Đề kiểm tra định kỳ lần 1 môn Toán lớp 8 năm 2015

UBND

iiXTI

DE KIF:,fr,{ TRA DINI{ KY T-AI-,{ 1
NXrn hqc 2oi4 - 2015
I\I6n: Toin - L6'p 8
Ti'td'i gian ldm hdi. 90 plnit (lchdng ke thdi gian gino

BZ\C NIN}I

so cIAo DU-c vA DAo

r,!o

d0)

Citu 1. Q,A ttiAm)
1) Thpc hiQn c6c phdp tinh

a) 8x3

- (4*' + 2x *

2) Cho x

PhAn

-

y

:

1).(2x

-

u1(ox'z

1);

2. H?.y tinh gi6 trf cria A

:

x3

.3

- oxy-y

-r6y')' (:x- 4y).

.

tich c6c da thfc sau thdnh nhdn tu.

1) l5x2 + iOx;

2)

*'-y'+2x-2y;

3) 3x2 +5xy +3y' -1222;

4)

*'- 5x - 6.

CAu 3. (2,0 di€m)
1)

Tim x bi6t:

a) 5(2x + 1)

b)ax(x + 5):3(x +

- 2x- l: 16;

2) Tirrrnrsao cho dathuc f (*)=10x2

Ciu

5).

-7x-m chiahtlt cho dathric g(x) =2x-3.

4" 6,A di6mt

Hinh thang ABCD (AB llCD) c6 f)C: 2AB. Ggi M, N, P, Q lAn luot ldtrung diOm ctra c6c
canh AB, BC, CD, DA.
1) Chii"ng minh cdc

2) Tim diOu kiQn

tir gi6c ABPD, MNPQ ld c6o hinh binh hdnh.

c'Jra

hinh thang ABCD

AC

L,fNfq ld hinh thoi.

3) Gpi E la giao di€rn eira BD vd AP. Chfng rninh ba rtiOm Q, N, E thing hdng.

Cho hai sO hUu ty a, b thoa rndn ding thric: a'b+ab3 + 2a'b'+2a+2b+l= 0. Chring minh

ring 1- ab ld binh phuong cira rnQt sO htu ty.
HET
(D€ gdm c6

0l

trang)

Thi sinh khong duoc sa dqng tdi li€u. Gidm thi khdng gidi th{Ch gi th€m.

Hg vd tOn thi

sinh:.........

....."....; S6 Uao danh:.......


UBND

HUoI.{G nAN cnAivl
LAx
KIEM TRA DINH
NIm hgc 2014 -2015
M6n: Toin - Lfp 8

TiN{ BAC NiNi{

rt

so crAo DUC vA DAO T4O

t

D6p 6n

CAu

Sxi

- 14x' + 2x+ l).(2x- 1): 8x'- (8x'- 1)

: d*r-8rrl

Di6m
0,25
0,25

i-:-1

(,, ' -16y') (r, -+y)= [{:,)'- (+y)'],( 3x-ay)

0 75

0 25

Vix-y:2,n€n
A : xr - 6xy - y3 :
----:--1-

:-(x-))

(r - f')(*' 1 xy + y'') - 6xy : 2(*' * xv * y') - 6*:'

'5

n

r5

0

r)

0 )5

;-;l _-;
- /./ - o

0

) -^
15x--l0x:5x(3x+2)

0,5

')+ (2.' -zy) = (* - y)(, * r-) +2(x - y)

= (r -y)(r* y+2)
3x2

=

:

:[(, * y)' - (2r)')

5(2x+

=

3[(r' +2ry + i)'+,')

= 3(x + v

a

o^Lx:3O

J

x=-

2

*

s) =3(x

vay

+

0,25

0,25

l)-2x- 1 : 16 a5(2x+ 1) - (2x+ 1): 16
1.

