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EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF
1
DENKLEM VE EŞİTSİZLİKSİSTEMLERİ
İkinci Dereceden İki Bilinmeyenli Denklem Sistemleri • 2
İkinci Dereceden Bir Bilinmeyenli Eşitsizlikler - I • 10
İkinci Dereceden Bir Bilinmeyenli Eşitsizlikler - II • 17
İkinci Dereceden Bir Bilinmeyenli Eşitsizlikler - III • 23
İkinci Dereceden Bir Bilinmeyenli Eşitsizlikler - IV • 30
Karma Testler • 41
Yazılı Soruları • 45
Yeni Nesil Sorular • 47
4. MODÜL11. SINIF
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF
2 3. {(5, –2)} 4. {(–13, 19), (1, 5)} 5. 31. , , , , , , ,5 2 5 2 5 2 5 2- - - -a a a ak k k k% / 2. {(3, 1), (2, 2)}
4. MODÜL
11.4.1.1 :
ax2 + +2 + + + = 0
-
-
-
TANIM
ÖRNEK 1
3x2 - 2 = 11
x2 + 2= 9
ÖRNEK 2
x + = 4
= x2 - 6x + 10
-
ÖRNEK 3
x2 - 2 = 9
x - = 9
ÖRNEK 4
2 - 2x2 = 23
x + = 6
-
ÖRNEK 5
x2 + 2 = 19
x + = 5
-
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
3 9. 10. {(2, 1), (1, 2)} 11. 66. {(4, 2), (–4, –2), (2, 4), (–2, –4)}
7. {(2, 2), (2, –2), (–1, 7 ), (–1, – 7 )} 8. 3
ÖRNEK 6
x2 + 2 = 20
= 8
-
ÖRNEK 7
x2 + 2 = 8
x + 2 = 6
-
ÖRNEK 8
x2 - = 2
2 - = 7
-
ÖRNEK 9
x2 - 2 = 5
= 6
-
ÖRNEK 10
x2 + +2 = 7
x + = 3
-
ÖRNEK 11
x2+
2 - 10x + + 41 = 0
+ -
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
412. { ( 3, –5 ), ( –3, – 5 ) } 13. /1 5 2+^ h 14. 38 15. 12 16. 6 5
ÖRNEK 12
x2 + 2 + - 9 = 0
x2 + + 1 = 0
-
ÖRNEK 13
-
-
ÖRNEK 14
2 -
ÖRNEK 15
--
ÖRNEK 16
= x2
= 2x +
y y = 2x + 8y = x2
xO
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
5 20. –2 21. 17. {(1, 1)} 18. 19. 2
1
ÖRNEK 17
= x2 + x - 1
= -2x2 + 7x - 4
-
ÖRNEK 18
= x2 - 4x + a
= 2x - 3
- -
( 6, -
= {( 3, 3 )}
ÖRNEK 19
a
= x2 - 5x + 5
= -x2 + x + a
-
ÖRNEK 20
y
xO B
C–10
A–2
–25
-
ÖRNEK 21
= 2x2+ x + a
= x2+ 5x +
-
<
+ 4 <
=
EĞİTİ
ME AYDINLA
TAN DESTEK
61. E 2. 3. 4. E 5. 6. 7. 8. E
TEST - 11. 2x2 + 2 = 17
x2 - 2 = -5
-
A) { - -2 } C) { -3, -2 }
D) { 2 } E) { -2, 2 }
2. x + = 3
= x2 + x - 12
A) - -40 C) -24
D) -15 E) -10
3. x + = 7
x2 - 2 = 21
-
4. 4x2 - 2 = 91
2x - = 7
y
x
A) -5
1- C) -1 D)
5
1 E) 5
5. - x = 3
2 - x2 = 7
A) - -6 C) 6 D) 10 E) 12
6. x2 + 2 = 26
x - = 6
A) - -3 C) 3 D) 5 E) 10
7. x2 - = 72
+2 = 7
- -
A) - -8 C) 0 D) 6 E)8
8. x2 + 2 = 10
= 3
-
A) { ( 3, 1 )} { ( -3, -1 ), ( 3, 1 ) }
C) { ( -3, -17 } D) { ( 3, 1 ), ( 3, -1 ) }
E) { ( 3, 1 ), ( -3, -1 ), ( 1, 3 ), ( -1, -3 ) }
EĞİTİ
ME AYDINLA
TAN DESTEK
71. 2. D 3. 4. D 5. 6. 7. 8.
