STT 01. ĐỀ THI CHỌN HSG TỈNH AN GIANG<br />
NĂM HỌC 2017-2018<br />
Câu 1:<br />
<br />
a)<br />
<br />
1 2x x 1 2x x x x <br />
1<br />
P<br />
<br />
<br />
<br />
:<br />
x 1 x<br />
1 x x<br />
1 x<br />
<br />
<br />
(<br />
<br />
v i x 0, x 1, x <br />
<br />
1<br />
4<br />
P<br />
<br />
b) (<br />
<br />
4<br />
10<br />
) Cho a, b, c<br />
x<br />
<br />
<br />
<br />
3 5 3 5<br />
<br />
<br />
a 2 b2 c2 12<br />
<br />
S 4 a3 b3 c3 a 4 b4 c4 <br />
<br />
Câu 2:<br />
x2 4 x <br />
x4<br />
<br />
5<br />
x<br />
x 1 <br />
x 1<br />
<br />
<br />
a)<br />
b)<br />
<br />
x 2 y 2 xy 1<br />
<br />
3<br />
3<br />
<br />
x y x 3y<br />
<br />
i<br />
<br />
Câu 3:<br />
<br />
BC<br />
<br />
O; R , M<br />
I q<br />
<br />
A<br />
<br />
K <br />
<br />
q<br />
<br />
a)<br />
b)<br />
<br />
AC<br />
<br />
M<br />
<br />
I <br />
<br />
M<br />
<br />
C<br />
<br />
AB<br />
<br />
B<br />
<br />
N<br />
<br />
K <br />
B, N , C<br />
AB ( D<br />
<br />
D<br />
<br />
CA sao cho BD CE<br />
q<br />
ADE<br />
O; R <br />
<br />
E<br />
<br />
Câu 4:<br />
<br />
A<br />
<br />
B<br />
x, y th<br />
<br />
2 x y xy 2 x y <br />
2<br />
<br />
2<br />
<br />
ĐÁP ÁN<br />
Câu 1:<br />
<br />
B<br />
<br />
A<br />
AB<br />
<br />
M<br />
M<br />
<br />
MAB<br />
<br />
Câu 5:<br />
<br />
A<br />
<br />
a) (<br />
1 2x x 1 2x x x x <br />
1<br />
P<br />
<br />
<br />
v i<br />
:<br />
x 1 x<br />
1 x x<br />
1 x<br />
<br />
1<br />
x 0, x 1, x <br />
4<br />
4<br />
x<br />
3 5 3 5<br />
P<br />
10<br />
b) (<br />
) Cho a, b, c<br />
a 2 b2 c2 12<br />
<br />
<br />
<br />
<br />
<br />
S 4 a3 b3 c3 a 4 b4 c4 <br />
<br />
1 2x x 1 2x x x x <br />
1<br />
P<br />
<br />
<br />
<br />
:<br />
x 1 x<br />
1 x x<br />
1 x<br />
<br />
<br />
<br />
P<br />
<br />
<br />
<br />
2<br />
<br />
x<br />
<br />
<br />
2<br />
<br />
x<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
x x 1 2 x 1 <br />
1 x x x 1 <br />
<br />
<br />
x 1 x x 1 2 x 1<br />
:<br />
<br />
x 1 x 1 x 1 x<br />
<br />
<br />
1<br />
x 1 <br />
: 2 x 1 <br />
<br />
1<br />
<br />
x<br />
x<br />
1 x <br />
<br />
<br />
<br />
<br />
x 1 <br />
2 x 1<br />
<br />
:<br />
<br />
<br />
1 x<br />
1 x x x 1 <br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
x<br />
<br />
x 1 <br />
<br />
<br />
<br />
x x 1<br />
x<br />
<br />
i<br />
x<br />
<br />
<br />
4<br />
10<br />
<br />
<br />
<br />
3 5 3 5<br />
<br />
5 1 5 1<br />
2<br />
<br />
y P<br />
<br />
.<br />
<br />
<br />
<br />
4<br />
4<br />
10<br />
<br />
4 4 1 3<br />
<br />
