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Math 110

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1 1 1

MATH110 دوري اول مـحـمـد عـمـران ست بنكتـ

1)the irrational numbers is

d)√ c)

√ b) a)√

3

2) the integer numbers is

d)√ c)

b) √ √

3a)

3) If the x =…….

d)

c) b) 2 a)-2

4)if then the solution set is

c) [ ]b) a) ]

5) If | | then x= ……

()C b)[

] a)[ ]

6)| | Then x=…..

d)-2 or -1 c)2or -1 b) -2or 1 a)2or 1

𝟐𝒙 𝟏 فك االقواس 𝟑 𝟒𝒙 -1 𝟐𝒙 𝟏 𝟐 𝟒𝒙

𝟐𝒙 𝟒𝒙 𝟐 𝟏 𝟔𝒙 𝟑 𝟔𝒙

𝟔

𝟑

𝟔

𝒙 𝟏

𝟐

𝟑 𝟓 𝟐𝒙 𝟕 → 𝟑 𝟓 𝟐𝒙 𝟕 𝟓 → 𝟖 𝟐𝒙 𝟐

[ 𝟏 𝟒]sol set 𝟒 ≥ 𝒙 ≥ 𝟏 𝟖

𝟐≥

𝟐𝒙

𝟐≥

𝟐

𝟐→

|3𝑥 | 3𝑥 3𝑥

3𝑥 6

𝑥

6

𝑥

Sol set

𝑥 3 𝑜𝑟 𝑥 3 𝑥 𝑥 𝑥 𝑥

2 2 2

7)the solution of inequality | | ≥

] [ d) c) 3 b) [ a)[ 3 ]

8)the solution of inequality is

c) b) ] a)

9)the distance between -2,

is

d) c)2 b)

a)

10)the distance between (-1,3) and (2,-5) is

d)√ c)√3 √ 3b) a)√

11)the mid-point between (-1,3) and (2,-5) is

c)

b)

a)

≥ ≥ ≥ 𝟖

≥

𝟖

≥

𝟐𝒙 𝟏 𝟕

𝟐𝒙 𝟕 𝟏

𝟐𝒙 𝟔 𝟐𝒙

𝟐

𝟔

𝟐

𝒙 𝟑

Sol set 𝟑] 𝟒 Or

𝒙𝟐 𝒙 𝟐 𝟎

𝒙 𝟐 𝒙 𝟏 𝟎

𝒙 𝟐 𝟎 𝒐𝒓 𝒙 𝟏 𝟎

𝒙 𝟐 𝒐𝒓 𝒙 𝟏

+ + --

Sol set (-1,2)

D=

5

0

5

5

5

5

D= 𝑥 𝑥 𝑦 𝑦 3 9 6 3

Midpoint= 𝑥1+𝑥2

𝑦1+𝑦2

+

+ 5

3 3 3

12)the slope between (3,2) and (5,-1) is

c)

b)

a)

13)the slope of perpendicular line pass through(2,5)and (3,-2) is

d)7 c)-7 b)7

7a)

14)the equation of vertical line "has no slope " passes through(3,-1) is

d)y=-1 c)y=3 b)x=-1 a)x=3

15)the equation of horizontal line "slope equal zero " passes through

(-1,5) is

d)y=5 c)y=-1 b)x=5 a)x=-1

16)the equation of the line with slope-

and passes through (-1,3) is

5=0-c)x+2y b)x-y+1=0 a)x+y+1=0

17)the equation of line with slope -3 and y-intercept is 8 is

d)3x-y+8=0 8=0-b)3x+y a)3x-y-8=0

18)the intersection point of and is

d)(1,-1) c)(-1,-1) 1,1)-b)( a)(1,1)

𝑚 𝑦 𝑦

𝑥 𝑥

3

3

7Perpendicular= 𝑚

5

𝑦 𝑚 𝑥 𝑥 𝑦 → 𝑦

𝑥 3 → 𝑦 𝑥 6 → 𝑦 𝑥

→ 𝑥 𝑦 0

𝑦 𝑚𝑥 𝑏 → 𝑦 3𝑥 → 3𝑥 𝑦 0

3𝑥 𝑦 0 → 𝑥 𝑦 3 0 →

𝑥 0 → 𝑥 → 𝑥

3 𝑦 0 → 𝑦 0 𝑦

x=-1عن 1معادله فًبالتعوٌض

1,1)-P=(

حل اخر

بالتعوٌض من االختٌاري والنقطة

التً تحقق معادله المستقٌم هً

الصحٌحة

4 4 4

19) [ [ is

[ c) b)[ ] a)(7,9)

20)[ [

)[ c) b)(2, ] a)(-1,2)