TEST - 21. x2 + 2 = 6
2 - 2x = 3
2. x2 - +2 = 17
2 - = 8
-
3.
x2 - = 0
- | x - 6 | = 0
-
A) - -6 C) 0 D) 6 E) 8
4. x2 - 2 = 15
= -4
A) { (4, 1 ) }
{ ( 4, -1 ), ( -4, 1 ) }
C) { ( -4, 1 ) }
D) { ( -4, 1 ), ( 4, - - - }
E) { ( -4, 1 ), ( 4, - - - }
5. x2 + +2 = 7
2x + = 5
-
A) -
6.
x2 + 2 - 4x + + 13 = 0
A) - -3 C) -2 D) 3 E) 6
7.
x2 - = 43
2- 21 =
- -
A) - -6 C) 4 D) 6 E) 16
8. 2x2 + 2 - + 2 = 0
x2 + + 4 = 0
EĞİTİ
ME AYDINLA
TAN DESTEK
81. 2. 3. 4. 5. E
TEST - 31. 2a2 + -
2 = 28
2a - = 4
+
2. = x2 - x - 6
= x - 2
-
y
xO
–6
–2 –1
A)
y
xO
–6
–2
–2
23
3
C)
y
xO
–6
–32
5
B)
y
xO
–6
–3
–2
2 3
D)
y
xO
–6
–22
3
E)
3. = x2 - x + 5
= 3x + a
A) -
4. = x2 + 2x - 3
= 4x +
-
A) - -4 C) -3 D) -2 E) -1
5. = x2 + + 1
= 4x - 8
A) ( - -1, 11 ) C) ( 2, 10 )
D) ( -10, 2 ) E) ( -2, 10 )
EĞİTİ
ME AYDINLA
TAN DESTEK
91. 2. 3. 4. 5. 6.
TEST - 41.
yx
3
2
=2 = x2
2
2.
= x + = x2 - 5x + 8
-
A) 2 2 4 2
D) 4 5 E) 8
3. y
xO
y = –2x + 5
5/2A
5
2
= 4 - ax2
= -2x +
A) 3
1
3
2 C) 1 D) 2 E) 3
4. -
-
y
xO
d: y + 2x – 8 = 0
4B
C
A–1
4
8
-
A ABC^ h& 2
5. = -x2 + 2x
= x2 - 4x - 8
A) - -11 C) -8 D) -3 E) 0
6. a
= x2 - 3x + a
= x + 1
-
-
a =
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
10 3. 4.
11.4.2.1 :
ax2 + + > 0 , ax2+ + < 0
ax2 + + $ 0 , ax2 + + # 0
-
TANIM
D >
(x1 < x
2
x x1
2 + bx + c
x2
ÖRNEK 1
x2 - 4x + 3
ÖRNEK 2
-x2 + 7x - 12 -
ÖRNEK 3
x2 - x > 0 -
ÖRNEK 4
-x2 + x + 6 # 0
D =
-
x x1 = x2
2 + bx + c
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
11 8. 9. (–6, 6) 10. 9 11. 7 6. R2
3- ( 2
ÖRNEK 5
x2 - 4x + 4
ÖRNEK 6
4x2 - 12x + 9 > 0
D <
-
x
2 + bx + c
ÖRNEK 7
x2 - 3x + 5
ÖRNEK 8
x2 - x + 4 # 0
ÖRNEK 9
x2 + + 9 > 0
ÖRNEK 10
ÖRNEK 11
3
2
4
9>
x x1 7– –2
f fp p
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
12 15. 52 18. 2712. 13. 14. (–4, 4)
ÖRNEK 12
a 2 - ( a + 2 ) x + 2 = 0
ÖRNEK 13
( )f x x x2 152
= - + +
ÖRNEK 14
f xx ax2 2
7
2=
- +
^ h-
ÖRNEK 15
= A2
= 13A - 22
--
ÖRNEK 16
-2
-
EĞİTİ
ME AYDINLA
TAN DESTEK
131. 2. 3. 4. 5. D 6. 7.
TEST - 51. x2 - 5x - 24 < 0
2. x2 - 2x - 15 # 0
3. 2x2 - 3x + 2 < 0
-
4. x x2 62
90
2#- +
-
5. x2 - 7x + 10 $ 0
A) ( - -
C) R - [ 2, 5 ] D) (- ] [
E) [ 2, 5 ]
6. x2 - 9x + 18 # 0
A) R - [ 3, 6 ]
C) ( 2, 9 ) D) R - [ 3, 6 ]
E) ( 3, 6 )
