tiT
ga A den ga B dai 645km.
•2(x + y) = 5(x - y)
20 20
b)
Giai he phi/dng
trinh:
•
X
+ y x-y ;, ,^ ,,,,, vf,-
Luy^n giai
iSi
truflc

k1
thi v^o
Iflp
10 ba miSn
Bjlc,
Trung, Nam mOn Toan _
NguySn
Dijfc
Tin
Bai 4. (3,0 diem) Cho nufa diTcIng tron (O) diTdng kinh BC. Lay diem A tren tia
doi cua tia CB. Ke tiep tuyen AF vdi nuTa dir5ng lr6n (O) (F 1^ tie'p diem), tia
' AF c^t tia tiep tuyen Bx cua nuTa diTdng tron (O) tai D (tia tiep tuye'n Bx nam
trong niJa mat phang bd BC chtfa niJa diTcJng tron (O)). Goi H la giao diem
cua BF vdi DO; K la giao diem ihuT hai cua DC vdi nuTa diTdng tr5n (O).
a) ChuTng minh rang: AO.AB = AF.AD.
b) Churng minh
tu"
giac KHOC noi tiep.
. , BD DM
c) Ke OM 1 BC (M thuoc doan thSng AD). Chtfng
mmh
Bai 5. (1,0 diem) Cho hinh chu' nhat OABC,
COB = 30*'. Goi CH la diTdng cao cua tam
giac CO, CH = 20cm. Khi hinh
chu"
nhat OABC
quay quanh mot vong quanh canh OC co dinh
ta diTdc mot hinh tru, khi do tam giac OHC tao
lhanh hinh (H). Tinh the tich cua phan hinh
try

nam ben ngoai hinh (H). (Cho n « 3,1416).
Hl/CfNG DAN GIAI
Bai 1.
N/5
V3 + 1
^/5 V3+1 ^ '
(V5.3)
b) 3Vx -2 - Vx^ -4 = Qo 3Vx -2 = Vx^ -4 o •
<=>
i
X > 2
9x -18 = x^ -4
X > 2
x(x - 2) - 7(x - 2) = 0
X > 2
<=>
i
fx > 2
x^ -9x + 14 = 0
X > 2
(X - 2)(x - 7) = 0
X -2 > 0
9(x - 2) = x^ - 4
X > 2
x^-2x-7x + 14 = 0
x-2 = 0
x-7 = 0
X = 2
X = 7
Vay nghiem cua phu'dng trinh la

Xi
= 2;
Xa
= 7
Nhan xet: Day la bai toan dc, cau b con c6 the giai nhiT sau:
DKXD: x>2
Cty
TNHH
MTV DVVii
r,t;ang
v'lu',
Ta
CO
3sjx - 2 - sjx^ - 4 = 0 o 3Vx - 2 - ^(x + 2)(x - 2) = 0
« Vx - 2 (3 - Vx + 2) = 0o
Vx-2
= 0
3 - Vx + 2 = 0
x - 2 = 0
+ 2 = 3
X = 2
X + 2 = 9
(+ x)<
x = 2
_x = 7
•-;a-:.
Bai 2. Phu'ring trinh du'Ctng thang (d) (c6 he so goc k 0) c6 dang y = kx + b:
Ta CO M e (d) 2 = k.l + b b = 2 - k
(d):y = kx + 2-k + !''- '
PhiTdng trinh hoanh do giao diem cua (d) va (P)

= kx + 2 - k o x' - kx - 2 + k = 0 (*)
A
= (-k}~ - 4(-2 + k) = k^ + 8 - 4k
= (k^ - 4k + 4) + 4 = (k - 2)^ + 4 > 0, vdi moi k
Do vay v(':ri moi gia tri k
;^
0, (d) luon cat (P) tai hai diem phan biet A va B.
b) Ta
CO
XA,
XIJ
la cac nghiem cua phiTcfng trmh (*)
Theo he thiJc Vi-et ta co XA + XB = k, XA-XH = -2 + k
Do do XA + XB - XA.XR - 2 = k-(-2 + k)-2 = k + 2- k- 2 = 0
Nlian xet: Day la bai loan vc ham so va do thi kc't hdp vdi phu'dng trinh bac
hai mot an va he ihu'c Vi-ct, can ghi nhd rang: (d) cat (P) lai hai diem phan
biet
<=>
Phifdng trinh hoiinh do giao diem co hai nghiem phan biet.
Bai 3. Doi
1
gid 40 phut = ^ gid
Quang du-dng {ii ga A den cho hai xc luTa gSp nhau tcii ga each B 300km la:
645 - 300 = 345 (km)
Goi van to'c cua xe lu^a thiJ nha't la x (km/gid) (Dieu kien x > 0)
Van toe cua xc liJa thu' hai la x + 5 (km/gi(<) ^•
ThcJi gian xe luTa thdr nhat da di la: 345 : x =
345
Thdi gian xe lufa
thu"

hai da di la: 300
:
(x + 5) =
(gi^)
300
X + 5
(gia)
Xe liJa thiir hai khdi hanh sau ^ gicJ, nen ta c6 phifcfng trinh:
345 300
5
3
69
X
60
X x+5 3 X x+5 3
207(x + 5) - 180x = x(x + 5) » 207x + 1035 - 180x = x^ + 5x
c:>x'- 22x- 1035 = 0
Luy$n
gi§i
dg
trutSc
kl thi vio lOp 10 ba
mjgn
BSc.
Trung,
Nam mOn
ToAn
_
Nguygn
Difc

Ta'n
A'= 121 + 1035 = 1156, ^/A' = 34
X|
= ^ 45 (thich hdp), xj =
^ ^
^ "^"^ = -23 (khong
ihich
hdp)
Vay van toe xc luTa
thu"
nha't (xe luTa
khdi
hanh
tu"
A) la 45 km/gid
Van toe xe
liJa
thu-
hai (xc lu'a
khdi
hanh
tu"
B) la:
45 + 5 = 50
(km/gid)
b) Dieu kien x y va x ;t -y '
Ta CO
2(x + y) = 5(x - y)
20
20

= 7
<=> <
<=> <
X + y X - y
'2(x+)
= 5(x - y)
20 100
2(x + y) = 5(x - y)
20 100
= 7
x + y 2(x + y)
2(x + y) = 5(x - y)
X + y = 10
x - y = 4
= 7
x + y
5(x-y)
2(x + y) = 5(x - y)
= 7
70
<=> <
x + y
2.10 = 5(x + y)
X + y = 10
X = 7
(thich
hdp)
2x = 14
X + y = 10 [x + y = 10 [y 3
Vay nghiem (x; y) cua he phu-cfng

trinh
la (7; 3)
Nhan xet:
a) Giai bai toan bang
each
lap phiTcfng
trinh
loai toan chuyen dong, dang bai
toan nay cung rat thifdng
xuift
hicn trong cac de kiem tra hoc ki hay thi vao
Idp 10.
b) Mau chot cua bai toan la bien doi
20 20 _ 20 100
x + y
20
X -y
100
= 7 thanh
= 7 de CO
X + y 2(x + y)
2(x + y) =
5(x-y)
,„,,;^.,
Bai
4. a) Ta co AF la tiep tuyen cua du-dng
tr6n(0)(gt)
=:> AF 1 OF => AFO = 90"
Va DB la tiep tuyen cua du^dng
tron

(O)
(gt) DB 1 OB => ABD = 90"
Xet
AAFO
va
AABD
co:
x + y 5(x - y)
= 7 vi phu'Ong
trinh
thiJ
nha't cua he phu-dng
trinh
la:
\
o
Cty
TMHH
MTV
DVVH
Khang
Vigt
FAO (Chung), AFO = ABD (= 90")
Do do
AAFO
AABD
(g.g) => 4^ = 4^
Vay
AO.AB
=

