Текст
E. B. CMb'KOAOSO
£
£
CAMOCTOSlTEAbHblE PA60Tbl
't.
a X 2 +2x
==O
X2-4
- -
........ ----
.
r
t
( + 3)( a + 5) < (a + 2)( + 6)
-- -- - -
2
2
-1 X-1
- :::
(2 + > b-
4
CaMOCTOATenbHaA pa60Ta N2 1
Bapuaum M 1
1. Haii,lJ;HTe qHCJIOBOe 3HaqeHHe BbIpa:meHHH: a 3 . b 4 . c 9
rrpH a=-3, b=-2, c=-I.
2. IIycTb a < 0, b> O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH
OTpHD;aTeJIbHO 3HaqeHHe BbIpa:meHHH: (3a - 4b)( 5b - 2a)
(b-a)?
3. IIycTb a < O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH O'TpH-
D;aTeJIbHO qHCJIO b, eCJIH 3ab = -5?
4. PemHTe ypaBHeHHe: (2x-5)(3x+l)=0.
x2-9
5. PemHTe ypaBHeHHe:
x-4
x 2 + 2x _ 0
6. PemMTe ypaBHeHMe: x2-4 - ·
1 2
7. PemHTe ypaBHeHHe: 2 = O.
x-I x-I
Bapuaum M 2
1. Haii,lJ;HTe qHCJIOBOe 3HaqeHHe BbIpa:meHHH:
a 4 · b 2 · c 7 rrpH a=-2, b=5, c=-I.
2. IIycTb a<O, b>O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH OT-
pHD;aTeJIbHO 3HaqeHHe BbIpa:meHHH: (2a-3b)(6b-a)(a-b)?
3. IIycTb b < O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH OTPH-
D;aTeJIbHO qHCJIO a, eCJIH 2ab = 7?
4. PemHTe ypaBHeHHe: (7x+ 1)(2x-7)=0.
x 2 _ 16
5. PemHTe ypaBHeHHe:
x+5
x 2 - 3x
6. PemHTe ypaBHeHHe: 2 = O.
x -9
1 4
7. PemHTe ypaBHeHHe: + = O.
x+2 x 2 _ 4
CaMOCTOATenbHaA pa60Ta N2 1
5
Bapuaum M 3
1. Haii,lJ;HTe qHCJIOBOe 3HaqeHHe BbIpa:meHHH: a 3 . b 4 . c 5
rrpH a= 3, b = -2, c = -1.
2. IIycTb a < 0, b > O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH
OTpHD;aTeJIbHO 3HaqeHHe BbIpa:meHHH: (5a-2b)(3b-4a)
(b-a)?
3. IIycTb a < O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH OTpH-
D;aTeJIbHO qHCJIO b, eCJIH 4ab=-9?
4. PemHTe ypaBHeHHe: (2x-3)(9x+ 1)=0.
x 2 - 25
5. PemHTe ypaBHeHHe: ·
x-2
x 2 + 5x _ _ O.
6. PemMTe ypaBHeHMe: x 2 _ 25
1 4
7. PemHTe ypaBHeHHe: - 2 = O.
x-2 x - 4
Bapuaum M 4
1. Haii,lJ;HTe qHCJIOBOe 3HaqeHHe BbIpa:meHHH:
a 4 · b 2 · c 6 rrpH a=2, b=-5, c=-I.
2. IIycTb a<O, b>O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH OT-
pHD;aTeJIbHO 3HaqeHHe BbIpameHHH: (4a-5b)(2b-3a)(a-b)?
3. IIycTb b < O. BbIHcHHTe, rrOJIo:mHTeJIbHO HJIH OTpH-
D;aTeJIbHO qHCJIO a, eCJIH 5ab=8?
4. PemHTe ypaBHeHHe: (6x+l)(2x-9)=0.
x 2 _ 4
5. PeIIIHTe ypaBHeHHe:
x+7
x 2 - 4x
6. PemMTe ypaBHeHMe: x 2 -16 = O.
1 2
7. PemHTe ypaBHeHHe: + = O.
x + 1 x 2 - 1
6
CaMOCTOATenbHaA pa60Ta N2 2
Bapuaum M 1
1
1. CpaBHMTe QMCJIa: 6 M 0,16.
2. CpaBHHTe qHCJIa a H b, eCJIH b-a=-0,3.
3. BepHo JIH YTBep:m,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
BepHO HepaBeHCTBO (a+3)(a+5»(a+2)(a+6)?
4. BepHo JIH YTBep:m,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
H b BepHO HepaBeHCTBO b( a + 3b) > ab - 1 ?
5. BepHo JIH YTBep:m,lJ;eHHe: eCJIH a H b - rrOJIo:mHTeJIbHbIe
qHCJIa, TO BbIrrOJIHHeTCH HepaBeHCTBO a 4 + b 4 > a 3 b + ab 3 ?
(x 2 -3x )(x - 5)
6. PemHTe ypaBHeHHe: 2 == O.
9-x
7. CYMMa ,lJ;BYX 3a,z:t;YMaHHbIX qHCeJI paBHa 35. ECJIH O,lJ;HO
H3 HHX YBeJIHqHTb B 4 pa3a, a ,lJ;Pyroe - Ha 30, TO CYMMa
rrOJIyqeHHbIx qHCeJI 6Y,lJ;eT paBHa 125. Ha30BHTe MeHbmee
H3 3TH X qHCeJI.
Bapuaum M 2
1
1. CpaBHHTe qHCJIa: - H 0,14.
7
2. CpaBHHTe qHCJIa a H b, eCJIH b-a=0,2.
3. BepHo JIH YTBep:m,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
BepHO HepaBeHCTBO (a+ 7)(a+ 1»(a+ 5)(a+ 3)?
4. BepHo JIH YTBep:m,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
H b BepHO HepaBeHCTBO a(2a+b»ab-2?
5. BepHo JIH YTBep:m,lJ;eHHe: eCJIH a H b - rrOJIo:mHTeJIb-
HbIe qHCJIa, TO BbIrrOJIHHeTCH HepaBeHCTBO b 4 - ab 3 > a 3 b - a 4 ?
(x 2 +2x)(x+7)
6. PemHTe ypaBHeHHe: 2 == O.
4-x
7. CYMMa ,lJ;BYX 3a,z:t;YMaHHbIX qHCeJI paBHa 25. ECJIH O,lJ;HO
H3 HHX YBeJIHqHTb B 5 pa3, a ,lJ;Pyroe - Ha 45, TO CYMMa
rrOJIyqeHHbIx qHCeJI 6Y,lJ;eT paBHa 110. -Ha30BHTe 60JIbmee
H3 3THX qHCeJI.
CaMOCTOATenbHaA pa60Ta N2 2
7
Bapuaum M 3
1
1. CpaBHHTe qHCJIa: - H 0,17.
6
2. CpaBHHTe qHCJIa a H b, eCJIH b-a=-0,4.
3. BepHo JIH YTBep:m,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
BepHO HepaBeHCTBO (a+3)(a+5)«a+2)(a+6)?
4. BepHo JIH YTBep:m,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
H b BepHO HepaBeHCTBO b( a + 5b) > ab - 5 ?
5. BepHo JIH yrBep:m,lJ;eHHe: eCJIH a H b - rrOJIo:mHTeJIbHbIe
qHCJIa, TO BbIrrOJIHHeTCH HepaBeHCTBO a 4 + b 4 < a 3 b + ab 3 ?
(x 2 _ 4x)(x-6)
6. PemHTe ypaBHeHHe: 2 == O.
16-x
7. CYMMa ,lJ;BYX 3a,n;YMaHHbIX qHCeJI paBHa 45. ECJIH O,lJ;HO
H3 HHX YBeJIHqHTb B 4 pa3a, a ,lJ;Pyroe - Ha 10, TO CYMMa
rrOJIyqeHHbIx qHCeJI 6Y,lJ;eT paBHa 115. Ha30BHTe MeHbmee
H3 3TH X qHCeJI.
Bapuaum M 4
1
1. CpaBHHTe qHCJIa: 7 H 0,15.
2. CpaBHHTe qHCJIa a H b, eCJIH b-a=0,5.
3. BepHo JIH YTBepm,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
BepHO HepaBeHCTBO (a + 7)(a + 1) < (a + 5)(a + 3)?
4. BepHo JIH YTBep:m,lJ;eHHe: rrpH JII06bIX 3HaqeHHHX a
H b BepHO HepaBeHCTBO a( 4a + b) > ab - 4 ?
5. Bepllo JIH yrBep:m,lJ;eHHe: eCJIH a H b - rrOJIo:mHTeJIbHbIe
qHCJIa, TO BbIrrOJIHHeTCH HepaBeHCTBO b 4 - ab 3 < a 3 b - a 4 ?
(x 2 + 5x )(x + 3)
6. PemHTe ypaBHeHHe: 2 == O.
25-x
7. CYMMa ,n;BYX 3a,n;YMaHHbIX qHCeJI paBHa 15. ECJIH O,lJ;HO
H3 HHX YBeJIHqHTb B 5 pa3, a ,lJ;Pyroe - Ha 55, TO CYMMa
rrOJIyqeHHbIX qHCeJI 6y,n;eT paBHa 110. Ha30BHTe 60JIbmee
H3 3THX qHCeJI.
8
CaMOCTORTenbHaR pa60Ta N2 3
Bapuaum M 1
1. BepHo JIH YTBep:m,n;eHHe: eCJIH a + 3 < b H b < 0,
TO a + 3 - OTpHD;a TeJIbHOe qHCJIO?
2. IIOJIo:mHTeJIbHbIM HJIH OTpHD;a TeJIbHbIM SlBJISleTCSI
qHCJIO a, eCJIH a+5>b H b>6?
3. IIycTb a<b. CpaBHHTe qHCJIa a+7-3c H b-3c+7.
Ha30BHTe 60JIbmee qHCJIO.
4. IIycTb a<b. CpaBHHTe qHCJIa -3(a+6) H -3(b+6).
Ha30BHTe MeHbmee qHCJIO.
5. BepHo JIH YTBep:m,n;eHHe: eCJIH (x-l)(x+ 2»(x+ 1)
(x-2), TO x<O?
6. Mo:meT JIH pa3HOCTb 2a - 3b 6bITb 60JIbme CYMMbI
2a+ 3b?
7. IIycTb a>b. BepHo JIH YTBep:m,n;eHHe:
1 1
->-, eCJIH ab<O?
a b
Bapuaum M 2
1. BepHo JIH YTBep:m,n;eHHe: eCJIH b + 1 < a H a < 0,
TO b + 1 - OTpHD;aTeJIbHOe qHCJIO?
2. IIOJIo:mHTeJIbHbIM HJIH OTpHD;aTeJIbHbIM SlBJISleTCSI
qHCJIO b, eCJIH b+2>a H a>3?
3. IIycTb a<b. CpaBHHTe qHCJIa a-4+7c H b+7c-4.
Ha30BHTe MeHbmee qHCJIO.
4. IIycTb a>b. CpaBHHTe qHCJIa -2(a+3) H -2(b+3).
Ha30BHTe 60JIbmee qHCJIO.
5. BepHo JIH YTBep:m,n;eHHe: eCJIH (x-3)(x+4»(x+3)
(x-4), TO x>O?
6. Mo:meT JIH pa3HOCTb 4a -7b 6bITb 60JIbme CYMMbI
4a+7b?
7. IIycTb a < b. BepHo JIH YTBep:m,n;eHHe:
1 1
->-, eCJIH ab<O?
a b
CaMOCTOATenbHaA pa60Ta N2 3
9
Bapuaum M 3
1. BepHo JIH YTBep:m,n;eHHe: eCJIH a + 5 < b H b < 0,
TO a + 5 - OTpHD;a TeJIbHOe qHCJIO?
2. IIOJIo:mHTeJIbHbIM HJIH OTpHD;aTeJIbHbIM HBJIHeTCH
qHCJIO a, eCJIH a+3>b H b>4?
3. IIycTb a<b. CpaBHHTe qHCJIa a+6-2c H b-2c+6.
Ha30BMTe 60JIbmee qHCJIO.
4. IIycTb a<b. CpaBHHTe qHCJIa -4(a-5) H -4(b-5).
Ha30BHTe MeHbmee qHCJIO.
5. BepHo JIH YTBep:m,n;eHHe: eCJIH (x-2)(x+3»(x+2)
(x-3), TO x<O?
6. Mo:meT JIH pa3HOCTb 5a - b 6bITb 60JIbme CYMMbI
5a+b?
7. IIycTb b < a. BepHo JIH YTBep:m,n;eHHe:
.! < .!.- , eCJIH ab < O?
b a
Bapuaum M 4
1. BepHo JIH YTBep:m,n;eHHe: eCJIH b + 2 < a H a < 0,
TO b + 2 - OTpHD;aTeJIbHOe qHCJIO?
2. IIOJIo:mHTeJIbHbIM HJIH OTpHD;a TeJIbHbIM HBJIHeTCH
qHCJIO b, eCJIH b+4>a H a>5?
3. IIycTb a<b. CpaBHHTe qHCJIa a-5+4c H b+4c-5.
Ha30BHTe MeHbmee qHCJIO.
4. IIycTb a>b. CpaBHHTe qHCJIa -7(a-l) H -7(b-l).
Ha30BHTe 60JIbmee qHCJIO.
5. BepHo JIH YTBep:m,n;eHHe: eCJIH (x-4)(x+5»(x+4)
(x-5), TO x>O?
6. Mo:meT JIH pa3HOCTb 6a - b 6bITb 60JIbme CYMMbI
6a+b?
7. IIycTb b > a. BepHo JIH YTBep:m,n;eHHe:
1 1
- < - , eCJIH ab < O?
b a
10
CaMOCTORTenbHaR pa60Ta N2 4
Bapuaum M 1
1. BepHo JIH, qTO eCJIH x<-8 H y<-2, TO x+y<-10?
2. BepHo JIH, qTO eCJIH x>4 H y>3, TO xy>7?
3. BbIrrOJIHHTe CJIo:meHHe HepaBeHCTB: 5x + y < 3x + 7
H 3y-4x<II-7x.
4. BepHo JIH HepaBeHCTBO 2X2 + 5> 0 rrpH JII06bIX 3Ha-
qeHHHX x?
5. BepHo JIH YTBep:m,lJ;eHHe: CYMMa paccToHHHii OT JIIO-
60ii TOqKH, JIe:maI.IJ;eii BHYTPH TpeyrOJIbHHKa, ,lJ;O ero
BepmHH 60JIbme rrepHMeTpa TpeyrOJIbHHKa?
6. M3BecTHo, qTO a> b. PaCrrOJIo:mHTe B rrOpH,lJ;Ke B03-
paCTaHHH qHCJIa: a+7, b-4, a+3, a, b-l, b.
7. IIycTb a H b - rrOJIo:mHTeJIbHbIe qHCJIa. BepHo JIH,
qTO eCJIH a>b, a 2 >b 2 ?
Bapuaum M 2
1. BepHo JIH, qTO eCJIH x<-5 H y<3, TO x+y<-8?
2. BepHo JIH, qTO eCJIH x > 2 H y> 3, TO xy > 6?
3. BbIrrOJIHHTe CJIo:meHHe HepaBeHCTB: 4x + y < 2x + 9
H 5y-3x<10-4x.
4. BepHo JIH HepaBeHCTBO -3X2 - 4 < 0 rrpH JII06bIX 3Ha-
qeHHHX x?
5. BepHo JIH YTBep:m,lJ;eHHe: CYMMa paccToHHHii OT JIIO-
60ii TOqKH, JIe:maI.IJ;eii BHYTPH KBa,z:t;paTa, ,lJ;O ero BepmHH
60JIbme rrOJIyrrepHMeTpa KBa,z:t;pa Ta ?
6. M3BecTHo, qTO a < b. PaCrrOJIo:mHTe B rrOpH,lJ;Ke y6bI-
BaHHH qHCJIa: a, a-8, b+l, b+4, b, a-3.
7. IIycTb a H b - rrOJIo:mHTeJIbHbIe qHCJIa. BepHo JIH,
qTO eCJIH a < b, a 3 < b 3 ?
CaMOCTOATenbHaA pa60Ta N2 4
11
Bapuaum M 3
1. BepHo JIH, qTO eCJIH x<4 H y<-3, TO x+y<l?
2. BepHo JIH, qTO eCJIH x>5 H y>l, TO xy>6?
3. BbIrrOJIHHTe CJIo:meHHe HepaBeHCTB: 7 x + 2 y < x + 5
H 6y-x<9-6x.
4. BepHo JIH HepaBeHCTBO 3x 2 + 1> 0 rrpH JII06bIX 3Ha-
qeHHHX x?
5. BepHo JIH YTBep:m,lJ;eHHe: CYMMa paccToHHHii OT JIIO-
60ii TOqKH, JIe:ma eii BHYTPH KBa,z:t;paTa, ,lJ;O ero BepmHH
60JIbme rrepHMeTpa KBa,lJ;paTa?
6. 113BecTHo, qTO a> b. PaCrrOJIo:mHTe B rrOpH,lJ;Ke B03-
paCTaHHH qHCJIa: a + 4, b, a, a + 9, b - 2, b - 8.
7. IIycTb a H b - rrOJIo:mHTeJIbHbIe qHCJIa. BepHo JIH,
qTO eCJIH a> b, a 4 > b 4 ?
Bapuaum M 4
1. BepHo JIH, qTO eCJIH x<-5 H y<-I, TO x+y<5?
2. BepHo JIH, qTO eCJIH x> 1 H y> 7, TO xy> 7?
3. BbIrrOJIHHTe CJIo:meHHe HepaBeHCTB: 6x + 5y < 4x + 3
H 7y-2x<8-5x.
4. BepHo JIH HepaBeHCTBO _2X2 - 7 < 0 rrpH JII06bIX 3Ha-
qeHHHX x?
5. BepHo JIH YTBep:m,lJ;eHHe: CYMMa paccToHHHii OT JIIO-
60ii TOqKH, JIe:ma eii BHYTPH TpeyrOJIbHHKa, ,lJ;O ero Bep-
llIHH 60JIbme rrOJIyrrepHMeTpa TpeyrOJIbHHKa?
6. 113BecTHo, qTO a < b. PaCrrOJIo:mHTe B rrOpH,lJ;Ke y6bI-
BaHHH qHCJIa: a-2, a-9, b+5, b+3, b, a.
7. IIycTb a H b - rrOJIo:mHTeJIbHbIe qHCJIa. BepHo JIH,
qTO eCJIH a<b, a 5 <b 5 ?
12
CaMOCTOATenbHaA pa60Ta N2 5
Bapuaum M 1
1. Haii,lJ;HTe HaH60JIbIIIee D;eJIOe qHCJIO n, Y,lJ;OBJIeTBO-
pSlIO ee HepaBeHCTBY: n < -4.
2. Haii,lJ;HTe HaHMeHbIIIee D;eJIOe qHCJIO n, Y,lJ;OBJIeTBO-
pSlIO ee HepaBeHCTBY: n > -5.
3. Haii,lJ;HTe HaH60JIbIIIee D;eJIOe qHCJIO n, Y,lJ;OBJIeTBO-
pSlIO ee HepaBeHCTBY: 3n < -2.
4. IIycTb a < b. BepHo JIH HepaBeHCTBO: a -7 < b -7?
5. IIycTb a > b. BepHo JIH HepaBeHCTBO: -6a < -6b?
6. BepHo JIH YTBep:m,lJ;eHHe:
eCJIH (x+2)(x-3) « x+3)(x-2), TO x > O?
a b
7. BepHo JIH YTBep:m,n;eHHe: eCJIH ab < 0, TO - + - > 2 ?
b a
Bapuaum M 2
1. Haii,lJ;HTe HaH60JIbIIIee D;eJIOe qHCJIO n, Y,lJ;OBJIeTBO-
pSlIO ee HepaBeHCTBY: n < -3.
2. Haii,lJ;HTe HaHMeHbIIIee D;eJIOe qHCJIO n, Y,lJ;OBJIeTBO-
pSlIO ee HepaBeHCTBY: n>-5.
3. Haii,lJ;HTe HaHMeHbIIIee D;eJIOe qHCJIO n, Y,lJ;OBJIeTBO-
pSlIO ee HepaBeHCTBY: 4n > -1.
4. IIycTb a > b. BepHo JIH HepaBeHCTBO: a-2 > b-2?
5. IIycTb a < b. BepHo JIH HepaBeHCTBO: -7a > -7b?
6. BepHo JIH YTBep:m,lJ;eHHe:
eCJIH (x+3)(x-4) « x+4)(x-3), TO x<O?
a b
7. BepHo JIH YTBep:m,lJ;eHHe: eCJIH ab>O, TO -+- > 2?
b a
CaMOCTOATenbHaJi pa60Ta N2 5
13
Bapuaum M 3
1. Haii,n;HTe HaH60JIbmee D;eJIOe qHCJIO n, y,n;OBJIeTBO-
pHIO ee HepaBeHcTBY: n < -7.
2. Haii,n;HTe HaHMeHbmee D;eJIOe qHCJIO n, y,n;OBJIeTBO-
pHIO ee HepaBeHcTBY: n > -2.
3. Haii,n;HTe HaH60JIbmee D;eJIOe qHCJIO n, y,n;OBJIeTBO-
pHIO ee HepaBeHCTBY: 6n < -5.
4. IIycTb a < b. BepHo JIH HepaBeHCTBO: a-3 < b-3?
5. IIycTb a > b. BepHo JIH HepaBeHCTBO: -4a < -4b?
6. BepHo JIH YTBep:m,n;eHHe:
eCJIH (x+3)(x-2» (x+2)(x-3), TO x > O?
a b
7. BepHO JIM YTBepm,ZJ;eHMe: eCJIM ab<O, TO t;+ a < 2?
Bapuaum M 4
1. Haii,n;HTe HaH60JIbmee D;eJIOe qHCJIO n, y,n;OBJIeTBO-
pHIOI.IJ;ee HepaBeHCTBY: n < -6.