7. -x2 + x + 12 # 0
A) - -7 C) -8 D) -9 E) -10
EĞİTİ
ME AYDINLA
TAN DESTEK
141. D 2. E 3. 4. 5. D 6.
TEST - 61. ( x - > x - 1
A) R- +
D) R - { 1 } E) R
2. -
3. x –6 2
+ – + ÇK = (–6, 2)
-
A) x2 - 4x + 12 > 2 - 4x + 12 < 0
C) x2 + 4x - 12 < 0 D) x2 - 4x - 12 > 0
E) x2 - 4x - 12 < 0
4. 39
1<
x x532
+ f p
A) ( - -3, 2 ) C) ( -3, -2 )
D) ( -6, 5 ) E) ( -1, 5 )
5. x2 - + 3 ) x + # 0
--
A) -
6. x2 + 2x + - 3 > 0
> < 4 C) -2 < < 4
D) -4 < < > 5
EĞİTİ
ME AYDINLA
TAN DESTEK
151. 2. E 3. 4. 5. D 6. D
TEST - 71. x2 - 2ax + a > 0
A) ( - -
-2, 3 )
2. ax2 + ( 4 - 2a ) x + a + 5 < 8
A) ( - -
3.6
5
5
6x x 2–2
#+f fp p
A) - -1 C) 2 D) 3 E) 5
4.
f x x x13 302
= - + -_ i
5.
f xx ax x
x
2 1
2 5
2=
- + +
+^ h
-
6.
f xx a x a
x
1 2
3
2=
+ - + +
-^^
hh
-
EĞİTİ
ME AYDINLA
TAN DESTEK
161. 2. 3. 4. D 5. 6. D
TEST - 81.
-x2 + 3x +
--
< m4
3< > 0
> 3 E) m3
2>
2. +
( x2 - 3x +
3.( 3a + 2 +
4. ax2 + 2ax - 2x2 - 5x + a > 0
A) -
5.
= 2x2 - - 2 ) x + 21
=
-
6.
--
-
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
17 3. 4. 5.
11.4.2.1 :
Çarpım Şeklindeki Eşitsizliklerin
Çözüm Kümesi
ÖRNEK 1
( 2x - + 2 ) $ 0
2x - 5 = 0 x + 2 = 0
x2
5= x = -2
x
(2x – 5) . (x + 2)
–2 5/2
+ – +
. , ,K 22
5Ç ,3 3= - -^ p>@
ÖRNEK 2
(x2 - - 1) # 0
x2 - 1 = 0 2x - 1 = 0
(x - 1) (x + 1) = 0 x2
1=
x = 1 x = -1
x
(x2–1) . (2x – 1)
–1 11/2
– + +–
. , ,K 12
11Ç ,3= - -^ >@ H
ÖRNEK 3
( 2x - - x ) < 0
ÖRNEK 4
( x - 2 - 4x - 5 ) # 0
ÖRNEK 5
( x - 2 )2 + 3 ) > 0
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
18 9. 12 10. {-2} 6. 7. ,b
c0d n 8. , –4) (–2, 3)
ÖRNEK 6
( x - x2 2 - 3x ) # 0
ÖRNEK 7
a < < 0 <
- < -
ÖRNEK 8
=
y
xO
–23
4
y = f(x)
+ > -
ÖRNEK 9
-
-
---
( 2x - 5) (x - 6 )
(Gol için topun çizgiyi tamamen geç-mesi gerekmektedir.)
ÖRNEK 10
=
y
xO–2–5 4
3
y = f(x)
2- $EĞ
İTİME AYDIN
LATAN D
ESTEK
191. 2. E 3. 4. E 5. 6. D 7. E 8.
TEST - 91. - 7 ) # 0
-
2. ( x + -2x + 5 ) > 0
A) - -1 C) 0 D) 1 E) 2
3. ( -x - -x - 5 ) # 0
A) - -8 C) -7 D) -4 E) -3
4. R,
a < < + + + > 0
, -
- -
D) ( -a, - - -
5. ( x + - - x ) < 0
A) - -3 C) 0 D) 3 E) 5
6. < a <
( ax + + a ) # 0
A) ,a
b3- -f H ,
b
a3- n<
C) ,b
a
a
b- -> H D) ,
a
b
b
a- -> H
E) ,b
a
a
b> H
7. R , a < < 0 <
( ax - - - > 0
-
A) ,c
a
a
bf p ,b
a
b
cf p
C) ,c
b
c
a-f p D) ,c
a3-d n
E) ,a
b3f p
8. x –2 2 6
+ – –+ ÇK = (– , –2] [2, 6]
-
A) ( x2 - - 6 ) $ 0
( x2 - 8x - + 2 ) $ 0
C) ( x2 - 4x - - x ) $ 0
D) ( x - 2 - 8x + 12 ) $ 0
E) ( x2 - 4x - + 2 ) $ x
EĞİTİ
ME AYDINLA
TAN DESTEK
20
TEST - 10
1. E 2. 3. 4. 5. 6. E 7. 8.
1. ( x - 3 )2 2 - 16 ) < 0
-
A) - -9 C) -1 D) 1 E) 3
2. ( x2 - -x2 - 6 ) $ 0
-
3. ( x + 2 - 5x + 6 ) $ 0
-
4. ( x2 - 3x + 2 - x - 2 ) # 0
5. x3 + 3x2 - 4x - 12 < 0
-
A) - -4 C) -5 D) -7 E) -9
6. x3 + 4x2 - 16x - 64 < 0
A) ( - -4, 4 ) C) ( 4, )
D) ( - , 4 ) E) ( - , 4 ) - { -4 }
7.