مه الرسم السابق حل سريع اكبر عدد واصغر عدد مه الفترتيه

21)[ [

C) (-1, ] b)(2,7) [ a)

رك وغير فتحتهمه الرسم السابق والحظ ان العدد المشت

22)[ [ =

[ c) b)(7,9] a)[ 9]

23)the equation of the line passes through (-2,3) and perpendicular the line

c)2x+y+1=0 b)2x+y-1=0 a)2x+y+5=0

24)the equation of the line passes through (1,5) and (-3,2) is

c)4y=3x+10 b)4y=3x+17 a)4y=3x-17

25) the slope and y-intercept of the line is

c)-2,3 b) 2,3 a)2,-3

→

صغر عدد من الفترة الثانٌةحل بدون الرسم اكبر عدد من الفترة األولى وا

𝒚 𝟐𝒙 𝟒 𝟑 → 𝒚 𝟐𝒙 𝟏 𝟐𝒙 𝒚 𝟏 𝟎

1-𝒎 𝟐

𝟒

𝟏

𝟐 →per then 𝒎𝟏 𝟐

2- eq is 𝒚 𝒎𝟏 𝒙 𝒙𝟏 𝒚𝟏 → 𝒚 𝟐 𝒙 𝟐 𝟑 →

𝑚

3

3

3

𝑦 3𝑥 3 0 → 𝑦 3𝑥

Eq 𝑦

𝑥 → 𝑦 3 𝑥 0

5 5 5

26)

-c)1 b)1-sinx a)

27)

c)

b) a)1

28)

c) √

b) a)

29)

c)√

√

b) a)

30)

c)√ √

b)

√ √6

√ +√6

a)

then

31) if

c)√

√5

b) a)

√5

𝜋

3

0

3 0 → 𝑐𝑜𝑠 0° cos 0 60 cos60°

𝜋

3

0

3 0° → 𝑠𝑖𝑛 0° sin 0 60 𝑠𝑖𝑛60

3

𝜋

0

° → 𝑠𝑖𝑛 ° sin 30

𝑠𝑖𝑛30𝑐𝑜𝑠 𝑐𝑜𝑠30𝑠𝑖𝑛

√

3

√

√

6

√ 6

𝑡𝑎𝑛𝜃

سالبه tanالزاوٌة بالربع الرابع

2

3 9

3

θ

6 6 6

32)if

then

c) b)

5 a)

5

33)the domain of √

c) ] [ [ ]b) a)[

34)the rang of √ is

c)[ ] [0 ]b) a)(0,∞)

35)the domain of √ √

[ ]c) b)(1,3) a)[

[ ] ol sets

36)the domain of

√ √ is

c)(0, ] [ b) a)(0,∞)

3 9

6

𝑡𝑎𝑛𝜃

3

سالبه tanالزاوٌة بالربع الثانً

θ

5

3

𝑥 ≥ 0 → 𝑥 ≥ → 𝑥 → |𝑥| → 𝑥 [ ]Sol set

𝑓 0 𝑓 0 → 𝑓 0

نعوض بطرفً المجال من المثال السابق

[0 ]Rang

𝑥 ≥ 0 3 𝑥 ≥ 0 𝑥 ≥ 𝑥 ≥ 3 → 𝑥 3

1 3

𝑥 > 0 𝑥 ≥ 0 → 𝑥 ≥

𝟏 Sol set 0 1

7 7 7

37)the rang of is

]∞,-c)( b)[9 a)R=(-∞,∞)

38)the function +

+ is

c)neither odd or even b)even a)odd

39)the function is decreasing in

c)R=(-∞,∞) ∞,0)-b)( a)(0,∞)

40)the function is increasing in

∞,∞)-c)R=( b)(-∞,0) a)(0,∞)

41) if √ √ +

] [ ]∞,-)(C b)[ 3] a)(-∞,- ]

42)if then

c) b) a)

43)if √ √ then

√

c) b)2-√ a) √

44) if √ then is

c)(-∞, ] [0 b) a)R=(-∞,∞)

𝐹 𝑔 3 𝑥 𝑥

𝑥 ≥ 3 → 𝑥 3 𝑥 ≥ → 𝑥 ≥ 𝑜𝑟𝑥

Domain 3 𝑥 ≥ 0 𝑥 ≥ 0

] [ 3]Sol set -1 1 3

𝐹 𝑔 𝑥 𝑥 3 𝑥 𝑥 𝑥

𝑓𝑜𝑔 𝑥 𝑓 𝑔 𝑥 𝑓 𝑥 𝑥 𝑥4

𝑫𝒇 ⋮ 𝒙 ≥ 𝟎 → 𝑫 𝟎 𝑫𝒈 𝓡 𝒕𝒉𝒆𝒏 𝑫𝒇𝒐𝒈 𝟎

8 8 8

45)