AF.AD
i- .
b) DB, DF lii cac tiep tuyen cua du'dng
tron
(O)
=i> DB = DF va DO la tia phan
giac
goc BDF
ADBF can tai D, DO la dUcfng phan
giac
?, r
DO cung la
du-ttng
cao => BH 1 OD.
ABOD
vuong tai B, BH la diTdng cao => DB' = DH.DO " - -
Mat
khac BKC = 90" (goc noi tiep chan nufa difdng tron)
ABDC
vuong
tiii
B, BK la difdng cao => DB^ = DK.DC
Ta CO DH.DO - DK.DC (= DB^)
DK DH
Xet ADKH va
ADOC
co KDH
(ehung),
= (vi DH.DO =
DK.DC)

DO DC
Do do ADKH ^
ADOC
(c.g.c)
=> DHK = DCO
Vay
tu"
giac
KHOC
noi tiep
c) Ta CO DB 1 BC, MO 1 BC (gl) =^ DB
//
MO BDO = DOM
Ma BDO = 6DM (Tinh chat cua hai tiep tuyen ca't nhau)
Do do DOM = ODM =>
AMDO
can tai M => DM = OM
BD AD
AAOM
CO OM//BD
OM AM
BD AM + DM BD , DM
Nen = => =
1
+
DM AM DM AM
^ . BD DM ,
Do vay = 1
DM AM J
Nhan xet: Cau a, b) ra't quen thuoc doi vdi moi hoc s- ih Idp 9. '

Cau c) chia khoa la DM = OM, do vay, day cung la ciu de lay diem.
Bai
5. Khi quay
hinh
chi? nhat
OABC
mot vong quanh canh OC thi tam
giac
OHC tao thanh
hinh
(H) gom 2
hinh
non up vao nhau co ciing ban
kinh
la
HK, chieu cao la OK va OC,
hinh
chu' nhat
OABC
tao thanh
hinh
tru co ban
kinh
day la CB, chieu cao la OC.
Ta CO
AHOC
vuong tai H => OH = CH cot COH = CH cot 30" = 20. S (cm)
Va sinHOC = ^ OC = = = ^ = 40 (cm)
OC sinHOC sin30" 1
2

_
Nguyen uac lan
ACOB
vuong tai
C
=> CB
=
OCtanCOB
=
40tan30"
= ^^y^ (cm)
AKOH
vuong tai
K
=> KH
=
OHsin KOH
=
20V3.i
=
10^
(cm)
The
tich
hinh
tru la:
V,
=
nBC^OC
= 7t

The
tich
hinh(H)
la:
V,
+ V, =
-Ti.HK^OK
+
-;i.HK^KC
^
3 3
40^3
64000
, .
.40
(cm
)
= ijT.HK-
(OK
+ KC) =
-7I(10N/3)' .40
=
40071
(cm')
The
tich
hinh
tru nam ngoai
hinh
(H)

lii:
V
= V, - (V. . VO = ^ -
4000.
. ^ .
8168,16
(cm"^)
Nhan
xet:
Chia khoa
bai
loan
la
nhan
ra
khi quay
hinh
chOr nhat
OABC
mot
vong quang canh
CO
thi tam
giac
OHC tao
thanh
hinh
(H)
gom
2

hinh
non
up
vac nhau, cung
ban
kinh
la HK,
chicu
cao la OK va OC;
hinh
chi? nhat
OABC
tcio thanh
hinh
tru
c6
ban
kinh
day la
CB, chieu
cao la OC.
DE
80 6
DE
THI TUYEN SINH VAO LdP 10 THPT, TP.CAN THd
NAM HOC 2012 - 2013
Cau 1.
(2,0
diem)
Giai

he
phu'dng
trinh,
cac
phu'rtng
trinh
sau
day:
fx
+ y = 43
1)
^
1
3x
-2y - 19
3)
x^-
12x
+
36
= 0
Cfiu2.
(1,5 diem)
Cho bieu thuTc:
K = 2
r 1 1 ^
rv^-fi]
,
Va -
1

^ya
y
2)
x + 5
=2x-18
4)
Vx
-2011
+
V4x
-
8044
= 3
(vdi
a
>
0, a
;^
1)
1)
Rut gpn bieu thiJc
K.
2)
Tim a de
K = V2012 .
Cau3.
(1,5
diem)
Cho phifdng
trinh

(an
so
x):
x^
-
4x
-
m^
+ 3 = 0 (*).
Cty
TNHH
MTV
DVVH
Khang
Vijt
1) Chiang minh phu'ctng
trinh
(*)
luon
c6
hai nghiem phan bict
vdi moi
.
2)
Tim gia
tri ciia
m de
phiftJng
trinh
(*) c6

hai nghiem
X|,
X2
thoa
X2
=
-5X|.
Cjiu4.
(l,5diem)
,
.ihX^.;;i
rns,,).,;;^
,
Mot
6 to
dii"
dinh
di
tif
A
dc'n
B
each
nhau 120km trong
mot
thdi
gian
quy
dinh.
.Sail khi

di
difOc
1 gid
Ihl
6 to
bi
chan
bdi
xe
cifii
hoa 10
phut.
Do do de
den
B
dung
han
xe
phai tang
van toe
Ihem
6km/li.
Tinh
van toe
liic dau eiia
6
i6.
Cau
5. (3,5
diem)

Cho
di/dng Iron
(O),
diem
A d
ngoai du'dng lion
ve
hai lie'p
luyen
AB va AC
(B,
C
lii
cac
iiep diem).
OA
cat BC lai H.
1) ChiJng minh
lu"
giac
AB( )C
noi
tiep.
r
2) ChiVng
Miiiih BC
vuong
gdc
\di OA va
BA.BE

=
AIE.BO
,^
3)
Goi
I la
triing
diem ciia BE, difdng lhang qua
I va
vuong
goc
OI cat cae lia AB,
AC theo
thi'r
liT lai
D
\
F.
Chifng minh
I'lX)
-
iTcO
va
ADOF
can
lai
O.
4) ChiVng minh
F
la

ining diem ciia
AC.
IMJ^NC;
DAN
GIAI
Cau
1.
|x
+ y = 43
[3x-2y
= 19
[3x-2y
= 19
fx
-21
^x =
21
[x-21
3.2!
- 2y - 19 [-2y -
-44
!y = 22
Vay nghiem ciia
he
phifdng
Iririli
la (x; y) =
(21;
22)
'2x-18>0 [2x>18

x
+ 5 - 2x -
18
o j X -
2x
=
-18
- 5
X
+ 5 = -2x +
18
1)
f2x
+
2v-86
f5x -
105
3x
- 2v = 19
2) |x
+
5
= 2x -
18
V
x
+ 2x -
18
- 5
X

> 9
-x
-
-23
o
3x
- 13
X
> 9
X
- 23
13
CJ> x = 23
X
=
3
Vay nghiem ciia phiAtng
Irinii
la:
x = 23
•'5)
X- - 12x +
36
= 0 <r> (X -
6)'
=
0
o X = 6
Vay phiftJng
trinh

CO nghiem
kep X
= 6
4)
BKXDx>2011
Ta CO
x/x - 2011 + 74x -
8044
- 3 o
N/X
- 201 1 +
^4(x
- 2011) = 1
o
Vx - 2011
^-
27x -
2T)TT
-
3
o
v/x
-
20 iT
= 1
Luy$n
giai
d6
trudc
kl thi vko I6p 10 ba

mign
B&c.
Trung,
Nam mOn To^n _
NguySn
DCfc
Ta'n
1
> 0
<=> \ « X = 2012
X -2011 = r
Vay
phuWng tnnh
CO
nghicm la X = 2012 y '
'.•'^^i^vv'.i';}
: j .
'
Nhan xet: Day la cac bai loan de,
quen
ihuoc. ' '
•
Va + 1
'
a(a-l)
;:-(irn
"fiticf*")
i i
2)
DKa>0,a^ 1

j-^
V
K
= V2G12
c^2^f^
=
sJlOll
<=> a = 503 (thich h(?p)
Nhan xet: Day la bai loan de,
quen
thuoc.
cau3.
1)
A' = 4 + - 3 = +
1
> 0, vdi moi m
Vay
phiTOng
trinh
(*) luon c6 hai nghicm
phan
bict vdi moi m.
2)
Theo he thiJc
Vi-ct,
ta co:
X| + X2 = 4, X1X2 =
-m"*
+ 3
Ma