2. Haii,n;HTe HaHMeHbmee D;eJIOe qHCJIO n, y,n;OBJIeTBO-
pHIOI.IJ;ee HepaBeHCTBY: n> -3.
3. Haii,n;HTe HaHMeHbmee D;eJIOe qHCJIO n, y,n;OBJIeTBO-
pHIOI.IJ;ee HepaBeHCTBY: 7n > -2.
4. IIycTb a > b. BepHo JIH HepaBeHCTBO: a-5 > b-5?
5. IIycTb a < b. BepHo JIH HepaBeHCTBO: -2a > -2b?
6. BepHo JIH YTBep:m,n;eHHe:
eCJIH (x+4)(x-3» (x+3)(x-4), TO x<O?
a b
7. BepHo JIH YTBep:m,n;eHHe: eCJIH ab > 0, TO - + - < 2 ?
b a
14
CaMOCTOJITenbHaJi pa60Ta N2 6
Bapuaum M 1
1. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: YTPO-
eHHaH CYMMa qHCeJI x H -5 60JIbme 19.
2. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: rrOJIY-
CYMMa qHCeJI 2x H 5 He MeHbme HX y,n;BoeHHoro qaCTHoro.
1
-; -4 HBJIHeTCH pemeHHeM
3
2
-6; - HBJIHeTCH pemeHHeM
7
3. KaKoe H3 qHCeJI: 12;
HepaBeHCTBa 5x - 3 > 4 ?
4. KaKoe H3 qHCeJI: 13;
HepaBeHCTBa x + 7 < 8x - 3?
5. IIpH KaKHX 3HaqeHHHX Y BepHO HepaBeHCTBO 5y> O?
6. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y+3)2 < 0?
7. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y-14)4 > 0?
Bapuaum M 2
1. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: y,n;BO-
eHHaH pa3HOCTb qHCeJI x H -4 MeHbme 20.
2. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: rrOJIY-
CYMMa qHCeJI 3x H 2 He 60JIbme HX YTpoeHHoro rrpoH3-
Be,n;eHHH.
3. KaKoe H3 qHCeJI: 11;
HepaBeHCTBa 8x - 3 < 2?
4. KaKoe H3 qHCeJI: 15;
HepaBeHCTBa x - 2 > 6x + 5?
5. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO -5y > O?
6. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y-l)2 > 0?
7. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y-12)4 < 0?
7
-; - 2 HBJIHeTCH pemeHHeM
9
2
-4; - HBJIHeTCH pemeHHeM
9
CaMOCTOATenbHaA pa60Ta N2 6
15
Bapuaum M 3
1. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: y,n;BO-
eHHaH CYMMa qHCeJI x H -3 60JIbme 18.
2. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: rrOJIY-
CYMMa qHCeJI 5x H 3 He MeHbme HX y,n;BoeHHoro qaCTHoro.
1
3. KaKoe M3 YIMCeJI: 10; 6 ; -2 HBJIHeTCH pemeHMeM
HepaBeHcTBa 4x - 5> 2? 3
4. KaKoe M3 YIMCeJI: 14; -5; 8 HBJIHeTCH pemeHMeM
HepaBeHCTBa x+6 < 7x-2?
5. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO 8y>0?
6. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y + 4)2 < O?
7. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y-ll)4 > 0?
Bapuaum M 4
1. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: YTPO-
eHHaH pa3HOCTb qHCeJI x H -2 MeHbme 15.
2. 3arrHmHTe B BH,n;e HepaBeHCTBa YTBep:m,n;eHHe: rrOJIY-
CYMMa qHCeJI 4x H 3 He 60JIbme HX YTpoeHHoro rrpoH3-
Be,n;eHHH. 6
3. KaKoe H3 qHCeJI: 13; -; -3 HBJIHeTCH pemeHHeM
7
HepaBeHCTBa 6x - 1 < 3? 7
4. KaKoe H3 qHCeJI: 11; -5; - HBJIHeTCH pemeHHeM He-
8
paBeHCTBa x - 3 > 5x + 7?
5. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO -4y>0?
6. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y- 5)2 > 0?
7. IIpH KaKHX 3HaqeHHHX y BepHO HepaBeHCTBO
(y-13)4 < 0?
16
CaMOCTOATenbHaA pa60Ta N2 7
Bapuaum M 1
1. PemHTe HepaBeHCTBO: 4 - 5x < 2.
2. PemHTe HepaBeHCTBO: 6(x-l)+5>2(2x+l).
3. HaH,n;HTe HaHMeHbmee D;eJIOe qHCJIO, HBJIHIOI.IJ;eeCH
pemeHHeM HepaBeHCTBa: 7 x + 2 > 3(x - 2) - 5x.
4x-3
4. IIpH KaKHX x 3HaqeHHe ,n;P06H 60JIbme 3Haqe-
2
x-2 4-3x
HHH pa3HOCTH ,n;po6eH H ?
5 4
5. IIpH KaKHX x 3HaqeHHH cpYHKD;HH Y = 4,5 - 0,5x
He 60JIbme 4,5?
6. O,n;Ha CTopOHa TpeyrOJIbHHKa 9 CM, a ,n;pyraH -
12 CM. KaKHM HaHMeHbmHM D;eJIbIM qHCJIOM caHTHMeTpOB
Mo:meT 6bITb ,n;JIHHa TpeTbeH CTOpOHbI?
7. CYMMa HeqeTHOrO qHCJIa C TpeMH rrOCJIe,n;YIOI.IJ;HMH
HeqeTHbIMH qHCJIaMH 60JIbme, qeM 51. HaH,n;HTe HaHMeHb-
mee HeqeTHOe qHCJIO, y,n;OBJIeTBOpHIOI.IJ;ee 3TOMY YCJIOBHIO.
Bapuaum M 2
1. PemHTe HepaBeHCTBO: 3-4x<6.
2. PemHTe HepaBeHCTBO: 8(x -1) + 3 > 2(3x + 1).
3. HaH,n;HTe HaH60JIbmee D;eJIOe qHCJIO, SlBJIHIOI.IJ;eeCH
pemeHHeM HepaBeHCTBa: 9 x - 7 < 2( x - 4) + 4x.
7x-2
4. IIpM KaKMX x 3HaqeHMe ,ZJ;P06M 4 MeHbme 3Haqe-
x-I 3-2x
HHH pa3HOCTH ,n;po6eH H ?
3 2
5. IIpH KaKHX x 3HaqeHHH cpYHKD;HH y=3,5-0,2x
He MeHbme 3,5?
6. O,n;Ha CTopOHa TpeyrOJIbHHKa 8 CM, a ,n;pyraH -
13 CM. KaKHM HaHMeHbmHM D;eJIbIM qHCJIOM caHTHMeTpOB
Mo:meT 6bITb ,n;JIHHa TpeTbeH CTOpOHbI?
7. CYMMa qeTHOrO qHCJIa C TpeMSI rrOCJIe,n;YIOI.IJ;HMH qeT-
HbIMH qHCJIaMH 60JIbme, qeM 53. HaH,n;HTe HaHMeHbmee
qeTHOe qHCJIO, y,n;OBJIeTBOpHIOI.IJ;ee 3TOMY YCJIOBHIO.
CaMOCTOATenbHaA pa60Ta N2 7
17
Bapuanm M 3
1. PemHTe HepaBeHcTBo: 6 - 5x < 3.
2. PemHTe HepaBeHcTBo: 4(x-l)+7>3(2x+3).
3. HaH,n;HTe HaHMeHbmee D;eJIOe qHCJIO, HBJIHIOIIJ;eeCH
pemeHHeM HepaBeHcTBa: 6x + 5 > 2(x - 3) - 8x.
5x-2
4. IIpH KaKHX x 3HaqeHHe ,n;P06H 60JIbme 3Haqe-
2
x-3 3-4x
HMH pa3HOCTM ,ZJ;po6eH 4 M 5 ?
5. IIpH KaKHX x 3HaqeHHH cpYHKD;HH Y = 2,5 - 0,3x
He 60JIbme 2,5?
6. O,n;Ha CTopOHa TpeyrOJIbHHKa 5 CM, a ,n;pyraH -
11 CM. KaKHM HaHMeHbmHM D;eJIbIM qHCJIOM caHTHMeTpOB
Mo:meT 6bITb ,n;JIHHa TpeTbeii CTOpOHbI?
7. CYMMa HeqeTHOrO qHCJIa C TpeMH rrOCJIe,n;YIOIIJ;HMH
HeqeTHbIMH qHCJIaMH 60JIbme, qeM 57. Haii,n;HTe HaHMeHb-
mee HeqeTHOe qHCJIO, y,n;OBJIeTBOpHIOIIJ;ee 3TOMY YCJIOBHIO.
Bapuanm M 4
1. PemHTe HepaBeHCTBO: 6 - 4x < 7.
2. PemHTe HepaBeHCTBO: 2(x-l)+4>2(2x+5).
3. Haii,n;HTe HaH60JIbmee D;eJIOe qHCJIO, HBJIHIOIIJ;eeCH
pemeHHeM HepaBeHCTBa: 8x - 3 < 4(x -1) + 2x.
8x-3
4. IIpH KaKHX x 3HaqeHHe ,n;P06H MeHbme 3Haqe-
4
x-4 1-2x
HHH pa3HOCTH ,n;po6eii H ?
2 3
5. II pH KaKHX x 3Ha qeHHH cpYHK HH Y = 5,5 - 0, 1 x
He MeHbme 5,5?
6. O,n;Ha CTopOHa TpeyrOJIbHHKa 7 CM, a ,n;pyraH -
14 CM. KaKHM HaHMeHbmHM D;eJIbIM qHCJIO 1 caHTHMeTpOB
MomeT 6bITb ,n;JIHHa TpeTbeii CTOpOHbI?
7. CYMMa qeTHOrO qHCJIa C TpeMH rrOCJIe,n;YIOIIJ;HMH qeT-
HbIMH qHCJIaMH 60JIbllIe, qeM 49. Haii,n;HTe HaHMeHbmee
qeTHoe qHCJIO, y,n;OBJIeTBopHIOIIJ;ee 3TOMY YCJIOBHIO.
18
CaMOCTOATenbHaA pa60Ta N2 8
Bapuanm M 1
1. KaKHe H3 qHCeJI: -2; 0; 6 HBJIHIOTCH pemeHHHMH
CHCTeMbI HepaBeHCTB: 7-x<10; 2-3x>3?
2. HaH,n;HTe Bce D;eJIbIe qHCJIa, HBJIHIOI.IJ;HeCH pemeHH-
HMH CHCTeMbI HepaBeHCTB: 2x> -6; -3x> 6.
3. II pHHa,z:t;JIe:mHT JIH OTpe30K [1; 4] HHTepBaJIY (-1; 5)?
4. IIMelOT JIH 06I.IJ;He TOqKH OTpe3KH [3; 6] H [5; 7]?
5. Ha O,n;HOH Koop,n;HHaTHoH rrJIOCKOCTH rrOCTpOHTb rpa-
CPHKH cpYHKD;HH y=-3x+5 H y=4-5x. OTMeTHTb Ha OCH
a6CD;HCC MHo:meCTBO 3HaqeHHH x, rrpH KOTOpbIX 3HaqeHHH
06eHX cpYHKD;HH OTpHD;aTeJIbHbI.
6. PemHTe HepaBeHCTBO:
(5 - 6x)(1 + 3x) + (1 + 3x)(3x + 1) < (1 + 3x)(I- 3x).
7. O,n;Ha CTopOHa TpeyrOJIbHHKa 4 M, a ,n;pyraH 7 M.
KaKoH Mo:meT 6bITb TpeTbH CTopOHa, eCJIH rrepHMeTp
TpeyrOJIbHHKa MeHbme 20 M H eCJIH H3BeCTHO, qTO OHa
BbIpa:maeTCH D;eJIbIM qHCJIOM MeTpOB?
Bapuaum M 2
1. KaKHe H3 qHCeJI: -1; 2; 4 HBJIHIOTCH pemeHHHMH
CHCTeMbI HepaBeHCTB: 5 - x < 7; 3 - 4x > 4 ?
2. HaH,n;HTe Bce D;eJIbIe qHCJIa, HBJIHIOI.IJ;HeCH pemeHH-
HMH CHCTeMbI HepaBeHCTB: 3x> -9; -2x> 4.
3. IIpHHa,z:t;JIe:mHT JIH OTpe30K [2; 5] HHTepBaJIY (-3; 6)?
4. IIMelOT JIH 06I.IJ;He TOqKH OTpe3KH [2;7] H [-1;1]?
5. Ha O,n;HOH Koop,n;HHaTHoH rrJIOCKOCTH rrOCTpOHTb rpa-
CPHKH cpYHKD;MH Y = - 2x + 3 H Y = 5 - 4x. OTMeTHTb Ha OCH
a6CD;HCC MHo:meCTBO 3HaqeHHH x, rrpH KOTOpbIX 3HaqeHHH
o6eHx cpYHKD;HH OTpHD;aTeJIbHbI.
6. PemHTe HepaBeHCTBO:
(5 - 4x)(1 + 2x) + (1 + 2x)(2x + 1) < (1 + 2x)(I- 2x).
7. O,n;Ha CTopOHa TpeyrOJIbHHKa 3 M, a ,n;pyraH 8 M.
KaKoH Mo:meT 6bITb TpeTbH CTopOHa, eCJIH rrepHMeTp
TpeyrOJIbHHKa MeHbme 21 M H eCJIH H3BeCTHO, qTO OHa
BbIpa:maeTCH D;eJIbIM qHCJIOM MeTpOB?
CaMOCTOATenbHaA pa60Ta N2 8
19
Bapuaum M 3
1. KaKHe H3 qHCeJI: -4; 0; 5 HBJIHIOTCH pemeHHHMH
CHCTeMbI HepaBeHCTB: 6-x<ll; 3-2x>5?
2. HaH,n;HTe Bce D;eJIbIe qHCJIa, HBJIHIOI.IJ;HeCH pemeHH-
HMH CHCTeMbI HepaBeHCTB: 2x>-8; -3x>9.
3. IIpHHMJIe:mHT JIH OTpe30K [0; 5] HHTepBaJIY (-2; 6)?
4. HMelOT JIH 06I.IJ;He TOqKH OTpe3KH [1; 5] H [4; 6]?
5. Ha O,n;HOH Koop,n;HHaTHoH rrJIOCKOCTH rrOCTpOHTb rpa-
CPHKH cpYHKD;HH Y = -3x + 4 H Y = 1 - 4x. OTMeTHTb Ha OCH
a6CD;HCC MHo:meCTBO 3HaqeHHH x, rrpH KOTOpbIX 3HaqeHHH
06eHX cpYHKD;HH OTpHD;aTeJIbHbI.
6. PemHTe HepaBeHCTBO:
(1 + 3x)(3x + 1) - (1 + 3x)(6x - 5) < (1-3x)(1 + 3x).
7. O,n;Ha CTopOHa TpeyrOJIbHHKa 5 M, a ,n;pyraH 9 M.
KaKoH Mo:meT 6bITb TpeTbH CTopOHa, eCJIH rrepHMeTp
TpeyrOJIbHHKa MeHbme 24 M H eCJIH H3BeCTHO, 'tITO OHa
BbIpa:maeTCH D;eJIbIM qHCJIOM MeTpOB?
Bapuaum M 4
1. KaKHe H3 qHCeJI: -7; 1; 3 HBJIHIOTCH pemeHHHMH
CHCTeMbI HepaBeHCTB: 4-x<12; 6-5x>7?
2. HaH,n;HTe Bce D;eJIbIe qHCJIa, HBJIHIOIIJ;HeCH pemeHH-
HMH CHCTeMbI HepaBeHCTB: 3x>-12; -2x>6.
3. IIpHHMJIe:mHT JIH OTpe30K [3; 6] HHTepBaJIY (-4; 7)?
4. HMelOT JIH 06I.IJ;He TOqKH OTpe3KH [-1; 4] H [6; 8]?
5. Ha O,n;HOH Koop,n;HHaTHoH rrJIOCKOCTH rrOCTpOHTb rpa-
CPHKH cpYHKD;HH Y = -2x + 5 H Y = 7 - 4x. OTMeTHTb Ha OCH
a6CD;HCC MHo:meCTBO 3HaqeHHH x, rrpH KOTOpbIX 3HaqeHHH
o6eHx cpYHKD;HH OTpHD;aTeJIbHbI.
6. PemHTe HepaBeHCTBO:
(1 + 2x)(2x + 1) - (1 + 2x)( 4x- 5) < (1-2x)(1 + 2x).
7. O,n;Ha CTopOHa TpeyrOJIbHHKa 6 M, a ,n;pyraH 8 M.
KaRoH Mo:meT 6bITb TpeTbH CTopOHa, eCJIH rrepHMeTp
TpeyrOJIbHHRa MeHbme 23 M H eCJIH H3BeCTHO, qTO OHa
BbIpa:maeTCH D;eJIbIM qHCJIOM MeTpOB?
20
CaMOCTOATenbHaA pa60Ta N2 9
Bapuaum M 1
1. PemHTe CHCTeMY HepaBeHCTB:
3x+2<2x-l; 3x-2<4x+3.
2. PemHTe CHCTeMY HepaBeHCTB:
5(x+l)-x>2x+5; 4(x-2)-6<3(2x-l).
3. PemHTe CHCTeMY HepaBeHCTB:
x-5 3x-l x+2 x+3
< >
6 4 3 5
4. PemHTe CHCTeMY HepaBeHCTB:
3(x + 2) > 4(7-x); (x+ 2)(x- 6) > (x+ 4)(x- 5).
5. CKOJIbKO D;eJIbIX pemeHHH HMeeT CHCTeMa Hepa-
x-I x x+l x
BeHCTB: <-. >-?
2 3' 2 5 ·
6. IIpH KaRHX x 3HaqeHHH <PYHKD;HH y=x-3 H y=2x+ 1
O,lJ;HOBpeMeHHo He 60JIbme 5?
7. IIpH KaKHX x 3HaqeHHH <PYHKD;Hii y=x+4 H y=-x+ 5
O,lJ;HOBpeMeHHO oTpHD;aTeJIbHbI?
Bapuaum M 2
1. PemHTe CHCTeMY HepaBeHCTB:
4x+ 1 <3x-l; 2x-7 < 5x+ 2.
2. PemHTe CHCTeMY HepaBeHCTB:
3(x+l)-x>4x+3; 5(2x-3)-5<2(3x-l).
3. PemHTe CHCTeMY HepaBeHCTB:
x-4 2x-l x+3 x+2
< >
5 3 3 4
4. PemHTe CHCTeMY HepaBeHCTB:
4(x + 3) < 3(3 - x); (x+ 3)(x- 5) > (x+ 2)(x- 6).
5. CKOJIbKO D;eJIbIX pemeHHH HMeeT CHCTeMa Hepa-
x-I x x+l x
BeHCTB: <-. >-?
4 5' 3 6.
6. IIpH KaKHX x 3HaqeHHH <PYHKD;HH y=x- 2 H y=3x+ 1
O,lJ;HOBpeMeHHo He MeHbme 4?
7. IIpH KaKHX x 3HaqeHHH <PYHKD;Hii y=x+ 5 H y=-x+ 2
O,lJ;HOBpeMeHHO rrOJIOmHTeJIbHbI?
CaMOCTOATenbHaA pa60Ta N2 9
21
Bapuanm M 3
1. PemHTe CHCTeMY HepaBeHCTB:
3x+l<2x-3; 3x-8<5x+4.
2. PemHTe CHCTeMY HepaBeHCTB:
4(x+l)-x>x+4; 5(x-2)-6<3(2x-l).
3. PemHTe CHCTeMY HepaBeHCTB:
x-5 3x-l x+2 x+4
< . >
5 4' 4 6
4. PemHTe CHCTeMY HepaBeHCTB:
3(x+ 1) > 4(6 - x); (x + 2)(x-7) > (x + 3)(x- 4).
5. CKOJIbKO D;eJIbIX pemeHHH HMeeT CHCTeMa Hepa-
x-I x x+l x
BeHCTB: <-. >-?
3 4' 4 6
6. II pH KaKHX X 3HaqeHHSI cpYHKD;HH y = x - 4 H Y = 2x + 1
O,lJ;HOBpeMeHHo He 60JIbme 7?
7. IIpH KaKHX x 3HaqeHHSI cpYHKD;HH y=x+3 H y=-x+4
O,lJ;HOBpeMeHHO oTpHD;aTeJIbHbI?
Bapuanm M 4
1. PemHTe CHCTeMY HepaBeHCTB:
4x+3<3x-l; 2x-9<5x+6.
2. PemHTe CHCTeMY HepaBeHCTB:
5(x+ 1)- x> 6x+ 5; 5(2x- 3)- 5 < 2(3x-l).
3. PemHTe CHCTeMY HepaBeHCTB:
x - 3 2x -1 x + 4 x + 1
< . >
6 3' 3 4
4. PemHTe CHCTeMY HepaBeHCTB:
4(x + 2) < 3( 4-x); (x + 4)(x - 6) > (x + 3)(x - 6).
5. CKOJIbKO D;eJIbIX pemeHHH HMeeT CHCTeMa Hepa-
x-I x x+l x
BeHCTB: < - · > - ?
2 4' 2 6.
6. ITPH KaKHX x 3HaqeHHSI cpYHKD;HH y = x -1 H Y = 3x-l
O,lJ;HOBpeMeHHO He MeHbme 2?
7. ITPH KaKHX x 3HaqeHHSI cpYHKD;HH y=x+6 H y=-x+ 1
O,lJ;HoBpeMeHHo rrOJIOmHTeJIbHbI?