( 4 - 4 + ax3 - 2 + # 0
[ ] {0} -+ +
A) - -8 C) -6 D) 2 E) 10
8. ( x + 2 - 6 ) < x2 - 2x - 8
-
A) -
EĞİTİ
ME AYDINLA
TAN DESTEK
21
TEST - 11
1. D 2. 3. 4. E 5. E 6.
1. y
xO 1
3
y = f(x)
=
( x - $ 0
2. y
xO
–23
y = f(x)
=
( x - $ 0-
3. y
xO
–3 3
–9
y = f(x)
=
( 2x + $ 0
4. y
xO–3
4 y = f(x)
=
( x2 - < 0 -
-
D) ( -3, 3 ) E) ( - - { -3 }
5. y
xO–4
96
y = f(x)
=
( x6 + > 0
6. y
xO–3 42
y = f(x)
=
( x2 + < 0 -
A) ( - -3, 2 ) C) ( 2, 4 )
D) ( -
EĞİTİ
ME AYDINLA
TAN DESTEK
22
TEST - 12
1. E 2. D 3. D 4. D 5. D 6.
1. y
xO
–16
4
5y = f(x)
y = g(x)
= =
> 0 -
2. y
xO
–3 –1 31
y = f(x)
y = g(x)
= =
2 -x2 + 5x - 9 ) # 0
3. y
xO
–2
–141
3
y = f(x)
y = g(x)
= =
( x2 + $ 0
A) -
4. y
xO
3
3
y = f(x)
=
- 4 ) < 0
x2 - 8x + 19 -
-
5. y
xO–2
–2
–56
y = f(x)
= -
+ - 3 ) < 0 -
6. y
xO–2
–2
–56
y = f(x)
= -
.fx
f x3
1 3 0$- -d _n i-
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
23 4. ( -3 , 1 ) , ( 4, 3) 5. ( -3 , –5 ) , [ 1, 3 ) , [ 5, 3 ) 6. ( –4 , –3 ) , ( 4, 5 )
11.4.2.1 :
Bölüm Şeklindeki Eşitsizliklerin
Çözüm Kümesi
ÖRNEK 1
xx
34 0–
#+
ÖRNEK 2
9 x
x 2 0–
2$
+
ÖRNEK 3
x
x
4
10<
-
+
ÖRNEK 4
x
x x
3
1 40<
+
- -_ _i i
ÖRNEK 5
x x
x x
3 5
1 50
–
–$
+
- +
_ __ _
i ii i
ÖRNEK 6
x x
x
2 15
160<
2
2
- -
-
1. 2. (–3 , –3) , [–2, 3) 3. ( –3 , –1 ) , ( 4, 3)
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
24 10. ( –3 , –3 ) , ( –1, 3 ) 11. ( –3 , –3 ) , ( 2, 3 ) 12. ( –3 , [ 1, 2 )7. ( –3 , 3 ) , [ 4, 3 ) – { –1 } 8. ( –3 , –1 ) , ( 0, 5 ) 9.