X2 = -5xi (gt). Do do -5xi + X| = 4 -4xi = 4
<=>
X| = -1
Ta
CO
X2
= -5xi = 5. Do vay -1.5 = -m' + 3<=>m' = 8<=>m =
±2>y2
Vay
m = 2%y2
hoac
m = -2^2
Nhan xet: Vi tong hai nghicm la
hang
so
(X|
+
X2
= 4) do vay nen kel hcfp
vdi
he thiJc nghicm cho trufdtc
(X2
= -5xi) de tim
du'dc
Xi,
X2
roi tiT do
nhanh
chong
CO

di/dc cac gia tn m can tim.
Cau4.
10phut=-gid
6
Goi
van toe luc dau cua 6 to la x (km/h)
(Dicu
kien x > 0)
Thdi
gian 6 l6 diT dinh di
tiT
A den B la: 120 : x = — (h)
X
Sau 1 gi5 6 to di
du'dc
la x.l = x (km)
Quang du-dng con lai dai la: 120 - x (km)
Van
toe cua 6 to sau khi tang la: x + 6 (km/h)
Thcli
gian 6 to di
quang
du'dng con lai \h:
Cty
TNHH
MTV DWH
Khang
Vi$t
(120-x):(x + 6)= (h)
X + 6

Theo dau bai, ta c6 phu'Ong
Irinh:
,
1 120-X
1
+ - +
6 X + 6
120
<=>
7x(x + 6) + 6x(120 -
X)
= 720(x + 6)
7x^
+ 42x + 720x - 6x' - 720x + 4320
o X' + 42x - 4320 = 0
A'
=441 +4320 = 4761,
VA'
= 69
-21 + 69
=
48 (nhan);
X2
=
-21-69
=
-90 (loai)
1
• - . ^
Vay

van toe luc dau cua 6 to la 48 km/h '
Nhan xet: Giai bai loan
bang
each
lap phUdng
Irinh,
loai loan chuyen dong,
dang
loan nay
quen
thuoc
doi vdi hoe sinh \6p 9. Can chu y d6n vi phai
thong
nha't.
Cau
5. 1) AB, AC la cac tiep tuyen cua
difcfng
tron (O) (gt)
^
AB 1 OB, AC 1 OC
=>
ABO = ACO = 90"
=>
Tu"
giac
ABOC noi tiep
2)
AB, AC la cac tiep tuyen cua du'dng
tron
(O) (gt) =^ AB = AC, AO la tia

phan
giac
cua goe BAC
(tinh
cha't
cua
hai tiep tuyen eat
nhau)
AABC
can lai
A,
AO la diTdng
phan
giac
nen AO
eung
.
la du'dng cao cua lam
giac
ABC.
=^
BCl OA
Xet
AEAB
va AEBO eo AEB = BEO (= 90")
Do
do
AEAB
^ AEBO (g.g)
Vay

BA.BE
= AE.BO
BAE
= EBO (cung phu vdi goe ABE)
BA
AE
BO
BE
3)
Ta
CO
OID = OBD = 90"
=>
Tvt
giac
OIBD
noi
licp
=>
Ma
OB = OC (= R) =^ AOBC can lai O
:=>
BCO = IBO
IDO
= IBO.
Do
vay DIO = BCO (= IBO)
Luy$n
giai 6i
truflc

k1
thi
vgio
lap 10 ba miSn BJc.
Trung,
Nam
mOn
loin
_ Nguygn DCic TSn
Mat
khac
OIF + OCF = 90" + 90" = 180"
.
Ttf
giac
lOCF noi tiep => BCO = IFO
Ta CO IFO = IDO (= BCO ) i ,
Vay
tarn
giac
DOF can tai O. A
4)
ADOF
can tai O c6 01 la di/ctng cao (011DF) nen 01 cung la difcJng trung tuyen.
Ti?
giac
BDEF co I la trung diem cua BE (gt) va I la trung diem cua DF
(chuTng minh trcn).
Do do BDEF la hinh binh
hanh

=> EF // BD
Xet
AABC
CO
E la trung diem cua BC
(AABC
can tai A diTdng cao AE cung
la
dirdng trung tuyen) va EF // BD
Vay
F la trung diem cua AC
Nhan xet: Day la bai loan de,
quen
thuoc.
DE
S67
DE
THI TUYEN SINH VAO L(3P 10 THPT,
TJNH
HAI PHONG
NAM HOC 2012 - 2013
Phan I.
Trac
nghi^m (2,0 diem)
Hay chon chi 1 chuT cai diJng trifdc cau tra 15i dung
Cau
1.
Dieu kien xac dinh cua bicu thuTc Vx -
1
la:

A.x>l;
B.x=l;
C.x<l;
CSu
2.
Diem
thuoc
do thj ham so y = -
x
+
1
thi:
D.
x <
1
va X ;^ I
A.
,
2J
B.
(2; 2);
C.
(0;-l);
-3y = -2
-2x + y = -1
A.
(-3;-l);
B. (1;-1); C. (1; 1);
D.
(-2;-l)

Cau
3.
Nghiem cua he phu'dng trinh
la:
D.
(l;-2)
CSu
4. Phifdng trinh (2m - l)x^ - mx - 1 = 0 la phiTdng trinh bac hai an x khi:
A.
m ^ -;
2
B.
m 5t 1;
C.
m5t2;
Cau
5. Tarn
giac
ABC vuong tai A, AH 1 BC,
BH
= 3,CH= 12(Hinhi).
Do dai
doan
thang
AH la:
A.
8; B. 12;
C. 25; D. 6.
Cty
TNHH MTV DWH Khang

Vigt
Cfiu 6. Tam
giac
MNP vuong tai M biet
MN
= 3a, MP = 3^/3a .
Khi
do
tanP
bang-
s
A ^
A.
—a;
B.
C.V3;
D.
3
cau 7. Trong hinh 2, biet DBA = 40",
s6'do
ACD
bang
A.
60";
C. 70";
O/
B.130";
D.65".
•B
Hinh

2
Cfiu
8. Cho hinh chi?
nhat
c6 AB = 4cm, BC = 3cm.
Quay
hinh chi?
nhat
do xung
quanh
AB ta difcJc mot hinh tru. The tich cua hinh tru do bkng:
A.
367icm^ B. 48TCm^ C. 247rcm^ D. 647icm^
Ph4n
II:
Phan tif luan (8,0 diem)
Bai
1.(1,5 diem)
1) Rut gpn cdc bieu thtfc sau:
a)
N = (l2N/2-3Vr8 +
2V8):
V2 b) N = J— '
^
' V5-1 75 + 1
2) Xac dinh ham so y = (a + l)x^ biet do thi ham so di qua diem
A(l;
-2).
Bai
2.

(2,5 diem)
1) Giai phifdng trinh + 2x - 3 = 0
2) Cho phiTdng trinh x^ + mx - m - 1 = 0 (1) (m la tham so)
a) Chu-ng minh r^ng vdi mpi m phu'dng trinh (1) luon c6 nghiem.
b) Tim cac gia
tri
cua m de phiTdng trinh (1) c6 it
nhat
mot nghiem khong diTdng.
3) Tim hai so biet tdng cua chiing b3ng 8 va so
thu"
nhat
gap 3 Ian so thi? hai.
Bai
3.
(3,0 diem) Cho tam gidc ABC c6 ba goc nhon va AB = AC. DiTdng tron
tarn O dirdng kinh AB = 2R c^t cdc
canh
BC, AC Ian
lirdt
tai
I,
K. Tiep tuyen
ciia
dirdng trdn (O) tai B c^t AI tai D, H la giao diem cua AI va BK.
a) Chu-ng minh tiJ
giac
IHKC
noi tiep.
b) Chu-ng minh BC la tia

phan
giac
cua DBH va tiJ
giac
BDCH la hinh
thoi.
c) Tinh dien Uch hinh thoi BDCH
theo
R trong tnrdng hdp tam
giac
ABC deu.
Bai
4. (1,0 diem)
1) Cho
X
> 0, y > 0. ChiJng minh r^ng - + - > . Dau xay ra khi
nao?
X
y X + y
2) Cho
X
> 0, y > 0 va 2x + 3y < 2. Tim gia trj nho
nhat
cua bicu thtfc:
4 9 ^^'y •'•
Luy^n
giSi
(SJ
truflc
k1

thi v^o I6p 10 ba
m\in
BJc,
Trung, Nam mOn Toan _ NguySn
Bijfe
TSn
Hifdng dSn giai
Ph^n
I.
Trdc
nghiem
A
caul.
A
Cfiu2.B Cfiu3.C CSu
4. A
CSu5.D
; r
Cfiu6.B Cfiu7.D
Cfiu
8.A
Phdn
II.
Ph^n trf
lu§n
Bai
1.1)
a) N =
(12V2
-

