+Algebra 2/Trig Final Exam Review Fall Semester€¦ · Final Exam Review – Fall Semester 8 63) Describe the transformation of the graph from f (x) x to f (x) x 5. [A] Shift up

+Algebra 2/Trig Final Exam Review – Fall Semester

1

1) Simplify:

3

2

25

z

yx [A]

1

18

z

yx [B]

6

615

y

zx [C]

12

5

yx

z [D]

6

615

z

yx

[E] None of these

2) Simplify: 432 xxx [A] 24x [B] 9x [C] 2793 xx [D] 10x [E] None of these

3) Simplify: 232a [A] 12a [B] 7a [C] 10a [D] 8a [E] None of these

4) Simplify: 2332 xx [A] 10x [B] 10x [C] 12x [D] 12x [E] None of these

5) Simplify: 432 xxx [A] 24x [B] 24x [C] 9x [D] 9x [E] None of these

6) Evaluate:

3/2

64

1

[A] 16 [B]

16

1 [C]

512

1 [D] 512 [E] None of these

7) Rationalize:27

5

[A]

47

2535 [B]

47

235 [C] 27 [D]

3

235 [E] None of these

8) Rationalize: 25

6

x [A]

23

256 x [B] 252 x [C]

23

230 x

[D]

21

256 x [E] None of these

9) Which of the following are polynomials?

[A] 123 2 xx [B] 1

1

x

x [C]

xx

1 [D] None [E] All

10) Which of the following are polynomials?

[A] 22

13

x

x [B] 12 1 xx [C] 2

3

2

4

1 3 xx [D] None [E] All


2

11) Simplify: 112524 2232 xxxxx

[A] 23 59 xx [B] 125 23 xxx [C] 66x [D] 2255 23 xxx [E] None of these

12) Simplify: )2(4)67(3 xxxx [A] xx 1017 2 [B] 234 14424084 xxx

[C] xx 1421 2 [D] 23 9672 xx [E] None of these

13) Expand: 24yx [A] 22 4 yxyx [B] 22 16yx [C] 22 168 yxyx

[D] 22 4yx [E] None of these

14) Expand: (2 )( )x y x y [A] 222 yx [B] 2 22x xy y [C] 222 yx

[D] xyyx 22 [E] None of these

15) Factor: 278 3 x [A] 3)32( x [B] 9124)32( 2 xxx [C] 964)32( 2 xxx

[D] 964)32( 2 xxx [E] None of these

16) Factor: 2163 x [A] 3)6( x [B] 36)6( 2 xx [C] 366)6( 2 xxx

[D] 366)6( 2 xxx [E] None of these

17) Factor: 49429 2 xx [A] 2)73( x [B] 2)79( x [C] 2)73( x

[D] )49429( xx [E] None of these

18) Factor: 16133 2 xx [A] )1)(163( xx [B] )1)(163( xx [C] )13)(16( xx

[D] )13)(16( xx [E] None of these

19) Factor completely: rtrrstrs 12832 [A] )12832( tstsr [B] )32)(4( trrs

[C] )32)(4( tsr [D] )32)(4( tsr [E] None of these


3

20) Factor completely: 483 4 x [A] 22 )4(3 xx [B] 4)2(3 x [C] 22 )2()2(3 xx

[D] )2)(2(43 2 xxx [E] None of these

21) Find the domain: xx

x

2

132

[A] ),0)(0,( [B] ),0)(2,( [C] ),2)(2,0)(0,(

[D] ),2)(2,0)(0,)(,(31

31 [E] None of these

22) Find the domain: 2x [A] ),( [B] ),0[ [C] ),2[ [D] )2,( [E] None of these

23) Identify the type(s) of symmetry: 012 224 yxyx

[A] x-axis [B] y-axis [C] origin [D] Both A and B [E] None of these

24) Identify the type(s) of symmetry: xxy 33

[A] x-axis [B] y-axis [C] origin [D] Both A and B [E] None of these

25) Identify the graph of the equation: 7y x

[A] [B] [C] [D]

26) Identify the graph of the equation: 3y x

[A] [B] [C] [D] 27) Determine the equation that is a circle with a center at (– 4, 3) and a radius of 5.

