hsg-2010-2011 (brvt)
TRANSCRIPT
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8/3/2019 HSG-2010-2011 (BRVT)
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S GIO DC & O TOTNH B RA VNG TU
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K THI CHN HC SINH GII CP TNHLP 10 THPT,NM HC 2010 2011
____________________
CHNH THC MN THI: TON LP 10Thi gian lm bi thi : 150 pht
Ngy thi : 30/3/2011
Cu 1(5 im) Cho pt: 3 2 24 4x x m x x + =
1.Gii pt khi m=-4
2.Tm m pt c nghim thuc [ ]0;4
Cu 2(5 im)
1. Gii bpt: 2 2 22 3 3 4 6 7x x x x x x+ + + +
2. CMR: vimi x,y khc 0 ta lun c:
2 2
2 23 10 8x y x y
y x y x
+ + +
Cu 3(4 im)
1.Gii h pt:2 2
3 2
8 12
2 12 0
x y
x xy y
+ =
+ + =
2.Tm tt c cc gi tr k bpt:2x x x k + c ng 2011 nghim nguyn
Cu 4(4 im)
1. Trong mp Oxy, cho ng thng d: (m-3)x+(1+2m)y+14=0, A(3;5). Tm m khang cch t A nd ln nht
2. Cho tam gic ABC vung ti A c AB=2AC=2a(a>0 khng i). Tm tp hp M tha:MA2+MB2+2MC2=12a2
Cu 5(2 im) :Cho tam gic ABC v M l 1 im bt k trong tam gic. Gi A 1, B1, C1 ln lt l hnh
chiu vug gc ca M ln BC,CA,AB. CM: 1 1 1
cot cot cotAA B BB C CC A+ + khng ph thuc v tr M
---------------------------------------------------HT------------------------------------------------
H v tn th sinh:. Ch k gim th 1:..
S bo danh :.
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8/3/2019 HSG-2010-2011 (BRVT)
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S GIO DC & O TOTNH B RA VNG TU
_____________
K THI CHN HC SINH GII CP TNHLP 11 THPT,NM HC 2010 2011
____________________
CHNH THC MN THI: TON LP 11Thi gian lm bi thi : 150 pht
Ngy thi : 30/3/2011
Cu 1(5 im) Cho pt:sin6x+cos6x+2cos3x.cosx-cos4x+m=0
1.Gii pt khi m=-2
2.Tm m pt c nghim thuc ;4 2
Cu 2(5 im)
3. Tm3
21
7 3 4lim
1xx x
x+ + +
4. CMR: Trong tam gic ABC ta lun c:sin3A+sin3B+sin3C 3 32
. Khi nao du = xy ra?
Cu 3(4 im)
Cho hnh lp phng ABCD.ABCD cnh a, M l mt im thay i trn cnh AB. Mp (AMC) ct cnhDC ti N.
1. T gic AMCN l hnh g? CM: MN CB
2. Gi H l hnh chiu vung gc ca C ln MN. Tm tp hp H.
Cu 4(2 im): Cho 3 tia Ox,Oy,Oz i mt vung gc v cc im A,B,C ln lt nm trn 3 tia saocho OA=OB+OC=1
1. CM: tng din tch cc mt ca t din OABC khng i khi B,C thay i
2. Tnh tng cc gc: OBA ABC OCB+ +
Cu 5(4 im) : Cho dy s (un), n=1,2,3 tha cc kin sau:
1. 0
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8/3/2019 HSG-2010-2011 (BRVT)
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S GIO DC & O TOTNH B RA VNG TU
_____________
K THI CHN HC SINH GII CP TNHLP 12 THPT,NM HC 2010 2011
____________________
CHNH THC MN THI: TON LP 12Thi gian lm bi thi : 180 pht
Ngy thi : 02/11/2010
Cu 1(4 im) Cho hm s y =2
2 1x mx m
x+ +
+( 1 ) .
Tm tt c cc gi tr ca m th hm s (1) ct trc honh ti 2 im phn bit v tip tuyn vi th(1) ti 2 im vung gc vi nhau .
Cu 2(5 im)
5. Gii h phng trnh :2 2 4
2 5 2 5 6
x y
x y
+ =
+ + + =
6. Tm gi tr nh nht v ln nht ca hm s : 2tan 16 cos y x x= + khi ;4 3x
Cu 3(4 im)
1. Cho hnh chp t gic u S.ABCD , cc mt bn c gc nh S s o l ( 0