22
CaMOCTOATenbHaA pa60Ta N2 10
Bapuaum M 1
1. PemHTe ypaBHeHHe: 12x-71=3.
2. PemHTe ypaBHeHHe: 18-2xl=-2.
3. IIpH KaKHX 3HaqeHHHX x BbIrrOJIHHeTCH paBeHCTBO:
Ix-51=5-x?
4. PemHTe HepaBeHCTBO: 12x + 71 < 3.
5. PemHTe HepaBeHCTBO: 15 - 3x 1 > 2.
6. PemHTe HepaBeHCTBO: Ix-31<-3.
7. BepHo JIH YTBepm,n;eHHe: reOMeTpHqeCKH 1 a - bl eCTb
paCCTOHHHe Mem,n;y TOqKaMH a H b qHCJIOBOii rrpHMoii?
Bapuaum M 2
1. PemHTe ypaBHeHHe: 12x - 91 = 1.
2. PemHTe ypaBHeHHe: 17-3xl=-I.
3. IIpH KaKHX 3HaqeHHHX x BbIrrOJIHHeTCH paBeHCTBO:
Ix-41=x-4?
4. PemHTe HepaBeHCTBO: 12x+51 < 1.
5. PemHTe HepaBeHCTBO: 17 - 3x I > 3.
6. PemHTe HepaBeHCTBO: Ix-81<-8.
7. BepHo JIH YTBepm,n;eHHe: reOMeTpHqeCKH la + bl eCTb
paCCTOHHHe Mem,n;y TOqKaMH a H b qHCJIOBOii rrpHMoii?
CaMOCTOATenbHaA pa60Ta N2 10
23
Bapuaum M 3
1. PemHTe ypaBHeHHe: 12x - 51 = 3.
2. PemHTe ypaBHeHHe: 19-4xl=-3.
3. IIpH KaKHX 3HaqeHHHX x BbIrrOJIHHeTCH paBeHCTBO:
Ix-31=3-x?
4. PemHTe HepaBeHCTBO: 12x+31 < 1.
5. PemHTe HepaBeHCTBO: 16-5xl>2.
6. PemHTe HepaBeHCTBO: Ix-41<-4.
7. BepHo JIH YTBepm,lJ;eHHe: reOMeTpHqeCKH la - bl eCTb
paCCTOHHHe Mem,lJ;Y TOqKaMH a H b qHCJIOBOii rrpHMoii?
Bapuaum M 4
1. PemHTe ypaBHeHHe: 12x-71=5.
2. PemHTe ypaBHeHHe: 16-5xl=-4.
3. IIpH KaKHX 3HaqeHHHX x BbIrrOJIHHeTCH paBeHCTBO:
Ix-21=x-2?
4. PemHTe HepaBeHCTBO: 12x+91 < 5_.
5. PemHTe HepaBeHCTBO: 18 - 5x I > 1.
6. PemHTe HepaBeHCTBO: Ix-71<-7.
7. BepHo JIH YTBepm,lJ;eHHe: reOMeTpHqeCKH la + bl eCTb
paCCTOHHHe Mem,lJ;Y TOqKaMH a H b qHCJIOBOii rrpHMoii?
24
CaMOCTOATenbHaA pa60Ta N2 11
Bapuaum M 1
1. Haii,lJ;HTe a6COJIIOTHYIO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 5: 7 qHCJIOM 1: 2 .
2. Haii,lJ;HTe a6COJIIOTHYIO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 25: 9 qHCJIOM 2,75.
3. IIycTb a - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x. Haii-
,lJ;HTe rrorpemHOCTb rrpH6JIHmeHHH, eCJIH x= 22,947; a= 23.
4. C rrOMO blO rpacpHKoB rrpHMbIX Y = 8x + 10 H Y = 1
rrOJIyqHJIH, qTO 3TH rrpHMbIe rrepeceKalOTCH B TOqKe C a6c-
D;HCcoii, paBHoii -1. qeMY paBHa rrorpemHOCTb 3Toro
rrpH6JIHmeHHH?
5. IIycTb 3 < a < 5 H 1 < b < 7. BepHo JIH ,lJ;BoiiHOe He-
paBeHCTBO: 7 < 2a + b < 1 7?
6. IIycTb 5,67 - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x,
a a6COJIIOTHaH rrorpemHOCTb rrpH6JIHmeHHH MeHbme 0,01.
B KaKOM rrpOMemYTKe 3aKJIIOqeHO TOqHOe 3HaqeHHe qHC-
JIa x?
7. PemHTe ypaBHeHHe: Ix-51=lx-81.
Bapuaum M 2
1. Haii,lJ;HTe a6COJIIOTHYlO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 5: 9 qHCJIOM 1: 2 .
2. Haii,lJ;HTe a6COJIIOTHYlO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 22: 7 qHCJIOM 3,14.
3. IIycTb a - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x. Haii-
,lJ;HTe rrorpemHOCTb rrpH6JIHmeHHH, eCJIH x = 23,962; a = 24.
4. C rrOMO blO rpacpHKoB rrpHMbIX Y = 7 x + 9 H Y = 1
rrOJIyqHJIH, qTO 3TH rrpHMbIe rrepeceKalOTCH B TOqKe C a6c-
D;HCcoii, paBHoii -1. qeMY paBHa rrorpemHOCTb 3Toro
rrpH6JIHmeHHH?
5. IIycTb 2 < a < 4 H 1 < b < 8. BepHo JIH ,lJ;BoiiHOe He-
paBeHCTBO: 7 < 3a + b < 20?
6. IIycTb 4,38 - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x,
a a6COJIIOTHaH rrorpemHOCTb rrpH6JIHmeHHH MeHbme 0,01.
B KaKOM rrpOMemYTKe 3aKJIIOqeHO TOqHOe 3HaqeHHe qHC-
JIa x?
7. PemHTe ypaBHeHHe: Ix+31=lx+41.
CaMOCTOATenbHaA pa60Ta N2 11
25
Bapuaum M 3
1. Haii,lJ;HTe a6COJIIOTHYIO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 4: 7 qHCJIOM 1: 2 .
2. Haii,lJ;HTe a6COJIIOTHYIO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 23: 9 qHCJIOM 2,52.
3. IIycTb a - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x. Haii-
,lJ;HTe rrorpemHOCTb rrpH6JIHmeHHH, eCJIH x=21,958; a=22.
4. C rrOMOI.IJ;blO rpacpHKoB rrpHMbIX Y = 9x + 11 H Y = 1
rrOJIytlHJIH, qTO 3TH rrpHMbIe rrepeceKalOTCH B TOqKe C a6c-
D;HCcoii, paBHoii -1. qeMY paBHa rrorpemHOCTb 3Toro
rrpH6JIHmeHHH?
5. IIycTb 4 < a < 6 H 1 < b < 9. BepHo JIH ,lJ;BoiiHOe He-
paBeHCTBO: 6 < a + 2b < 24?
6. IIycTb 3,84 - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x,
a a6COJIIOTHaH rrorpemHOCTb rrpH6JIHmeHHH MeHbme 0,01.
B KaKOM rrpOMemYTKe 3aKJIIOqeHO TOqHOe 3HaqeHHe qHC-
JIa x?
7. PemHTe ypaBHeHHe: Ix-21=lx-71.
Bapuaum M 4
1. Haii,lJ;HTe a6COJIIOTHYlO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 7: 9 qHCJIOM 1: 2 .
2. Haii,lJ;HTe a6COJIIOTHYlO rrorpemHOCTb rrpH6JIHmeHHH
qHCJIa 20: 7 qHCJIOM 2,84.
3. IIycTb a - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x. Haii-
,lJ;HTe rrorpemHOCTb rrpH6JIHmeHHH, eCJIH x = 24,97 4; a = 25.
4. C rrOMOI.IJ;blO rpacpHKoB rrpHMbIX Y = 6x + 8 H Y = 1
rrOJIyqHJIH, qTO 3TH rrpHMbIe rrepeceKalOTCH B TOqKe C a6c-
HCCOi1:, paBHoii -1. qeMY paBHa rrorpemHOCTb 3Toro
rrpH6JIHmeHHH?
5. ITYCTb 2 < a < 7 H 1 < b < 5. BepHo JIH ,lJ;BoiiHOe He-
paBeHCTBO: 5 < a + 3b < 22?
6. ITYCTb 2,63 - rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x,
a a6COJIIOTHaH rrorpemHOCTb rrpH6JIHmeHHH MeHbme 0,01.
B KaKOM rrpOMemYTKe 3aKJIIOqeHO TOqHOe 3HaqeHHe qHC-
JIa x?
7. PemHTe ypaBHeHHe: I x + 41 = Ix + 71.
26
CaMOCTOATenbHaA pa60Ta N2 12
Bapuaum M 1
1. YKamHTe rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x, paBHoe
cpe,n;HeMY apHcpMeTHqeCKoMY rrpH6JIHmeHHii C He,lJ;OCTaT-
KOM H C H36bITKOM: 12 < x < 13.
2. HBJIHeTCH JIH qHCJIO 3,8 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 3,8365 C TOqHOCTblO ,lJ;O 0,5?
3. HBJIHeTCH JIH qHCJIO 0,14 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 7: 51 C TOqHOCTblO ,lJ;O 0,0001?
4. BbICOTa co6opa 113 M. 3KCKYPCOBO,n; TypHCTaM
CKa3aJI, qTO BbICOTa co6opa rrpH6JIHmeHHO paBHa 110 M.
KaKoBa rrorpemHOCTb TaKoro rrpH6JIHmeHHH?
5. 3a 8 peiicoB aBTo6yc rrepeBe3 60JIbme 185 rraccamH-
pOB, a 3a 15 peiicoB - MeHbme 370 rraccamHpOB. CKOJIbKO
MeCT B aBTo6yce, eCJIH B Kam,lJ;OM peiice aBTo6yc rrepeB03HT
pOBHO CTOJIbKO rraccamHpOB, CKOJIbKO MeCT B aBTo6yce?
6. BepHo JIH YTBepm,lJ;eHHe: a- 2b> 3a+ 2b Tor,n;a H TOJIb-
KO TOr,lJ;a, KOr,lJ;a a + 2b < O?
7. PemHTe ypaBHeHHe: Ix+21=lx-41.
Bapuaum M 2
1. YKamHTe rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x, paBHoe
Cpe,lJ;HeMY apHcpMeTHqeCKoMY rrpH6JIHmeHHii C He,lJ;OCTaT-
KOM H C H36bITKOM: 13 < x < 14.
2. HBJIHeTCH JIH qHCJIO 3,6 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 3,6285 C TOqHOCTblO ,lJ;O 0,5?
3. HBJIHeTCH JIH qHCJIO 0,1 7 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 9: 52 C TOqHOCTblO ,lJ;O 0,0001?
4. BbICOTa co6opa 98 M. 3KCKYPCOBO,lJ; TypHCTaM CKa3aJI,
qTO BbICOTa co6opa rrpH6JIHmeHHO paBHa 100 M. KaKoBa
rrorpemHOCTb TaKoro rrpH6JIHmeHHH?
5. 3a 7 peiicoB aBTo6yc rrepeBe3 60JIbme 174 rraccamH-
pOB, a 3a 14 peiicoB - MeHbme 352 rraccamHpOB. CKOJIbKO
MeCT B aBTo6yce, eCJIH B Kam,n;OM peiice aBTo6yc rrepeB03HT
pOBHO CTOJIbKO rraccamHpOB, CKOJIbKO MeCT B aBTo6yce?
6. BepHo JIH YTBepm,n;eHHe: a - 2b 3a + 2b Tor,n;a H TOJIb-
KO TOr,lJ;a, Kor,n;a a + 2b > O?
7. PemHTe ypaBHeHHe: I x -71 = Ix + 31.
CaMOCTOATenbHaA pa60Ta N2 12
27
Bapuaum M 3
1. YKamHTe rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x, paBHoe
cpe,lJ;HeMY apHcpMeTHqeCKoMY rrpH6JIHmeHHii C He,lJ;OCTaT-
KOM H C H36bITKOM: 14 < x < 15.
2. flBJIHeTCH JIH qHCJIO 3,4 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 3,4378 C TOqHOCTblO ,lJ;O 0,5?
3. flBJIHeTCH JIH qHCJIO 0,15 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 7: 46 C TOqHOCTblO ,lJ;O 0,0001?
4. BbICOTa co6opa 81 M. 3KCKYPCOBO,lJ; TypHCTaM CKa3aJI,
qTO BbICOTa co6opa rrpH6JIHmeHHO paBHa 80 M. KaKoBa
rrorpemHOCTb TaKoro rrpH6JIHmeHHH?
5. 3a 8 peiicoB aBTo6yc rrepeBe3 60JIbme 183 rraccamH-
pOB, a 3a 15 peiicoB - MeHbme 358 rraccamHpOB. CKOJIbKO
MeCT B aBTo6yce, eCJIH B Kam,lJ;OM peiice aBTo6yc rrepeB03HT
pOBHO CTOJIbKO rraccamHpOB, CKOJIbKO MeCT B aBTo6yce?
6. BepHo JIH YTBepm,lJ;eHHe: a-3b> 5a+3b TOr,lJ;a H TOJIb-
KO TOr,lJ;a, KOr,lJ;a 2a + 3b < O?
7. PemHTe ypaBHeHHe: Ix+21=lx-81.
Bapuaum M 4
1. YKamHTe rrpH6JIHmeHHOe 3HaqeHHe qHCJIa x, paBHoe
cpe,lJ;HeMY apHcpMeTHqeCKoMY rrpH6JIHmeHHii C He,lJ;OCTaT-
KOM H C H36bITKOM: 15 < x < 16.
2. HBJIHeTCH JIH qHCJIO 3,2 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 3,2418 C TOqHOCTblO ,lJ;O 0,5?
3. flBJIHeTCH JIH qHCJIO 0,16 rrpH6JIHmeHHbIM 3HaqeHHeM
qHCJIa 9: 55 C TOqHOCTblO ,lJ;O 0,0001?
4. BbIcoTa co6opa 86 M. 3KCKypCOBO,lJ; TypHCTaM CKa3aJI,
qTO BbICOTa co6opa rrpH6JIHmeHHO paBHa 90 M. KaKoBa
rrorpemHocTb TaKoro rrpH6JIHmeHHH?
5. 3a 7 peiicoB aBTo6yc rrepeBe3 60JIbme 180 rraccamH-
POB, a 3a 14 peiicoB - MeHbme 367 rraccamHpOB. CKOJIbKO
MeCT B aBTo6yce, eCJIH B Kam,lJ;OM peiice aBTo6yc rrepeB03HT
POBHO CTOJIbKO rraccamHpOB, CKOJIbKO MeCT B aBTo6yce?
6. BepHo JIH YTBepm,lJ;eHHe: a-3b> 5a+3b TOr,lJ;a H TOJIb-
KO Tor,lJ;a, KOr,lJ;a 2a + 3b > O?
7. PemHTe ypaBHeHHe: Ix-91=lx+ll.
28
CaMOCTOATenbHaA pa60Ta N2 13
Bapuaum M 1
1. OKpyrJIHTe ,n;o e,n;HHHD;: 264,587.
2. OKpyrJIHTe ,n;o ,n;eCHTbIX: 138,469.
3. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
5
,n;o 0,01 qHCJIO -.
19
4. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
3
,n;o 0,001 qHCJIO 2-.
11
5. CKOPOCTb aBTo6yca 13,8 M/c. BbIpa3HTe STY CKOpOCTb
B KHJIOMeTpaX B qaC H oKpyrJIHTe C TOqHOCTblO,n;O 1 KM/q.
6. Haii,n;HTe HaH60JIbmee 3HaqeHHe BbIpameHHH b - 3a 2 ,
eCJIH -3 < a < 4 H -1 < b < 2.
7. PemHTe HepaBeHCTBO: 12x - 51 < 1.
Bapuaum M 2
1. OKpyrJIHTe ,n;o e,n;HHHD;: 317,485.
2. OKpyrJIHTe ,n;o ,n;eCHTbIX: 125,359.
3. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
5
,n;o 0,01 qHCJIO -.
17
4. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
4
,n;o 0,001 qHCJIO 3-.
11
5. CKOPOCTb aBTo6yca 12,6 M/c. BbIpa3HTe STY CKOpOCTb
B KHJIOMeTpax B qac H oKpyrJIHTe C TOqHOCTblO,n;O 1 KM/q.
6. Haii,n;HTe HaH60JIbmee 3HaqeHHe BbIpameHHH b-4a 2 ,
eCJIH - 2 < a < 3 H -1 < b < 1.
7. PemHTe HepaBeHCTBO: 12x+ll < 3.
CaMOCTOATenbHaA pa60Ta N2 13
29
Bapuaum M 3
1. OKpyrJIHTe ,n;o e,n;HHHD;: 493,529.
2. OKpyrJIHTe ,n;o ,n;eCHTbIX: 109,483.
3. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
3
,n;o 0,01 qHCJIO 19 .
4. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
5
,n;o 0,001 qHCJIO 1-.
11
5. CKOpOCTb aBTo6yca 14,8 M/c. BbIpa3HTe 3TY CKOpOCTb
B KHJIOMeTpax B qac H oKpyrJIHTe C TOqHOCTblO,n;O 1 KM/q.
6. Haii,n;HTe HaHMeHbmee 3HaqeHHe BbIpameHHH b-3a 2 ,
eCJIH -3 < a < 4 H -1 < b < 2.
7. PemHTe HepaBeHCTBO: 12x-31 < 5.
Bapuaum M 4
1. OKpyrJIHTe ,n;o e,lJ;HHHD;: 528,496.
2. OKpyr JIHTe ,n;o ,n;eCHTbIX: 117,257.
3. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
3
,lJ;O 0,01 qHCJIO -.
17
4. IIpe,n;cTaBbTe B BH,n;e ,n;ecHTHqHOii ,n;P06H C TOqHOCTblO
2
,n;o 0,001 qHCJIO 4-.
11
5. CKOPOCTb aBTo6yca 12,8 M/c. BbIpa3HTe 3TY CKOpOCTb
B KHJIOMeTpax B qac H oKpyrJIHTe C TOqHOCTblO,n;O 1 KM/q.
6. Haii,lJ;HTe HaHMeHbmee 3HaqeHHe BbIpameHHH b - 4a 2 ,
eCJIH -2 < a < 3 H -1 < b < 1.
7. PemHTe HepaBeHCTBO: 12x + 31 < 1.
30
CaMOCTOATenbHaA pa60Ta N2 14
Bapuaum M 1
1. OKpyrJIHTe qHCJIO 4,85 ,n;o e,n;HHHD; H Haii,n;HTe a6co-
JIIOTHYIO rrorpemHOCTb oKpyrJIeHHH.
2. OKpyrJIHTe qHCJIO 2,58 ,n;o e,n;HHHD; H Haii,n;HTe OT-
HOCHTeJIbHYIO rrorpemHOCTb oKpyr JIeHHH.
3. Haii,n;HTe OTHOCHTeJIbHYIO rrorpemHOCTb rrpH6JIHme-
1
HHH qHCJIa - qHCJIOM 0,14.
7
4. IIpH6JIHmeHHoe 3HaqeHHe qHCJIa x paBHO a. OTHOCH-
TeJIbHaH rrorpemHOCTb 3Toro rrpH6JIHmeHHH paBHa 0,01
(1 0/0). Haii,n;HTe a6COJIIOTHYlO rrorpemHOCTb, eCJIH a = 2,65.
5. IIpH KaKHX 3HaqeHHHX x o6e cpYHKD;HH y=-x+5
H y = 3x + 6 rrpHHHMalOT rrOJIOmHTeJIbHbIe 3HaqeHHH?
6. PemHTe CHCTeMY HepaBeHCTB: 5-x>0; x+3>0;
2x<8.
7. PemHTe HepaBeHCTBO: I x-51> 3.
Bapuaum M 2
1. OKpyr JIHTe qHCJIO 3, 74 ,n;o e,n;HHHD; H Haii,n;HTe a6co-
JIIOTHYIO rrorpemHOCTb oKpyrJIeHHH.
2. OKpyrJIHTe qHCJIO 4,55 ,n;o e,n;HHHD; H Haii,n;HTe OT-
HOCHTeJIbHYIO rrorpemHOCTb oKpyr JIeHHH.
3. Haii,n;HTe OTHOCHTeJIbHYIO rrorpemHOCTb rrpH6JIHme-
1
HHH qHCJIa - qHCJIOM 0, 11.
9
4. IIpH6JIHmeHHoe 3HaqeHHe qHCJIa x paBHO a. OT-
HOCHTeJIbHaH rrorpemHOCTb 3Toro rrpH6JIHmeHHH paBHa
0,001 (0,1 0/0). Haii,n;HTe a6COJIIOTHYlO rrorpelliHOCTb, eCJIH
a=I,38.
5. IIpH KaKHX 3HaqeHHHX x o6e cpYHKD;HH y=4x+ 12
H y=-x+ 1 rrpHHHMalOT rrOJIOmHTeJIbHbIe 3HaqeHHH?
6. PemHTe CHCTeMY HepaBeHCrB: x - 2 > 0; 7 - x > 0;
3x < 9.
7. PemHTe HepaBeHCTBO: I x + 61 > 2.
CaMOCTOATenbHaA pa60Ta N2 14
31
Bapuaum M 3
1. OKpyr JIHTe qHCJIO 5,29 ,lJ;O e,lJ;HHHD; H HaH,lJ;HTe a6co-
JIIOTHYIO rrorpemHOCTb oKpyrJIeHHH.
2. OKpyr JIHTe qHCJIO 3,52 ,lJ;O e,lJ;HHHD; H HaH,lJ;HTe OT-
HOCHTeJIbHYIO rrorpemHOCTb oKpyr JIeHHH.
