CVADAOT ao

S

I

Ki

THr

ruyfN

srNH vAo Lop r.0 NAM
rvrol rul: TOAN (CHUytN)

C

e

Thti gian ldm bdi:

Glli

L50

KHAO

OA

phit

202s-2026

(Kh6ng kd thdi gian phtil dA)

02 trang)

CAu 1. (2,0 didm) Cho cdc bi6u thuc p = 2x

a) Rrit gqn c6c bi6u thrlc p

vA

-)G,- z ue g ='F -zJi P,
Jx -2
G+z

- +, v6 x > 0,x *
4.

e.

b) Tim cilc gi6 tri cia x dd p = e.
CAU 2. (2,s

didm)

. l5r' -l*y'
-2(x+
l)CiaihQphuongrrinh:]
'.
;. -,
lwlx'+ r')+2=(** y)'
y

2)

Cho da thuc

P(x)

c6 bQc a vA

+3y3

thoi min

y) =o

cdc diEu kiQn:

p(-t) = 0 vn p(r)-r(x_r)=x(x+r)(2x+t),vxe!

d

Ch(mg minh rlng:

x=0,x=-2

b) Tim tdt ca da thrlc p(x)
CAU 3. (1,0

a) Thi

lA

nghiQm cua da thrlc

p(x).

thoA man cdc cliEu kiQn tr6n.

didm)
10 chidc dinh kh6ng thd'm nu6c c6 kich thu6c nhu hinh du6i

vio

mQt cdc nudc

thuf

tinh. Dinh chim h&n xudng vir nu6c trong cdc kh6ng bi tran ra ngoii. H6i thd tich nu6c
trong cdc tdng th6m bao nhi€u ml (lAm trdn kdt quA ddn hlng phhn mucri)?
.F

l4 mm

8mm

,L
2mm

25 mm

5mm

b) Tron m{t phing voi h6 truc tea do oxy cho hinh chit
A(0;3),8(4;3), C(a;D. Gqi O

li

t6p hqp tdt ca cec di6m

(r;y)

nhit 1ABC sao cho

vot

x,y li

c6c sdnguyOn

nim bon trong (kh6ng kdtr6n c4nh) cua hinh chir .,t.at )ABC. Ldy ngau nhi6n
di6m cua tip h_qp O. Tinh xiic sudt de"di6m (x;y) ldy ra rhoi mdn x+ y <5.
vA

CAu a. (2,5 didm) Cho tam

giiic ABC rhqn nQi ti6p ducmg trbn

trung di6h c,a BC, AM cit (o) tai dicm D (D khric
MDC cit duong thrng
A,r;,nc +hi-.} r'R ti

l).

(o) voi AB < AC . Gqi M li

Duong trbn ngo4i ridp tam gi6c

AC t4i E (E khric c ). Duong rrbn ngo4i tidp tam

F tE t hin R\

mQt

giac

MDB cit

2

a)

dbng d4ng voi tam gi6c CDE ;badie'm
Ch(mg minh ring tam gi6c BDF

h)ng vir OA vu6ngg6c EF

E'M'F thing

'

Erw va EFN hn
tai didm N ' PhAn gi6c cua c6c gac
EF
c{t
b)
minh rlng PQ songsong v6i BC'
lugt cit CN,BN tai P vir p. chung
bingtdngtdtcacdcu6cnguy6n
v6im6isdnguyOnduong r >2'ddts(n)
Phan gi6c

cua

goc WA'c

CAu5.(1,0rtidm)
duong ctra r

.

thd
mOt sd nguy€n td thr s(n) kh6ng
cua
phuong
binh
lir
n
ndu
a) Chtug minh ring,

iA

s6

chinh phucrng
b) Chung mhh

ring ndu n li hqP sd thi S(n)

"*

Ji

'

CAu 6. (1,0 didm)

a)

Cho 3 sd thuc a,b,c >

LI

nhdt cia bidu thuc:
th6a a + b + c= 3' Tim gie td nh6

b'c c'a
2b-1 2c-1 2a-l

a'b
D--+-

'
b) MOt nEn nhir hinh
vi
1

x

chCr

nhit duqc 16t kin bing

c6c vi6n gach

hinh

chCr

nhdt kich thu6c

1x 3

nhir dy chi bing mQt 1o4i g4ch
I x 1 . H6i c6 thd I6t lai n'6n
thu6c
kich
nh4t
chir
3 vi6n gach

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HET