Sx/Ts + 2V8)
:
72 -
(12V2
-
3^3^ +
2V2^j
:
V2
=(l2V2-9V2+4>/2): V2 =7^/2 : V2-7
5-V5
4
4(V5-l)
5-1
b)
N =
V5-1
V5+
1
%/5-1
=
V5-(V5-l)-V5-V5
+ l = l
^
2)
Do thi ham
so y = (a +
l)x^
di qua
A(l;

-2)
<=>
-2 = (a +
l).l^
o a +
1
= -2 o a = -3
Nhan xet: Bai toan nay
de
doi vdi mpi hoc sinh Idp
9.
Bai
2.1)
a + b
+
c =
1
+
2
+
(-3)
= 0
Phircfng
trinh
co
hai nghiem phan biet X|
=
1; X2
= -3
2)

a)
A
= m^
-
4(-m
-
1) = m^ + 4m +
4
= (m + 2)^ >
0
Vay
phifdng
trinh
(1) luon c6 nghiem
vcti
moi m.
b)
De
phifdng
trinh
(1)
c6
it
nha't
mot nghiem khong diTcfng khi
va
chi khi.
•
PhiTdng
trinh

(1)
c6
hai nghiem
trdi
da'u
o
P
< 0 o
-m
-
1
< 0 o m > - 1
•
PhiTdng
trinh
(1)
c6
mot nghiem b^ng 0.
1
Ta
CO
P =
0 o
-m
-
1 =
0 o
m =
-1
•

PhiTdng
trinh
(1)
c6
hai nghiem am
<=>
i
A
> 0
S < 0
<=>
P
> 0
(m
-if > 0
-m
< 0
<=>
<!
-m
-
1
> 0
(m
-2)^
> 0
m
> 0 o m e 0
m
< -1

Vay
v(Ji
m >
-1 thi phifOng
trinh
c6 it
nha't
mot nghiem khong diTdng
3)
Gpi
so
thi?
nha't
la x, so
thi? hai
la
8
- x
Vi
so
thuf
nha't
gap
3 Ian
so
thiJ hai, nen
ta c6
phiTdng
trinh
x =

3(8
- x)
X =
3(8
-
x)
o X =
24
-
3x
o
4x
=
24
o X = 6
So thiJ
nha't
la 6
So thiJ hai
la
8
- 6 = 2
Nhan xet:
Cau 1 va 3 de, cau 2
tim
cac gia
tri
cua m de (1) co it
nha't
mot

nghiem khong diTOng
ta
tim m
de co
1 nghiem bing 0,
co
hai nghiem am.
Cty
TNHH
MTV^jwnjviiang VjQt
Bai
3.
a) Ta co
AIB
=
90" (Goc noi tiep chan
nijfa
diTcJng iron)
AI1
BC
^
HIC
=
90|^
va
AKB
=
90"
(Goc noi
tie'p

ch^n n^a
di^cJng
•BK_LAC
iron)
r:> BK
_L
AC => HKC
= 90"
Ti?
giac
IHKC
co
HIC
+
HKC
=
I8O".
Do
do tiJ giac
IHKC
npi tie'p
b)
Ta
CO
AABC
can
tai
A
(gt), AI
la

diTdng
cao
nen AI la tia
phan giac
cua goc
BAG
=^ BAI
=
lAC
Ma
BAI
=
DBI (He
qua tao
bdi tia tie'p
tuyen
va
day cung)
lAC
=
KBI (Hai goc npi tie'p cilng ch^n cung KI)
Do
do
DBI
=
KBI.
Vay BC la tia
phan giac
cua goc
DBH.

ABHD
co BI
dUcfng
phan giac
va la
du^dng
cao
nen tarn giac BHD can tai B => BI
la
di/dng
trung tuyen => IH
=
ID
TiJ
giac
BDCH
co I la
trung diem
cua
BC, HD.
Nen
tiJ giac
BDCH
la
hinh
binh
hanh. Ma HD
1
BC.
" *

Vay
tiJ giac BHCD
la
hinh
thoi.
c)
AABC
deu => AC
=
BC
=
AB
=
2R, ABI
= 60"
.
,
AIAB
vuong tai
I ^
AI
=
ABsinABI
=
2Rsin60"
=
2R.—
= V3R " '
2
H

la
triTc tam
cua
tam
giAc
ABC
(AI
1
BC, BK
1
AC)
ma
AABC
deu.
. .
Do
do
H la
irpng tam
cua
tam giac ABC
,L
=>iH
=
iAi
= :^
3
3
HD
=

2IH
=
2V3R
Dien
tich
hinh thoi
BDCH
la:-BC.HD
= 1.2R.^^ =
(dvdt)
2
2 3 3
Nhan xet: Day
la
bai toan quen thupc.
^al4.
1) Vdi mpi
x,y>().
Ta
CP i + i >
x
+ y
<=>
>
y x + y xy x + y
o
(x +
y)^
>
4xy

<=>
(x +
y)^
-
4xy
> 0 (x -
y)^
> 0
(BDT dung)
LuyQn
giai
ai
truflc
kl thi
vito
Iflp
10 ba
m\in
BJc,
Trung,
Nam
mOn
Toan
_
Nguygn
Ditc
Tan
Vay vdi moi
x; y > 0 ta co
—

+
—
>
X
y X + y
Da'u "="
xay
ra <=>
(x -
y)^
= 0
<=>
x = y
2) Ap
dung
bat
dang
thuTc
Co-si
cho hai so
dUdng
Ta CO
2x + 3y > 272x.3y <=> 276xy < 2x + 3y
Ma
2x + 3y
<
2.
Do
do T^xy <
1 <=>

6xy < 1.
Kct hdp ke't qua
d cau 1)
ta
c6:
A
=
>
4.
4x^
+ 9y'
4
xy
1
[4\^
+ 9y'
52
12xy,
+
—
+ — - 16. • ^ +
4x^
+
9y^
+
12xy
6xy (2x +
3y)
6xy
26

3xy
52
.16
' .^ = 56
Da'u xay ra
o
2x
= 3y
2x
+
3y
= 2
X
= —
2
'
= 3
Vay gia tri nho nhat cila bieu
thiJc
A la 56
Nhan
xet:
1) Dung
cac
phcp bicn ddi tiTdng diTdng
dc c6
Kli giai.
2)
Van dung cau
1) dc

tim gia trj nho nhat cua A,
lilf
gia thic't
2x + 3y < 2
cho
ta
dir
doan
A
dat gid nho nhat khi
2x = 3y = 1.
Do vay,
ap
dung
bat
d^ng thufc
Co-si
cho hai
so
diTdng
ta c6 2x + 3y > 2
72x.3y
<=>
2x
-i-
3y > 2
,j6xy
.
Day
cung

la
mot nut th^l cua bai toan.
Oti
SO 8
KY
THI
TUYEN
SINH
VAO
LCiP
10
THPT,
TJNH
NGHE
AN
NAM HQC 2012
-
2013
CSu 1.
(2,5
diem):
Cho bieu thtfc
A =
Vx-2
Vx+2
"
N/X-2J'
Vx
a) Tim dieu kicn
xac de A xac

djnh va rut gon A.
b) Tim tat
ca cac
gia tri
x
de
A > ^
Cty
TNHH
MTV DWH
Khang
Vigt
c) Tim tat
ca cac
gia
Iri
cua
x de B =
—A dat gia tri nguyen.
C&u 2. (1,5 diem) Quang dtfdng AB dai
156km.
Mot ngiTdi di
xe
may tCr A, mot
ngi/cti
di
xe
dap tu"
B.
Hai

xe
xuat
phat
ciing mot luc
va
sau
3
gicJ
gap nhau.
Biet
rang van
toe cua
ngU'di di
xe
may nhanh hcfn van
toe cua
ngtfdi di
xe
dap la 28km/h. Tinh van toe cua moi
xe.
CSu 3.
(2
diem) Cho phiTdng
trinh:
x^
-
2(m
-
l)x
-i-

m^
- 6 = 0
(m
la
tham so).
a) Giai phU'dng trinh khi m
= 3. f-
b) Tim
m de
phu'dng
trinh
c6
hai nghiem X|, X2
thoa
man
x^ + Xj = 16
CSu 4.
(4
diem) Cho diem
M
nam ngoai diTcfng tron tam O.
Ve
tiep tuyen MA, MB
vcfi dirdng tron (A,
B la cac
tiep diem).
Ve
cat tuyen MCD khong di qua tam
O
(C n^m giOra