2 5 1 X

7 2 3 f(x)

4 1 5 G(x)

From the table f(g(5))=

c)3 b)7 a)2

46)the function √

)algebraicc b)power a)polynomial

47)if then the new function is……………………..if

shifting 2 unite to right

c) b) a)

48) | | then f(x)=………………………such that is

c)-x-2 2)-(x–b) a)x-2

49)√

| |c) b) –x a)x

50)| | then

c)-a<x≤a a≤x≤a-b) a)-a<x<a

51){ } is

c)[ ] ]2,-b)( a)(-2,5)

52)if

>

then

c)a<b b)a≤b a)a>b

53)| √ |

c)0 b)√ √ -a)2

54)

sin

𝑔 𝑥 𝑥 𝑥 𝑥 𝑥

اعاده تعرٌف للقٌمة المطلقة

𝑥 0 → 𝑥

X=2

x>2 x<2

(x-2) x+2-2)=-(x-

9 9 9

s c sin

)

[ 𝟖 A) ]

𝟖 > >

𝟖

57)| | | | | |

B)false A)True

𝟖

B)false A)True

B) false A)True

60) this graph is function

B)false A)True

𝟖

{ } {6} { 3}

𝟖

{ }

11 11 11

62) The accompanying figure shows the graph of

√

1) and is , An equation for the line passes through (0 63)

12 =y 4 −x perpendicular to the line 8

64) +

+

c)

65)

3 3

3

66) The number 1.23 Is

C)integer B)rational number A)irrational number

67)

The accompanying figure shows the graph of a line an equation of this line is

3 3

11 11 11

68) If the graph of y =√ is shifted 4 units to the right and 1 unit up. An

equation for the shifted graph is

√ √ √

69) [ ]

[ 3] [ ] [0 ]

70

The domain of f(x) is

[ [ ] [ [ ]

12 12 12

+

رانــمــع ـد ــمـمـح

سارـلالستف 0507017098

0580535304 او زياره الموقع

خصم خاص للمجموعات

والمادةعدم الرد نرجو ترك رساله باالسم حاله في

1

1) Find the domain of 2

1( )

2 15

xf x

x x

.

a { 5 and 3}x x x

b { 3 and 5}x x x

c { 3 and 5}x x x

d { 5 and 3}x x x

2) 5

sin3

a3

2

b2

3

c2

3

d3

2

3) Solve 3 5 7x .

a

2 or 43

b2

or 43

c2

4 or 3

d 2

4 or 3

4) Solve 14 5 4 11x .

a 2,3

b 2,3

c 2,3

d 2,3

5) Solve 2 5 24 0x x .

a , 3 8,

b , 8 3,

c ,3 8,

d , 8 3,

6) Find the domain of 2( ) 3f x x .

a 3, 3

b 3, 3

c , 3 3, d , 3 3,

7) Solve 2 5 7x .

a , 6 1,

b , 1 6,

c , 1 6,

d , 6 1,

8) 1

a

1

b 1

c 1

d 1

First Exam

First Semester 2013-2014

Math 110 - 30 Marks

Time Allowed: 90 Minutes

Higher Education Ministry

King Abdul-Aziz University Faculty of Science

Department of Mathematics

A ID Name

2

9) Solve 2 5 7x .

a

1,6

b 1,6

c 6,1

d 6,1

10) Find the slope of the line through the points (3, 1) and ( 1,9) .

a5

2

b2

5

c5

2

d 1

11) Find the equation of the line through the points (3, 1) and ( 1,9) .

a 5 2 1y x

b 2y x

c 2 5 13y x

d 2 5 13y x

12) Find the equation of the line through the point (2, 1) with slope 3

5

.

a 5 3 11 0y x b 5 3 7 0y x c 5 3 1 0y x

d 5 3 5 0y x

13) The function 3( ) 2 3 1f x x x is

a Constant

b Linear

c quadratic

d Cubic

14) Find the slope and y intercept of the line 2 3 5 0y x .

a3 5

slope , intercept2 2

y

b3 5

slope , intercept 2 2

y

c2 5

slope , intercept3 3

y

d

2 5slope , intercept

3 3y

15) The equation for the line passes through 4, 1 and perpendicular to the line

2 3 3x y is

a 2 3 3x y b 2 3 10x y c 3 2 2x y d 3 2 10x y

16) Find the domain of 2( ) 4f x x .

a 2,2

b ,

c 2,2

d , 2 2,

17) Find the domain of ( ) 1f x x x .