ÖRNEK 7
x x
x x
2 3
1 40
2$
- -
+ -_ _i i
ÖRNEK 8
x x x
x x
4 5
40<
3 2
2
- -
+ +
ÖRNEK 9
x
x x
1
1 20
4 7
#+
- -_ _i i
ÖRNEK 10
x
x
1
12<
+
-
ÖRNEK 11
x x3
1
2
1#
+ -
ÖRNEK 12
x
x
21
2
$-
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
2513. { –5 } , , [ 5, 3) 14. 27
ÖRNEK 13
x
x x x
3 3
5 4 50
·
·
x 1
2
$
+
+ - -
+ __
ii
ÖRNEK 14
-
"Negatif”
–1 0
"Pozitif”
+1
• -
•
• +
x
x
2 3
8
+
-
+ -
ÖRNEK 15
= = -
–5O–1 3
y = f(x)
y
x
y = g(x)
g x
f x0#^
^hh
ÖRNEK 15
=
–4
y
x1–1
5
y = f(x)
O
f x 2
f x 20
–#
+
^^
hh
-
15. [ –5 , –1 ) , [ 3, 3) 16. , , ( 1, 7 ) – { 3 }
EĞİTİ
ME AYDINLA
TAN DESTEK
26
TEST - 13
1. 2. 3. 4. E 5. 6. 7. 8. D
1. x 4
x 30
–>
+
-5 C) -4 D) -3 E) -2
2. x
01
9 x
–
–$
-
3. x
x
25
30
–2
#-
-
4. x
01
x 2
– –
–
2$
A) ( - -1, 2 ] C) ( 1, 2]
D) [ 2, 3 ) E) (-3, 2]
5. x 5x 6
x 10
–
–
2
2
#
+
6. x x
x x
2
3 50>
2- -
- -_ _i i
7. a < < 0 <
ax b
cx b0$
+
+
A) ,a
b–3-f p ,
c
b3- i>
C) ,a
b
c
b- -f H D) ,
b
a
b
c- - n>
E) R
8. x 3
x x 2
x 3
x x 2– –2 2
+
+=
+
+
A) [ -2, 1 ]
( -3, -3 ] , [ -2, 1 ]
C) ( -3, 1 ]
D) ( -3, -2 ] , [ 1, 3 )
E) ( - 3, 1 ]
EĞİTİ
ME AYDINLA
TAN DESTEK
271. 2. D 3. D 4. 5. D 6. 7. 8.
TEST - 14
1. x
5 x0
· 3 x– –1907 1988
2^ ^h h
-
2. bx
x a
90#
-
+
[ -
+
3. x
1x<
A) ( -1, 1 )
( -1, 0 )
C) ( -3, -1 ) , ( 0, 1 )
D) ( -1, 0 ) , ( 1, 3 )
E) R
4. x 3
x 5
x 8
x 3– –$
+ +
5. 16 x
71
–2
$
A) ( -3, 3 )
( 3, -3 ) , [ 3, 3 )
C) ( -4, -3 )
D) ( -4, -3 ] , [ 3, 4 )
E) ( -4, 4 )
6. x x
x
2 7 6
21
2$
- +
-
7. x
x
4
20
2#
-
-
-
8. x b
x ax 350
–
2
$+ +
[ -7, -6 ) , [ -5, 3 )
+
A) - -6 C) 6 D) 12 E) 18
EĞİTİ
ME AYDINLA
TAN DESTEK
28
TEST - 15
1. D 2. 3. 4. 5. 6. E
1. x 1
x 40
· x 13x 14
–
– –2 2
#+
^^ ^
hh h
2. x x
x
9 2 3
3 20
2#
- + -
- +
_ ai k
3. x 4
x 20
4 x 2 3
–
– – –<
2+^ h
-
4. x 2
18 9x1
–
–>
2^ h
A) - -20 C) -15 D) -14 E) -6
5. =
y
xO
3
4
y = f(x)
x
f x
2 502
+
^ h
6. =
y
x–2
1
O
y = f(x)
f x
x 90<
2-
_ i
EĞİTİ
ME AYDINLA
TAN DESTEK
291. 2. D 3. D 4. D
TEST - 161. =
y
x–1 3
y = f(x)
O
9 x
f x0
· x 4
–2
$+^ ^h h
-
2. =
y
x–3
4–1
O
y = f(x)
x 2
f x x 2x 50
· –2
$+
+^ ^h h
-
A) [ -2, 1 ]
[ -1, 3 )
C) [ -3, 4 ]
D) ( -3, -3 ] , ( -2, -1 ] , { 4 }
E) R
3. = = -
y
–2 4
y = f(x)
y = g(x)
O
x
f x0
g>^
^hh
-
4. = = -
y
x–1
3
4
1 2
y = g(x)
y = f(x)
O
g x
x f x250
·>
2-
__ _
ii i
-
EĞİTİ
ME AYDINLA
TAN DESTEK
30 3. (–5, –2) , (2, 5) 4. (–3, –2) , (3
7, 3)1. [–4,
3
5 ) 2. (–3, –1)
11.4.2.2 :
-
-
TANIM
-
ÖRNEK 1
x + 4 $ 0
3x - 5 < 0
ÖRNEK 2
x - 3 < 0
x2 - 5x - 6 > 0
ÖRNEK 3
x2 - 4 > 0
x2 - 25 < 0
ÖRNEK 4
x2 + x - 2 > 0
3x2 - 4x - 7 > 0
www.aydinyayinlari.com.tr4. MODÜL
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
31
ÖRNEK 5
x2 - 5x + 6 < 0
-x2 + 2x + 8 > 0
ÖRNEK 6
2x2 - 5x - 3 0
8x2 - 9x - 17 > 0
ÖRNEK 7
x2 - 6x + 15 > 0
3x2 + 5x - 2 < 0
-
ÖRNEK 8
-3x2 + 4x - 10 > 0
x2 - 7x + 10 < 0
-
7. ( –2, 1
3 ) 8. 5. ( 2, 3 ) 6. (
8
17
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
32
ÖRNEK 9
4x2 - 12x + 9 > 0
-x2 + 5x - 7 < 0
-
ÖRNEK 10
( x - 1 )2 > 0
5x - x2 > 0
x2 - x - 12 < 0
-
ÖRNEK 11
- 6 < x2 - 7x < 18
-
ÖRNEK 12
!