M
va D), OM c^t AB va (O) Ian liTdt tai H va I. ChuTng minh.
a) Tvt
giac
MAOB noi tiep.
b) MC.MD
=
MA^
c) OH.OM
-I-
MC.MD
=
MO^
d) CI
la
lia phan
giac
goc MCH.
Hl/OfNG
DAN
GIAI
Cfiu
1.
a) A xac
dinh <=>
Dieu kien:
x > 0
va
x ;t 4
x > 0

Vx
+ 2 7t 0
A/X-2
^ 0
Vx
^ 0
<=>
i
X
> 0
N/X
^ -2
7^ ^ 2
X
;t 0
X
> 0
X
7t 4
A
=
N/X-2
N/X-2
+
VX+2
VX-2
lV^ + 2 ^ (V^ +
2)(V5^-2)'
sf^
=

2N/X
N/X
-2 _ 2
(V5(^
+
2)(Vx-2)'
Vx
~Vx+2
b) Dieu kien
x > 0 va x ;t 4
1
2
+ 2
>-<=>Vx+2<4oVx<2<=>0<x<4
2
Vay0<x<4thi
A >
2
Mid (^Vv
i<
Dieu kien
x > 0
va
x 4.
B
= ZA = Z 2 ^ 14_
4
3Vx+2
3V^
+ 6

•mi
('V/ )'•'
Luy?n giai dg trmSc kl thi vao Idp 10 ba
m'tin
BSc, Trung, Nam mOn Toan _ NguySn Dijfc Tin
Vi
Vx > 0. Nen sVx +
6>6.Dod6
0<B < —
c^0<B<2
6
3
Ma
B la so
nguyen.
•
Do
do B =
1
hoac
B =
2.
/ i,.
•
B =
l.Tac6——
=
lo3Vx+6
=
14

'• ''^
3Vx
+ 6
riifi'l
'.iJ-
.
/-
8 64
^
, , , . ,
<=>Vx=-ox
= —
(thich hcJp)
3
9 • £
•
B =
2.
Ta
CO
— = 2c^3Vx+6 = 7
y- 3Vx
+ 6
0
ii!
<=>^/x=-ox
=
— (thich hc(p)
Vay
X = ^

hoSc
x = ^
thi
B =
dat gia Iri nguyen.
"ban
xet:
("au
a), b) de, cau c)
nham giup phan loai
hoc
sinh,
chia khoa
bai
toan
la
nhan
ra B > 0 va vi 3>/x + 6 > 6 nen B < — o B < 2- de c6
difdc
B = 1
6
3
hoSc
B =
2. Tif do tim diTdc
gia
trj ciia
x de B la so
nguyen
CSu 2. Goi van toe cua ngtfdi di

xe
dap
la
x(km/h) (Dieu kien
x > 0)
Van
toe
cua ngU'di di
xe
may
la x +
28 (km/h)
>• Trong
3
gid
xe
may di du'dc quang du'dng la:
3(x
+
28)
= 3x +
84 (km/h)
Trong
3
gid
xe
dap di dUdc quang du'dng la: 3x(km/h)
Theo
dau bai ta
c6

phu'cfng
trinh:
^
3x
+
84
+
3x=156
o
6x +
84
=
256
6x
= 72
<=>
X =
12 (thich hdp)
Vay van
toe
cua ngurdi di
xe
dap
la
12 (km/gi6)
Van toe cua ngU'di di
xe
may la:
'"
12+ 28

=
40 (km/h)
Nhan xet: Giai bai toan b^ng each lap phu'cfng
trinh,
loai toan chuyen dong
rat
quen thuoc do'i
vdi
hoc sinh Idp 8,
9.
C&u 3.
a) m =
3, phiTdng
trinh
trd thanh x^
= 4x + 3 = 0
C6a
+ b + c= l+ (-4) +
3
= 0
Cty
TNHH
MTV
DVVH
Khang
Vi?t
PhiTdng
trinh
c6
hai nghiem phan biet X|

= 1, X2 = - = 3
a
•1
r
b)
A' =
(m
- 1) -
(m
- 6) = m -
2m
+
1
-
m^
+ 6 =
-2m
+ 7 ^ : , ,:
Phu'dng
trinh
CO hai nghiem X,,
X2
<:>
A' > 0 «
-2m
+
7>0<=>m<-
Theo
he
thuTc Vi-et ta c6:

Xi +
X2
=
2(m
- 1) =
2m
- 2;
X1X2
=
m^
- 6.
Do do xf + X2 = 16x <=> (x, + X2)^-
2x1X2
= 16
<:> (2m
-
2)^
- 2
(m^
- 6) =
16
o
4m^
-
8m
+ 4 -
2m^
+
12
= 16

o 2m^
-
8m
= 0
<=> 2m(m
- 4) = 0
m
= 0
"
11
m
= 0
(thich hdp)
m-4
= 0 [m = 4
(khong
thich
hdp)
Vay
m = 0 la gia
tri bai toin
ve
phu'dng
trinh
bac hai mot an
va
van dung
he
thtfc
Vi-et, bai toan nay eung

de va
quen thuoc
Cfiu
4. a) MA, MB Ih cic
tiep tuyen
cua
diTdng
tron
(O) (gt)
MA
1
OA, MB
1
OB.
Ta
c6 MAO =
90", MBO
=
90"
.
Do
do
tiJ
giac
MAOB noi tiep.
b) Xet
AMAC
va
AMDA
eo AMC

(chung),
MAC
= MDA (He
qua
gdc
tao bdi tiep tuyen
va
day cung)
Do
do
AMAC
AMDA
(g.g) =^ — = —
MD
MA
Vay MC.MD
=
MA^
c) MA,
MB la cac
tiep tuyen cua diTdng
tr6n
(O) => MA =
MB,
MO la
tia phan
giac
goc
AMB, AMAB can tai
M, MO la

dudng phan
giac
nen
MO la
diTdng
cao cua tam
giac
MAB =>
MO 1
AB.
AMAO
vuong tai
A eo AH la
diTdng
cao =>
OH.OM
= 0A^
MH.MO
= MA^
va
MA.OA
=
AH.MO.
AAMO
vuong tai
A =>
OA^
+
MA^
=

MO^ (dinh li
Py-ta-go).
Do d6: OH.OM
+
MC.MD
=
MO^
d)
Ta
CO MC.MD
=
MH.MO
(=
MA^)
;
Xet AMCH
va
AMOD
c6 CMH
(chung),
MC
MH
MO
MD
(vi MC.MD
=
MH.MO)
Luy§n
gici
6n

Join
_ NguySn
Bute
Ta'n
Do do
AMCH
^
AMOD
(c.g.c)
=>
Mat
khic
OM
1
AB
=>
lA
=
IB
^
AAMH
CO
AI la difdng phan
giac
=
MA
MC
CH MC MO
MO
"

OD
^
CH
"
OD
(1)
MAI
=
lAB
MI
MA
Ta
CO
MA.OD
=
AH.MO
Tir(l),
(2) va
(3)tac6
AH
MC
MI
HI
MO
OD
AH
(2)
CH
HI
Gpi