a 1,

b ,1

c 1,

d ,1

18) The equation of the Horizontal line passes through the point ( 3, 2) is

a 2y

b 2x

c 3y

d 3x

19) The Range of ( ) 5f x x is

a ,

b ,5

c 0,

d 0,

20) Find the intersection point of the lines 4 2y x and 7y x .

a 6,1

b 1,6

c 1, 6

d 6, 1

3

21) If 2

tan( )3

x , and 02

x

, then cos( )x

a2

13

b13

2

c 13

3

d3

13

22) The irrational number is

a 3

b 0.333...

c 3

d 3

23) The solution of the equation 6 2( 3) 10x x is

a

4x

b 1x

c 4x

d 1x

24) 1,6 \ 3,9

a 3,6 b 1,3 c 1,3 d 6,9

25) 1,6 3,9

a 3,6 b 3,6 c 1,9 d 6,9

26) The midpoint of the segment with endpoints 7, 1 & 3 7,7 is

a 2 7,5 b 7,2 c 2 7, 3 d 2 7,3

27) Find the distance between the points ( 1,2) and (2, 1) is

a 2 3

b 3 2

c 9

d 3

28) 2sec x

A21 tan x

B21 tan x

C

21 tan x

D21 tan x

29) 0330

a11

rad 6

b4

rad 3

c

5rad 

3

d7

rad 6

30) Find the distance between the numbers 6 and 17 .

a 11

b 23

c 23

d 11

Instructions : (33 points). Solve each of the following problems and choose the correct answer.

(1) The domain of the function f x |3x 6| is(a) 2(b) 2,(c) 2(d) *

(2) The domain of the function f x x 2x2 x 6

is

(a) 2,3(b) 2,3(c) 2,3 *(d) 2,3

(3) The domain of the function f x 4 x2 is(a) 2,2(b) 2,2 *(c) ,2 2,(d) 2,

(4) The range of the function f x 25 x2 is(a) , 5(b) , 5(c) 5,(d) 5, *

(5) The range of the function f x 9 x2 is(a) , 9 *(b) 9,(c) ,9(d) 9,

(6) The function f x 10 x3 is even.(a) True(b) False *

(7) The function f x x 23 x2 is

(a) Algebraic function *(b) Power function(c) Polynomial function(d) Exponential function

(8) If h x |cosx | , f x cosx ,g x |x | , then(a) h f g(b) h g f *(c) h f.g(d) h f f

(9) The function f x 7 x2x3 3x

is symmetric about the origin.

(a) True *(b) False

(10) The function f x x 12 is

1

(a) increasing on 1, *(b) increasing on , 1(c) decreasing on 1,(d) decreasing on 1,

(11) The degree measure of 76 is

(a) 100

(b) 120

(c) 210 *(d) 75

(12) The radian measure of 150 is(a) 5

6 *

(b) 103

(c) 109

(d) 43

(13) If f x x2 and g x 2 x , then f gx (a) 2 x2

(b) 2 x2

(c) 2 x2

(d) 2 x *

(14) If f x x and g x 3x2 x , then fg x

(a) x3x2 1

(b) 13x 1 *

(c) 13x 1

(d) x3x2 1

(15) If f x x and g x 2 x , then the domain of f gx is(a) , 2(b) 0,2 *(c) 0,(d) 0,2

(16) The graph of the function f x x 12 2 is

2

(a)* -4 -2 2 4

2468

(b) -4 -2 2 4

2468

(c)

-4 -2 2 4

-4-2

24

(d)

-4 -2 2 4

-4-2

24

(17) The graph of g x |x 4| is a shifting of the graph of f x |x |(a) 4 units to the left(b) 4 units to the right *(c) 4 units downward(d) 4 units upward

(18) If the graph of f x 3x is reflected about the y axis, then the equation of the new function is(a) 13

x

(b) 3x

(c) 13 x *

(d) 3x (19) If cosx 3

2 , sinx 12 , then sin2x

(a) 32 *

(b) 2(c) 4(d) 3

4(20) The function f x 1

2xis increasing on R .

