Đề kiểm tra năng lực giáo viên THCS môn Toán Bắc Ninh

iNH
aAC
NINI-{
of xrtnn rna
NANG LVc
cnuvtN
na0N
ctAo
vltll
UBND
TiNH BAC
NINI-{
sO clAo
DUC
vA DAo rAo
oE cniNu rHfc
NAnn Hec
zotz -zot3
Mdn:
Toin
- THCS
Thdi
gian
ldm bdi:/5 0
philt
(hhdng
kd thdt
gianphdt di)
Ngny ki6m
tra
!4

thdng
4
ndm
20i3
Cflu
I
(1.5
tli6m):
l)Tfnhgi6tricriabi6uthrlc
P=x2(x
+y)-2y'(x+y) +2013x2-4026y2+2(x+y)+4036,bii6t
rang
x+y+ 2013:0.
2)
Tim
sO
qu
nhien n biiSt
r[ng
khi chia 147 vi 193 cho
n
thi
c6 sO du
l6n
luqt
ld 17 vi
1 1.
Cflu 2
(2,0
tli6m):

l)Tim
x,y,z biiit: x
:
4y
:
*
vdx*
y+z
:
2A29.
"
125
2)
Cho
c6c
don
thrlc: M: xy2z3; N
:
yzzt3;
P
:
zt?x3;
Q
:
ft't'.
Chtlng
t6 r6ng
vdi
gi6
tri

cria c6c
biSn hm 2
trong
4 tlon thrtc tr0n
c6
gi6
tri
kh6c d6u thi
2 dsathtc
cdn
l4i cfing
c6
gi6
tri
kh6c d6u.
C6u
3
(2.0
di6m):
1)
Phan
tich da
thrlc
sau thanh nhdn
tt:
x2 +Zxy
-15y'
.
2)
ChoA: 13

+
23
+33
+

+
1003
vdB
:
L
+
2
+3 +

+
100. ChfmgminhrdngA
chia
htit
cho B.
3) Giai
phucrng
trinh:
Bf
**1)' ++(*'*+)'
-+(*'+.1
\r I \2 t
I
x./
(
x'

)
(
P,J{,".*J
=(x+4)''
Cflu 4
(3"0
di6m):
Tt m$t
eli€m D nim ngodi dudrng
trdn
(O;
R) kE hai tii5p tuyi5n
DA
vd DB
di5n
dudng
trdn
(A
vd B Ii
c6c
ti6p di6m). K6
tia
Di
nim
gita
hai tia
DAvi
DO, tia
Dx
c6t

dudng
trdn
t4i
hai
di€m C vi E
(E
nim
gita
C vi D). Doan thing OD cft ctoan
thdng
AB
tai
M.
Chung
minh
reng:
l) DC.DE
:
DO.DM
vi trt
gi6c
OMEC
nQi
tii5p.
2)m[:Em
^,
(N,B)'
DE
"
Ino.J

:nc'
Cf,u 5
(1.5
tliSm):
1)
Vdi
a,
b
li c6c
si5 nguy€n. Ch{mg minh
rang
n6u 4a2+3ab-11b2chia
hiit
cho
5
thi
ao
-
bo chia hiSt cho
5.
2)Chfngminhring:
4*-L*-L*4* *,
1
=,
<l,vdineN[*.
3Jt sJ3 7^ls
gJt
(2n+
L)Jzn-l
nEr

Th[
sinh kh6ng
tttrgc srb dyng
tdi liQu Cdn
b$
coi thi khdng
girti
fiich
gi
thdm.