- 3 ) x2 - ( 2 - + 6 - = 0
1 2
1 2 1 < 0 <
2
9. {2
3} 10. ( 0, 1 ) , ( 1, 4 ) 11. (–2, 1) ( 6, 9 ) 12. ( –3, 2 ) , ( 3, 3 )
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
33
ÖRNEK 13
+ 1 ) x2 - + 1 ) x - - 3 = 0
1 2
1 < 0 <
2 | 1 | < | 2
| -
-
ÖRNEK 14
!
- 1 ) x2 + + - 3 = 0
1 2
1 2<
1 <
2
ÖRNEK 15
- 2 ) x2 + 4x + < 5
-
ÖRNEK 16
= = -
y y
x
y = f(x)
y = g(x)
–1
–5
6
5
x
$ 0,
< 0
13. (–3, –3 ) , ( 3
1– , 3 ) 14. (
4
3, 1 ) 15. ( –3, 1 ) 16 [–1, 6 )
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
34 19. ( –6, –1 ) , ( 6, 9 ) (–4, –2) (3, 5) (6, 8)17. ( –2, 1 ) 18. { –3 } , [ 5, 3 )
ÖRNEK 17
= = -
y
xO–231
–5
–5
4
y = g(x)
y = f(x)
< 0
> 0
ÖRNEK 18
x
y
53
4
–1–3
–3y = f (x)
y = g (x)
= = -
# 0
> 0
ÖRNEK 19
=
y = f (x)
x
y
74–3
5
+ 3 ) > 0
- 2 ) < 0
- + 1) < 0
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr 11. SINIF4. MODÜL
35
> ax2 + +
= ax2 + +
y = ax2+bx+ca > 0
y = ax2+bx+c
a < 0
x x
yy
OO
< ax2 + +
= ax2 + +
y = ax2 + bx + ca > 0
y = ax2 + bx + ca < 0
x x
y y
O O
$ ax2 + + # ax2 + + -
-
ÖRNEK 20
> x2 -
ÖRNEK 21
# -2x2 -
ÖRNEK 22
$ -2 ( x - 1 )2 -
ÖRNEK 23
# x2 - 4x + 3
EĞİTİ
ME AYDINLA
TAN DESTEK
www.aydinyayinlari.com.tr11. SINIF 4. MODÜL
36 28.
ÖRNEK 24
# x + 1
$ x2 - 2
-
ÖRNEK 25
< x2 - 1
$ -x2 + 2
-
ÖRNEK 26
x2 - 2x < # x2 + 4x
-
ÖRNEK 27
# x2
x + # 2
- x < 1
-
ÖRNEK 28
y
A
x
B
E
C
O
D
F
x + 1 < < -x2 + 2x + 3
EĞİTİ
ME AYDINLA
TAN DESTEK
37
TEST - 17
1. 2. 3. 4. 5. 6. D 7. 8.
1. x2 - 4x + 4 > 0
x2 - 5x - 14 < 0
2. x2 + x + 2 > 0
x2 - 16 # 0
-
A) [ -2, 4 ] -4, 4 )
C) [ -4, 4 ] D) R
E) ( - 3, -4 ] , [ 4, 3 )
3. x
x
3
20
2
$-
-
| x - 2 | $ 0
4. x2 - x - 12 # 0
x
x
1
60
3
#-
-_ i
5. x
x
3
3 10$
-
+
x x4 3
10
2#
- -
-
A) ,2
12-f p ,
3
11- i> C) ,
3
12-f p
D) [ -4, -2 ) E) 2
1, 2f p
6. x
x
1
20>
- +
+
x
x x
4
3 40
2
2
#
-
- -
-
-2, 4 ) C) ( 2, 4 ]
D) ( -2, -1 ] E) [ -1, 1 )
7. x2 - 4 < 0
x2 - x - 6 # 0
x3 · | x + 1 | 2 $ 0
8. x2 + 2x + 3 > 0
x · ( x2 - 3x + 2 ) > 0
-1, 0 )
D) ( -3, 1 ) E) ( 0, 2 )
EĞİTİ
ME AYDINLA
TAN DESTEK
38
TEST - 18
1. 2. D 3. 4. 5. D 6. D 7. D 8. E
1. x2 + 3x < 4
x
11<
-
A) ( - 3 ) C) ( -4, 0 )
D) ( -3, -4 ) E) ( 0, 1 )
2. x2 # -6x - 8
x < x
4
A) - -9 C) -8 D) -7 E) -6
3. x x2
1
2
2<
+ -
x 1
12#
+
-
A) ( -6, -2 ) , ( 2, 3 [ 2, 3 )
C) [ 2, 4 ) D) ( 0, 2 ]
E) ( -6, -1 ) , ( 2, 3 )
4. -2 < x2 - 6 # 19
-
5.