(a) True(b) False *

(21) If sin 34 and 0

2 , then cos

(a) 37

(b) 74

(c) 37

(d) 74 *

(22) If 3 , then sin

(a) 12

(b) 32

3

(c) 32 *

(d) 12

(23) The range of the function f x sinx is(a) R(b) 1,1(c) R 1,1(d) 1,1 *

(24) The function f x cotx is(a) even(b) odd *(c) even and odd(d) neither even nor odd

(25) If a is a positive number and x , y are real numbers, then ax y (a) axy(b) ax.y *(c) ax.ay(d) ax /y

(26) The range of the function y 2x 1 is(a) 1, *(b) 1,(c) , 1(d) , 1

(27) The following graph represents the function f x

-4 -2 2 4

-10

-5

(a) ex 1(b) e x 1(c) e x 1(d) 1 ex *

(28) The domain of the function f x 11 e2x is

(a) 0 *(b) 1(c) 0,1(d)

(29) If f x 3x 2 , then f 1x (a) x 3

2(b) x 3

2

4

(c) x 23 *

(d) x 23

(30) The following graph represents one - to - one function

-2 2

5

10

1. (a) true(b) false *

(31) The range of the function f x x is(a) R(b) R 0(c) 0, *(d) 0,

(32) One of the following identities is true(a) cos2x cos2x sin2x *(b) cos2x cos2x sin2x(c) cos2x cos22x sin22x(d) cos2x 2sinx. cosx

(33) The following graph

-4 -2 2 4-2

2

4

6

8

10

represents the function :

(a) f x x2 2 if x 0x 1 if x 0

(b) f x x2 2 if x 0x 1 if x 0

*

(c) f x x2 2 if x 0x 1 if x 0

(d) f x x2 2 if x 0x 1 if x 0

5

Kingdom of Saudi ArabiaKing AbdulAziz UniversityFaculty of ScienceDept. of Mathematics

� � � � � � � � � � � � � � � � � � � � � � � � � �Instructions: (30 points) Solve each of the following problems and choose

the correct answer :

1. The number 4:417417417:::::: is(a) Integer (b) RationalF(c) Irrational (d) Natural

2. If a < b and c > 0; then

(a) ac < bc F (b) ac > bc(c) ac � bc (d) ac � bc

3. If x < 2; then jx� 2j =(a) x� 2 (b) 2� xF(c) x+ 2 (d) �x� 2

4. If x2 � x� 20 � 0 , then x 2(a)[�4; 5] F (b) (�1;�4) [ (5;1)(c) (�4; 5) (d) (�1;�4] [ [5;1)

5. The solution of the inequality jx� 4j < 1 is the interval(a) (3; 5) F (b) (�5;�3)(c) (�1; 3) [ (5;1) (d) (�1; 5)

6. The distance between the points (6;�2) and (�1; 3) is equal to(a)

p70 (b)

p74 F

(c)p50 (d)

p26

7. The slope of the line that passes through the points (�1; 6) and (4;�3)is equal to

(a)�59

(b) 1

(c)3

2(d)

�95F

1

8. The slope m and the y-intercept b of the line 9x� 3y = 4 are :(a) m = 9 ; b = �4 (b) m = 3 ; b = 4

3(c) m = 3 ; b = � 4

3F (d) m = �9 ; b = 4

9. If two lines L1 and L1 with slopes m1 and m2 , respectively, have theproperty that m1 = m2 then the lines

(a) Are parallel F (b) Are perpendicular(c) Intersect (d) Are not parallel

10. The equation of the line that passes through the point (4;�5) andparallel to the x� axis is

(a) y = 5 (b) x = 4(c) x = �4 (d) y = �5 F

11. sin(15�

2+ 2�) = sin

15�

2

(a) True F (b) False

12. 135� =(a)2�3 rad (b) 4�3 rad(c) 3�2 rad (d) 3�4 rad F

13. If the raduis of a circle is 3cm; then the angle subtended by an arc oflength 6cm is

(a) 18 rad (b) 2 rad F(c) 1

2 rad (d) 3 rad

14. If tan � = 12 ; 0 < � <

�2 ; then cos � =

(a) 12 (b) 2(c) 2p

5F (d)

p52

15. If cos �3 =12 ; sin

�3 =

p32 ; then cos 2

�3 =

(a) � 12 F (b) 2p

3

(c) 2 (d)p32

2

16. If f(x) = 3x2 + 2x� 5 , then 3f(a) =

(a) 27a2 + 6a� 15 (b) 9a2 + 6a� 15F(c) 9a2 + 6a� 5 (d) 27a2 + 2a� 5

17. The domain of the function f(x) =px+ 3 is

(a) [3;1) (b) (�1;�3](c) [�3;1) F (d) (�1; 3]

18. The range of the function f(x) = jxj+ 1 is

(a) [0;1) (b) [�1;1)(c) (�1;�1] (d) [1;1) F

19. The accompanying �gure shows the graph of

­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5

1

2

3

4

5

6

7

8

9

10

x

y

(a) f(x) =�x2 if x < 2x if x > 2 (b) f(x) =

�x2 if x < 2x if x � 2

(c) f(x) =�x2 if x > 2x if x < 2 (d) f(x) =

�x2 if x � 2x if x > 2 F

20. The function f(x) =x3�xx4 + x2

is

3

(a) An even function (b) An odd function F(c) An even and odd function (d) Neither even nor odd