Cr la
diTcfng phan
giac
cua tam
giac
MCH.
MI'
MC
^ ^, Ml Ml
. Do do
Ta CO
r
= I
HI'
CH HI' HI
Vay CI la tia phan
giac
cua goc MCH.
Nhan xet: Cac cau a), b),
c)
de va quen
thuoc. Cau
d)
la
cau
kho, day
la
phan
M
kho nhat

cua do thi
nhim
giiip
phan
loai,
phai that sir Unh
hoat
mdi nhan ra
ding
thiJc
MC
MI
CO
diTcJc
tir
AMCH
^
AMOD, AI
la
diTdng phan gidc
CH
HI
cua tam
giac
AMH va MA.OD
=
AH.MO.
Co mot
Icfi
giai rat hay, neu phat hien siT xuat hien ciia diem

E
la
diem doi
xiJng
cua diem
I
qua O.
Cdc ban
c6
phat hien
diTcJc
Idi giai sau
khong?
Ve dirdng
kinh
IE cua dtfdng tron (O). OD
=
OE
(= R)
=> A ODE can tai O
=>
HOD
=
20ED.
Ma MCH
=
HOD (Tu-
giac
CDOH npi tiep).
Nen

MCH
=
26ED
.
Mat khdc MCI
=
OED (Ttf gidc CDEI noi tiep)
Do d6 MCH
=
2Ma . Nen MCI
=
ICH
Vay CI
la
tia phan
giac
cua goc MCH.
oiy iNnn
ivii
v uvvn
^^a^g
vi?t
so
9
KY
THI
TUYEN
SINH
VAO
LdP

10
THPT,
TINH QUANG NINH
NAM HOC
2012
-
2013
cau
1.
(2,0 diem)
^ ,„ ,
1) Riit gon
cac
bieu thufc sau:
a)
A
=
2./^ + 718
b)
B
= ,
^
+
J—
-
vdi
x
>
0,
x

^
1
V2 Vx
-1
Vx
+
1
x-I
r2x
+
y
=
5
2) Giai he phiTdng
trinh:
<^
[x
+
2y
=
4
'
cau
2.
(2,0 diem) Cho phiTdng
trinh
(an x): x^
-
ax
-

2
=
0 (*)
" '
1) Giai phu'dng
trinh
(*)
vdi
a
= 1.
2) ChuTng minh rang phu'cfng
trinh
(*)
c6
hai nghiem phan biet vdi mpi gia tri
cua
a.
3) Gpi
Xi, X2
la
hai nghiem cua phu'Png
trinh
(*). Tim gia tri cua
a
de bieu
thiJc
N
=
xf
+

(X|
+
2)(X2
+ 2) +
X2 CO
gia tri nho nhat.
cau
3.
(2,0 diem) Giai bai toan bkng
each
lap phu'cfng
trinh,
he phiTdng
trinh.
Quang
dU'cJng
song
AB dai 78km. Mot
chiec
thuyen may di
tijr
A
ve phia
B.
Sau do
1
gicJ,
mot
chiec
ca

no di
tijf
B ve
phia A. Thuyen va
ca
no gap nhau
tai
C
each
B
36km. Tinh
thdi
gian cua thuyen,
thdi
gian ciia
ca
no da di tuf
luc
khdi
hanh den khi gap nhau, biet van toe cua
ca
no Idn hcfn van toe cua
thuyen
la 4km/h.
cau
4. (3,5
diem) Cho tam giic ABC vuong tai A, tren
canh
AC lay diem
D

(D
^
A,
D
C). Dirdng tron (O), diTdng
kinh
DC
cil
BC tai
E
(E
^
C).
1)
ChiJng
minh ti?
giac
ABED npi tiep.
2) Dufdng thing BD c^t
dirdng
tron (O) tai diem thiJ hai I. Chtfng minh ED la tia
phan
giac
cua goc AEI.
3) Gia sur tan ABC
=
V2
.
Tim vi tri cua
D

tren AC
de EA
la
tiep tuyen
cua
du-dng
tron diTdng
kinh
DC.
Cfiu
5.
(0,5 diem) Giai phiTdng
trinh:
7 +
27^
-
x
=
(2 +
sf^)y/l
-
x
.
Hl/OfNG DAN
GIAI
cau 1. 1. a)
A
=
2,
-

+
Vis
=
2,
^ + =
yjl +
3J2
=
4yf2
2
V22
b)
B
= 1 1
_ _2_
_
N/^
+
1
+V^-1-2
^
2V^-2
+
1 x-i~
(v;;;_i)(v^ +1)
(V^-i)(Vr + i)
LuyQn
giai
OJ
triOc

kl thi vAo
Ii3p
10
ba
mign
6^0,
Trung,
Nam mOn
ToAn
_
Nguygn
Bijfc
Ta'n
2(^-1)
2)
" (7^
-
i)(V5r
+1) ^ + 1
2x + y
= 5 {4\ 2y = 10
_x +
2y = 4
X
= 2
2 +
2y = 4
<=>
i
X

+ 2y
=
4
3x
= 6
X
+ 2y = 4
X
= 2
<=>
i
<=>
i
X
= 2
y
= 1
1
'^V;
fier.
UJH
'
f
r,
[2y
= 2
Vay nghiem (x; y) cua he phiTdng
trinh
la
(2; 1)

Nhan
xet: Bao toan nay de va rat quen thuoc.
CSu 2.
1)
Khi
a
=
1.
PhiTdng
trinh
trd thanh x^
-
x
- 2
=
0.
Via-b + c=l-(-l) +
(-2)
=
0
Q
PhU'dng
trinh
c6 hai nghiem phan bi^t Xi
= -1,
Xj
= —=2
a
2) a = 1 > 0, c =
-2

<
0
a,
c
trai
dau nen phu'cfng
trinh
c6 hai nghiem phan biet vdi moi
a.
3)
Theo
he thuTc Vi-et, ta c6: x, +
X2
= a, X1X2
= -2
Do do N = xf + (X| +
X2)(X2
+ 2) + X2
=
(x?+x^)
+ (x,
+2)(x2+2)
= (X|
+
Xj)^
-
2X|X2
+
X|X2
+ 2x, + 2x2 + 4

= a^ +
2
+ 2a +
4 =
(a^ + 2a +
1)
+ 5
=
(a + 1)^ + 5
> 5
Dau "=" xay ra
o
a +
1
<=>
a =
-1
Vay gia tri nho nha't cua N la
5
khi va chi khi a =
-1.
Nhan
xet: Day la bai toan ve phu'cfng
trinh
bac hai va he thufc Vi-et, bai toan
nay cung quen
thuoc
va de, can
liTu
y x^ + X2

=
(x,
+
X2)^
-
2x,X2.
CSu
3.
Goi
thcJi
gian ciia
ca
no di ttr luc khcli hanh den khi gSp nhau la
x(gicJ)
(Dieu kien
x
>
0)
Thdi
gian cua thuyen mdi di
tiJf
luc
khdi
hanh khi gap nhau la
x
+
1
(gid)
Quang diTcfng
tiJf

A
den C dai: 78
-
36 = 42 (km)
V^ntdc cua thuyen may
la:42:
(x-i-l)
=
Van toe cua ca no 1^:
42
X
+ 1
(km/gicJ)
36
:
X
= —
(kmAi)
Theo
dau bai ta c6 phu'cfng
trinh:
Cty
TNHH MTV DWH
Khang
Vigt
36
X
42
X
+

1
4 «•
—
X
21
X
+
1
=
2c^l8(x
+
l)-21x
=
2x(x
+ l)
O
18a
=
18
-
21x
=
2x^ + 2x <=> 2x^ + 5x
-
18
^^25 +
144-169,
VA=13
-5 + 13
_ -5-13 -9

=
2
(thich hop).
(khong thich hOp)
2.2
' 2.2 2
Vay
thdi
gian cua
ca
no di tiT luc
khdi
hanh den khi gSp nhau
la 2
gid,
thcJi
gian cua thuyen may di
tijT
luc
khdi
hanh den khi gap nhau la:
2
+ 1 =
3
(gid)
Nhan
xet: Day
la
bai toan: giai bai toan b^ng
each

lap phUdng
trinh,
loai
todn
chuyen dong rat quen
thuoc
va de.
CSu 4.
1) Ta CO DEC
=
90" (Goc noi tiep ch^n nuTa du-dng tron)
A
DEC
=
BAD (= 90").
Do do ti?
giac
ABED noi tiep.
2) Die
=
90"
(Goc noi
tiep ch^n nufa
dirdng
tron). Ta
c6
BAC
=
BIC
= 90"