0,25

0,25

- 6(x+1): (x + 1Xx - 6)

e4(2x + 1): 16a2x)-

4x(x

-22)(x + v +22)

-6- x'+x -6x-6

x(x+1)

?i

0 25

+6xy+3y'-1222

x'-5x

n

7;

0,25

=4

t': I
xel-l

5) <+

0,25

l2)

4x(x +

5)-3(, + 5)=0.e(ax-:X, + 5):s

0,25


O4x-3-

a

0 ho{c

x * 5=0

4x=3 hoic x :-

5ex-1

:__

------T----ir
vay x.

o)5

:-

no4. x

I-- --

5

0,25

t-t'aj

(*) = 10x2 - 7 x - m chia h€t cho da thric g(x) =2x -3
<+ T6n t4i da thricp(x) sao cho "f (*)= l0x2 - 7x-m=(2x-l) a(*),V, (*)

Da thric: -f

Vi (*) dirng Vx, n€n (t) cflng dtng khi
3

Thay

e10
Vay

vio (*) ta duoc: ,(i)= Q

2
/a\2
IJ]

[;]

-

l.-

1

ltl

-

0em

-

, = ].
2

14).Q(,)

=o
0 ?5

=12

m: i2 thi da th[Lc -f *)= 10x2 - Jx-m chia h6t cho da thuc g(*)=2*-z
VC hinh dilng

+ GT

0,25

0,25

- KL

- L4p lu4n,chi ra tu gi6c ABPD

I

I

PD

0

?i

0

?i

"0,{A,B
IAB = PD

l-lPl?-l:l49ttt*- -- Chi MN ld trung binh cua AABC n6n MN//AC (1) vd Mli
ra

0,25
I

=

-

AC
o ?5

- Chi ra PQ/AC (2)
rt (1) vn (2) MN// PQ (3)

=

- Tuong t.u chi ra MQ
-

Tt (3) vn (a) =

/

NP(4) vir MN =), ao
2

MNPQ ld hinh binh hanh.

Theo cAu 1) thi tir gi6c MNPQ da le hinh binh henh'
MN: MQ
Oe ttr ei6c MNPQ ld hinh thoi

e

=

0?5

i.: ", G; ^ =!^r,^
=!ro)
22

0,25

0,25


Khi d6 hinh thang ABCD c6 2 ducrng ch6o AC: BD
= ABCD la hinh thang cdn.
Vfly hinh thang ABCD ld hinh thang cAn thi MNPQ ld hinh thoi.

0,25

(cmt)= E li trung di6m cria BD.
- Chi ra NQ le trung binh cira hinh thang ABCD

= NQ/CD(*)
- Chi ra NE ld ducrng trung binh cria ABCD
= NE//CD(**)
- Tt (*) va (**) :+ Ba diOm Q, N, E thing ha"g( Theo ti6n OA Octit;.
- Vi ABPD le hinh binh hdnh

0,25
0,25
0,25

o)5

*) N6u ab = 0 l- ab =l e
Q(Hi6n nhi6n dirng )
=
*) N6u ab + O, ta c6:
at b + ab3 + 2a'

e
o
e

1t2,

a' b-

b' + 2a + 2b + l-

r.l
a

lo + b)' +2ab1a
r

+

hS

:

e

ab(ct +

b)' + 2(a + b) = -l

0 ?5

-o6

a' b' (a + b)2 + 2ab(a + b) + | = |

1- 66 =lab.(a +b) +1]'

0

0,25

-

ctb

0 r5

. Q (la binh phuong c[ta sO hlrLr ry*)

Tu 2 truong hqp tr€n thi bdi tofn duoc chtmg minh.

0.25

Luu y:
- Thi sinh ldm theo cdch riAng nhtrng clap tfug dtroc

-

ViQc c'h.i tiet hoa di€m

yAtL

,ir, ,o ban vdn cho di --';.nt,

to 6et, co) So vot bi€tt di€m phai dam bao khong

,:
htr,tng dan cltttn; r'a dr.roc thong

nhdt trong to

chan'1.

sai

le:L voi