21. The function f(x) =px+ 1 + x2 is

(a) A root function (b) An algebric function F(c) An exponential function (d) A polynomial function

22. The function f(x) = x14 + 3x4 + x3 + 5 is polynomial of degree 4

(a)True (b)False F

23. The range of the function g(x) =p5 is

(a)�p5

F (b) [0;1)(c) (�1; 0) (d) (�1;1)

If f (x) = cosx and g (x) =px� 1 ,then �nd

f

gand the domain

off

gin questions (24) and (25) respectively :

24.f

g=

(a)cosxpx� 1

F (b)1p

cosx� 1(c)

px� 1cosx

(d)

px+ 1

cosx

25. The domain off

gis

(a) [1;1) (b) (�1;�1](c) (�1;1) (d) (1;1)F

26. If h(x) = sin 3px , f(x) = 3

px and g(x) = sinx , then

(a) h = f � g (b) h = g � f F(c) h = gf (d) h = f � f

4

27. If f(x) = x2 and g(x) = 3x , then (f � g)(3)

(a) 9 (b) 13

(c) 1F (d) 3

28. The equation of the function y = 3px whose graph is shifted 2 units right

and 3 units up is

(a) y = 3px� 2� 3 (b) y = 3

px+ 2 + 3

(c) y = 3px+ 2� 3 (d) y = 3

px� 2 + 3F

29. If f(x) = x2 , then f(x) is decreasing on the interval (�1; 0]a)True F b) False

30. Choose the �gure that shows the graph of a function f(x) = � jxj+ 2

(a)F

­4 ­2 2 4

­4

­2

2

4

x

y

(b)

­4 ­2 2 4

­4

­2

2

4

x

y

(c)

­4 ­2 2 4

­4

­2

2

4

x

y

(d)

­4 ­2 2 4

­4

­2

2

4

x

y

5

King Abdul Aziz University

Faculty of Sciences

Mathematics Department

Math 110 A Name : ID No.:

1) The real number in R is

A 2 B 1

C 3 D 49

2) 2

A 2 B 2

C 2 D 2

3) The solution of 4 10x is

A , 6 14, B , 14 6,

C 6,14 D 6,14

4) The solution set of 2 3 15x is

A 9, B ,9

C ,9 D 9,

5) The solution set of 2 2 0x x is

A 1,2 B ( , 2) (1, )

C 2,1 D ( , 1) (2, )

6) The solution set of 1 2x is

A ( , 1] [3, ) B ( , 3) (1, )

C 1,3 D ( , 1) (3, )

7) The distance between the points (1, 2) and ( 3,1) is

A 5 B 5

C 5 D 13

8) The function 2 1

( ) ; 33

x xf x x

x

is

A Quadratic B Polynomial

C Radical D Rational

9) The function 3 2( ) 3 2 1f x x x x is

A Quadratic B Cubic

C Linear D Constant

10) The solution of the equation 2 6 0x x is A 2,3 B 3,2

C 1,6 D 6,1

11) The points of intersection of the parabola 2 2 5y x x

and the line 1y x are

A (3,4) &( 2, 1) B (2,3)

C ( 3, 2) &(2,3) D ( 3, 2)

12) The domain of 2( ) 4f x x is

A ( , ) R B ( , 2] [2, )

C [ 2,2] D ( 2,2)

13) The domain of 2

5( )

5 6

xf x

x x

is

A ( 2, 3) B (2,3)

C \ 2,3R D \ 2, 3 R

14) The domain of 2

3( )

1

xf x

x

is

A ( 1,1) B \ 1R

C \ 1R D ( , ) R

15) The domain of 3( ) 1f x x is

A [1, ) B ( , ) R

C ( ,1] D (1, )

16) Let ( ) 2f x x , and ( )g x x . Then g

f

D is

A (2, ) B [2, )

C ( ,2] D (0, )

17) The y intercepts of 2 2 8y x x is

A 8y B 4,2y

C 8x D 8y

18) Let ( ) 2f x x , and ( )g x x . Then ( )f gD

is

A ( , ) R B [2, )

C ( ,2] D (2, )

19) Let ( ) 2f x x , and 2( ) 1g x x . Then ( )( )g f x is

A ( )( ) 1g f x x B 2( )( ) ( 1) 2g f x x x

C 2( )( ) 1g f x x D ( )( ) 1g f x x

20) Let ( ) 2f x x , and 2( ) 1g x x . Then ( )g fD is

A [0,2] B (2, )

