Пробный ГИА 2014
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. 90501 |
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21 |
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3x − y = 2, |
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x2 − 4x + 8 = y. |
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3x − y = 2, |
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y = 3x − 2, |
y = 3x − 2, |
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− 4x + 8 |
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− 4x + 8 = 3x − 2; |
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( x − 2)( x − 5) = 0, |
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x = 2, |
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x = 5, |
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y = |
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y = 13. |
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: (2; 4); (5;13). |
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225% , – 13% .4 . ,10% . .
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x . |
( x + 4) , |
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( 2x + 4) |
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0,05x |
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0,13( x + 4) . |
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0,1( 2x +4) , :
0,05x +0,13( x + 4) =0,1( 2x + 4) ; 0,02x = 0,12 , x = 6 .
16 .
: 16 .
© |
2014 . |
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. 9 |
. 90501 |
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y = x2 − 5x + 10 − 3 |
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x − 2 |
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a , y = a + 3. |
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y = x2 − 2x + 4 x < 2 |
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y = x2 − 8x + 16 x ≥ 2 . |
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y = a + 3 a = 0 a = 1.
: 0; 1. |
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© |
2014 . |
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. 9 |
. 90501 |
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» « |
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BC |
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A ABCD |
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E . |
ABCD , BE =7 , EC =3 , |
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ABC =150°. |
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BEA EAD , AE – BAD ,, BEA = EAD = BAE . , BEA -AB = BE =7 .
SABCD = AB BC sin ABC =7 10 1 =35. |
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: 35. |
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25O AC BD ,AB CD . , O – BD .
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ADB , CBD , ACB DAC ,, .
© |
2014 . |
. 9 |
. 90501 |
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, O AOD ;AO : OC . AO =OC , -, , BO =OD .
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26,12, 18.
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C ABCCM CH.
CM = 12 AB = 6 ; CH = 2SABABC = 21218 = 3.
CHM CH CM , CMH =30 .
, H AM . CMH –BMC , ,
ABC = MBC = 1 CMH = |
1 30°= 15° |
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, BAC = 75 . |
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: 15 , 75 . |
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© |
2014 . |
21
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. 9 |
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. 90502 |
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2x + y = 1, |
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x2 − 11x + 14 = 2 y. |
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2x + y = 1, |
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y = 1− 2x, |
y = 1− 2x, |
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− 11x + 14 |
= 2 y; |
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− 11x + 14 = 2 − 4x; |
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( x − 3)( x − 4) = 0, |
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x = 3, |
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x = 4, |
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y = − |
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y = − 7. |
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: (3; − 5); (4; − 7). |
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5% , – 11% .4 . ,10% . .
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x . ( x + 4) ,– ( 2x + 4) . 0,05x , -– 0,11( x + 4) . 0,1( 2x + 4), :
0,05x +0,11( x + 4) = 0,1( 2x + 4) ; 0,04x = 0,04 , x = 1.
6 .
: 6 .
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© |
2014 . |
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. 9 |
. 90502 |
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23y = x2 − x + 3 − 3 x a ,y = a − 4 .
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y = x2 + 2x + 3 |
x < 0 |
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y = x2 − 4x + 3 x ≥ 0 . |
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y = a − 4 a = 6 a = 7 .
: 6; 7. |
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© |
2014 . |
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. 9 |
. 90502 |
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» « |
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A ABCD |
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BC |
24 |
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E . |
ABCD , BE =5 , EC =2, |
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ABC =150°. |
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BEA EAD , AE – BAD ,, BEA = EAD = BAE .
, BEA AB = BE =5 .
SABCD = AB BC sin ABC =5 7 1 |
= 35 . |
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2 |
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: 17,5. |
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25O BD AC ,AB CD . , O – AC .
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ADB , CBD , ACB DAC , -, .
© |
2014 . |
. 9 |
. 90502 |
4 |
, COB AOD ;BO : OD . BO =OD , -, , AO =OC .
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26,16, 32 2 .
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C ABC CM CH .
CM = |
1 |
AB = 8 ; |
CH = |
2S ABC = |
2 32 2 |
= 4 |
2 . |
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AB |
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CHM sin CMH = |
CH |
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CM |
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CMH = 45 .
, H AM . CMH –BMC , ,
ABC = MBC = 12 CMH = 12 45°= 22,5°.
, BAC =67,5 .
: 22,5 ; 67,5 .
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© |
2014 . |
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. 9 . |
. 9 . |
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90501 |
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90502 |
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© |
2014 . |
© |
2014 . |
21
22
. 9 . 90503 1
« »
3x − y = 2,
x2 − 4x + 8 = y.
.
3x − y = 2, |
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y = 3x − 2, |
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y = 3x − 2, |
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2 |
− 4x + 8 |
= y; |
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2 |
− 4x + 8 |
= 3x − 2; |
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x |
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x |
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( x − 2)( x − 5) = 0, |
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x = 2, |
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x = 5, |
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y = |
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y = 13. |
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: (2; 4); (5;13). |
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, . |
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5% , – 11% .4 . ,10% . .