2<br />
4<br />
<br />
S 4 a 3 b3 c 3 a 4 b 4 c 4 <br />
4a3 a 4 4b3 b4 4c3 c 4 <br />
<br />
Ta ch<br />
<br />
4a<br />
<br />
3<br />
<br />
a 4 4a 2<br />
<br />
4a<br />
<br />
3<br />
<br />
a 4 4a 2<br />
<br />
a 4 4a 3 4a 2 0<br />
a2 a 2 0<br />
2<br />
<br />
T<br />
<br />
4b<br />
4c<br />
<br />
3<br />
<br />
b 4 4b 2<br />
<br />
3<br />
<br />
c 4 4c 2<br />
<br />
y<br />
S 4 a 3 b3 c 3 a 4 b 4 c 4 <br />
4a 3 a 4 4b3 b 4 4c3 c 4 <br />
4 a 2 b 2 c 2 48<br />
<br />
a, b, c 2, 2, 2<br />
Câu 2:<br />
x2 4 x <br />
x4<br />
<br />
5<br />
x<br />
x 1 <br />
x 1<br />
<br />
<br />
a)<br />
b)<br />
<br />
2<br />
2<br />
<br />
x y xy 1<br />
3<br />
3<br />
<br />
x y x 3y<br />
<br />
i<br />
<br />
x 1<br />
y<br />
<br />
x x 4<br />
x4<br />
x4<br />
suy ra x <br />
x4<br />
4 y4<br />
x 1<br />
x 1<br />
x 1<br />
<br />
Ph<br />
y y 4 5<br />
y 1<br />
y 5<br />
<br />
<br />
V<br />
<br />
<br />
5 21<br />
x1 <br />
2<br />
y 1 <br />
<br />
5 21<br />
x2 <br />
<br />
2<br />
<br />
<br />
1 21<br />
x1 <br />
2<br />
y 5 <br />
<br />
1 21<br />
x2 <br />
<br />
2<br />
<br />
V<br />
<br />
x3 y 3 x 3 y .1<br />
<br />
x3 y 3 x 3 y x 2 y 2 xy <br />
2 y 3 4 xy 2 4 x 2 y 0<br />
2 y y 2 2 xy 2 x 2 0<br />
2 y 0<br />
2<br />
2<br />
2<br />
y 2 xy x x 0<br />
<br />
<br />
<br />
1;0 <br />
<br />
y 0 x 1<br />
<br />
V<br />
<br />
x y<br />
<br />
2<br />
<br />
x2 0<br />
<br />
x 0<br />
<br />
y 0<br />
<br />
1;0 ; 1;0<br />
Câu 3:<br />
<br />
BC<br />
<br />
O; R , M<br />
I q<br />
<br />
A<br />
<br />
K <br />
<br />
q<br />
<br />
M<br />
<br />
I <br />
a)<br />
b)<br />
<br />
C<br />
<br />
AB<br />
<br />
N<br />
<br />
K <br />
D<br />
<br />
E<br />
<br />
AC<br />
<br />
M<br />
<br />
B , N ,C<br />
AB ( D<br />
CA sao cho BD CE<br />
q<br />
ADE<br />
<br />
A<br />
<br />
B<br />
A<br />
<br />
B<br />
<br />
A<br />
<br />
D<br />
<br />
O<br />
N<br />
<br />
B<br />
<br />
C<br />
<br />
I<br />
K<br />
<br />
E<br />
<br />
M<br />
x<br />
<br />
BNM MBx<br />
<br />
a)<br />
<br />
MNC MCE<br />
<br />
Do t<br />
<br />
ABMC<br />
<br />
Suy ra: ABM ACM 1800<br />
MBx MCE 1800<br />
<br />
Nên : BNM CNM 1800 suy ra B, N , C<br />
b)<br />
<br />
BDM<br />
<br />
CEM<br />
<br />
BD CE ( gt )<br />
<br />
DBM ECM ( ABMC nt) BDM CEM c.g.c <br />
BM MC gt<br />
<br />
<br />
BDM CEM t<br />
<br />
ADME<br />
<br />
Do M<br />
<br />
q<br />
<br />
ADE<br />
M<br />
<br />
Câu 4:<br />
<br />
O; R <br />
A<br />
<br />
B<br />
<br />
AB<br />
M<br />
<br />
M<br />
MAB<br />
<br />