C (0,2] D [2, )

21) Let 2( ) 1f x x , and 2( ) 2g x x . Then ( )( )fg x is

A 4 2( )( ) 2fg x x x B 4 2( )( ) 2fg x x x

C 4 2( )( ) 2fg x x x x D 4 2( )( ) 3 2fg x x x

22) The equation of the line passes through the point

( 2,1) with slope 2 is

A 2 5y x B 2 3y x

C 2 5y x D 2 3y x

23) The equation of the line passes through the point ( 2,1)

and Parallel to the line 5 3y x is

A 5 11y x B 5 9y x

C 5 1y x D 5 11y x

24) The equation of the line passes through the point ( 2,1)

and perpendicular to the line 5 3y x is

A 1 3

5 5y x B

13

5y x

C 1 7

5 5y x D

1 3

5 5y x

25) If

3 4( )

3 2

xf x

x

, then ( 4)f

A 1

7 B

2

9

C undefined D 1

7

26) The equation of the line passes through the points (1, 2) and

( 3,1) is

A 3 5

4 4y x B

3 5

4 4y x

C 1 5

4 4y x D

3 3

4 4y x

27) 2sin x

A 1 cos(2 )

2

x B

1 cos(2 )

2

x

C 1 cos( )

2

x D 1 cos(2 )x

28) sin( )4

A 2 B 1

2

C 2

2 D

2

2

29) If 4

3x

, then x

A 270 B 120

C 180 D 240

30) If 270x , then x

A 2

3

B

6

C

3

2

D

4

3

With best wishes

Math 110, 17/11/1430H Exam1–A 1 of 5

Instructions. (30 points) Solve each of the following problems.

(1pts) 1. The slope m and the y−intercept b of the line 6x − 2y = 4 are

(a)✔ m = 3, b = −2 (b) m = −3, b = −2

(c) m = 3, b = 2 (d) m = −3, b = 2

(1pts) 2. The center and the radius of the circle x2 + y2 + 2x = 3 are

(a) (0,−1), 2 (b)✔ (−1, 0), 2

(c) (1, 0), 2 (d) (0,−1), 2

(1pts) 3. The accompanying figure shows the graph of y = |x|shifted to new position. An equation for the new posi-tion is

(a) y = |x + 2| + 1

(b) y = |x + 2| − 1

(c)✔ y = |x − 2| + 1

(d) y = |x − 2| − 1

1

2

3

4

-11 2 3 4-1-2-3-4-5

y = ∣x∣

y

x

(1pts) 4. The domain of f(x) =x + 1x2 − 4

is

(a) (−∞,−2) ∪ (−2,∞) (b) (−∞, 2) ∪ (2,∞)

(c)✔ (−∞,−2) ∪ (−2, 2) ∪ (2,∞) (d) (−∞,−2) ∪ (2,∞)

(1pts) 5. The accompanying figure shows the graph of

(a)✔ f(x) = x

(b) f(x) = |x|

(c) f(x) = x3

(d) f(x) = x2

1

2

3

-1

-2

-3

-4

1 2 3-1-2-3-4

y

x

Math 110, 17/11/1430H Exam1–A 2 of 5

(1pts) 6. The solution of |4x − 3| = 9 are

(a)✔ x = 3,−3/2 (b) x = −3,−3/2

(c) x = 3, 3/2 (d) x = −3, 3/2

(1pts) 7. If the domain of y = f(x) is [−2, 6] and g(x) = f(x − 2), then domain g is

(a) [−4, 4] (b)✔ [0, 8]

(c) [−4, 12] (d) [−1, 3]

(1pts) 8. If f(x) = x + 1, and g(x) =√

x2 − 1 , then(

f

g

)(x) =

(a)1

x − 1(b)✔

x + 1√x2 − 1

(c)1

x + 1(d)

√x2 − 1x + 1

(1pts) 9. If f(x) = x + 1, and g(x) =√

x2 − 1 , then domain(

f

g

)is

(a) R (b) (1,∞)

(c) (−∞,−1] ∪ [1,∞) (d)✔ (−∞,−1) ∪ (1,∞)

(1pts) 10. An equation for the line passing through (1, 0) and is parallel to the line 8x − 4y = 12 is

(a)✔ y = 2x − 2 (b) y = −2x + 2

(c) y =−12

x +12

(d) y =12x − 1

2

(1pts) 11. The distance between (1, 2) and (3,−2) is

(a) 7 (b)√

7

(c) 4√

5 (d)✔ 2√

5

(1pts) 12. The solution set of the inequality∣∣∣∣x + 1

2

∣∣∣∣ > 1

(a) (−1, 3) (b) (−∞,−1) ∪ (3,∞)

(c) (−3, 1) (d)✔ (−∞,−3) ∪ (1,∞)

Math 110, 17/11/1430H Exam1–A 3 of 5

(1pts) 13. The function f(x) = x3 + x is

(a)✔ Odd (b) Neither even nor odd

(c) Even and odd (d) Even

(1pts) 14. A formula for the function graphed to the right is

(a) f(x) =

{x − 2, if 0 < x ≤ 2;−13

x − 53, if 2 < x ≤ 5.