[A] 25)3()4( 22 yx [B] 5)3)(4( yx [C] 5)3()4( 22 yx

[D] 25)3()4( 22 yx [E] None of these


4

28) Find the center and radius of the circle: 36)1()4( 22 yx

[A] Center: )1 ,4( , Radius: 36 [B] Center: )1 ,4( , Radius: 36 [C] Center: )1 ,4( , Radius: 6

[D] Center: )1 ,4( , Radius: 6 [E] None of these

29) Solve: 221332 xx [A] 5

2x [B]

2

5x [C] 0x [D] No Sol. [E] None of these

30) Solve: 682374 xxx [A] No Sol [B] 0x [C] 1x [D] 2x [E] None of these **YOU MAY SKIP 31 AND 32**

31) Solve: 64

1

2

3

xx [A] 5x [B]

5

23x [C]

2

1x [D]

8

35x [E] None of these

32) Solve: 3

14

3

46

5

23

xx [A]

21

44x [B]

12

37x [C] 5x [D] 4x [E] None of these

33) Use the discriminant to determine the number of real solutions for: 01537 2 xx [A] 0 [B] 1 [C] 2 [D] 3 [E] None of these

34) Use the discriminant to determine the number of real solutions for: 0323

1 2 xx

[A] 0 [B] 1 [C] 2 [D] 3 [E] None of these

35) Solve: )5(3)1(52 2 xxx [A] 2

391x [B]

3

15x [C] 5 ,1 ,0 x

[D] 5 ,1x [E] None of these

36) Solve: 9522x [A] 1,4 x [B] 1x [C] 38x

[D] 8 ,14x [E] None of these

37) Solve: 2)3()1)(2( xxx [A]

5

11x [B] 9 ,2x [C] 11x

[D] 2,7 x [E] None of these


5

38) Solve: 152 22 xxx [A] 5 ,0x [B] 11

4x [C]

2

295x

[D] 2


39) Write the answer as a complex number in standard form:i

i

41

4

[A] i

17

8 [B] i [C] i

[D] i17

8 [E] None of these

40) Solve: 328 2 xx [A] 8

32 x [B]

16

231 ix

[C]

16

232

ix

[D] 8

231 ix

[E] None of these

41) Simplify: 31i [A] 1 [B] – 1 [C] i [D] i [E] None of these

42) Solve: 01025 23 xxx [A] 5 ,2 x [B] 5x [C] 5 ,2x

[D] 5 ,2 x [E] None of these

43) Solve: 016249 24 xx [A] 3

32 x [B]

3

32 x [C]

3

32 0, x

[D] 3


44) Solve: 2316 xx [A] 3 x [B] 4

17 x [C]

2

1 x

[D] No Solution [E] None of these

45) Solve: 13|103| x [A] 1 x [B] 1 x [C] 3

23 1, x

[D] 3

23 1, x [E] None of these


6

46) Solve: 5214 x [A]

2

9, [B]

2

9, [C]

,

2

9 [D]

,

2

9 [E] None of these

47) Solve: 7132 x [A] 2 ,1 [B]

3

8 ,

3

1 [C] ,2 [D] 2 ,1 [E] None of these

48) Solve: 9)1( 2 x [A] 2 ,4x [B] ,2 4 , [C] 4 ,2

[D] ) ,4( 2 , [E] None of these

49) Solve: 063 23 xx [A] ) ,2( 0 , [B] 2) (0, [C] 0 , [D] ,2 [E] None of these

50) Solve: 532 2 xx [A] 1] ,5.2[ [B] 1, 5.2 , [C] 5, 5.2 ,

[D] 2.5, [E] None of these

51) Find the equation of the line parallel to: 13 yx and passing through the point: ).10 ,3(

[A] 93

1 xy [B] 13 xy [C] 193 xy [D] 11

3

1 xy [E] None of these

52) Find the equation of the line perpendicular to: 223 yx and passing through the point: ).2 ,6(

[A] 112

3 xy [B] 6

3

2 xy [C] 7

2

3 xy [D] 2

3

2 xy [E] None of these

53) In which equation(s) is y a function of x? [A] 0132 yx [B] 73 22 yx [C] 72 2 yx

[D] Both A and B [E] Both A and C

54) Given: .43)( 2xxg Find: ).2(g [A] – 13 [B] 19 [C] – 61 [D] – 3 [E] None of these

55) Given:

2 ,1

2 ,43)(

2 xx

xxxf . Find ).3(f [A] 13 [B] 10 [C] 5 [D] 3 [E] None of these


7

56) Given:

5 |,3|

5 ,19)(

xx

xxxf . Find ).4(f [A] – 15 [B] 1 [C] – 1 [D] – 23 [E] None of these

57) You invest $12,000 to start a business. Each unit you produce costs $3.40 and is sold for $5.60. Which equation

represents the profit of the business?