3. HaH,lJ;HTe OTHOCHTeJIbHYIO rrorpemHOCTb rrpH6JIHme-
4
HHH qHCJIa - qHCJIOM 0,44.
9
4. IIpH6JIHmeHHoe 3HaqeHHe qHCJIa x paBHO a. OTHO-
CHTeJIbHaH rrorpemHOCTb 3Toro rrpH6JIHmeHHH paBHa 0,01
(1 0/0). HaH,lJ;HTe a6COJIIOTHyro rrorpemHOCTb, eCJIH a=0,543.
5. IIpH KaKHX 3HaqeHHHX x o6e cpYHKD;HH y = -x + 3
H Y = 2x + 4 rrpHHHMalOT rrOJIOmHTeJIbHbIe 3HaqeHHH?
6. PemHTe CHCTeMY HepaBeHCTB: 4 - x > 0; x + 7> 0;
3x < 9.
7. PemHTe HepaBeHCTBO: 1 x - 31 > 6.
Bapuaum M 4
1. OKpyr JIHTe qHCJIO 6,38 ,lJ;O e,lJ;HHHD; H HaH,lJ;HTe a6co-
JIIOTHYIO rrorpemHOCTb oKpyrJIeHHH.
2. OKpyr JIHTe qHCJIO 5,64 ,lJ;O e,lJ;HHHD; H HaH,lJ;HTe OT-
HOCHTeJIbHYIO rrorpemHOCTb oKpyr JIeHHH.
3. HaH,lJ;HTe OTHOCHTeJIbHYIO rrorpemHOCTb rrpH6JIHme-
2
HHH qHCJIa - qHCJIOM 0,22.
9
4. ITpH6JIHmeHHOe 3HaqeHHe qHCJIa x paBHO a. OT-
HOCHTeJIbHaH rrorpemHOCTb 3Toro rrpH6JIHmeHHH paBHa
0,001 (0,1 0 /0 ). HaH,lJ;HTe a6COJIIOTHYlO rrorpemHOCTb, eCJIH
a=0,123.
5. ITPH KaKHX 3HaqeHHHX x o6e cpYHKD;HH Y = 3x + 9
H Y = - x + 4 rrpHHHMalOT rrOJIOmHTeJIbHbIe 3HaqeHHH?
6. PemHTe CHCTeMY HepaBeHCTB: x - 4 > 0; 6 - x > 0;
2x < 10.
7. PemHTe HepaBeHCTBO: 1 x + 71> 4.
32
CaMOCTOATenbHaA pa60Ta N2 15
Bapuaum M 1
1. 3arrHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 37056.
2. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 0,0000539.
3. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 136080 H Ha-
30BHTe MaHTHCCY 3Toro qHCJIa.
4. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 0,0002634
H Ha30BHTe nOpH,lJ;OK.
5. PemHTe ,lJ;BoiiHOe HepaBeHCTBO: -1 < 2x + 3 < 7.
6. PemHTe CHCTeMY ypaBHeHHii: x - 2> 4; 3 - x < 5;
4-2x>10.
7. PemHTe HepaBeHCTBO: 12 - xl > 7.
Bapuaum M 2
1. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 4815.
2. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 0,00000627.
3. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 283400 H Ha-
30BHTe MaHTHCCY 3Toro qHCJIa.
4. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 0,005927
H Ha30BHTe nOpH,lJ;OK.
5. PemHTe ,lJ;BoiiHOe HepaBeHCTBO: -3 < 2x-l < 5.
6. PemHTe CHCTeMY ypaBHeHHii: x - 3 > 6; 2 - x < 4;
5-2x>5.
7. PemHTe HepaBeHCTBO: 11-xl > 6.
CaMOCTOATenbHaA pa60Ta N2 15
33
BapuaKm M 3
1. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 53 082.
2. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 0,0000745.
3. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 482610 H Ha-
30BHTe MaHTHCCY 3Toro qHCJIa.
4. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 0,0008139
H Ha30BHTe nOpH,lJ;OK.
5. PemHTe ,lJ;BoiiHOe HepaBeHCTBO: -7 < 2x + 1 < 3.
6. PemHTe CHCTeMY ypaBHeHHii: x-I> 5; I-x < 3;
6-3x> 3.
7. PemHTe HepaBeHCTBO: 13-xl > 5.
BapuaKm M 4
1. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 6394.
2. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO: 0,00000482.
3. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 395600 H Ha-
30BHTe MaHTHCCY 3Toro qHCJIa.
4. 3anHmHTe B CTaH,lJ;apTHOM BH,lJ;e qHCJIO 0,001857
H Ha30BHTe nOpH,lJ;OK.
5. PellIHTe ,lJ;BoiiHOe HepaBeHCTBO: -5 < 2x - 3 < 7.
6. PemHTe CHCTeMY ypaBHeHHii: x - 4 > 3; 5 - x < 1 ;
7 -3x> 7.
7. PemHTe HepaBeHCTBO: 14-xl > 8.
34
CaMOCTOATenbHaA pa60Ta N2 16
BapuaKm M 1
1. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 144.
2. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 0,09.
3. BepHo JIH paBeHCTBO: .J625 == 25 ?
1
4. BblqMCJIMTe: 3 · 0,81 +0,7.
5. Haii,lJ;HTe 3HaqeHHe BbIpameHH,a: 7. .J 10x - 2 npH
1
x= 5 .
6. IIp H KaK HX 3HaqeHH,ax a HMeeT CMbICJI BbIpameHHe:
-5. .J 3-2a?
7. PemHTe ypaBHeHHe: £ + 3 == 11.
BapuaKm M 2
1. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 169.
2. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 0,25.
3. BepHo JIH paBeHCTBO: .J400 == -20?
1
4. BblqMCJIMTe: 6 · 0,36 +0,2.
5. Haii,lJ;HTe 3HaqeHHe BbIpameHH,a: 8. .J 10x - 5 npH
1
x= 2 .
6. II pH Ka KHX 3HaqeHH,ax a HMeeT CMbICJI BbIpameHHe:
-8+ .J 5-2a?
7. PemHTe ypaBHeHHe: £ - 2 == 7 .
BapuaKm M 3
1. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 225.
2. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 0,04.
3. BepHo JIH paBeHCT BO: .J196 = 14 ?
4. BbPIMCJIMTe: · .J O,64 +0,8.
5. Haii,lJ;HTe 3HaqeHHe BbIpameHH,a: 6. .J 8x - 2 npH
1
x=-
4.
6. IIp H KaK HX 3HaqeHH,ax a HMeeT CMbICJI BbIpameHHe:
-2 · .J 9-2a ?
7. PemHTe ypaBHeHHe: £ + 2 = 9.
BapuaKm M 4
1. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 121.
2. Haii,lJ;HTe apHcpMeTHqeCKHii KBa,lJ;paTHbIii KopeHb
H3 qHCJIa: 0,16.
3. BepHo JIH paBeHCTBO: .J900 = -30?
1
4. BbIqHCJIHTe: -. .J 0,49 +0,4.
7
5. Haii,lJ;HTe 3HaqeHHe BbIpameHH,a: 9 · .J 8x-4 npH
1
X=-
2.
6. IIPH K aKHX 3HaqeHH,ax a HMeeT CMbICJI BbIpameHHe:
4 - 7 - 2a ?
7. PellIHTe ypaBHeHHe: £ - 5 = 6.
36
CaMOCTOATenbHaA pa60Ta N217
Bapuaum M 1
1. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;HqeCKOii
2
,lJ;eCHTHqHOii ,lJ;P06H: -.
3
2. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;HqeCKOii
1
,lJ;eCHTHqHOii ,lJ;P06H: -4 - .
11
3. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: 0,(5).
4. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: -1,2(3).
5. CpaBHHTe qHCJIa: 0,32 H 0,3(2).
6. CpaBHHTe qHCJIa: -1,0(25) H -1,025.
1
7. PemHTe ypaBHeHHe: £ = 1--
4.
Bapuaum M 2
1. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;H"tIeCKOii
2
,lJ;eCHTHqHOii ,lJ;P06H: -.
9
2. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;HqeCKOii
,AeCSlTMQHOH ,AP06M: -1 .
11
3. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: 0,(4).
4. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: -2,1(6).
5. CpaBHHTe qHCJIa: 0, 78 H 0,(78).
6. CpaBHHTe qHCJIa: -2,03(7) H -2,037.
2
7. PemMTe ypaBHeHMe: £ = 1- 5 ·
CaMOCTOJITenbHaJi pa60Ta N2 17
37
BapuaKm M 3
1. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;HqeCKOii
1
,lJ;eCHTHqHOii ,lJ;P06H: 3 .
2. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;HqeCKOii
2
eCHTHqHOii ,lJ;P06H: -3-.
11
3. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: 0,(2).
4. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: -4,3(6).
5. CpaBHHTe qHCJIa: 0,59 H 0,5(9).
6. CpaBHHTe qHCJIa: -4,0(17) H -4,017.
1
7. PemHTe ypaBHeHHe: £ = 1--
3.
BapuaKm M 4
1. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;HqeCKOii
1
,lJ;eCHTHqHOii ,lJ;P06H: -.
9
2. 3anHmHTe B BH,lJ;e 6eCKOHeqHOii nepHO,lJ;HqeCKOii
u 2 4
,lJ;eCHTHqHOH ,lJ;P06H: - -.
11
3. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: 0,(7).
4. 3anHmHTe B BH,lJ;e 06bIKHoBeHHoii ,lJ;P06H: -5,1(3).
5. CpaBHHTe qHCJIa: 0,14 H 0,(14).
6. CpaBHHTe qHCJIa: -3,06(8) H -3,068.
7. PemMTe ypaBHeHMe: £ = 1- 3 .
5
38
CaMOCTOATenbHaA pa60Ta N2 18
Bapuaum M 1
1. Haii,lJ;HTe 3HaqeHHe BbIpameHHH N npH x=-3.
2. BbIqHCJIHTe: H.
3. YnpocTMTe BbIpameHMe
(4-J5)2.
4. Haii,lJ;HTe ,lJ;Ba IIOCJIe,lJ;OBaTeJIbHbIX D;eJIbIX qHCJIa,
Mem,lJ;Y KOTOpbIMH 3aKJIIOqeHO qH CJIO -J150 .
5. BepHOJIMpaBeHCTBO a +3-
(a -3)2 =2a, eCJIMa < 3?
6. PemMTe ypaBHeHMe:
(X-6)2 =6-x.
7. BbPIMCJIMTe Ha MMKpOKaJIbKYJIHTope:
(5-2J3).
,n:aiiTe OTBeT C TOqHOCTblO ,lJ;O 0,01.
Bapuaum M 2
1. Haii,lJ;HTe 3Haq eHHe BbIpameHHH N IIPH x= 5.
2. BbIqMCJIMTe:
(_4)6.
3. YnpocTMTe BbIpameHMe
(6-J7)2.
4. Haii,lJ;HTe ,lJ;Ba IIOCJIe,lJ;OBaTeJIbHbIX D;eJIbIX qHCJIa,
Mem,lJ;Y KOTOpbIMH 3aKJIIOqeHO q HCJIO -J130 .
5. BepHOJIMpaBeHcTBo a+ 4-
(a -4)2 =2a, eCJIMa > 4?
6. PemMTe ypaBHeHMe:
(X-5)2 =x-5.
7. BbIqMCJIMTe Ha MMKpOKaJIbKYJIHTope:
(6-3J2).
,n:aiiTe OTBeT C TOqHOCTblO ,lJ;O 0,01.
CaMOCTOATenbHaA pa60Ta N2 18
39
BapuaHm M 3
1. Haii,lJ;HTe 3HaqeHHe BbIpameHHH .j;2 rrpH x = -4.
2. BbIqHCJIHTe: 9.
3. YnpocTMTe BbIpameHMe (2-J3)2.
4. Haii,lJ;HTe ,lJ;Ba nOCJIe,n;OBaTeJIbHbIX eJIbIX qHCJIa,
Mem,n;y KOTOpbIMH 3aKJIIOqeHO qH CJIO .J180 .
5. BepHO JIM paBeHCTBO a + 5- (a -5)2 = 2a, eCJIM a < 5?
6. PemMTe ypaBHeHMe: (X-4)2 =4-x.
7. Bb1<IMCJIMTe Ha MMKpOK8JIbKym1Tope: (9-4J3).
aiiTe OTBeT C TOqHOCTblO ,lJ;O 0,01.
BapuaHm M 4
1. Haii,lJ;HTe 3Haq eHHe BbIpameHHH .j;2 npH x = 6.
2. Bb1<IMCJIMTe: (_5)6.
3. YnpocTMTe BbIpameHMe (1-J2)2.
4. Haii,lJ;HTe ,lJ;Ba nOCJIe,lJ;OBaTeJIbHbIX eJIbIX qHCJIa,
Mem,n;y KOTOpbIMH 3aKJIIOqeHO qH CJIO .J120 .
5. BepHOJIMpaBeHcTBo a +6- ( a-6)2 =2a,eCJIMa > 6?
6. PemMTe ypaBHeHMe: (X-7)2 =x-7.
7. Bb1<IMCJIMTe Ha MMKpOK8JIbKYJIHTope: (8-4J2).
,D:aiiTe OTBeT C TOqHOCTblO ,n;o 0,01.
40
CaMOCTOATenbHaA pa60Ta N2 19
Bapuaum M 1
1. BbIqHCJIHTe: (144.0,25.4 9).
2. BbIqMCJIMTe: (132 .3 4 .1 10 ).
3. CpaBHHTe: 2 .J45 H 4 .J20 .
4. BbIqHCJIHTe: (m -.J7)(.J7 +m)-(M _.J3)2.
5. YnpocTHTe BbIpameHHe: 3 .J45 - .J125 + .J80 .
25-a
6. COKpaTHTe ,lJ;p06b r ' eCJIH a > O.
5+\Ia
7. BepHo JIH pa Be HCTBO
J (2a+2 (a2-b» = (a+Jb) + (a-Jb). eCJIMa > Jb. b > O?
Bapuaum M 2
1. BbIqHCJIHTe: (121. 0, 04. 25).
2. BbIqMCJIMTe: (122 .5 4 .18).
3. CpaBHHTe: 3 .J80 H 5 .J45 .
4. BbIqHCJIHTe: (.J13 - J6)( J6 +.J13) + (.J3 + M)2 .
5. YnpocTHTe BbIpameHHe: 4 .J20 +2 .J125 -3 .J80 .
64-b
6. COKpaTHTe ,lJ;p06b ' eCJIH b > O.
8-\Ib
7. BepHo JIH p aBe HCTBO
(2b+2 (b2 -a» = (a+Jb) + (b- ). ec.rrMa> Jb. b > O?
CaMOCTOATenbHaA pa60Ta N2 19
41
BapuaKm M 3
1. BbIqHCJIHTe: .j(196.0,25.6 4).
2. BbPIMCJIMTe: (102 .3 6 .1 12 ).
3. CpaBHHTe: 3 .J45 H 5 .J20 .
4. BbIqHCJIHTe: (J5 - .J45 )2 -(J13 +m)(m -J13).
5. YrrpocTHTe BbIpameHHe: 2 .J27 - 3 .J300 + 4J3.
16-a
6. COKpaTHTe ,lJ;p06b J: ' eCJIH a > O.
4+-va
7. BepHo JIH p aBeH CTBO
(2 (a2-b) +2a) = (a-Jb) + (a+Jb), eCJIMa > Jb, b > O?
BapuaKm M 4
1. BbIqHCJIHTe: .j(25 0 0,16 o 49 ).
2. BbI'IMCJIMTe: (14 2 .2 4 .1 15 ).
3. CpaBHHTe: 4 .J80 H 6 .J45 .
4. BbIqHCJIHTe: (J13 + m)( J13 - m) - (J5 - .J 45 )2 .
5. YrrpocTHTe BbIpameHHe: 5J27 + 2 .J300 - 4J3.
36-b
6. COKpaTMTe .AP06b Jb ' eCJIM b > O.
6- b
7. BepHo JIH p aBe HCTBO
(2b+2 (b2 -a» = (a-Jb) + (b- ), eCJIM a>Jb, b > O?
42
CaMOCTOJITenbHaJi pa60Ta N2 20
Bapuaum M 1
3 2 r;;
J7 -2 J7 +3 2"\17.
6. YnpocTHTe BbIpameHHe: (a +b-/b) : (a- .Jab +b).
7. IIJIow;a,lJ;b O,lJ;HOrO KBMpa Ta 72 CM 2 , a nJIOW;Mb ,lJ;py-
roro KBMpaTa 2 CM 2 . Bo CKOJIbKO pa3 CTopOHa nepBoro
KBa,lJ;paTa 60JIbme CTOpOHbI BToporo KBMpaTa?
1. BbIqHCJIHTe: 49: 144 - 16: 81 .
30Ji8
2. BbIqHCJIHTe:
5J2 ·
3. BbPIMCJIMTe: 5 4 : 11 14 .
9 25
4. MCKJIlOqHTb HppaD;HOHaJIbHOCTb H3 3HaMeHaTeJI.H:
J7-J5
J7+J5.
5. BbIqHCJIHTe:
Bapuaum M 2
1. BbIqHCJIHTe: 36:121- 9:49.
10 .J50
2. BbIqHCJIHTe:
25J2 ·
3 2
r;;+ J6 3.
3+,-,6 2+ 6
6. YnpocTHTeBbIpameHHe: (n -mJi;;): (n+ .Jnm + m).
7. IIJIow;a,lJ;b O,lJ;HOrO KBMpaTa 75 CM 2 , a nJIOw;a,lJ;b ,lJ;PY-
roro KBa,lJ;paTa 3 CM 2 . Bo CKOJIbKO pa3 CTopOHa nepBoro
KBa,lJ;paTa 60JIbme CTOpOHbI BToporo KBMpaTa?
3. BbPIMCJIMTe: 7 1 . 7 9 .
9 16
4. MCKJIlOqHTb HppaD;HOHaJIbHOCTb H3 3HaMeHaTeJI.H:
J5+J3
J5-J3.
5. BbIqHCJIHTe:
CaMOCTOfiTenbHafi pa60Ta N2 20
43
BapuaKm M 3
1. BblqHCJIHTe: .J 25: 144 - .J 4: 81 .
50m
2. BbI MCJlMTe: 10J8 ·
3. BbI MCJlMTe: 5 4 . 11 14 .
9 25
4. HCKJIlOqHTb HppaD;HOH8.JIbHOCTb H3 3HaMeHaTeJI.H:
J6-J5
J6+J5.
2 7
5. BbI MCJlMTe: J1i J1i + 1 ·
11-3 11-2
6. YrrpocTHTe BbIpameHHe: (a -bJb) : (a+ .Jab +b).
7. IIJIOI.IJ;Mb O,lJ;HOrO KBMpaTa 72 CM 2 , a rrJIOI.IJ;Mb ,lJ;PY-
roro KBMpaTa 8 CM 2 . Bo CKOJIbKO pa3 CTopOHa rrepBoro
KBMpaTa 60JIbme CTOpOHbI BToporo KBMpaTa?
BapuaKm M 4
2- 2 + 3
2+J6 3+J6.
6. YrrpocTHTe BbIpameHHe:(n +m ):(n- .Jnm +m).
7. IIJIOI.IJ;Mb O,lJ;HOrO KBMpaTa 150 CM 2 , a rrJIOI.IJ;Mb ,lJ;PY-
1'01'0 KBMpaTa 6 CM 2 . Bo CKOJIbKO pa3 CTopOHa rrepBoro
KB paTa 60JIbme CTOpOHbI BToporo KBMpaTa?
1. BblqHCJIHTe: .J 64: 121- .J 16: 49 .
10 .J72
2. BbIqHCJIHTe:
3J2 ·
3. BbI MCJlMTe: 7!: 7 .
9 16
4. HCKJIlOqHTb HppaD;HOH8.JIbHOCTb H3 3HaMeHaTeJI.H:
J8+J7
J8-J7.
5. BbIqHCJIHTe:
44
CaMOCTOfiTenbHafi pa60Ta N2 21
Bapuaum M 1
1. PemHTe ypaBHeHHe: x 2 - 121 = O.
2. PemHTe ypaBHeHHe: x 2 + 32 = O.
3. PemHTe KBMpaTHoe ypaBHeHHe, pa3JIOmHB ero JIe-
BYIO qaCTb Ha MHOmHTeJIH: x 2 - 4x + 4 = O.
4. PemHTe KBa,lJ;paTHOe ypaBHeHHe, pa3JIOmHB ero JIe-
BYIO qaCTb Ha MHOmHTeJIH: x 2 + 5x = o.
5. PemHTe ypaBHeHHe:
(x + 1)(x 2 - x + 1)- x 2 (x + 4) = O.
6. HMelOT JIH O,lJ;HH H Te me KOpHH ypaBHeHHH: x 2 =-9
H Ixl=3?
7. PemHTe ypaBHeHHe: x 2 + 3x + 2 = O.
Bapuaum M 2
1. PemHTe ypaBHeHHe: x 2 - 144 = O.
2. PemHTe ypaBHeHHe: x 2 +36=0.
3. PemHTe KBMpaTHoe ypaBHeHHe, pa3JIOmHB ero JIe-
BYIO qaCTb Ha MHOmHTeJIH: x 2 + 10x + 25 = O.
4. PemHTe KBMpaTHoe ypaBHeHHe, pa3JIOmHB ero JIe-
BYIO qaCTb Ha MHOmHTeJIH: x 2 -6x=0.
5. PemHTe ypaBHeHHe:
(x 2 - x + 1)(x + 1)- x 2 (x - 5) = O.
6. HMelOT JIH O,lJ;HH H Te me KOpHH ypaBHeHHH: x 2 = 25
H Ixl=5?
