[r]
(1)so crAo D TAO xi rm rUYEN sINH LoP to rHPT NAU Hec zozo - zozt
Kh6a ngiry 171712020
oAp Ax-THANG DIEM
M6n thi: TOAN
0'5
1)
T{nh gid tr! cfto bi6u thrbc A khi r - 4
Thay r - 4 (thoa mdn DKXD) vdo bitiu thric A, tinhdugc: .4
4
GI
0t
lr0
2)
r-Vr+1
1
1
2
-
(c-r)(.6+r)
(c
(l;
B-
J" -t
3 +
)-( Ch*ngminh B - +
Jr +t
.6+r)
J-" +s
,(l; - r)
0'5 BNi I
2,0 didm
3)
Tim ttit crt gid tr! crta r it| bi\u thtbc P - 2A.B + J " dqt gid tr! nhd nhdt
P-2A.B+J;:#r+J;
Tac6: P -2 -++J; -2- +> 0 voimoi r > 0
Jr +z Jr
+2-Suy ra P > 2 Dingthric xtty rakhi vd chi khi r - 0 KL: r - 0 thi bi6u thric P dqt gi6 tri nhO nh6t
l15
VAn t6c di xe dpp cira An la r * I (km/h)
Thdi gian An di b9 ttr nhe An dtin nhd Binh l' a - 3 (gio)
+ r' +9r - 36: o <+ (r - 3)(" +12) - o <+
,
Tinh vQn tbc iti b? crta An.
LAp lupn d6n d6n phucrng trinh
Thcri gian An di xe d4p tir nha Binh v0
Gqi v0n di b0 cua An lir r (dcrn vi: km/h, u > 0).
r-3 r t2
3
nhaAnh r+g Gio).
33
r r*9 Bii II
2,0 diam
I
1)
Di6m
v Dfp 6n
(2)kiQn lopi r 12 , thu 14i r - 3 thoa mdn y6u u bii to6n
KL
hqrp di
t6c di ctra An la 3 km/h
0,5
2)
Tinh diQn tich bi mfit cfia qud bdng bdn
S - 4trR2 x 4x 3,14 x22 - 50,24(.-'). bc mdt cira qui b6ng ban li:
DiQn tfch
Ir0
r)
Vdi b - 1 + + - 1 + u : 2(thoam6nDKXD).
y -l v
KL: hQ phucrng trinh co nghiQm nh6t le (r; y): (r'r).
Gidi hQ phwong trinh
<+ e
2r * 3b - 5
4r - b : 3
2r* :b
y -l
4r- :3
y -l
DKXD: U =L.
1
DAt
- -b,
tac6hq
y-I Giai he
b:l
f:l 2r * 3b :5
4r-b:3
0,75
2a)
Ggi tgadO diem ,4 la (rr;Ao) Do cli6m ,4 thu6c tryc Oy n€n ro - 0.
Do di6m ,4 thuQc dudrng thing (d),A : n'Lr * 4 n6n
ut: ffine * 4 - m.0 * 4 - 4
KL: tsa d0 di6m A la (0;a)
fim cua m A
0,75
b) Tim tiit cd gid tr! cfia m AO dwong thdng (d) cdt tryc Or tgi itilm B sao cho
tam gidc OAB ld tam gidc cfrn
(*utrr) oo di6m B thuQc tryc or ndn vo - 0. Vi di6m B thuQc ducmg theng (d),y rrln + dan d6n - mna * 4
Yt m*O + nB:a * OB -prl -
l#l
Vi A OB - 900 n€nclOtam giitc OAB ldtam gitrccdnthi OA - OB Md OA:4 n€n OB - 4
KL:m-l
Ggi tga <t0 cli6m B le
m-l m l
m L
Giai phuong trinh: - l=l - 4 e * [
l*l t
BNi III ^ -.;
./,) drcm
2b)
BNi IV
a
00(
rl(
1r0
l) Chirng minh trb gitic BHEK ld ttb gitic nQi tiiip
2
Di6rr
D6p 6n
Bei Y
)
(3)Chtmg minh dugc BHE - 900 vir
Suy ra BHE + BKE - 1800
Lap luan d6n Aen fr giAc BHEK la ffi
^, ,.i
grac nQl trep
BKE : 900
A
H
E F
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2)
Ap dgng he thftc lugng cho L,AEB vu6ng tqi E, dulng cao EH c6:
BH,BA _ BE2
Chtmg minh tuong tg c6: BK.BC : BE2
Y$Y BH,BA : BK,BC,
Chftng minh BH.BA: BK.BC.
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3)
-
-^
chtmg minh dusc BHK - BEK (l) ( BHBK le tf gitrc nQi ti6p) Chimg minh dugc BEK : BCE (2) (Cung phU voi EBC )
Chimg minh dusc frE - ffi (3) ( BCEF la tri gitcnQi ti6p)
^ ^
chimg minh dusc HFE - FHI (4) (tam giitc FHI c6n tai / )
Ttr ( l),(2),(3), (4) suy ra ffiK -frt Do A.ABCnhqn, hai di6m I vd K
nim ctrng phia AOi vOi duong thing HF n6n I/, I, K li ba ili6m thing hing. hdng
Ch*ng minh ba 'm H ,I,K ld ba th 3,0 diam
0r5
Bni v
0,5 diam
Gidiphwongtrinh J" +,h 1- 12 *!
Lap luan dan Aen r - | (thoa mfrn DKXD).
KL: phuong trinh co nghiQm ntr6t lir r - 1
-0.
3r -2 -l ,
+ zJr +z 3r -2 -2r2 *2
3r -2 - 12 +L
<+,(* -r)' * (.6- r)' * (
2
DKXD: r ) -3-.
Ji+
Luu f:.c6c c6ch ldm kh6c n6u dring hqc sinh v6n tluqc di6m tuong img vdi bitiu ditim cria ddn ch6m
uong H
J
Di6m
Ddp 6n
Bii f
K
2
3
a
,(
, /
o