( a - 7 ) x2 - ( 2a - 8 ) x + a + 6 = 0
A) ( -3, - 3 ) C) ( -6, 4 )
D) ( -6, 7 ) E) ( -8, -6 )
6. a
x2 - 3 ( a - 4 ) x - 5a = 0
1 2
1 2 1 < 0 <
2 | 1 | > | 2
| -
-
A) ( -3 3 ) C) ( 0, 5 )
D) ( 0, 4 ) E) ( -4, 3 )
7.2 + + 4x + 1 = + 5x
1 2
1 2<
1 <
2
A) -
8. a
ax2 - 2 ( a - 4 )x + a - 6 = 0
-
A) (-3, 0 ) , , ( 4, 6 ]
C) ( 4, 6 ) , ( 6, 8 ] D) ( 6, 8 ) , ( 8, 3 )
E) (-3, 0 ) , ( 6, 8 ]
EĞİTİ
ME AYDINLA
TAN DESTEK
39
TEST - 19
1. 2. D 3. 4. 5.
1.
O O
yy
x
y = f(x)
y = g(x)
–3
4
5
3
x
= = -
$ > 0 -
2. = = -
y
x–1
4
4
3
y = f(x)
y =g(x)
O
$ $ 0 -
3. = = -
y = g (x)y = f (x)
x
y
732–2
–1
–7 O
# > 0
D) 5 E) 6
4. = = -
x
y
1–3
5
–9
–4O
y = f (x)
y = g (x)
--
$ x2 + # x2 + 4x
# -( x + 3 )2 $ -( x + 3 )2
> - ( x + 3 )2 # - ( x + 3 )2
< x2 + # x2 + 4x
< x2 + 4x
> -( x + 3 )2
5. = = -
Ox
5
5
1
y
M L
E
TK
y = f(x)y = x
# x2 - 6x + 5
- x $ 0
> 0
EĞİTİ
ME AYDINLA
TAN DESTEK
40
KARMA TEST - 1
1. 2. 3. E 4. E 5. E 6. 7. 8. E
1. x2 + 2 = 26
= 5
-
A) - - 3 C) 0 D) 5 E) 10
2. 2 52
-
3. x
x x
2
8 70<
2
2
-
- +
_ i
4. x b
x ax 180
2
$+
+ -
[ -9, -3 ) , [2, 3 --
A) - - 2 C) -1 D) 1 E) 4
5. x x
x x x
2
40
2
4 2
$
-
-_ i
A) [ -2, 3 -2, 3 )
C) [ 2, 3 ) D) [ -2, 2 ]
E) [ -2, 3 ) - { 0, 2 }
6. x x
x
4 3
4 160
·
·x
3
2 2–
#
- +
-
_ __i i
i
7. x x3 2 15 02
2- + -
-
A) - -4 C) -2 D) 0 E) 3
8. x x
x x
12 13
4 20
·
2#
+ -
+ -
-
A) - -13 C) -12 D) -11 E) -10
EĞİTİ
ME AYDINLA
TAN DESTEK
41
KARMA TEST - 2
1. 2. E 3. 4. 5. 6. 7. 8.
1.1
2-
A) 2
1 5+
2
5 1– C)
2
1 5–
D) 2
1 E) 1
2. x 3
x x 20
–2019
2017
2018
#
+^^hh
-
A) [ -
D) [ -3, 0 ] E) ( -3, 0 ] , { 2 }
3. x
x x x
3 12
1 10
· –
2
2 2
$
-
+ +^ ^h h
4. x x2
3
1
1$
- +
5. < 0 <
ax
ax bx
40<
2
2
-
+
A) ,a
b0 -f p ,
a
20-f p C) ,
a a
b2- -f p
D) ,a a
b2-f p E) ,
a
b
a
2-f p
6. -1 < x 2
1
+ # 4
-
A) ,34
7- -f p - ,3
4
7- - p7
C) ,34
7- - p7 D) R - ,3
4
7- -f H
E) R
7.2- 5x -14, x2 + x -12 )
8.2 - + 3 ) x + 1 = 0
1 2
x1 < 0 < x
2 | x1 | > | x2
|
A) - - - 1 E) 2
EĞİTİ
ME AYDINLA
TAN DESTEK
42
KARMA TEST - 3
1. 2. 3. 4. D 5. 6.