7. PemHTe ypaBHeHHe: x 2 - 3x + 2 = O.
CaMOCTOfiTenbHafi pa60Ta N2 21
45
BapuaKm M 3
1. PemHTe ypaBHeHHe: x 2 -169=0.
2. PemHTe ypaBHeHHe: x 2 + 24 = O.
3. PemHTe KBMpaTHoe ypaBHeHHe, pa3JIOmHB ero JIe-
BYIO qaCTb Ha MHOmHTeJIH: x 2 - 6x + 9 = O.
4. PemHTe KBMpaTHoe ypaBHeHHe, pa3JIOmHB ero JIe-
BYIO qaCTb Ha MHo:mHTeJIH: x 2 + 8x = o.
5. PemHTe ypaBHeHHe:
(x+ 1)(x 2 - x + 1)- x 2 (x + 9) = O.
6. HMelOT JIH O,lJ;HH H Te me KOpHH ypaBHeHHH: x 2 =-16
H Ixl=4?
7. PemHTe ypaBHeHHe: x 2 + 5x + 4=0.
BapuaKm M 4
1. PemHTe ypaBHeHHe: x 2 - 100 = O.
2. PemHTe ypaBHeHHe: x 2 +64=0.
3. PemHTe KBMpaTHoe ypaBHeHHe, pa3JIOmHB ero JIe-
Byro qaCTb Ha MHo:mHTeJIH: x 2 + 8x + 16 = O.
4. PemHTe KBMpaTHoe ypaBHeHHe, pa3JIOmHB ero JIe-
BYIO qaCTb Ha MHo:mHTeJIH: x 2 - 7 x = o.
5. PemHTe ypaBHeHHe:
(x 2 - x+ 1)(x + 1)- x 2 (x -7) = O.
6. HMelOT JIH O,lJ;HH H Te :me KOpHH ypaBHeHHH: x 2 =36
H Ixl=6?
7. PemHTe ypaBHeHHe: x 2 - 5x + 4 = O.
46
CaMOCTOfiTenbHafi pa60Ta N2 22
BapuaKm M 1
1. PemHTe ypaBHeHHe: -3x 2 =0.
2. PemHTe ypaBHeHHe: 4x 2 -64=0.
3. PemHTe ypaBHeHHe: 2x 2 +8=0.
4. PemHTe ypaBHeHHe: 5x 2 -15x=0.
5. PemHTe ypaBHeHHe: (x-7)(x+3)+(x-l)(x+5)= 102.
6. Haii,lJ;HTe qHCJIO, KBMpaT KOToporo paBeH YTpoeH-
HOMY 3TOMY qHCJIY.
x 2 -9
7. PemHTe ypaBHeHHe: - 0
x-3 - ·
BapuaKm M 2
1. PemHTe ypaBHeHHe: 7x 2 =0.
2. PemHTe ypaBHeHHe: 5x 2 - 125 = O.
3. PemHTe ypaBHeHHe: 3x 2 +5=0.
4. PemHTe ypaBHeHHe: 2X2 + 14x = o.
5. PemHTe ypaBHeHHe: (x-l)(x+4)+(x- 5)(x+ 2)= 58.
6. HaH,lJ;HTe qHCJIO, KBMpaT KOToporo paBeH y,lJ;BOeH-
HOMY 3TOMY qHCJIY.
x 2 -16
7. PemHTe ypaBHeHHe: = O.
x+4
CaMOCTOfiTenbHafi pa60Ta N2 22
47
BapuaKm M 3
1. PemHTe ypaBHeHHe: -6x 2 =0.
2. PemHTe ypaBHeHHe: 2x 2 -18=0.
3. PemHTe ypaBHeHHe: 5x 2 + 11 = O.
4. PemHTe ypaBHeHHe: 3x 2 -12x=0.
.5. PemHTe ypaBHeHHe: (x+3)(x-7)+(x+5)(x-l)=24.
6. Haii,lJ;HTe qHCJIO, KBMpaT KOToporo, YMeHbmeHHbIii
Ha 4, paBeH O.
x 2 - 36
7. PemHTe ypaBHeHHe: - 0
x-6 - ·
BapuaKm M 4
1. PemHTe ypaBHeHHe: 8x 2 =0.
2. PemHTe ypaBHeHHe: 2x 2 -72=0.
3. PemHTe ypaBHeHHe: 4x 2 +9=0.
4. PemHTe ypaBHeHHe: 6x 2 + 30x = o.
5. PemHTe ypaBHeHHe: (x+4)(x-l)+(x+2)(x-5)=84.
6. Haii,lJ;HTe qHCJIO, KBMpaT KOToporo, YMeHbmeHHbIii
Ha 9, paBeH O.
x 2 -25
7. PemHTe ypaBHeHHe: - 0
x+5 - ·
48
CaMOCTOATenbHaA pa60Ta N2 23
Bapuaum M 1
1. PemHTe ypaBHeHHe: x 2 +4x-12=0.
2. PemHTe ypaBHeHHe: x 2 -10x+ 16=0.
3. PemHTe ypaBHeHHe: x 2 - 3x - 10 = O.
4. PemHTe ypaBHeHHe: 2x 2 +3x-5=0.
5. IIpH KaKHX 3HaqeHHHX x 3HaqeHHH ,lJ;po6eii
4x2-3x x 2 +5x ?
3 H 2 paBHbI.
6. PemHTe ypaBHeHHe:
(2x+ 1)(x- 3)- (l-x)(x- 5)= 29 -llx.
2x+x 2 - -0.
7. PemHTe ypaBHeHHe:
x+2
Bapuaum M 2
1. PemHTe ypaBHeHHe: x 2 - 8x + 15 = O.
2. PemHTe ypaBHeHHe: x 2 +9x+14=0.
3. PemHTe ypaBHeHHe: x 2 -x-12=0.
4. PemHTe ypaBHeHHe: 9x 2 +6x-8=0.
5. IIpH KaKHX 3HaQeHHHX x 3HaQeHHH ,lJ;po6eii
3x 2 +7x 7x 2 -5x ?
4 H 3 paBHbI.
6. PemHTe ypaBHeHHe:
(3x- 8)2 - (4x- 6)2 + (5x - 2)(5x+ 2) = 96.
x 2 - 5x
7. PemHTe ypaBHeHHe: == O.
x-5
CaMOCTOATenbHaA pa60Ta N2 23
49
BapuaKm M 3
1. PemHTe ypaBHeHHe: x 2 + 6x - 16 = O.
2. PemHTe ypaBHeHHe: x 2 -9x+20=0.
3. PemHTe ypaBHeHHe: x 2 +3x-18=0.
4. PemHTe ypaBHeHHe: 25x 2 -10x-3=0.
5. IIpH KaKHX 3HaqeHHHX x 3HaqeHHH ,lJ;po6eii
5x+x 2 4X2-3x ?
2 H 3 paBHbI.
6. PemHTe ypaBHeHHe:
(x- 3)(2x + 1) - 29 + llx = (x-l)(5 - x).
4x+x 2 - - O.
7. PemHTe ypaBHeHHe:
x+4
BapuaKm M 4
1. PemHTe ypaBHeHHe: x2-9x+ 18=0.
2. PemHTe ypaBHeHHe: x 2 +10x+16=0.
3. PemHTe ypaBHeHHe: x 2 +x-30=0.
4. PemHTe ypaBHeHHe: 5x 2 - 7 x - 6 = o.
5. IIpH KaKHX 3HaqeHHHX x 3HaqeHHH ,lJ;po6eii
7x 2 -5x 7x+3x 2
3 M 4 paBHbI?
6. PemHTe ypaBHeHHe:
(5x- 2)(5x + 2) + (3x- 8)2 - 96 = (4x - 6)2.
x2-7x
7. PemHTe ypaBHeHHe: = O.
x-7
50
CaMOCTOATenbHaA pa60Ta N2 24
Bapuaum M 1
1. PemHTe ypaBHeHHe: 2X2 + 3x + 1 = O.
2. PemHTe ypaBHeHHe: 2x 2 -7x+3=0.
3. PemHTe ypaBHeHHe: 3x 2 +2x-l=0.
4. PemHTe ypaBHeHHe: 16x 2 - 8x + 1 = o.
5. CKOJIbKO KopHeii HMeeT ypaBHeHHe 2X2 + 5x - 7 = O?
6. CKOJIbKO KopHeii HMeeT ypaBHeHHe 9x 2 - 6x + 2 = O?
x 2 -3x 11
7. PemHTe ypaBHeHHe: + x = .
7
Bapuaum M 2
1. PemHTe ypaBHeHHe: 2X2 - 3x + 1 = O.
2. PemHTe ypaBHeHHe: 2x 2 -7x-4=0.
3. PemHTe ypaBHeHHe: 5x 2 -8x-4=0.
4. PemHTe ypaBHeHHe: 9x 2 - 6x + 1 = o.
5. CKOJIbKO KopHeii HMeeT ypaBHeHHe 2X2 + 5x + 7 = O?
6. CKOJIbKO KopHeii HMeeT ypaBHeHHe 9x 2 - 6x - 2 = O?
x 2 +3x x+7
7. PemHTe ypaBHeHHe:
2
4
CaMOCTOfiTenbHafi pa60Ta N2 24
51
BapuaKm M 3
1. PemHTe ypaBHeHHe: 2X2 + 5x + 2 = O.
2. PemHTe ypaBHeHHe: 3x 2 +x-4=0.
3. PemHTe ypaBHeHHe: 8x 2 - 6x + 1 = O.
4. PemHTe ypaBHeHHe: 25x 2 +10x+l=0.
5. CKOJIbKO KopHeii HMeeT ypaBHeHHe 3x 2 - 7 x - 8 = O?
6. CKOJIbKO KopHeii HMeeT ypaBHeHHe 7 x 2 - 5x + 2 = O?
7. PemMTe ypaBHeHMe: 1+ 5x = 6x+2 .
x+l (X+1)2
BapuaKm M 4
1. PemHTe ypaBHeHHe: 2X2 + 5x - 3 = O.
2. PemHTe ypaBHeHHe: 2x 2 -x-l=0.
3. PemHTe ypaBHeHHe: 4x 2 + 4x - 3 = O.
4. PemHTe ypaBHeHHe: 36x 2 + 12x+ 1 =0.
5. CKOJIbKO KopHeii HMeeT ypaBHeHHe 3x 2 - 7 x + 8 = O?
6. CKOJIbKO KopHeii HMeeT ypaBHeHHe 7 x 2 - 5x - 2 = O?
7. PemMTe ypaBHeHMe: 2+ x = 12-x
x+2 (X+2)2.
52
CaMOCTOATenbHaA pa60Ta N2 25
Bapuaum M 1
1. PemHTe ypaBHeHHe: x 2 +6x-40=0.
2. PemHTe ypaBHeHHe: x 2 -7x+12=0.
3. Pa3JIOmHTe Ha MHOmHTeJIH: x 2 +x-42.
4. Pa3JIOmHTe Ha MHOmHTeJIH: x3-9x2_22x.
X2 +6x-7
5. COKpaTHTe ,n;P06b: 2 ·
x -7x+6
3 1
6. YnpOCTMTe: 2 6 - 3 ·
x + x+9 x+
7. He BbIqHCJIHH KopHeH Xl H X 2 ypaBHeHHH
1 1
3x 2 -8x-15=0, HaH,n;HTe -+-.
Xl X 2
Bapuaum M 2
1. PemHTe ypaBHeHHe: x 2 -6x-7=0.
2. PemHTe ypaBHeHHe: X2 + 5x + 6 = O.
3. Pa3JIOmHTe Ha MHOmHTeJIH: x2+5x-24.
4. Pa3JIOmHTe Ha MHOmHTeJIH: x3-3x2+2x.
x 2 -8x-9
5. COKpaTHTe ,n;po6b: 2 ·
X + 9x + 8
4 1
6. YnpocTMTe: x 2 +8x+16 x+4
7. He BbIqHCJIHH KopHeH Xl H x 2 ypaBHeHHH
1 1
2x 2 -3x-5=0, HaH,n;HTe -+-.
Xl x 2
CaMOCTOATenbHaA pa60Ta N2 25
53
Bapuaum M 3
1. PelIIHTe ypaBHeHHe: x 2 +4x-5=0.
2. PelIIHTe ypaBHeHHe: x2-8x+ 15=0.
3. Pa3JIo:mHTe Ha MHo:mHTeJIH: x 2 -5x+6.
4. Pa3JIo:mHTe Ha MHo:mHTeJIH: x3+4x2-21x.
X2 +7x+12
5. COKpaTHTe ,n;P06b: 2 ·
X + 6x + 8
3 1
6. YrrpOCTHTe: 2 + ·
x -6x+9 x-3
7. He BbIqHCJIHH KopHeH Xl H X 2 ypaBHeHHH
1 1
5x 2 -11x+2=0, HaH,n;HTe -+-.
Xl X 2
Bapuaum M 4
1. PemHTe ypaBHeHHe: x 2 -8x-9=0.
2. PelIIHTe ypaBHeHHe: X2 - 6x + 5 = O.
3. Pa3JIo:mHTe Ha MHo:mHTeJIH: x2-7x+ 12.
4. Pa3JIo:mHTe Ha MHo:mHTeJIH: x3+4x2-12x.
x 2 +8x+15
5. COKpaTHTe ,n;po6b: 2 .
X +9x+20
4 1
6. YrrpOCTHTe: 2 +.
X -8x+16 x-4
7. He BbIqHCJIHH KopHeH Xl H x 2 ypaBHeHHH
1 1
2x 2 +5x-3=0, HaH,n;HTe -+-.
Xl x 2
54
CaMOCTOATenbHaA pa60Ta N2 26
Bapuaum M 1
1. PemHTe ypaBHeHHe: x 4 -10x 2 +9=0.
2. PemHTe ypaBHeHHe: x 4 -3x 2 -4=0.
3. PemHTe ypaBHeHHe: x 4 + 6x 2 - 7 = O.
4. PemHTe ypaBHeHHe: x 4 + 6x 2 + 5 = O.
5. PemMTe ypaBHeHMe: 10
== 1 .
x-3 x
x 2
6. PemHTe ypaBHeHHe:
x-I
2x
I-x
3
x-I
7. HMeeT JIH
eiiCTBHTeJIbHbIe KOpHH ypaBHeHHe:
x 4 +8x 2 + 7?
Bapuaum M 2
1. PemHTe ypaBHeHHe: x 4 - 5x 2 + 4 = O.
2. PemHTe ypaBHeHHe: x 4 +3x 2 -4=0.
3. PemHTe ypaBHeHHe: x 4 + 3x 2 + 2 = O.
4. PemHTe ypaBHeHHe: x 4 +9x 2 -10=0.
5. PemMTe ypaBHeHMe: 40 _ 40 == 1.
x - 20 X
x 2 2x 3
6. PemHTe ypaBHeHHe: -
x+l l+x x+l
7. HMeeT JIH
eiiCTBHTeJIbHbIe KOpHH ypaBHeHHe:
x 4 -11x 2 + 18?
CaMOCTOATenbHaA pa60Ta N2 26
55
Bapuanm M 3
1. PemHTe ypaBHeHHe: x 4 -13x 2 +36=0.
2. PemHTe ypaBHeHHe: x 4 +x 2 -20=0.
3. PemHTe ypaBHeHHe: x 4 + 7 x 2 - 8 = O.
4. PemHTe ypaBHeHHe: x 4 + 5x 2 + 4 = o.
5. PemMTe ypaBHeHMe: 10 = 1+
.
x-3 x
x 2 3x
6. PemHTe ypaBHeHHe: -
x-I I-x
4
x-I ·
7. HMeeT JIH ,n;eiicTBHTeJIbHbIe KOpHH ypaBHeHHe:
x 4 + llx2+ 10?
Bapuaum M 4
1. PemHTe ypaBHeHHe: x 4 -50x 2 +49=0.
2. PemHTe ypaBHeHHe: x 4 + 5x 2 - 6 = O.
3. PemHTe ypaBHeHHe: x 4 + 4x 2 + 3 = O.
4. PemHTe ypaBHeHHe: x 4 +10x 2 -11=O.
5. PemMTe ypaBHeHMe: 40 = 1 + 40 .
x-20 X
x 2 3x 4
6. PemHTe ypaBHeHHe: -
x+l l+x x+l
7. HMeeT JIH ,n;eiicTBHTeJIbHbIe KOpHH ypaBHeHHe:
x 4 -7x 2 + 12?
56
CaMOCTOATenbHaA pa60Ta N2 27
Bapuaum M 1
1. Haii,n;HTe ,n;Ba rrOCJIe,n;OBaTeJIbHbIX HaTYPaJIbHbIX qHC-
JIa, rrpOH3Be,n;eHHe KOTOpbIX paBHO 210.
2. IIepHMeTp rrpHMoyrOJIbHHKa paBeH 1 M, a rrJIO-
W;Mb - 4 ,n;M 2 . Haii,n;HTe ,n;JIHHY rrpHMoyrOJIbHHKa.
3. PaccToHHHe B 400 KM CKOpbIii rroe3,n; rrpomeJI Ha qac
6bIcTpee TOBapHoro. KaKoBa CKOpOCTb CKoporo rroe3,n;a,
eCJIH OHa Ha 20 KM/q 60JIbme, qeM CKOpOCTb TOBapHoro
rroe3,n;a?
4. PemHTe ypaBHeHHe: 2x 2 -9x=35.
5. PemHTe ypaBHeHHe: x 4 + x 2 - 2 = o.
6. PemHTe ypaBHeHHe:
3x 1 4
+ 2 .
x+2 x-2 x-4
x 2 +7x+12
7. COKpaTHTe ,n;P06b:
x 2 +6x+8 ·
Bapuaum M 2
1. Haii,n;HTe ,n;Ba rrOCJIe,n;OBaTeJIbHbIX HaTYPaJIbHbIX qHC-
JIa, rrpOH3Be,n;eHHe KOTOpbIX paBHO 240.
2. IIepHMeTp rrpHMoyrOJIbHHKa paBeH 1 M 20 CM, a rrJIO-
W;Mb - 8 ,n;M 2 . Haii,n;HTe mHpHHY rrpHMoyrOJIbHHKa.
3. PaCCTOHHHe B 180 KM CKOpbIii rroe3,n; rrpomeJI Ha qac
6bIcTpee TOBapHoro. KaKoBa CKOpOCTb CKoporo rroe3,n;a,
eCJIH OHa Ha 30 KM/q 60JIbme, qeM CKOpOCTb TOBapHoro
rroe3,n;a?
4. PemHTe ypaBHeHHe: 2X2 + x = 3.
5. PemHTe ypaBHeHHe: x 4 - x 2 - 12 = o.
6. PemHTe ypaBHeHHe:
3 = 4+ 3 .
x+2 x-I
x 2 - x - 2
7. COKpaTHTe ,n;po6b: 2 ·
X - 2x - 3
CaMOCTOATenbHaA pa60Ta N2 27
57
Bapuaum M 3
1. Haii,n;HTe ,n;Ba rrOCJIe,n;OBaTeJIbHbIX HaTypaJIbHbIX qHC-
]la, rrpoH3Be,n;eHHe KOTOpbIX paBHO 156.
2. IIepHMeTp rrpHMoyrOJIbHHKa paBeH 1 M 60 CM, a rrJIO-
a,n;b - 15 ,n;M 2 . Haii,n;HTe ,n;JIHHY rrpHMoyrOJIbHHKa.
3. PaccToHHHe B 240 KM CKOpbIii rroe3,n; rrpomeJI Ha qac
6bIcTpee TOBapHoro. KaKoBa CKOpOCTb CKoporo rroe3,n;a,
eCJlH OHa Ha 20 KM/q 60JIbme, qeM CKOpOCTb TOBapHoro
noe3,n;a?
4. PemHTe ypaBHeHHe: 2x 2 -3x=5.
5. PemHTe ypaBHeHHe: x 4 + 3x 2 + 2 = o.
6. PemHTe ypaBHeHHe:
2x 1 6
2 ·
x-3 x+3 x-9
x 2 + x - 2
7. COKpaTMTe ,lI;P06b: x 2 -3x+2 ·
Bapuaum M 4
1. HaH,n;HTe ,n;Ba rrOCJIe,n;OBaTeJIbHbIX HaTypaJIbHbIX qHC-
JIa, npOH3Be,n;eHHe KOTOpbIX paBHO 182.
2. IIepHMeTp rrpHMoyrOJIbHHKa paBeH 1 M 40 CM, a rrJIO-
IQa,n;b - 12 ,n;M 2 . HaH,n;HTe mHpHHY rrpHMoyrOJIbHHKa.
3. PaccToHHHe B 360 KM CKOpbIii rroe3,n; rrpomeJI Ha qac
6bIcTpee TOBapHoro. KaKOBa CKOpOCTb CKoporo rroe3,n;a,
eCJIH OHa Ha 30 KM/q 60JIbme, qeM CKOpOCTb TOBapHoro
I10e3,n;a?
4. PemHTe ypaBHeHHe: 2x 2 +5x=3.
5. PemHTe ypaBHeHHe: x 4 +6x 2 +5=0.
6. PemHTe ypaBHeHHe:
1 3
=3+ .
x + 1 3x -1
x 2 -2x-3
7. COKpaTHTe ,n;P06b:
x 2 +3x+2 ·
58
CaMOCTOATenbHaA pa60Ta N2 28
Bapuanm M 1
1. PemHTe CHCTeMY ypaBHeHHii: x 2 + y2 = 5; x + Y = 1.
2. PemHTe CHCTeMY ypaBHeHHii: x + y = 5; xy = 6.
3. PemHTe CHCTeMY ypaBHeHHii: x - y = 5; x 2 - y2 = 5.
4. PemHTe CHCTeMY ypaBHeHHii: X 2 +y2= 17; xy=4.
CKOJIbKO pemeHHii HMeeT cHcTeMa?
5. CYMMa ,n;BYX qHCeJI paBHa 8, a pa3HOCTb HX KBMpaTOB
paBHa 32. qeMY paBHa CYMMa KBMpaTOB 3THX qHCeJI?