Ti?
giac
ABCI noi tiep
=> ABI
=
ACI. Ma DEI
=
DCI (hai goc noi tiep cilng ch^n cung DI)
Mat
khac
ABD
=
AED (TiJ gidc ABCD noi tiep). Do do AED
=
DEI.
Vay ED la tia phan
giac
cua goc AEI.
3) Gia sijr EA la tiep tuyen cua diTdng tron duTdng
ki'nh
DC.
Ta CO AED
=
ACE (He qua goc tao bdi tiep tuyen va day cung).
Ma ABD
=
AED. Dodo ABD
=
ACE. Nen ADB
=

ABC
Ta CO tanADC = tanABC =
V2 .
tan ADB
= .
Nen
^ = V2
AD
AD
=
ABV2
Vay khi
D
tren
canh
AD sao cho: AD
=
ABV2
thi
EA
la
tiep tuyen
ciaa
di^dng
tron diTdng
kinh
DC
NhSn xet: Bai toan hinh hoc nky cQng la dang toan quen thupc, cSu
3 se c6
IfJi giai neu phat hi$n ADB

=
ABC c6 di/dc
tiJf
ABD
=
ACE.
5. Digu kien
0 <
X
<
7
Bat
y = V7 - X
(y > 0). Do do
, , .
LuyOn
giii
66
tn;.,.
IM vio
Iflp
10
ba mign
iguySn
DiJc
TSn
<=>
7
+
2Vx

-
X
= (2 +
>/x)V7
-
X
(7
-
x)
+ = (2 +
Vx)>/7
-
X
+2V^
= (2 +
V^)y
y^
+
2Vx
-
(2
+
Vx)
= 0:
<=>
y^ +
2Vx
-
2y
-

Vxy
= 0
o y(y
- 2) +
Vx(2
-
y)
- 0 o (y -
V5^)(y
-
2)
= 0
-
Vx
= 0
y
-
2
= 0
"2x
= 7
y
=
Vx
y
= 2
<=>
V7
- X =
Vx

x>0va7-x
= x
2>0va7-x
= 2^
^V7-x
= 2
X
- 3,5
X
= 3 [x = 3
Vay
phifdng
trinh
da
cho c6 hai nghiem
X]
=
3,5;
X2
= 3
Nhan xet: Day
la
bai todn phiTdng
trinh
chiJa
can, bai toan kho
nha't
cua
de
thi

nh^m
de
phan loai hoc sinh,
dat y =
V7
- x de c6 {y -
Vx j(y
-
2)
= 0
giup
CO
diTdc Idi giai cua bai toan.
S6
10
KY
THI TUYEN
SINH
VAO
L(3P 10
THPT, TINH
THANH
HOA
NAM
HQC
2012
-
2013
Bai
1. (2,0 diem)

1)
Giai
cac
phi/dng
trinh
sau:
a) X
-
1
=
0 b)
x^
-
3x + 2 =
0
f2x-y
= 7
2) Giai
he
phiTdng
trinh:
\
[x
+ y = 2
Bai
2. (2,0 diem) Cho bieu thu-c:
A =
1 1
a^+l
2

+
2Va 2
-
2Va
1
-
a
1)
Tim dieu kien xac dinh
va
rut gon bieu thiJc A.
2) Tim gia tri ciia
a;
bie't
^ < 'J
Bai
3. (2,0 diem)
1)
Cho difdng thing (d):
y = ax + b.
Tim
a; b de
diTdng th^ng (d)
di qua
diem
A(-l;
3) va
song song
vdi diTdng thing (d'):
y =

5x
+ 3
CtyTNHH
MTV DWH Khang
Vijt
2)
Cho phu'dng
trinh:
ax^
+
3(a
+
l)x
+ 2a + 4 = 0
(x
la an
so). Tim
a de
phiTdng
trinh
da cho c6 hai nghiem phan biet
Xi;
X2
thoa man
xf +
Xj
= 4 '
Bai
4.
(3,0 diem) Cho tam

giac
deu
ABC
c6
diTdng
cao
AH. Tren
canh
BC
lay
diem
M
ba't ky (M khong trung B;
C;
H).
TiT
M
ke
MP; MQ Ian
liTdt
vuong
g6c vdi
cac
canh
AB;
AC (P thuoc
AB;
Q
thuoc AC)
1)

Chi?ng minh: Tvt
giac
APMQ noi tiep
du'Sng
tron.
2)
Gpi O
la
tam du'dng tron ngoai tiep
tu*
giac
APMQ. ChiJng minh OH 1PQ
3)
Chtfng minh r^ng: MP + MQ
=
AH.
Bai
5. (1,0 diem) Cho hai
so
thtfc
a; b
thay ddi, thoa man dieu kien
a + b >
1
va
a
>
0. Tim gia tri nho
nha't
cua bieu thiJc

A = ^ ^ +
b^
, .
4a
V'",,""''
'
HUdNG
DAN
GIAI
Bai
1. 1.
a)
x
-
1
= 0
<=>
x =
0
+
1
<=>
x =
1
Phu'dng
trinh
da
cho c6 nghiem
la x = 1
b)

Phifdng
trinh
x^-3x
+ 2 =
0c6a
+ b + c = l+ (-3) + 2 = 0 nen c6 hai
c
2 ^
nghiem:
xi
=
l;x2=-
= - = 2
a
1
2)
'2x
-
y
= 7
3x
= 9
fx
= 3
[x
= 3
o
-
o • o
•

X +
y = 2
X
+ y = 2
3 +
y = 2
y
= -1
Vay
nghiem (x; y) cua
he
phiTdng
trinh
la
(3;
-1)
Nhan xet: Bai toan
nay qua de
doi vdi moi
hoc
sinh Idp
9,
thi sinh diT thi
ch^c chin
CO
tron
2
diem
6
bai toan nay.

Bai
2.
1.
A xac dinh
<=> <
A
=
a
> 0
2
+
2Va
0
2-2Va
^ 0
1
-
a^
^0
a^+l
a
> 0
2
+
2Va
0
2Va
^ 2
a^^l
1

a
> 0
a
7t
1
<=>
a^
+ l
a
> 0
a
^ 1
2
+
2V^
2-2V^ l-a^
2(1+ V^) 2(1-V^)
1-a'
_
(1
-
Va)(l
+
a) + (1
+
Va)(1
+
a)
-
2(a^

+
1)
'i
2(1
+
Va)(l
-
Va)(l+
a)
_
1
+
a
-
Va
-
aVa
+
1
+
a
+
Va + aVa
-
2a^
- 2 ,,i ; -
2(l-a)(l
+ a)
=
2a -a^

_
2a(l
-
a)
_ a
j
•
;
2(1
-
a)(l
+
a)
~
2(1
-
a)(l
+
a)
~
1
+
a
'
Luygn
giai
6i
tru6c kl thi vAo I6p 10 ba
miSn
B^c, Truiig, r^jm mfln

lo&n
_
Nguygn
Dire
Ta'n
2) Dieu kien
a >
0,
a 1
3 1
+ a 3 3
1
+ a
a
+
1
-
3a
^
1
-
2a
^
<r>
> 0
<=>
> 0
<=>
3(1
+ a)

3(1
+ a)
1
-
2a
> 0
va 1
+ a > 0
1
-
2a
< 0
va 1
+ a < 0
<=>
-2a
>
-1 va
a > -1
1 ^
a
<
— va
a > -1
a
>
— va
a < -1
2
-2a

<
-1 va
a < -1
1 <
'1 4-
i.
<=> -1
< a < -
2
Ket hdp vdi dieu kien ta
c6
vdi
0 < a <
thi
A <
Nhan xet: Day la bai toan de.
a
= 5
b
^ 3
Ma
A e
(d)
3 =
5(-l)
+
b
o
b
= 8