[A] 120009 xP [B] 120009 xP [C] 120002.2 xP [D] 120002.2 xP [E] None of these 58) To produce x units of a product, there are fixed costs of $23,000 and a production cost of $4.78 per unit. Which

equation represents the total cost as a function of x?

[A] 2300078.4 xC [B] xC 78.423000 [C] 2300078.4

x

C [D] xC 78.23004 [E] None of these

59) Determine which of the following are EVEN functions. [A] [B] [C] [D] All are even [E] None are even 60) Determine which of the following are ODD functions. [A] [B] [C] [D] All are odd

[E] None are even

61) If the following function EVEN or ODD? 23 32)( xxxf

[A] Even [B] Odd [C] Neither [D] Both

62) If the following function EVEN or ODD? 133)( 24 xxxf

[A] Even [B] Odd [C] Neither [D] Both


8

63) Describe the transformation of the graph from xxf )( to .5)( xxf

[A] Shift up 5 [B] Shift down 5 [C] Shift left 5 [D] Shift right 5 [E] None of these 64) What kind of reflection has taken place from ||)( xxf to 7|5|)( xxf ?

[A] over x-axis [B] over y-axis [C] through origin [D] over xy [E] None of these

65) Given 42)( xxf and ,31)( xxg find ).)(( xgf

[A] 35 x [B] 3x [C] )3( x [D] 0 [E] None of these

66) Given 6)( xf and ,12)( 2 xxg find ).)(( xgf

[A] 52 2 x [B] 72 2 x [C] 72 2 x [D] 52 2 x [E] None of these 67) Given xxf 2)( and ,1)( xxg find ).)(( xfg

[A] 1x [B] xx 22 2 [C] 13 x [D] 12 2 x [E] None of these

68) Given x

xf1

)( and ,5)( 2 xxg find ).)(( xfg

[A] 52 x

x [B] 52 xx [C]

x

x 52 [D] 5x [E] None of these

69) Given 7)( xxf and ,4)( xxg find ).)(( xgf

[A] 73 x [B] xx 74 2 [C] 74 x [D] )7(4 x [E] None of these

70) Given 4)( xxf and ,3)( xxg find .)2(gf


71) If )(xf is one-to-one, then )(1 xf is a reflection of )(xf …

[A] over x-axis [B] over y-axis [C] through origin [D] over xy [E] None of these

72) Find ).(1 xf

7

54)(

xxf

[A] )4(

5

7)(1 xxf [B] )47(

5

1)(1 xxf

[C] x

xf5

7

4

7)(1 [D]

xxf

54

7)(1

[E] None of these


9

73) Find ).(1 xf 12)( xxf [A] 12)(1 yxf [B] 41)( 21 xxf

[C] 12

1)( 21 xxf [D] 1)( 21 xxf [E] None of these

74) Which quadratic equation represents the parabola graphed below?

[A] 1)4(2

1 2 xy [B] 1)4( 2 xy

[C] 1)4(2

1 2 xy [D] 4)1( 2 xy

[E] None of these

75) Write the quadratic in vertex form: .282 xxy

[A] 18)4( 2 xy [B] 14)4( 2 xy [C] 66)8( 2 xy [D] 18)4( 2 xy [E] None of these

76) Find the minimum of the parabola: 982 2 xxy

[A] 1 ,2 [B] 33 ,2 [C] 17 ,2 [D] 17 ,2 [E] None of these

77) Find the maximum of the parabola: 1123 2 xxy

[A] 5 ,6 [B] 19 ,2 [C] 13 ,2 [D] 14 ,1 [E] None of these

78) Find the x- and y-intercepts of the parabola: .432 xxy

[A] 0 ,1 ,0 ,4 ,4 ,0 [B] 0 ,1 ,0 ,4 ,4 ,0 [C] 1 ,0 ,0 ,4 ,4 ,0

[D] 0 ,1 ,4 ,0 ,0 ,4 [E] None of these

79) Determine the end behavior of the graph of: .123 4 xxy

[A] Rise left and right [B] Fall left and right [C] Rise left, fall right [D] Fall left, rise right [E] None of these