6.
JIHHa rrpHMoyrOJIbHHKa Ha 5 CM 60JIbme mHpHHbI,
a rrJIOw;a,n;b rrpHMoyrOJIbHHKa paBHa 84 CM 2 . Haii,n;HTe
,n;JIHHY rrpHMoyrOJIbHHKa.
7. CKOpOCTb BeJIOCHrre,n;HCTa Ha rrepBoii rrOJIOBHHe rrYTH
6bIJIa Ha 3 KM/q 60JIbme, qeM ero CKOpOCTb Ha BTOpoii
rrOJIOBHHe rrYTH. C KaKoii CKOpOCTblO BeJIOCHrre,n;HCT rrpo-
eXaJI BTOPYIO rrOJIOBHHY rrYTH, eCJIH BeCb rrYTb B 90 KM OH
rrpeo,n;OJIeJI 3a 5,5 q?
Bapuanm M 2
1. PemHTe CHCTeMY ypaBHeHHii: x+2y=l; x+y2=4.
2. PemHTe CHCTeMY ypaBHeHHii: x + y = 8; xy = 7 .
3. PemHTe CHCTeMY ypaBHeHHii: x + y = 3; x 2 - y2 = 15.
4. PemIITe CHCTeMY ypaBHeHHii: X 2 +y2=29; xy=10.
CKOJIbKO pemeHHii HMeeT cHcTeMa?
5. CYMMa ,n;BYX qHCeJI paBHa 9, a pa3HOCTb HX KBMpaTOB
paBHa 45. qeMY paBHa CYMMa KBMpaTOB 3THX qHCeJI?
6. IIIHpHHa rrpHMoyrOJIbHHKa Ha 6 CM MeHbme ,n;JIHHbI,
a rrJIOw;a,n;b rrpHMoyrOJIbHHKa paBHa 72 CM 2 . Haii,n;HTe
mHpHHY rrpHMoyrOJIbHHKa.
7. PaCCTOHHHe Me:m,n;y rrOCeJIKaMH 36 KM rrepBbIii BeJIO-
CHrre,n;HCT rrpeo,n;OJIeBaeT Ha 1 q 6bIcTpee BToporo. Haii,n;HTe
CKOpOCTb rrepBoro BeJIOCHrre,n;HCTa, - eCJIH H3BeCTHO, qTO
CKOpOCTb rrepBoro Ha 3 KM/q 60JIbme CKOpOCTH BToporo.
CaMOCTOATenbHaA pa60Ta N2 28
59
Bapuaum M 3
1. PeIIIHTe CHCTeMY ypaBHeHHii: x 2 + y2 = 1 7; x - y = 3.
2. PeIIIHTe CHCTeMY ypaBHeHHii: x + y = 12; xy = 11.
3. PeIIIHTe CHCTeMY ypaBHeHHii: x+y=4; x 2 _y2=24.
4. PeIIIHTe CHCTeMY ypaBHeHHii: x 2 + y2 = 10; xy = 3.
CKOJIbKO peIIIeHHii HMeeT cHcTeMa?
5. CYMMa ,lJ;BYX qHCeJI paBHa 7, a pa3HOCTb HX KBa,n;paTOB
paBHa 21. qeMY paBHa CYMMa KBa,lJ;paTOB 3THX qHCeJI?
6. AJIHHa rrpHMoyrOJIbHHKa Ha 9 CM 60JIbIIIe IIIHPHHbI,
a rrJIOw;a,lJ;b rrpHMoyrOJIbHHKa paBHa 70 CM 2 . Haii,lJ;HTe
,n;JIHHY rrpHMoyrOJIbHHKa.
7. CKOpOCTb BeJIOCHrre,lJ;HCTa Ha rrepBoii rrOJIOBHHe rrYTH
6bIJIa Ha 3 KM/q MeHbIIIe, qeM ero CKOpOCTb Ha BTOpoii
rrOJIOBHHe rrYTH. C KaKoii CKOpOCTblO BeJIOCHrre,lJ;HCT rrpo-
exaJI BTOPYIO rrOJIOBHHY rrYTH, eCJIH BeCb rrYTb B 90 KM OH
rrpeO,lJ;OJIeJI 3a 5,5 'II?
Bapuaum M 4
1. PemHTe CHCTeMY ypaBHeHHii: x + y2 = 32; x + y = 2.
2. PemHTe CHCTeMY ypaBHeHHii: x+y=-7; xy=10.
3. PeIIIHTe CHCTeMY ypaBHeHHii: x - y = 2; x 2 - y2 = 8.
4. PemHTe CHCTeMY ypaBHeHHii: x 2 + y2 = 26; xy = 5.
CKOJIbKO pemeHHii HMeeT cHcTeMa?
5. CYMMa ,lJ;BYX qHCeJI paBHa 20, a pa3HOCTb HX KBa,n;pa-
TOB paBHa 80. qeMY paBHa CYMMa KBa,n;paTOB 3TH X qHCeJI?
6. IIIHpHHa rrpHMoyrOJIbHHKa Ha 11 CM MeHbme ,lJ;JIH-
HbI, a rrJIOw;a,n;b rrpHMoyrOJIbHHKa paBHa 80 CM 2 . Haii,lJ;HTe
IIIHPHHY rrpHMoyrOJIbHHKa.
7. PaCCTOHHHe Me:m,lJ;y rrOCeJIKaMH 36 KM rrepBbIii BeJIO-
CHrre,lJ;HCT rrpeO,lJ;OJIeBaeT Ha 1 'II 6bIcTpee BToporo. Haii,lJ;HTe
CKOpOCTb BToporo BeJIOCHrre,lJ;HCTa, eCJIH H3BeCTHO, qTO
CKOpOCTb BToporo Ha 3 KM/q MeHbme CKOpOCTH rrepBoro.
60
CaMOCTOATenbHaA pa60Ta N2 29
Bapuaum M 1
1. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH x, rrpH KOTO-
pbIX KBa,n;paTHqHaH cpYHKD;HH Y = X2_X - 3 rrpHHHMaeT
3HaqeHHe, paBHoe -3.
2. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH x, rrpH KOTO-
pbIX KBa,z:t;paTHqHaH cpYHKD;HH Y = X2 + 7 x + 5 rrpHHHMaeT
3HaqeHHe, paBHoe 5.
3. Haii,n;HTe HYJIH KBa,z:t;paTHqHOii cpYHKD;HH
y=3x 2 -5x+8.
4. HaH,n;HTe HYJIH KBa,z:t;paTHqHOii cpYHKD;HH
Y = -6X2 + 7 x - 2.
5. Haii,n;HTe K03cpcpHD;HeHTbI b H C KBMpaTHqHOii cpYHK-
D;HH y=x 2 +bx+c, eCJIH H3BeCTHbI HYJIH cpYHKD;HH: -4; 1.
6. Haii,n;HTe 3HaqeHHH x, rrpH KOTOpbIX cpYHKD;HH
Y = X2 + 2x - 3 H Y = 2x + 1 rrpHHHMalOT paBHbIe 3HaqeHHH.
7. HaH,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
cpYHKD;Hii: y=x 2 -4 H y=2x-4.
Bapuaum M 2
1. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH x, rrpH KOTO-
pbIX KBa,n;paTHqHaH cpYHKD;HH y = X2 + x + 4 rrpHHHMaeT
3HaQeHHe, paBHoe 4.
2. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH x, rrpH KOTO-
pbIX KBa,z:t;paTHqHaH cpYHKD;HH Y = X2 - 8x - 6 rrpHHHMaeT
3HaqeHHe, paBHoe -6.
3. Haii,n;HTe HYJIH KBa,n;paTHqHOii cpYHKD;HH
y=2x 2 -3x+ 7.
4. Haii,n;HTe HYJIH KBa,n;paTHqHOii cpYHKD;HH
y=-2x 2 + 3x+ 5.
5. Haii,n;HTe K03cpcpHD;HeHTbI b H C KBMpaTHQHOii cpYHK-
D;HH y=x 2 +bx+c, eCJIH H3BeCTHbI HYJIH cpYHKD;HH: 2; -4.
6. Haii,n;HTe 3HaqeHHH x, rrpH KOTOpbIX cpYHKD;HH
Y = X2 + 3x - 8 H Y = 3x + 1 rrpHHHMalOT paBHbIe 3HaqeHHH.
7. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
cpYHKD;Hii: y=x 2 +5 H y=3x+5.
CaMOCTOATenbHaA pa60Ta N2 29
61
Bapuaum M 3
1. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH x, rrpH KOTO-
pbIX KBa,n;paTHqHaH cpYHKD;HH Y = X2_X - 5 rrpHHHMaeT
3HaqeHHe, paBHoe -5.
2. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH x, rrpH KOTO-
pbIX KBa,n;paTHqHaH cpYHKD;HH Y = X2 + 3x + 4 rrpHHHMaeT
3HaqeHHe, paBHoe 4.
3. Haii,n;HTe HYJIH KBa,z:t;paTHqHOii cpYHKD;HH
y=4x 2 -2x+9.
4. Haii,n;HTe HYJIH KBa,z:t;paTHqHOii cpYHKD;HH
y=-2x 2 -3x+ 2.
5. Haii,n;HTe K03cpcpHD;HeHTbI b H C KBa,z:t;paTHqHOii cpYHK-
HH Y = X2 + bx + c, eCJIH H3BeCTHbI HYJIH cpYHKD;HH: -1; 3.
6. Haii,n;HTe 3HaqeHHH x, rrpH KOTOpbIX cpYHKD;HH
Y = X2 + 5x - 2 H Y = 5x + 2 rrpHHHMalOT paBHbIe 3HaqeHHH.
7. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
cpYHKD;Hii: y=x 2 -3 H y=4x-3.
Bapuaum M 4
1. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH X, rrpH KOTO-
pbIX KBa,n;paTHqHaH cpYHKD;HH y = X2 + x + 6 rrpHHHMaeT
3HaqeHHe, paBHoe 6.
2. Haii,n;HTe ,n;eiicTBHTeJIbHbIe 3HaqeHHH x, rrpH KOTO-
pbIX KBa,n;paTHqHaH cpYHKD;HH Y = X2 - 4x - 5 rrpHHHMaeT
3HaqeHHe, paBHoe -5.
3. Haii,n;HTe HYJIH KBa,z:t;paTHqHOii cpYHKD;HH
Y= 5X2-4x+ 3.
4. Haii,n;HTe HYJIH KBa,z:t;paTHqHOii cpYHKD;HH
y=-2x 2 -7x+4.
5. Haii,n;HTe K03cpcpHD;HeHTbI b H C KBa,z:t;paTHqHOii cpYHK-
HH y=x 2 +bx+c, eCJIH H3BeCTHbI HYJIH cpYHKD;HH: 2; -3.
6. Haii,n;HTe 3HaqeHHH x, rrpH KOTOpbIX cpYHKD;HH
y=x 2 +4x-6 H y=4x+3 rrpHHHMalOT paBHbIe 3HaqeHHH.
7. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
cpYHKD;Hii: y= x 2 + 7 H y= 5x + 7.
62
CaMOCTOATenbHaA pa60Ta N2 30
Bapuaum M 1
1. IIpHHa,z:t;JIe:mHT JIH TOqKa A(-2; -4) rpacpHKY cpYHK-
D;HH Y = x 2 ?
2. Haii,n;HTe Koop,n;HHaTbI TOqKH, cHMMeTpHqHOii TOq-
Ke A(-5; 15) OTHOCHTeJIbHO OCH op,n;HHaT.
3. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rrapa60JIbI
y=x 2 H rrpHMoii y=9.
4. HBJIHeTCH JIH TOqKa A(2; 4) TOqKOii rrepeCeqeHHH
rrapa60JIbI y=x 2 H rrpHMoii y=5x-6?
5. BepHo JIH YTBep:m,n;eHHe, qTO cpYHKD;HH Y = x 2 B03-
paCTaeT Ha HHTepBaJIe (-1; I)?
6. Ha o,n;Hoii Koop,n;HHaTHoii rrJIOCKOCTH rrocTpoiiTe rra-
pa60JIY y=x 2 H rrpHMYIO y=4. IIpH KaKHX 3HaqeHHHX x
TOqKH rrapa60JIbI JIe:maT HH:me rrpHMoii?
7. IIpH KaKHX x 3HaqeHHe cpYHKD;HH y = x 2 He MeHb-
me 16?
Bapuaum M 2
1. IIpHHa,z:t;JIe:mHT JIH TOqKa A(-5; 25) rpacpHKY cpYHK-
D;HH Y = x 2 ?
2. Haii,n;HTe Koop,n;HHaTbI TOqKH, cHMMeTpHqHOii TOq-
Ke A(4; 12) OTHOCHTeJIbHO OCH op,n;HHaT.
3. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rrapa60JIbI
y=x 2 H rrpHMoii y= 16.
4. HBJIHeTCH JIH TOqKa' A(3; 9) TOqKOii rrepeCeqeHHH
rrapa60JIbI y = x 2 H rrpHMoii y = 2x + 7?
5. BepHo JIH YTBep:m,n;eHHe, qTO cpYHKD;HH Y = x 2 B03-
paCTaeT Ha HHTepBaJIe (2; 8)?
6. Ha o,n;Hoii Koop,n;HHaTHoii rrJIOCKOCTH rrocTpoiiTe rra-
pa60JIY y=x 2 H rrpHMYIO y=4. IIpH KaKHX 3HaqeHHHX x
TOqKH rrapa60JIbI JIe:maT BbIme rrpHMoii?
7. II pH KaKHX x 3HaqeHHe cpYHKD;H_H y = x 2 He 60JIbme 1 ?
CaMOCTOATenbHaA pa60Ta N2 30
63
Bapuaum M 3
1. IIpHHa,n;JIe:mHT JIH TOqKa A( -3; -9) rpacpHKY cpYHK-
IJ;HH Y = x 2 ?
2. Haii,n;HTe Koop,n;HHaTbI TOqKH, cHMMeTpHqHOii TOq-
Ke A(-4; 13) OTHOCHTeJIbHO OCH op,n;HHaT.
3. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rrapa60JIbI
Y = x 2 H rrpHMoii y = 25.
4. HBJIHeTCH JIH TOqKa A( 1; 1) TOqKOii rrepeCeqeHHH
rrapa60JIbI y = x 2 H rrpHMoii y = 3x - 2?
5. BepHo JIH YTBep:m,n;eHHe, qTO cpYHKD;HH Y = x 2 y6bIBaeT
Ha HHTepBaJIe (-2; 2)?
6. Ha o,n;Hoii Koop,n;HHaTHoii rrJIOCKOCTH rrocTpoiiTe rra-
pa60JIY y=x 2 H rrpHMYIO y=9. IIpH KaKHX 3HaqeHHHX x
TOqKH rrapa60JIbI JIe:maT HH:me rrpHMoii?
7. IIpH KaKHX x 3HaqeHHe cpYHKD;HH y = x 2 He MeHb-
me 36?
Bapuaum M 4
1. IIpHHa,z:t;JIe:mHT JIH TOqKa A( -1; 1) rpacpHKY cpYHK-
D;HH Y = x 2 ?
2. Haii,n;HTe Koop,n;HHaTbI TOqKH, cHMMeTpHqHOii TOq-
Ke A(6; 11) OTHOCHTeJIbHO OCH op,n;HHaT.
3. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rrapa60JIbI
y=x 2 H rrpHMoii y=4.
4. HBJIHeTCH JIH TOqKa A(4; 16) TOqKOii rrepeCeqeHHH
rrapa60JIbI y = x 2 H rrpHMoii y = 6x - 5?
5. BepHo JIH yrBep:m,n;eHHe, qTO cpYHKD;HH Y = x 2 y6bIBaeT
Ha HHTepBaJIe (-5; -I)?
6. Ha o,n;Hoii Koop,n;HHaTHoii rrJIOCKOCTH rrocTpoiiTe rra-
pa60JIY y = x 2 H rrpHMYIO Y = 9. IIpH KaKHX 3HaqeHHHX x
TOqKH rrapa60JIbI JIe:maT HH:me rrpHMoii?
7. IIpH KaKHX x 3HaqeHHe cpYHKD;HH Y = x 2 He 60JIb-
me 25?
64
CaMOCTOATenbHaA pa60Ta N2 31
Bapuaum M 1
1. Ha o,lJ;Hoii KOOp,lJ;HHaTHOii rrJIOCKOCTH rrOCTpOHTb
rpacpHKH cpYHKD;Hii: y=2x 2 H y=-2x 2 . KaKaH H3 3THX
cpYHKD;Hii B03paCTaeT Ha rrpOMe:mYTKe x > O?
2. Haii,lJ;HTe K03cpcpHD;HeHT a, eCJIH rrapa60JIa y = ax 2
rrpOXO,lJ;HT qepe3 TOqKY A(3; -1).
3. C rrOMOI.IJ;blO rpacpHKa cpYHKD;HH y = -3X2 pemHTe
HepaBeHCTBO: -3X2 > -3.
4. IIpH KaKHX x 3HaqeHHH cpYHKD;HH y= 5x 2 60JIbme 20?
5. IIpH KaKHX x 3HaqeHHH cpYHKD;HH y=2x 2 He 60JIb-
me 50?
6. Haii,lJ;HTe KOOp,lJ;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
1 1
«PYHKII;liH: Y= - 2 x 2 Ii Y= 2 x-3.
7. Haii,lJ;HTe 3HaqeHHe a, rrpH KOTOpOM O,lJ;Ha H3 TOqeK
rrepeCeqeHHH rrapa60JIbI y = ax 2 H rrpHMoii y = 5x - 2 HMeeT
a6cD;Hccy x = 2.
Bapuaum M 2
1. Ha o,lJ;Hoii KOOp,lJ;HHaTHOii rrJIOCKOCTH rrOCTpOHTb
rpacpHKH cpYHKD;Hii: y = 3x 2 H Y = -3x 2 . KaKaH H3 3THX
cpYHKD;Hii y6bIBaeT Ha rrpOMe:mYTKe x > O?
2. Haii,lJ;HTe K03cpcpHD;HeHT a, eCJIH rrapa60JIa y = ax 2
rrpOXO,lJ;HT qepe3 TOqKY A(2; 1).
3. C rrOMOI.IJ;blO rpacpHKa cpYHKD;HH y = _2X2 pemHTe
HepaBeHCTBO: _2X2 < -2.
4. IIpH KaRHX x 3HaqeHHH cpYHKD;HH y=3x 2 MeHbme 12?
5. IIpH KaKHX x 3HaqeHHH cpYHKD;HH y=2x 2 He MeHb-
me 50?
6. Haii,lJ;HTe KOOp,lJ;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
1 1
«PYHKII;liH: Y= - 3 x 2 Ii Y= 3 x- 2.
7. Haii,lJ;HTe 3HaqeHHe a, rrpH KOTOpOM O,lJ;Ha H3 TOqeK
rrepeCeqeHHH rrapa60JIbI y = ax 2 H rrpHMoii y = 5x + 3 HMeeT
a6cD;Hccy x = 3.
CaMOCTOATenbHaA pa60Ta N2 31
65
Bapuaum M 3
1. Ha o,n;Hoii Koop,n;HHaTHoii rrJIOCKOCTH rrOCTpOHTb
rpacpHKH cpYHKD;Hii: y = 4x 2 H Y = -4x 2 . KaKaH H3 STHX
cpYHKD;Hii B03paCTaeT Ha rrpOMe:mYTKe x > O?
2. Haii,n;HTe KOscpcpHD;HeHT a, eCJIH rrapa60JIa y = ax 2
rrpoxo,n;HT qepe3 TOqKY A(5; -1).
3. C rrOMOW;blO rpacpHKa cpYHKD;HH Y = -3X2 pemHTe
HepaBeHCTBO: -6X2 > -6.
4. IIpH KaKHX x 3HaqeHHH cpYHKD;HH Y = 2X2 60JIbme 18?
5. IIpH KaKHX x 3HaqeHHH cpYHKD;HH y=5x 2 He 60JIb-
me 80?
6. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
1 1
«PYHKII;liH: Y= - 2 x 2 Ii Y=- 2 x-3.
7. Haii,n;HTe 3HaqeHHe a, rrpH KOTOpOM o,n;Ha H3 TOqeK
rrepeCeqeHHH rrapa60JIbI y = ax 2 H rrpHMoii y = 5x + 2 HMeeT
a6cD;Hccy x = 2.
Bapuaum M 4
1. Ha o,n;Hoii Koop,n;HHaTHoii rrJIOCKOCTH rrOCTpOHTb
rpacpHKH cpYHKD;Hii: y = 5x 2 H Y = -5x 2 . KaKaH H3 STHX
cpYHKD;Hii y6bIBaeT Ha rrpOMe:mYTKe x > O?
2. Haii,n;HTe KOscpcpHD;HeHT a, eCJIH rrapa60JIa y = ax 2
rrpoxo,n;HT qepe3 TOqKY A(4; 1).
3. C rrOMOW;blO rpacpHKa cpYHKD;HH y = -3X2 pemHTe
HepaBeHCTBO: -7 x 2 < -7.
4. II pH KaKHX x 3HaqeHHH cpYHKD;HH y = 3x 2 MeHbme 27?
5. IIpH KaKHX x 3HaqeHHH cpYHKD;HH Y = 5x 2 He MeHb-
me 80?
6. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rpacpHKoB
1 1
«PYHKII;liH: Y= - 3 x 2 Ii Y=- 3 x-2.
7. Haii,n;HTe 3HaqeHHe a, rrpH KOTOpOM o,n;Ha H3 TOqeK
rrepeCeqeHHH rrapa60JIbI Y = ax 2 H rrpHMoii y = 1 Ox - 3 HMeeT
a6cD;Hccy x = 3.