1.
O
y
x
y = f(x)
5
3
=
( x +
2. = = -
y = f (x)
y = g (x)
x
y
53
4
O–4
–3
g x
f x0<^
^hh
3. y
y = f(x)
–1
3
7x
O
=
+ 2 ) > - x ) < 0
4. y = f (x)
x
y
4–7–1
=
( 5 - - -
5. x –3 –2 0 2 3
– – + +
+
– +
– –+ ––
-
A) x2 > 9
x < x
4x2 < 9
x > x
4C) x2 < 4
x < x
3
D) x2 < 4
x < x
9E) x2 > 9
x > x
4
6.
x
y
–1
–2
2O
2
--
A) # x2 - x - 2
# 2x + 2
$ x2 - x - 2
# 2x + 2
C) # x2 + x - 2
# 2x + 2
D) $ x2 + x - 2
$ 2x + 2
E) $ x2 - x - 2
$ -2x + 2
EĞİTİ
ME AYDINLA
TAN DESTEK
43
KARMA TEST - 4
1. 2. 3. 4. 5. 6. D
1. = -x2 + ax + -
< 0 <2
ab–<
=
- > 0
| x2 - x -20 | $ 0
2. "
= { } -
-2
+ 4 ) ) = - 2
A) - -3 C) 0 D) 7 E) 9
3. 2 + - 2 )
( 2x -
-
4. R+
=2 + 2 - 5 ) x - 25
=
x1 2
1 2 1 < 1 <
2
5. =
O
y
x
7
–5
16
y = f(x)
= x2 + 6x
0 < < 7 -
A) - -6 C) -3 D) -2 E) 0
6. x x a
x ax
2
360
–>
2
2
+ +
+ +
A) [ - -6, -1 ] C) [ -12, -6 ]
D) [ -12, -1 ] E) [ -1, 12 ]
EĞİTİ
ME AYDINLA
TAN DESTEK
YAZILI SORULARI
44 4. 5. (–2, 0) 1. (–2, 1) 2. {0, 3, 4} 3. (3, 5)
1. ( a - 2) x2 - 2ax - 1 < 0
--
2. 5 x
x · 3 x0
–
–2
3
5
#^^hh
-
3. ( a - 5 ) x2 - 4ax + a - 3 = 0
4.
y = f(x)
–4 3O
x
y
=
x 16
x 20
f x
–2
#+^ ^h h
5. x 4
x 4x0
x 2x 8
x 160
–
– –
–
>
>
2
2
2
+
EĞİTİ
ME AYDINLA
TAN DESTEK
YAZILI SORULARI
45 9. {3} 6. 7. 5 8. {–4, 4}
6. 9 # ( x - 1 )2 # 49
7. x2 - = 44
-2 = 19
-
8. 2x 12x 18
x 160
–
–
2
2
#
+
-
9.
y = f(x)
x
y
3O
O
–1
y = g(x)
x
y
1–2
-
( x2 + $ 0
10. $ x2 - 3x - 4
+ 1
$ 0
-
EĞİTİ
ME AYDINLA
TAN DESTEK
461. D 2. D 3. 4.
1. x
Buna göre;
x
x
x3x +1
-
A) ,14
1-> H -1, 4 ] C) [ -4, 1 ]
D) ,4
11-> H E) [ 1, 4 ]
2. -
-
-
-
a
a Z
Yaz " a
Yaz "
x 9
1
–2
A) - -5 C) -7 D) -9 E) -11
3.
-
2" 3¨
" 2¨
-
¨
-
4.
- -
-2 -
EĞİTİ
ME AYDINLA
TAN DESTEK
471. 2. 3. D 4.
1.--
B
C
A
a
AYDIN YAYINLARI
| |= 2 - --
2 -
2.
f(x) = x2 + (k +1)x + k + 16
-
--
3.
-
-
A B
--
= -2 - - + 1
-
-
4. --
= - -
EĞİTİ
ME AYDINLA
TAN DESTEK
48
1. -
+ + 3
200 cm
-
2. -
-
2 + 1) bin
-
-
3. -
2 - ax +
-
4.
1. kefe 2. kefe
---
-
-
1. 2. D 3. D 4.
EĞİTİ
ME AYDINLA
TAN DESTEK
EĞİTİ
ME AYDINLA
TAN DESTEK
EĞİTİ
ME AYDINLA
TAN DESTEK