10

80) Determine the end behavior of the graph of: .12 25 xxy

[A] Rise left and right [B] Fall left and right [C] Rise left, fall right [D] Fall left, rise right [E] None of these

81) Find all of the real zeros for the function: .43)( 23 xxxxf [A] 4 ,1x [B] 1 ,4x [C] 4 ,0x

[D] 4 ,0 ,1x [E] None of these

82) Find all of the real zeros for the function: .48163)( 23 xxxxf

[A] 3x [B] 3x [C] 4 3, ,4 x [D] 4 ,3x [E] None of these

83) Divide: 233869 23 xxxx [A] 233

83 3

72

xxx [B]

23

7243 2

xxx

[C] 233

1643 3

232

xxx [D]

23

343 2

xxx [E] None of these

84) Divide: 1125 24 xxx [A] 1

43355 23

xxxx [B] 875 2 xx

[C] 1

43355 23

xxxx [D] 435 2 xx [E] None of these

85) Use the given factor of (x + 2) to factor completely: .81023 xxx [A] )1)(4)(2( xxx [B] 1 ,4 ,2 [C] )4)(1)(2( xxx [D] )1)(4)(2( xxx [E] None of these

86) List the possible rational zeros of: .5323 35 xxx

[A] 53

51

31

35 ,,1,5,,3, [B]

53

51 ,,1,3 [C]

35

31 ,,1,5 [D]

53

35 ,,1,3 [E] None of these

87) Find all of the real roots: .1552 23 xxx

[A] 1 ,1 ,3 [B] 2 ,2

3 ,1 [C] 2 ,

2

3 ,2 [D] 5 ,2 ,6 [E] None of these

88) Find all of the zeros: .14425 24 xx

[A] 5,32 [B] 32 ,1 [C] ii 3 ,4 [D] ii 3 ,4 [E] None of these


11

89) 90) 91) 92) Which of the following has an inverse? 93) 94) `


12

95) 96) 97) 98) A twenty pound mixture of two kinds of candy sells for $30.52. One of the candies sells for $1.35 per pound and the

other sells for $1.79 per pound. How many pounds of the cheaper candy are in the mixture? 99) 100) 101) 102) Eleanor invests $18,000 in two accounts that pay 9.25% and 10.5% simple interest respectively. How much is invested

at 9.25% if the annual interest earned is $1827.50? [A] $1300 [B] $5000 [C] $8000 [D] $10,000 [E] None of these 103) Maria inherited $15,000 and decided to invest it in two separate accounts. One of them pays 9.25% simple interest and

the other pays 11.5%. Her annual interest is $1623.75. How much did she invest at 9.25%?


13

0

42

x

yx

yx

0

42

y

xy

yx

0

42

y

xy

yx

0

42

y

yx

yx

0

0

1052

1

3

y

x

yx

yx

yx

[A] $4500 [B] $10,500 [C] $488 [D] $14,512 [E] None of these 104) Match the graph with the correct system of inequalities. [A] [B] [C] [D] [E] None of these 105) Find the maximum of the objective function: yxZ 69 given the following constraints:



14

ANSWERS 1) B 2) B 3) A 4) C 5) D 6) E 7) A 8) A 9) A 10) C 11) D 12) A 13) C 14) B 15) C 16) C 17) A 18) E 19) D 20) D 21) C 22) C 23) B 24) C 25) D 26) B 27) D 28) C 29) E 30) B 31) A 32) D 33) A 34) B 35) D 36) A 37) A 38) C 39) C 40) D 41) D 42) D 43) A 44) B 45) C 46) D 47) D 48) B 49) D 50) B 51) A 52) D 53) E 54) A 55) B 56) B 57) D 58) A 59) B 60) C 61) C 62) A 63) D 64) A 65) A 66) C 67) B 68) C 69) C 70) B 71) D 72) B 73) C 74) B 75) B 76) A 77) C 78) A 79) A 80) C 81) D 82) C 83) D 84) A 85) C 86) C 87) E 88) D 89) A 90) A 91) C 92) A 93) A 94) A 95) B 96) D 97) B 98) C 99) A 100) A 101) A 102) B 103) A 104) A 105) C

+Algebra 2/Trig Final Exam Review Fall Semester€¦ · Final Exam Review – Fall Semester 8 63) Describe the transformation of the graph from f (x) x to f (x) x 5. [A] Shift up

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