66
CaMOCTOATenbHaA pa60Ta N2 32
Bapuaum M 1
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI rrapa60JIbI
y=x 2 -6x-7.
2. IIpoxo,n;HT JIH OCb CHMMeTpHH rrapa60JIbI y=x 2 -10x
'tIepe3 TO'tlKY A(-5; -8)?
3. Haii,n;HTe Koop,n;HHaTbI TO'tleK rrepeCe'tleHHH rrapa60JIbI
y = _2X2 + 3x - 1 C OCHMH Koop,n;HHaT.
4. HanHmHTe ypaBHeHHe rrapa60JIbI, eCJIH H3BeCTHO, 'tITO
rrapa60JIa rrpoxo,n;HT 'tIepe3 TO'tlKY (-1; 6), a ee BepmHHoii
HBJIHeTCH TO'tlKa (1; 2).
5. IIpHHMJIe:>KHT JIH TO'tlKa (1; -9) rrapa60JIe
y=-5x 2 +3x-7?
6. 3arrHmHTe ypaBHeHHe rrapa60JIbI, rrOJIyqeHHoii H3 rra-
pa60JIbI y = 3x 2 c,n;BHrOM B,n;OJIb OCH OX Ha 5 e,n;HHHD;
BrrpaBO.
7. 3arrHmHTe ypaBHeHHe rrapa60JIbI, rrOJIyqeHHoii H3 rra-
pa60JIbI y=4x 2 c,n;BHrOM B,n;OJIb OCH Oy Ha 7 e,n;HHHD; BBepx.
Bapuaum M 2
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI rrapa60JIbI
y=x 2 -4x+ 5.
2. IIpoxo,n;HT JIH OCb CHMMeTpHH rrapa60JIbI y = x 2 - 8x
'tIepe3 TO'tlKY A(4; -9)?
3. Haii,n;HTe Koop,n;HHaTbI TO'tleK rrepeCe'tleHHH rrapa60JIbI
y = 2X2 - 3x - 2 C OCHMH Koop,n;HHaT.
4. HarrHmHTe ypaBHeHHe rrapa60JIbI, eCJIH H3BeCTHO, 'tITO
rrapa60JIa rrpoxo,n;HT 'tIepe3 TO'tlKY (-1; 8), a ee BepmHHoii
HBJIHeTCH TO'tlKa (2; -1).
5. IIpHHa,n;JIe:>KHT JIH TO'tlKa (-1; -10) rrapa60JIe
y=-4x 2 +5x-9?
6. 3arrHmHTe ypaBHeHHe rrapa60JIbI, rrOJIyqeHHoii H3 rra-
pa60JIbI y = 5x 2 c,n;BHrOM B,n;OJIb OCH OX Ha 3 e,n;HHHD;bI
BJIeBO.
7. 3arrHmHTe ypaBHeHHe rrapa60JIbI,_rrOJIyqeHHoii H3 rra-
pa60JIbI y = 7 x 2 c,n;BHrOM B,n;OJIb OCH Oy Ha 2 e,n;HHHD;bI BHH3.
CaMOCTOATenbHaA pa60Ta N2 32
67
Bapuaum M 3
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI rrapa60JIbI
y=x 2 -6x-5.
2. IIpoxo,n;HT JIH OCb CHMMeTpHH rrapa60JIbI y = x 2 - 4x
qepe3 TOQKY A( -4; -I)?
3. Haii,n;HTe Koop,n;HHaTbI TO'tleK rrepeCeQeHHH rrapa60JIbI
y=-2x 2 -x+3 C OCHMH Koop,n;HHaT.
4. HanHmHTe ypaBHeHHe rrapa60JIbI, eCJIH H3BeCTHO, 'tITO
rrapa60JIa rrpoxo,n;HT 'tIepe3 TO'tlKY (-1; 0), a ee BepmHHoii
HBJIHeTCH TO'tlKa (1; -4).
5. IIpHHa,ltJIe:>KHT JIH TO'tlKa (1; -2) rrapa60JIe
y=-6x 2 + 5x-l?
6. 3arrHmHTe ypaBHeHHe rrapa60JIbI, rrOJIyqeHHoii H3 rra-
pa60JIbI y = 4x 2 c,n;BHrOM B,n;OJIb OCH OX Ha 2 e,n;HHHD;bI
BrrpaBO.
7. 3arrHmHTe ypaBHeHHe rrapa60JIbI, rrOJIyqeHHoii H3 rra-
pa60JIbI y = 3x 2 c,n;BHrOM B,n;OJIb OCH Oy Ha 8 e,n;HHHD; BBepx.
Bapuaum M 4
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI rrapa60JIbI
y=x 2 -4x+ 3.
2. IIpoxo,n;HT JIH OCb CHMMeTpHH rrapa60JIbI y = x 2 - 6x
Qepe3 TO'tlKY A(3; -12)?
3. Haii,n;HTe Koop,n;HHaTbI TO'tleK rrepeCe'tleHHH rrapa60JIbI
y = 2X2 + 5x + 3 C OCHMH Koop,n;HHaT.
4. HarrHmHTe ypaBHeHHe rrapa60JIbI, eCJIH H3BeCTHO, 'tITO
rrapa60JIa rrpoxo,n;HT 'tIepe3 TO'tlKY (-1; 2), a ee BepmHHoii
HBJIHeTCH TO'tlKa (2; -7).
5. IIpHHMJIe:>KHT JIH TO'tlKa (-1; -12) rrapa60JIe
y=-3x 2 +8x-2?
6. 3arrHmHTe ypaBHeHHe rrapa60JIbI, rrOJIyqeHHoii H3 rra-
pa60JIbI y = 6x 2 c,n;BHrOM B,n;OJIb OCH OX Ha 4 e,n;HHHD;bI
BJIeBO.
7. 3arrHmHTe ypaBHeHHe rrapa60JIbI, rrOJIyqeHHoii H3 rra-
pa60JIbI y = 5x 2 c,n;BHrOM B,n;OJIb OCH Oy Ha 6 e,n;HHHD; BHH3.
68
CaMOCTOATenbHaA pa60Ta N2 33
Bapuaum M 1
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI napa60JIbI
y=x 2 +8x-6.
2. Haii,n;HTe Koop,n;HHaTbI TOqeK nepeCeqeHHH napa60JIbI
y=-2x 2 -8x+ 10 C OCHMH Koop,n;HHaT.
3. IIocTpoHTb rpacpHK cpYHKD;HH Y = -3X2 - 6x - 4 H
no rpacpHKY BbIHCHHTb, npH KaKOM 3HaqeHHH x cpYHKD;HH
npHHHMaeT HaH60JIbmee 3HaqeHHe.
4. He CTpOH rpacpHK, onpe,n;eJIHTb, npH KaKOM 3Haqe-
HHH x cpYHKD;HH Y = x 2 - 2x - 4 npHHHMaeT HaHMeHbmee
3HaqeHHe. Ha30BHTe 3TO HaHMeHbmee 3HaqeHHe.
5. qHCJIO 16 npe,n;CTaBHTb B BH,n;e CYMMbI ,n;BYX qHCeJI
TaR, qTo6bI npOH3Be,n;eHHe 3THX qHCeJI 6bIJIO HaH6oJIbmHM.
6. IIepHMeTp npHMoyrOJIbHHKa paBeH 60 CM. Ha30BHTe
HaH6oJIbmyIO B03MO:>KHYIO nJIOw;a,n;b 3Toro npHMoyrOJIb-
HHKa.
7. Haii,n;HTe 3HaqeHHH p H q, eCJIH napa60JIa Y = x 2 + px + q
nepeceKaeT OCb a6cD;Hcc B TOqKe x = 1 H OCb op,n;HHaT
B TOqKe y=3.
Bapuaum M 2
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI napa60JIbI
y=x 2 -6x+4.
2. Haii,n;HTe Koop,n;HHaTbI TOqeK nepeCeqeHHH napa60JIbI
y = -8X2 - 2x + 1 C OCHMH Koop,n;HHaT.
3. IIocTpoHTb rpacpHK cpYHKD;HH Y = -3X2 + 12x - 4 H
no rpacpHKY BbIHCHHTb, npH KaKOM 3HaqeHHH x cpYHKD;HH
npHHHMaeT HaH60JIbmee 3HaqeHHe.
4. He CTpOH rpacpHK, onpe,n;eJIHTb, npH KaKOM 3Haqe-
HHH x cpYHKD;HH Y = x 2 - 4x - 3 npHHHMaeT HaHMeHbmee
3HaqeHHe. Ha30BHTe 3TO HaHMeHbmee 3HaqeHHe.
5. qHCJIO 14 npe,n;CTaBHTb B BH,n;e CYMMbI ,n;BYX qHCeJI
TaK, qTo6bI npOH3Be,n;eHHe 3THX qHCeJI 6bIJIO H8.H6oJIbmHM.
6. IIepHMeTp npHMoyrOJIbHHKa paBeH 40 CM. Ha30BHTe
HaH6oJIbmyIO B03MO:>KHYIO nJIOw;a,n;b 3Toro npHMoyrOJIb-
HHKa.
7. Haii,n;HTe 3HaqeHHH p H q, eCJIH napa60JIa Y = x 2 + px + q
nepeceKaeT OCb a6cD;Hcc B TOqKe x = 1 H OCb op,n;HHaT
B TOqKe y=-5.
CaMOCTOATenbHaA pa60Ta N2 33
69
Bapuaum M 3
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI rrapa60JIbI
y=x 2 +4x- 5.
2. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rrapa60JIbI
y = -5X2 - 3x + 2 C OCHMH Koop,n;HHaT.
3. IIocTpoHTb rpacpHK cpYHKD;HH Y = -4X2 - 8x + 7 H
no rpacpHKY BbIHCHHTb, rrpH KaKOM 3HaqeHHH x cpYHKD;HH
npHHHMaeT HaH60JIbmee 3HaqeHHe.
4. He CTpOH rpacpHK, orrpe,n;eJIHTb, rrpH KaKOM 3Haqe-
HHH x cpYHKD;HH Y = x 2 - 8x + 5 rrpHHHMaeT HaHMeHbmee
3HaqeHHe. Ha30BHTe 3TO HaHMeHbmee 3HaqeHHe.
5. qHCJIO 20 rrpe,n;CTaBHTb B BH,n;e CYMMbI ,n;BYX qHCeJI
TaK, qTo6bI rrpOH3Be,n;eHHe 3THX qHCeJI 6bIJIO HaH6oJIbmHM.
6. IIepHMeTp rrpHMoyrOJIbHHKa paBeH 44 CM. Ha30BHTe
HaH6oJIbmyIO B03MO:>KHYIO rrJIOW;Mb 3Toro rrpHMoyrOJIb-
HHKa.
7. Haii,n;HTe 3HaqeHHH p H q, eCJIH rrapa60JIa Y = x 2 + px + q
rrepeceKaeT OCb a6cD;Hcc B TOqKe x = 1 H OCb op,n;HHaT
B TOqKe y=4.
Bapuaum M 4
1. Haii,n;HTe Koop,n;HHaTbI BepmHHbI rrapa60JIbI
y=x 2 -l0x+3.
2. Haii,n;HTe Koop,n;HHaTbI TOqeK rrepeCeqeHHH rrapa60JIbI
y=-2x 2 +5x-2 C OCHMH Koop,n;HHaT.
3. IIocTpoHTb rpacpHK cpYHKD;HH y=-4x 2 + 16x-9 H
rro rpacpHKY BbIHCHHTb, rrpH KaKOM 3HaqeHHH x cpYHKD;HH
rrpHHHMaeT HaH60JIbmee 3HaqeHHe.
4. He CTpOH rpacpHK, orrpe,n;eJIHTb, rrpH KaKOM 3Haqe-
HHH x cpYHKD;HH y = x 2 - 6x + 4 rrpHHHMaeT HaHMeHbmee
3HaqeHHe. Ha30BHTe 3TO HaHMeHbmee 3HaqeHHe.
5. qHCJIO 18 rrpe,n;CTaBHTb B BH,n;e CYMMbI ,n;BYX qHCeJI
TaK, qTo6bI rrpOH3Be,n;eHHe 3THX qHCeJI 6bIJIO HaH6oJIbmHM.
6. IIepHMeTp rrpHMoyrOJIbHHKa paBeH 48 CM. Ha30BHTe
HaH6oJIbmyIO B03MO:>KHYIO rrJIOw;a,n;b 3Toro rrpHMoyrOJIb-
HHKa.
7. Haii,n;HTe 3HaqeHHH p H q, eCJIH rrapa60JIa y = x 2 + px + q
rrepeceKaeT OCb a6cD;Hcc B TOqKe x = 1 H OCb op,n;HHaT
B TOqKe y=-6.
70
CaMOCTOATenbHaA pa60Ta N2 34
Bapuaum M 1
1. PemHTe HepaBeHCTBO: (x -1)(x - 5) > O.
2. PemHTe HepaBeHCTBO: (x+2)(x-4)<0.
3. PemHTe HepaBeHCTBO: x 2 - 9 > O.
4. PemHTe HepaBeHCTBO: x 2 +6x<0.
5. PemHTe HepaBeHCTBO: x 2 +2x-3>0.
6. PemHTe HepaBeHCTBO: 3x 2 + 2x -1 < O.
7. PemHTe HepaBeHCTBO: (x-l)(x+3»5.
Bapuaum M 2
1. PemHTe HepaBeHCTBO: (x-3)(x-4)<0.
2. PemHTe HepaBeHCTBO: (x- 2)(x+ 1» O.
3. PemHTe HepaBeHCTBO: x 2 -16<0.
4. PemHTe HepaBeHCTBO: x 2 +8x>0.
5. PemHTe HepaBeHCTBO: x 2 + 4x - 5 < O.
6. PemHTe HepaBeHCTBO: 3x 2 -2x-l>0.
7. PemHTe HepaBeHCTBO: (x+2)(x+4)<8.
CaMOCTOATenbHaA pa60Ta N2 34
71
Bapuaum M 3
1. PemHTe HepaBeHCTBO: (x-2)(x-6»0.
2. PemHTe HepaBeHCTBO: (x+3)(x-5)<0.
3. PemHTe HepaBeHCTBO: x 2 - 25 > O.
4. PemHTe HepaBeHCTBO: x 2 +9x<0.
5. PemHTe HepaBeHCTBO: x 2 -3x+2>0.
6. PemHTe HepaBeHCTBO: 3x 2 -5x-2<0.
7. PemHTe HepaBeHCTBO: (x-3)(x+2»-4.
Bapuaum M 4
1. PemHTe HepaBeHCTBO: (x-4)(x-5)<0.
2. PemHTe HepaBeHCTBO: (x-3)(x+l»0.
3. PemHTe HepaBeHCTBO: x 2 - 4 < O.
4. PemHTe HepaBeHCTBO: x 2 + 7 x> o.
5. PemHTe HepaBeHCTBO: x 2 -5x+4<0.
6. PemHTe HepaBeHCTBO: 3x 2 -2x-5>0.
7. PemHTe HepaBeHCTBO: (x+l)(x+9)<9.
72
CaMOCTOATenbHaA pa60Ta N2 35
Bapuaum M 1
1. PemHTe HepaBeHCTBO: x 2 - 3x + 2 < 0.
2. PemHTe HepaBeHCTBO: x 2 -3x-4 > 0.
3. PemHTe HepaBeHCTBO: x 2 -6x+9<0.
4. PemHTe HepaBeHCTBO: x 2 +10x+25 < 0.
5. PemHTe HepaBeHCTBO: x 2 - 14x + 49 > O.
6. PemHTe HepaBeHCTBO: 4x 2 -20x+25 > 0.
7. PemHTe HepaBeHCTBO: -x 2 +x-l<0.
Bapuaum M 2
1. PemHTe HepaBeHCTBO: x 2 -5x+4 > 0.
2. PemHTe HepaBeHCTBO: x 2 -2x-3 < 0.
3. PemHTe HepaBeHCTBO: x 2 -4x+4 < 0.
4. PemHTe HepaBeHCTBO: x 2 + 6x + 9 < o.
5. PemHTe HepaBeHCTBO: x 2 +10x+25>0.
6. PemHTe HepaBeHCTBO: 9x 2 -24x+16 > 0.
7. PemHTe HepaBeHCTBO: -x 2 +2x-3>0.
CaMOCTOATenbHaA pa60Ta N2 35
73
Bapuaum M 3
1. PemHTe HepaBeHCTBO: x 2 -4x+3 < 0.
2. PemHTe HepaBeHCTBO: x 2 -6x-7 > 0.
3. PemHTe HepaBeHCTBO: x 2 - 8x + 16 < O.
4. PemHTe HepaBeHCTBO: x 2 +14x+49 < 0.
5. PemHTe HepaBeHCTBO: x 2 -6x+9>0.
6. PemHTe HepaBeHCTBO: 25x 2 -20x+4 > 0.
7. PemHTe HepaBeHCTBO: -x 2 +2x-5<0.
Bapuaum M 4
1. PemHTe HepaBeHCTBO: x 2 -6x+5 > 0.
2. PemHTe HepaBeHCTBO: x 2 -7x-8 < 0.
3. PemHTe HepaBeHCTBO: x 2 -10x+25 < 0.
4. PemHTe HepaBeHCTBO: x 2 + 12x + 36 < o.
5. PemHTe HepaBeHCTBO: x 2 +4x+4>0.
6. PemHTe HepaBeHCTBO: 16x 2 -24x+9 > 0.
7. PemHTe HepaBeHCTBO: -x 2 +3x-4>0.
74
CaMOCTOATenbHaA pa60Ta N2 36
Bapuaum M 1
1. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x+3)(x-4»0.
2. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x-2)(x+5)<0.
3. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 - 7 x > O.
4. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x 2 -1)(x + 6) < o.
5. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 3 -9x > 0.
6. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x - 5)(x + 2)(x 2 - 4) < 0.
7. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 -3x-4
2 > 0.
x +x-6
Bapuaum M 2
1. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x+2)(x-3)<0.
2. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x-l)(x+7»0.
3. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 +5x<0.
4. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x 2 -1)(x-8»0.
5. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 3 -16x > 0.
6. PemHTe MeTO,l];OM HHTepBaJIOB HepaBeHCTBO:
(x -7)(x + 3)(x 2 - 9) < 0.
7. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 - x - 2
2 < 0.
x + 2x - 3
CaMOCTOATenbHaA pa60Ta N2 36
75
Bapuaum M 3
1. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x+4)(x-2»0.
2. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x-6)(x+l)<0.
3. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 - 3x> O.
4. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x 2 -4)(x + 7) < O.
5. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 3 -25x > 0.
6. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x - 8)(x + 4)(x 2 -16) < O.
7. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 -4x-5
> O.
x 2 + x - 2
Bapuaum M 4
1. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x+l)(x-6)<0.
2. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x-4)(x+3»0.
3. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 + 8x < O.
4. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x 2 -4)(x-5»0.
5. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 3 -36x > 0.
6. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
(x - 2)(x + 1)(x 2 -1) < 0.