(b) f(x) =

{x − 2, if 0 ≤ x ≤ 2;−13

x − 53, if 2 ≤ x ≤ 5.

(c)✔ f(x) =

{ −x + 2, if 0 < x ≤ 2;−13

x +53, if 2 < x ≤ 5.

(d) f(x) =

{ −x + 2, if 0 ≤ x ≤ 2;−13

x +53, if 2 ≤ x ≤ 5.

1

2

-11 2 3 4 5-1

��

�

��

�

y

x

(1pts) 15. The domain of f(x) =√

(1 − x)2 is

(a) (−∞, 1) ∪ (1,∞) (b)✔ R

(c) [1,∞) (d) (−∞, 1]

(1pts) 16. If g is an odd function defined at 0, then g(0) =

(a) 1 (b) −1

(c)✔ 0

(1pts) 17. The vertex of the parabola y = 2x2 − 12x + 1 is

(a) (−3,−17) (b) (−3, 17)

(c) (3, 17) (d)✔ (3,−17)

(1pts) 18. The domain of f(x) =x

x − 7is

(a) (−∞,−7) ∪ (−7,∞) (b) R

(c) (7,∞) (d)✔ (−∞, 7) ∪ (7,∞)

Math 110, 17/11/1430H Exam1–A 4 of 5

(1pts) 19. The domain of f(x) =√

x − 2 +√

5 − x is

(a)✔ [2, 5] (b) [2,∞)

(c) (−∞, 5] ∪ [2,∞) (d) (−∞, 5]

(1pts) 20. A particle starts at A(−2, 3) and its coordinate change by increments Δx = 2, Δy = −2. Its newposition is

(a) (1, 0) (b) (−1, 0)

(c)✔ (0, 1) (d) (0,−1)

(1pts) 21. The domain of the function f(x) = 2x + 4 is

(a) (−∞, 0) ∪ (0,∞) (b)✔ R

(c) (−∞,−2) ∪ (−2, 0) ∪ (0,∞) (d) (−∞,−2) ∪ (−2,∞)

(1pts) 22. The domain of f(x) =√

x2 − 2x − 3 is

(a) [3,∞) (b) (−∞,−1]

(c)✔ (−∞,−1] ∪ [3,∞) (d) [−1, 3]

(1pts) 23. The solution set of the inequality 2x − 12≥ 7x +

76

(a)(−∞,

13

](b)✔

(−∞,

−13

]

(c)[−13

,∞)

(d)(−13

,∞)

(1pts) 24. The domain of f(x) =1√

2x − 12is

(a) (−∞, 6) ∪ (6,∞) (b) R

(c)✔ (6,∞) (d) (−∞, 6)

(1pts) 25. If f(x) = x2 − 1 and g(x) =√

x + 1, then (g ◦ f)(x) =

(a) x (b) (x2 − 1)√

x + 1

(c)√

x + 1 + x2 − 1 (d)✔ |x|

Math 110, 17/11/1430H Exam1–A 5 of 5

(1pts) 26. If f(x) = x2 − 1 and g(x) =√

x + 1, then domain (g ◦ f) is

(a) [−1,∞) (b) (−1,∞)

(c) (−∞,−1) ∪ (−1,∞) (d)✔ R

(1pts) 27. The domain of the function f(x) = 3√

12x + 36 is

(a) (−∞, 0) ∪ (0,∞) (b) [−3,∞)

(c) (−∞,−3) ∪ (−3,∞) (d)✔ R

(1pts) 28. If a is a none-zero real number, then |a| = | − a|.

(a)✔ True (b) Fales

(1pts) 29. The x−intercept and y−intercept of the line12x − 1

3y =

16

(a) x − intercept =13, y − intercept =

12

(b) x − intercept =−12

, y − intercept =13

(c) x − intercept =−13

, y − intercept =12

(d)✔ x − intercept =13, y − intercept =

−12

(1pts) 30. If the graph of y = x2 − 1 is reflected about the x−axis. An equation for the new graph is

(a) y = x2 + 1 (b) y = −x2 − 1

(c) y = x2 − 1 (d)✔ y = −x2 + 1