Vaya
=
5,b
= 8.
2) Phifdng
trinh
c6 hai nghiem phan biet X|, \i
Bai 3. 1) (d) // (d')
^
. Ta c6 (d): y
=
5x
+ b
o
A
=
f3(a
+
1)1
-
4a(2a
+ 4) > 0
a
5t 0
9a^+18a
+
9-8a^-16a>0
[a^
+
2a

+ 9 > 0
a
^ 0
. <=>
a 9t 0
(a
+
1)^
+ 8 > 0
Vay phifdng
trinh
c6 hai nghiem phan biet vdi
a
;^
0
<=>
{
Theo
he
thiJc
Vi-6t ta
c6
X,
+X2 = -
3(a
+
1)
X|X2
=
2a

+ 4
Do do xf + X2 = 4 o (x, + Xj)^ - 2x,X2 = 4
-3(a
+
1)
n2
^ 2a
+ 4
9(a
+ \f
4a
+ 8 , ^
- 2.
<=> T-^ 4 = 0
Cty
TNHH
MTV
DWH
Khang
Vi^t
<=> 9(a
+
I)^
-
(4a^
+
8a)
-
4a^
=0

<^ 9a^
+
18a
+ 9 -
4a^
-
8a
-
4a^
= 0
<=>a^+10a
+ 9 =
0<=>a^+a
+
9a
+ 9 = 0
o a(a
+
1)
+
9(a
+
1)
= 0 o
(a
+
l)(a
+
9)
= 0 «

a
= -1
a
= -9 v.;«
a
=
-1 (thich hdp),
a = -9
(thich hdp)
Vay
a =
-1
hoSc
a = -9
Nh§nxet:
1) Day la bai toan ve do thj h^m so' bac nhat rat quen thuoc va de.
v
i
i
-
2) Day
la
bai toan
ve
phifdng
trinh
bac hai mot an
he
thtfc Vi-et.
Lufu

y
rang
fa ;^
0
phiTdng
trinh
hai nghiem phan bi$t <=>
A
=
b'^
-
4ac
> 0
Bai 4. 1) Ta c6: MP 1AB (gt) => MPA
=
90"
Va MQ
1
AC (gt) MQA
=
90"
.
TiJ
giac
APMQ cd MPA
+
MQA
=
90", MPA
=

90"
.
Do
do trJ
giac
APMQ noi tiep diTdng tron
dirdng
kinh
AM, tarn la trung diem cua AM.
2)
Ta cd O la
tarn diTdng tron ngoai tiep
tiJ
gi^c APMQ. Mat
khac
AHM
=
90"
=> M thuoc du-dng tron difdng
kinh
OM.
Do vay
H e
diTdng tron. Ma BAH
=
HAC
(AABC deu, AH
la
diTdng cao nen cung 1^
dirdng

phan
giac)
=> HP
=
HQ
Vay PO IHQ
3) SMAB + SMAC =
SABC
=>-MP.AB
+-MQ.AC
=-AH.BC
2
2 2
=>
^MP.BC
+
^MQ.BC
=
^AH.BC (AABC deu => AB
=
BC
=
AB)
DoddMP
+
MQ
=
AH
Nhfin
xet: Day la bai toan hinh hoc qua de vk rS't quen thuoc.

Bai 5. Ta c6
a >
0,
a +
b
=
1. Do do
A =
^^-^
+
b^
=
2a
+ +
b^
4a
, ,j 4a
•nr'
1
Luy^n
giSi
ai
truOc
k1
thi
vao Idp 10 ba
miSn
Bjc,
Trung,
Nam mOn

Join
_
Nguyln Dufc
Tin
=
(a
+
b)
+
=
(a +
b)
+
a
+
4a
b^
-
b
+ i
]_
2
a
+
4a
b

2 2
V 4a 2 2
Dau xay ra

«
a
=
b =
—
r
1 ^
P
2
1
a
+ —
+
b
I
4a;
v
2y
"
2
Vay gia tri nho nhat cua
A
la
^ ,
Nhan
xet: Day
la
bai
toan
ciTc

tri dai
so, cac
bien
c6
dieu kien rang bupc
(a
> 0, a + b >
1), bai
toan
nay
kho nhat trong
de
thi
nay
nh^m giup phan
loai
hpc
sinh, bang diT doan
a = b = ^
thi
A
dat gia trj nho
nhat, chung
ta
kheo
leo
viet
A
thanh
A

= (a
+
b)
+
Tur do
giiip
CO
Idi giai bai toan.
Dlfe
S6 11
KY
THI TUYEN
SINH
VAO LdP
10
THPT, TJNH YEN BAI
NAM HOC
2012
-
2013
Cau 1.
(2,0
diem)
1)
Chohamsoy
= x +
3(l)
a) Tinh gia tri
cua
y

khi
x = 1
b) Vedo thi
cua
ham
so (1)
2) Giai phiTdng
trinh:
4x^
- 7x + 3 = 0
Cau
2.
(2,0
diem) Cho bieu thtfc
M =
—^=
+ =
^^-^
3-Vx
3 +
Vx
x-9
1) Tim dieu kien
cua
x
dc
bieu thtfc
M
c6
nghla. Rut gpn bieu thtfc M.

2) Tim
cac
gia tri cua
x
de M
> 1
Cfiu
3. (2,0 diem) Mot dpi the* mo phai khai
thac
260
tan than trong mot thcfi gian
nha't
dinh.
Trcn ihiTc
tc,
moi ngay dpi deu khai
thac
vu'dt
dinh
mtfc
3
tan, do
do
hp
da
khai
thac
du'dc
261
tan than

va
xong trufctc
thdi
han mot ngay.
Hoi
theo
ke
hoach
moi ngay dpi thd phai khai
thac
bao
nhicu ta'n
than?
Cau
4. (3,0
diem) Cho nuTa
di/dng
Iron
tarn
O,
diTcJng
kinh
AB
=
12cm. Tren
nuTa
mat phang
bd AB
chuTa
nuTa diTcfng tr6n

(O)
ve
cdc
tia tiep tuyen Ax,
By.
M
~my^i\inn
rvnv uvvn r\naiiy viyt
la mot
diem
thupc nCfa
diTdng
iron
(O),
M
khong
trung vdi
A
va
B.
AM
cj(t
gy
tai
D,
BM cMt Ax tai
C,
E
la
trung

diem
cua doan thang BD.
1) Chtfng
minh:
AC,
BD
= AB\
2) ChiJng
minh:
EM
la
tiep tuyen cua
nijTa
diTdng
tron tam O.
•
3)
Keo
dai
EM c^t Ax tai
F.
Xac
dinh
vi tri
cua
diem
M
tren
nuTa
du"5ng tron

tam
O
sao cho
dien
tich
tu' giac
AFEB
dat gia
tri
nho
nha't.
Tim gi^
tri
nho
nhat
do.
Cfiu
5. (1-0
<3iem) Tinh gid tri cua
bieu
thiJc:
T =
x^
+
y^
+ - 7
biet:
X
+ y + z
=

2 Vx
-
34
+
-21+
6>/z
-4 + 45
Hl/ClNG
DAN GIAI
Cfiu
1.
1. a) X
=
llhi
y =
X
+ 3 =
1
+ 3 = 4
b)
Bang
gia tri
X
-3 0
y
=
X
+ 3
0 3
2)

4x'
-
7x
+ 3
=
0
a
+ b +
c
=
4 + (-7) + 3
=
0
Phi/dng
trinh
c6
hai
nghiem
phan biet:
c
3
X,
=
1, X2
= - = -
a
4
Nhan xet: Day
la bai
toan qua

de
Cfiu
2.
1)
M
CO
nghia
<=>
X
> 0
3-Vx
^
0
x
-9 ^ 0
X
> 0
X
?t
9
X
> 0
X
;^
9
M
= -
1
six x + 9 3 + Vx +
>yx(3

-
Vx]
+
X
+ 9
3-N/^^3
+
V^~X-9
" (3
+
V^)(3-Vr)
_
3 +
x/x+3Vx-x
+ x + 9
4Vx+12
(3
+
V5^)(3
-
(3
+
V^)(3
-
N/^)
4(75^ + 3)
4
(3
+
V^)(3

-
V^)
3-^/^.^^^,^
45