De va dap an thi hk1 nam 2011

Truong
THPT Nguyen Hue
·Ta
toan
***
DE
KIEM TRA HQC
KI
I
Kh3i IOAB
Thai gian: 60
phut
Bilt I: (3 di~m)
II
Giai
phuong
trinh:
~2X2 - 3x +
1
=
x-I
2/G
o" •
bie 1
A
x+m
lal va len uan:
= 111
° °
x-I
, Bai 2: (3 di~m)

{
)
,
I
/G
"oh
A
h • h
x-+y+3xy=11
rai
y
p irong
trtn :
x+y-xy=1
~ 21
Tim m d~ h~
phuong
trinh sau
co
vo s6 nghiern:
{
mx+ y
=
m+1
x+my
=
2
Bili 3: (2 di~m)
Trong m?~
phang toa

dQ
qxy
~ho
cac
di~m A(
-3; I),
B(2;4)o
1/ Tim diem C tren true Ox de tam giac ABC vuong tai C.
21
Khi C(
I;0)
hay
tinh dien tich
.0.ABC
va
ban
kinh duong
trim
ngoai
ti~~ .0.ABC.
Bili 4: (1 di~m)
Cho tam
giac
ABC
co
AB
=
.fi,AC
=
2,A

=
45".
Tinh
dQ
dai
canh
Be
va dien tich
tam
giac
ABC.
Bili 5: (Idi~m)
Cho a,
b,c
la
cac
s6
dirong.
Chung minh r~ng:
a be.,
a+1
b+1
e+1
-+-+-+-' ~ + +
be ae ab a b e
Dang thirc xay
ra khi
nao?
H~t
nAp AN MON ToAN KHOI

lOAB
~
csu:
Bai 1
N(>i dung
{
X
-I> 0
I
I
.J2X2 -
3x
+ I
=
x -
I¢:::>, ,. ()2
2x - - 3x +
I
=
x -
I
{
X ~
I
x>1
¢:::>{ 2- ¢:::>
[X
=
0 ¢:::>
X

=
I
x -x=O
x=
I
(co th~ trinh bay each khac)
Diem
21
x + m
=
m
(I)
x-I
(I) ~
X
+117
=
mx
-/11
¢:::>
(I-m)x
=
-2111 (2)
. - 2Jn
Khi
m
-:I:
I: (2)
¢:::>
x

=
I-m
- 2m
I' hi ,
(I)
khi -
2m
I I
x
=
a
ng
I~m cua 11
-:I:
¢:::>
m
= - \
I-m I-m
Khi
m
=
I: (2) ¢:::>O.x = -2 vo
nghiern ~
(I) vo
nghiern
K
~ 1 ' P 'h" -
2m
et uan: m
-:I:

±I: t co ng rem x
=
. . I-m
m= 1vm=-I:
Pt
vo
nghiern
(khong co
tru'o'ng
hop m
=
-1 thl cho 1 di~m)
£)K:
x-:l:l
0,5d
Id
(3d)
0,25d
Bai 2:
(3d)
{
s=x+
y
J
{S2+P=11 [S=-4,P=-5
II £)at
(S- ~
4P)
He ¢:::> ¢:::>
. P =

xy .
S - P = I
S
= 3, P = 2
" {S
= 3
{x
+
y
= 3
[x
= 2,
y
= I
VOl
P = 2
=>
xy
= 2 ¢:::> ¢:::>
x
= I;
y
= 2
" {S
= -4
{x
+
y
= -4
[x

=
+
I,
y
=-S
VOl
P
= -5 ~
xy
= -5 ¢:::> ¢:::>
x =-5;y
= t-I
V~y h~
co
4
nghiern: .
0,25d
0,5d
0,5d
O,Sd
Id
{
mx+ y
=
m+
I
21
x+my
=
2

D
=
m'
-I;
D =m2+m-2'
r '
O,Sd
0,5d
0,5d
i.
Bai 3:
(2d)
D =m-I

{
m2
-I
=
0
H~
co
vo 56
nghiern
¢:::>D =
D,
=D} =0 ¢:::>
m'
+
111-
2 = 0

m-I =0
,
0,2Sd
0,5d
0,25d
¢:::> ' ¢:::>
111
= I
a/
A(-3;1), B(2;4).
C
EOX ~
CCa,O)
AC
=
(a
+
3;-1);
Be
=
(a -
2;-4)
[a=1
.!'lASC
vuong tai C
¢:::>
AC'.BC
= 0¢:::>(a+3)(a-2)+4=0¢:::>
a
=-2

V~y
CC
I ;0)
hoac CC
-2;0)
bl
TLf
cau
a ta thay .!'lASC
vuong
t~i C
AS=.JS
2
+3
2
=J34,AC=~42+(-1)2 =J17,BC=J(-1)2+(-4)2 =J17
0,5d
D
·•
i ,
h S I
AC BC 17
lel1tlc:
=- . =-
. . 2 2
B
' 'k' h
a . .~
R
AB

J34
an In t ngoai uep:
= - ~
. 2 2
(chi tinh durrc AB, AC thl cho O,25d)
0,5a
Bai 4:
10
, . 2
J J
1\
r;:::12
ApdungDI
COSIn: BC
=
AB-
+
AC- - 2AB.AC cos A
=2+4-2.,,2.2'2=2
BC=12
D
'" . 1 S ) AB C· )
r;:::?
2
12
1
I~n tic 1 tam glac: = - .A .sII1A=-" L -
=
i
2 2 2

0,50
0,50
Bili
5:
10
~+~+~+3~a+l+b+l+e+1
be ac ab a b
e
a
be) )
I
~-+-+-~-+-+-
be ac ab a b
e
Ap dung
b<1t
o~ng thirc Cosi:
(1
blab)
bel
e
a )
be + (1e ~
2fb-;:'-;;;;
=
2 ;:;
ae + ab ~
2 ;;;
ab + be ~
2'

b
Cong v~ theo v~ ~ Dpcrn
Dang thirc xay ra ~ a
=
b
=
c
0,750
0.250
<;, '
'r
I'" . \