.
x . ( x + 4) ,– ( 2x + 4) . 0,05x , -– 0,11( x + 4) . 0,1( 2x + 4), :
0,05x +0,11( x + 4) = 0,1( 2x + 4) ; 0,04x = 0,04 , x = 1.
6 .
: 6 .
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© |
2014 . |
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. 9 |
. 90503 |
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23 |
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y = x2 |
− 5x + 10 − 3 |
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x − 2 |
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a , y = a + 3. |
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y = x2 |
− 2x + 4 x < 2 |
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y = x2 − 8x + 16 x ≥ 2 . |
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y = a + 3 a = 0 a = 1.
: 0; 1. |
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© |
2014 . |
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. 9 |
. 90503 |
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» « |
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A ABCD |
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BC |
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E . |
ABCD , BE =5 , EC =2, |
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ABC =150°. |
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.
BEA EAD , AE – BAD ,, BEA = EAD = BAE .
, BEA AB = BE =5 .
SABCD = AB BC sin ABC =5 7 1 |
= 35 . |
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2 |
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: 17,5. |
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, , |
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25O AC BD ,AB CD . , O – BD .
.
ADB , CBD , ACB DAC ,, .
© |
2014 . |
. 9 |
. 90503 |
4 |
, O AOD ;AO : OC . AO =OC , -, , BO =OD .
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16, 32 2 . |
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ABC CM CH . |
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CM = 1 |
AB = 8 ; CH = 2S ABC = |
2 32 2 = 4 |
2 . |
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AB |
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CHM sin CMH = |
CH |
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CM |
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CMH = 45 .
, H AM . CMH –BMC , ,
ABC = MBC = 12 CMH = 12 45°= 22,5°.
, BAC =67,5 .
: 22,5 ; 67,5 .
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© |
2014 . |
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. 9 |
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. 90504 |
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2x + y = 1, |
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x2 − 11x + 14 = 2 y. |
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2x + y = 1, |
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y = 1− 2x, |
y = 1− 2x, |
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− 11x + 14 |
= 2 y; |
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− 11x + 14 = 2 − 4x; |
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x |
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x |
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( x − 3)( x − 4) = 0, |
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x = 3, |
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x = 4, |
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y = − |
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y = − 7. |
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: (3; − 5); (4; − 7). |
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, . |
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225% , – 13% .4 . ,10% . .
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x . |
( x + 4) , |
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– |
( 2x + 4) |
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0,05x |
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– |
0,13( x + 4) . |
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0,1( 2x +4) , :
0,05x +0,13( x + 4) =0,1( 2x + 4) ; 0,02x = 0,12 , x = 6 .
16 .
: 16 .
© |
2014 . |
. 9 |
. 90504 |
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, . |
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23y = x2 − x + 3 − 3 x a ,y = a − 4 .
. |
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y = x2 + 2x + 3 |
x < 0 |
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y = x2 − 4x + 3 x ≥ 0 . |
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y = a − 4 a = 6 a = 7 .
: 6; 7. |
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© |
2014 . |
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. 9 |
. 90504 |
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3 |
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» « |
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BC |
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24 |
A ABCD |
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E . |
ABCD , BE =7 , EC =3 , |
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ABC =150°. |
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BEA EAD , AE – BAD ,, BEA = EAD = BAE . , BEA -AB = BE =7 .
SABCD = AB BC sin ABC =7 10 1 =35. |
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2 |
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: 35. |
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, , |
2 |
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, , |
1 |
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, . |
0 |
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2 |
25O BD AC ,AB CD . , O – AC .
.
ADB , CBD , ACB DAC , -, .
© |
2014 . |
. 9 |
. 90504 |
4 |
, COB AOD ;BO : OD . BO =OD , -, , AO =OC .
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, . |
3 |
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26,12, 18.
.
C ABCCM CH.
CM = 12 AB = 6 ; CH = 2SABABC = 21218 = 3.
CHM CH CM , CMH =30 .
, H AM . CMH –BMC , ,
ABC = MBC = 1 CMH = |
1 30°= 15° |
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2 |
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, BAC = 75 . |
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: 15 , 75 . |
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© |
2014 . |
. 9 . |
. 9 . |
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1 |
270 |
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11 |
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324 |
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1 |
64 |
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11 |
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270 |
2 |
3 |
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12 |
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-1,5 |
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2 |
2 |
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12 |
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-3 |
3 |
2 |
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13 |
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13 |
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3 |
4 |
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13 |
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23 |
4 |
6 |
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14 |
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4 |
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4 |
36 |
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14 |
|
3 |
5 |
142 |
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15 |
|
3 |
|
5 |
413 |
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|
15 |
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9 |
6 |
-4,5 |
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|
16 |
|
840 |
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6 |
1 |
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16 |
|
810 |
7 |
84 |
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17 |
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2,22 |
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7 |
60 |
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17 |
|
1,05 |
8 |
4 |
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|
18 |
|
3 |
|
8 |
3 |
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18 |
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2 |
9 |
106 |
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|
19 |
|
0,9604 |
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9 |
126 |
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19 |
|
0,9409 |
10 |
10 |
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|
20 |
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7 |
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10 |
8 |
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20 |
|
5 |
© |
2014 . |
© |
2014 . |