7. PemHTe MeTO,lJ;OM HHTepBaJIOB HepaBeHCTBO:
x 2 -2x-3
2 < 0.
x - 2x - 8
76
OTBeTbl
CaMOCTOJlTeJILHaJl pa60Ta eM 1
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 432 -400 -432 400
2 OTpHn;a TeJIb- IIoJIomHTeJIb- OTpHn;aTeJIb- IIoJIomHTeJIb-
HO HO HO HO
3 IIoJIomHTeJIb- OTpHn;aTeJIb- IIoJIomHTeJIb- OTpHn;a TeJIb-
HO HO HO HO
4 1 1 1 1
2 5. -- --. 3 5 1 5. -- --. 4 5
" 3 7' , " 9 6' ,
5 3;-3 4;-4 5;-5 2;-2
6 0 0 0 0
7 KopHeH HeT KopHeH HeT KopHeH HeT KopHeH HeT
CaMOCTOJlTeJILHaJl pa60Ta eM 2
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 1 1 1 1
- >0,16 7 >0,14 6 <0,17 7 <0,15
6
2 b<a b>a b<a b>a
3 .l];a HeT HeT .l];a
4 ,lJ;a .l];a .l];a .l];a
5 .l];a .l];a HeT HeT
6 0; 5 0;-7 0;6 0;-3
7 15 15 20 10
OTBeTbl
77
CaMOCTOJlTeJILHaJl pa60Ta eM 3
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 ,lJ;a ,lJ;a ,lJ;a ,lJ;a
2 IIoJIomHTeJIb- IIoJIomHTeJIb- IIoJIomHTeJIb- IIoJIomHTeJIb-
Hoe Hoe Hoe Hoe
3 b - 3c + 7 a-4+7c b - 2c + 6 a - 5+4c
4 -3(b+6) -2(b+3) -4(b-5) -7(b-1)
5 HeT ,lJ;a HeT ,lJ;a
6 ,lJ;a ,lJ;a ,lJ;a ,lJ;a
7 ,lJ;a HeT ,lJ;a HeT
CaMOCTOJlTeJILHaJl pa60Ta eM 4
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 ,lJ;a HeT ,lJ;a HeT
2 HeT ,lJ;a HeT ,lJ;a
3 5x+4y< 18 3x+6y< 19 11x+8y< 14 5x+ 12y< 11
4 ,lJ;a ,lJ;a ,lJ;a ,lJ;a
5 HeT ,lJ;a HeT ,lJ;a
b-4; b-1; b+4; b+1; b-8; b- 2; b+5; b+3;
6 b;a;a+3; b; a; a-3; b; a; a + 4; b; a; a - 2;
a+7 a-8 a+9 a-9
7 ,lJ;a ,lJ;a ,lJ;a ,lJ;a
78
OTBeTbl
CaMOCTOJlTeJILHaJl pa60Ta M 5
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 -5 -3 -8 -6
2 -5 -4 -2 -2
3 -1 0 -1 0
4 .l];a .l];a .l];a .l];a
5 .l];a .l];a .l];a .l];a
6 .l];a HeT .l];a HeT
7 HeT .l];a .l];a HeT
CaMOCTOJlTeJILHaJl pa60Ta M 6
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 3(x-5» 19 2(x+4)<20 2(x-3» 18 3(x+2)<15
2 2x + 5
2 . 2x 3x + 2
3 . 3x . 2 5x + 3
2 . 5x 4x + 3
3 . 4x . 3
2 5 2 2 3 2
3 12 -2 10 -3
4 13 -4 14 -5
5 y>O y<O y>O y<O
6 -3 y - JII060e -4 y - JII060e
7 y - JII060e 12 y - JII060e 13
OTBeTbl
79
CaMOCTOSTeJILHaS pa60Ta M 7
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 x>0,4 x>-0,75 x>0,6 x>-0,25
2 x> 1,5 x>3,5 x<-3 x<-4
3 0 -1 0 -1
2 7
4 x>- x<-3,2 x>-- x<-1,9
21 29
5 x O x O x O x O
6 4 CM 6 CM 7 CM 8 CM
7 11 12 13 10
CaMOCTOSTeJILHaJl pa60Ta M 8
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 -2 -1 -4 -7
2 HeT TaKHX HeT TaKHX HeT TaKHX HeT TaKHX
qHCeJI qHCeJI qHCeJI qHCeJI
3 .l];a .l];a .l];a .l];a
4 .l];a HeT .l];a HeT
5 5 x> 1,5 4 x> 2,5
x>- x>-
3 3
6 1 x<-0,5 1 x<-0,5
x<-- x<--
3 3
4 M; 5 M; 6 M; 7 M; 5 M; 6 M; 3 M; 4 M;
7 6 M; 7 M; 8 M 8 M; 9 M 7 M; 8 M; 9 M 5 M; 6 M;
7 M; 8 M
80
OTBeTbl
CaMOCTOJlTeJILHaJl pa60Ta M 9
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 -5<x<-3 -3<x<-2 -6<x<-4 -5<x<-4
2 x>O x<O x>O x<O
3 x>-0,5 x>-1 x>2 1
x>--
3
4 PemeHHH HeT PemeHHH HeT PemeHHH HeT PemeHHH HeT
5 4 6 6 3
6 x 2 x 6 x 3 x 3
7 PemeHHH HeT -5<x<2 PemeHHH HeT -6 < x < 1
CaMOCTOJlTeJILHaJl pa60Ta eM 10
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 5; 2 5;4 4; 1 6; 1
2 PemeHHH HeT PemeHHH HeT PemeHHH HeT PemeHHH HeT
3 x 5 x 4 x 3 x 2
4 -5 x -2 -3 x -2 -2 x -1 -7 x -2
4
7 x< -. x<0,8; x< 1,4;
5 3 '
x<1.x>-
, 3 10 x> 1,6 x> 1,8
x>-
3
6 PemeHHH HeT PemeHHH HeT PemeHHH HeT PemeHHH HeT
7 .l];a HeT .l];a HeT
OTBeTbl
81
CaMOCTOSTeJILBaS pa60Ta M 11
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 3 1 1 5
- - - -
14 18 14 18
1 1 8 3
2 - - - -
36 350 225 175
3 0,053 0,038 0,042 0,026
4 1 1 1 1
- - - -
8 7 9 6
5 .l];a .l];a .l];a .l];a
6 5,66<x<5,68 4,37<x<4,39 3,83 < x < 3,85 2,62<x<2,64
7 6,5 -3,5 4,5 -5,5
CaMOCTOSTeJILBaS pa60Ta M 12
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 12,5 13,5 14,5 15,5
2 .l];a .l];a .l];a .l];a
3 HeT HeT HeT HeT
4 3M 2M 1M 4M
5 24 25 23 26
6 .l];a HeT .l];a HeT
7 1 2 3 4
82
OTBeTbl
CaMOCTOSTeJILBaS pa60Ta M 13
Ba pHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 265 317 494 528
2 138,5 125,4 109,5 117,3
3 0,26 0,29 0,16 0,18
4 2,273 3,364 1,455 4,182
5 50 KM/q 45 KM/q 53 KM/q 46 KM/q
6 -25 -15 -49 -37
7 2
x
3 -2
x
1 -1
x
4 -2
x
-1
CaMOCTOSTeJILBaS pa60Ta M 14
BapHaBT 1 BapHaBT 2 BapHaBT 3 Ba pHaBT 4
1 0,15 0,26 0,29 0,38
2 140/0 9°1o 120/0 6°1o
3 1 1 1 1
-
20/0 -
10/0 -
1°/0 -
10/0
49 99 99 99
4 0,0265 0,00138 0,00543 0,000123
5 -2<x<5 -3 < x < 1 -2<x<3 -3 < x < 4
6 -3 < x < 4 2<x<3 -7<x<3 4<x<5
7 x>8; x<2 x>-4; x<-8 x>9; x<-3 x>-3;
x<-11
OTBeTbl
83
CaMOCTOSTeJILBaS pa60Ta M 15
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 3,7056.10 4 4,815.10 3 5,3082.10 4 6,394.10 3
2 5,39.10- 5 6,27.10- 6 7,45.10- 5 4,82.10- 6
3 1,3608 2,834 4,8261 3,956
4 -4 -3 -4 -3
5 -2<x<2 -1<x<3 -4 < x < 1 -1<x<5
6 PemeHHH PemeHHH PemeHHH PemeHHH
HeT HeT HeT HeT
7 x
-5;x
9 x
-5; x
7 x
-2;x
8 x
-4;x
12
CaMOCTOSTeJILBaS pa60Ta M 16
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 12 13 15 11
2 0,3 0,5 0,2 0,4
3 .l];a HeT .l];a HeT
4 1 0,3 1 0,5
5 0 0 0 0
6 a
1,5 a
2,5 a
4,5 a
3,5
7 64 81 49 121
84
OTBeTbl
CaMOCTOSTeJILHaS pa60Ta M 17
BapHaHT 1 Ba pHaHT 2 BapHaHT 3 Ba pHaHT 4
1 0,(6) 0,(2) 0,(3) 0,(1)
2 -4,(09) -1,(27) -3,(18) -2,(36)
5 4 2 7
3 - - - -
9 9 9 9
4 7 1 11 2
-1- -2- -4- -5-
30 6 30 15
5 0,32 < 0,3(2) 0,78 <0,(78) 0,59 < 0,5(9) 0,14 <0,(14)
6 -1,0(25) < -2,03(7) < -4,0(17)< -3,06(8) <
-1,025 -2,037 -4,017 -3,068
7 9 9 4 4
- - - -
16 25 9 25
CaMOCTOSTeJILHaS pa60Ta M 18
Ba pHaHT 1 BapHaHT 2 Ba pHaHT 3 BapHaHT 4
1 3 5 4 6
2 16 64 81 125
3 4-J5 6-J7 2-J3 J2-1
4 12; 13 11; 12 13; 14 10; 11
5 .l];a HeT .l];a HeT
6 x 6 x 5 x 4 x 7
7 1,24 1,33 1,44 1,53
OTBeTbl
85
CaMOCTOSTeJILBaS pa60Ta M 19
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 42 11 56 14
2 117 300 270 56
3 2 45 < 4 20 3 80 < 5 45 3 45 < 5 20 4 80 < 6 45
4 1 34 22 -18
5 8J5 6J5 -20J3 31J3
6 5- 8+Jb 4- 6+Jb
7 .l];a HeT .l];a HeT
CaMOCTOSTeJILBaS pa60Ta M 20
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 5 9 7 12
- - - -
36 77 36 77
2 18 2 10 20
3 35 1 14 32
- 7- 7- -
51 3 15 33
4 6 - 35 4+Ji5 11-2 30 15+2 56
5 -1 -2 2 1
6 +Jb - -Jb +
7 B6pa3 B5pa3 B 3 pa3a B5pa3
86
OTBeTbl
CaMOCTOSTeJILBaS pa60Ta M 21
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 11; -11 12;-12 13; -13 10;-10
2 KopHeR HeT KopHeR HeT KopHeR HeT KopHeR HeT
3 2 -5 3 -4
4 0;-5 0;6 0;-8 0; 7
5 0,5; -0,5 KopHeR HeT 1 1 KopHeR HeT
-. --
3 ' 3
6 HeT .l];a HeT .l];a
7 -1;-2 1; 2 -1;-4 1; 4
CaMOCTOSTeJILBaS pa60Ta M 22
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 0 0 0 0
2 4;-4 5;-5 3;-3 6;-6
3 KopHeR HeT KopHeR HeT KopHeR HeT KopHeR HeT
4 0;3 0;-7 0;4 0;-5
5 8;-8 6;-6 5;-5 7;-7
6 0; 3 0; 2 2;-2 3;-3
7 -3 4 -6 5
OTBeTbl
87
CaMOCTOSTeJILBaS pa60Ta M 23
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 2;-6 3; 5 2;-8 3; 6
2 8; 2 -2;-7 5;4 -2;-8
3 5;-2 4;-3 3;-6 5;-6
4 1- -2 5 1 2 0,6; -0,2 2; -0,6
-1-. -
, , 3 ' 3
5 0; 4,2 3 0; 4,2 3
0.2- 0.2-
, 19 ' 19
6 3;-3 2;-2 3;-3 2;-2
7 0 0 0 0
CaMOCTOSTeJILBaS pa60Ta M 24
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 -1; -0,5 1; 0,5 -0,5; -2 0,5; -3
2 3; 0,5 4; -0,5 1 1; -0,5
1. -1-
, 3
3 1 2 0,5; 0,25 0,5; -1,5
-. -1 2. --
3 ' , 5
4 0,25 1 -0,2 1
- --
3 6
5 2 0 2 0
6 0 2 0 2
7 7; -11 1; -3,5 1 1
-. -0 5 -. -4
3 ' , 3 '
88
OTBeTbl
CaMOCTOSTeJILBaS pa60Ta M 25
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 4;-10 7;-1 1;-5 9;-1
2 3;4 -2;-3 3; 5 1; 5
3 (x+7)(x-6) (x+8)(x-3) (x- 2)(x- 3) (x-3)(x-4)
4 x(x+2)(x-11) x(x-1)(x-2) x(x+ 7)(x-3) x(x+6)(x-2)
x+7 x-9 x+3 x+3
5 x-6 x+8 x+2 x+4
6 -x -x x x
(x + 3)2 (X + 4)2 (x - 3)2 (X - 4)2
8 3 5,5 2
7 -- -- 1-
15 5 3
CaMOCTOSTeJILBaS pa60Ta M 26
BapHaHT 1 BapHaHT 2 BapHaBT 3 BapHaHT 4
1 + 1; + 3 + 1; + 2 + 2; + 3 + 1; + 7
2 + 2 + 1 + 2 + 1
3 + 1 KopHeH HeT + 1 KopHeH HeT
4 KopHeH HeT + 1 KopHeH HeT + 1
5 8;-3 40;-20 8;-3 40; -20
6 -3 3 -4 4
7 HeT ,lJ;a HeT ,lJ;a
OTBeTbl
89
CaMOCTOSTeJILBaS pa60Ta M 27
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 14; 15 15; 16 12; 13 13; 14
2 40 CM 20 CM 50 CM 30 CM
3 100 KM/q 90 KM/q 80 KM/q 120 KM/q
4 7; -2,5 1; -1,5 2,5; -1 -3; 0,5
5 + 1 :f:2 KopHeH HeT KopHeH HeT
6 1 -0,5 0,5 1
-- --
3 3
7 x+3 x-2 x+2 x-3
x+2 x-3 x-2 x+2
CaMOCTOSTeJILBaS pa60Ta M 28
BapHaBT 1 BapHaBT 2 BapHaBT 3 BapHaBT 4
1 (2; -1); (-5; 3); (4; 1); (7; -5);
(-1; 2) (3; -1) ( -1; -4) (-4; 6)
2 (2; 3); ( 1; 7); (11; 1); (-2; -5);
(3; 2) (7; 1) (1; 11) (-5; -2)
3 (3; -2) (4; -1) (5; -1) (3; 1)
4 4 4 4 4
5 40 53 29 208
6 12 CM 6 CM 14 CM 5 CM
7 15 KM/q 12 KM/q 18 KM/q 9 KM/q
90
OTBeTbl
CaMOCTOSTeJILBaS pa60Ta M 29
BapHaBT 1 BapHaBT 2 BapHaBT 3 Ba pHaBT 4
1 0; 1 0;-1 0; 1 0;-1
2 0;-7 0;8 0;-3 0;4
3 HYJIeH HeT HYJIeH HeT HYJIeH HeT HYJIeH HeT
2
4 -. 0 5 -1; 2,5 0,5; -2 0,5; -4
3' ,
5 b=3;c=-4 b=2; c=-8 b=-2; c=-3 b=1; c=-6
6 + 2 + 3 + 2 + 3
7 (0; -4); (0; 5); (0; -3); (0; 7);
(2; 0) (3; 14) (4; 13) (5; 32)
CaMOCTOSTeJILBaS pa60Ta M 30
Ba pHaBT 1 BapHaBT 2 Ba pHaBT 3 BapHaBT 4
1 HeT ,lJ;a HeT ,lJ;a
2 (5; 15) (-4; 12) (4; 13) (-6; 11)
3 (3; 9); (4; 16); (5; 25); (2; 4);
(-3; 9) (-4; 16) (-5; 25) (-2; 4)
4 ,lJ;a HeT ,lJ;a HeT
5 HeT ,lJ;a HeT ,lJ;a
6 -2<x<2 x<-2; x>2 -3 < x < 3 x<-3; x>3
7 x -4;x 4 -1 x 1 x -6; x 6 -5 x 5
OTBeTbl
91
CaMOCTOSTeJILHaS pa60Ta M 31
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 y = 2X2 Y = -3X2 Y = 4X2 y=-5x 2
1 1
2 -- 0,25 -0,04 -
9 16
3 -1 x 1 x -1;x 1 -1 x 1 x -1; x 1
4 x<-2; x>2 -2<x<2 x<-3; x>3 -3<x<3
5 -5 x 5 x -5; x 5 -4 x 4 x -4;x 4
(-3; -4,5); (-3; -3); (3; -4,5); (3; -3);
6 (2; -2) 4 (-2; -2) 4
(2; - 3 ) (-2; - 3 )
7 2 2 3 3
CaMOCTOSTeJILHaS pa60Ta M 32
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 (3; -16) (2; 1) (3; -14) (2; -1)
2 HeT .l];a HeT .l];a
(1; 0); (2; 0); (1; 0); (-1; 0);
3 (0,5; 0); (-0,5; 0); (-1,5; 0); (-1,5; 0);
(0; -1) (0; -2) (0; 3) (0; 3)
4 y=x 2 -2x+3 y=x 2 -4x+3 y=x 2 -2x-3 y=x 2 -4x-3
5 .l];a HeT .l];a HeT
6 y=3(x-5)2 y=5(x+3)2 Y = 4(x - 2)2 y=6(x+4)2
7 y=4x 2 + 7 y= 7x 2 - 2 y=3x 2 +8 y= 5X2-6
92
OTBeTbl
CaMOCTOSTeJILHaS pa60Ta M 33
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 (-4; -22) (3; -5) (-2; -9) (5; -22)
(1; 0); (-0,5; 0); (-1; 0); (2; 0);
2 (-5; 0); (0,25; 0); (0,4; 0); (0,5; 0);
(0; 10) (0; 1) (0; 2) (0; -2)
3 -1 2 -1 2
4 x= 1; y=-5 x=2; y= 7 x=4; y=-11 x=3; y=-5
5 16=8+8 14=7+7 20= 10+ 10 18=9+9
6 225 CM 2 100 CM 2 121 CM 2 144 CM 2
7 p=-4; q=3 p=4; q=-5 p=-5; q=4 p=5; q=-6
CaMOCTOSTeJILHaS pa60Ta M 34
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 x<1;x>5 3<x<4 x<2; x>6 4<x<5
2 -2<x<4 x<-1; x>2 -3 < x < 5 x<-1; x>3
3 x<-3; x>3 -4 < x < 4 x<-5; x>5 -2<x<2
4 -6 < x < 0 x<-8; x>O -9 < x < 0 x<-7; x>O
5 x<-3; x> 1 -5<x< 1 x<1;x>2 1<x<4
1 1 1 2
6 -1<x< - x<--.x>1 -- <x<2 x<-1. x>1-
3 3 ' 3 ' 3
7 x<-4; x>2 -6 < x < 0 x<-1; x>2 -10<x<0
OTBeTbl
93
CaMOCTOSTeJILHaS pa60Ta M 35
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 1 x 2 x 1;x 4 1 x 3 x 1;x 5
2 x -1;x 4 -1 x 3 x -1;x 7 -1 x 8
3 PemeHHH x=2 PemeHHH x=5
HeT HeT
4 x=-5 PemeHHH x=-7 PemeHHH
HeT HeT
5 x*7 x*-5 x*3 x*-2
x - JII060e x - JII060e x - JII060e x - JII060e
6 eHCTBHTeJIb- eHCTBHTeJIb- eHCTBHTeJIb- eHCTBHTeJIb-
Hoe qHCJIO Hoe qHCJIO Hoe qHCJIO Hoe qHCJIO
x - JII060e PemeHHH x - JII060e PemeHHH
7 eHCTBHTeJIb- HeT eHCTBHTeJIb- HeT
Hoe qHCJIO Hoe qHCJIO
CaMOCTOSTeJILHaS pa60Ta M 36
BapHaHT 1 BapHaHT 2 BapHaHT 3 BapHaHT 4
1 x<-3; x>4 -2<x<3 x<-4; x>2 -1<x<6
2 -5<x<2 x<-7; x> 1 -1<x<6 x<-3; x>4
3 x<O; x> 7 -5<x<O x<O; x>3 -8 < x < 0
4 x<-6; -1 <x< 1; x<-7; -2<x<2;
-1 <x< 1 x>8 -2<x<2 x>5
5 -3 x O; -4 x O; -5 x O; -6 x O;
x 3 x 4 x 5 x 6
6 x=-2; x=-3; x = -4; x=-1;
2 x 5 3 x 7 4 x 8 1 x 2
x<-3; -3 <x -1; x<-2; -2<x -1;
7 -1 x<2; 1<x 2 -1 x<1; 3 x<4
x 4 x 5
co,n:EPmAHHE
II pe
HCJIOBHe. . . . . . .. .... .... 3
CaMoCTOHTeJIbHaH pa60Ta N2 1 . . . . . . . . .. 4
CaMoCTOHTeJIbHaH pa60Ta N2 2 . . . . . . . . . . . . 6
CaMoCTOHTeJIbHaH pa60Ta N2 3 . . . . . . . . 8
CaMoCTOHTeJIbHaH pa60Ta N2 4. . . . . . . . . . . . 10
CaMoCTOHTeJIbHaH pa60Ta N2 5. . . . . . . . . . . . 12
CaMoCTOHTeJIbHaH pa60Ta N2 6. . . . . . . . 14
CaMoCTOHTeJIbHaH pa60Ta M 7. . . .. ..... 16
CaMoCTOHTeJIbHaH pa60Ta M 8. . . . . . . . . . . . 18
CaMoCTOHTeJIbHaH pa60Ta M 9.. ........ 20
CaMoCTOHTeJIbHaH pa60Ta N2 10 . . . . . . . 22
CaMoCTOHTeJIbHaH pa60Ta M 11 . . . . . 24
CaMoCTOHTeJIbHaH pa60Ta N2 12 . . . . . . . 26
CaMoCTOHTeJIbHaH pa60Ta N2 13 . . . . . . . . . . . 28
CaMoCTOHTeJIbHaH pa60Ta N2 14 . .. ... . 30
CaMoCTOHTeJIbHaH pa60Ta N2 15 . . . . . . . . . . . 32
CaMoCTOHTeJIbHaH pa60Ta N2 16 . . . .. .... 34
CaMoCTOHTeJIbHaH pa60Ta N2 1 7 . . . . . . . 36
CaMoCTOHTeJIbHaH pa60Ta N2 18 . . . .. 38
CaMoCTOHTeJIbHaH pa60Ta M 19 . . . . . . . 40
CaMoCTOHTeJIbHaH pa60Ta N2 20 . . . .. .... 42
CaMoCTOHTeJIbHaH pa60Ta N2 21 . . . . . . .. . 44
CaMoCTOHTeJIbHaH pa60Ta N2 22 ... .... 46
CaMoCTOHTeJIbHaH pa60Ta N2 23 . . . . . . . . . . . 48
CaMoCTOHTeJIbHaH pa60Ta N2 24 . . . . . . . 50
CaMoCTOHTeJIbHaH pa60Ta N2 25 ... .... 52
CaMoCTOHTeJIbHaH pa60Ta N2 26 . . . . . . . . . . . 54
CaMoCTOHTeJIbHaH pa60Ta N2 27. ........ 56
CaMoCTOHTeJIbHaH pa60Ta N2 28 . . . . . . . . . . . 58
CaMoCTOHTeJIbHaH pa60Ta N2 29 . . . . . . . 60
CaMoCTOHTeJIbHaH pa60Ta N2 30 . .. ... . 62
CaMoCTOHTeJIbHaH pa60Ta N2 31 . .. ... . 64
CaMoCTOHTeJIbHaH pa60Ta N2 32 . . .. ..... 66
CaMoCTOHTeJIbHaH pa60Ta N2 33 . . . . . . . . . . . 68
CaMoCTOHTeJIbHaH pa60Ta N2 34 . . . . . 70
CaMoCTOHTeJIbHaH pa60Ta N2 35 . . . . .. ... 72
CaMoCTOHTeJIbHaH pa60Ta N2 36 ......... 74
OTBeTbI. . . . . . . . . . . . . . .. .... 76
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