Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Algebra 2 - Spring Final 2013 Review

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Classify –2x4 – x3 + 8x2 + 12 by degree.a. quartic c. quadratic b. quintic d. cubic

What are the zeros of the function? What are their multiplicities?

____ 2. f(x) x4 4x3 3x2

a. the numbers –1 and –3 are zeros of multiplicity 2; the number 0 is a zero of multiplicity 1b. the number 0 is a zero of multiplicity 2; the numbers 1 and 3 are zeros of multiplicity 1c. the numbers 0 and 1 are zeros of multiplicity 2; the number 3 is a zero of multiplicity 1d. the number 0 is a zero of multiplicity 2; the numbers –1 and –3 are zeros of multiplicity 1

____ 3. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation x3 4x2 7x 8 0. Do not find the actual roots.a. –8, –1, 1, 8 c. 1, 2, 4, 8b. –8, –4, –2, –1, 1, 2, 4, 8 d. no possible roots

How many roots do the following equations have?

____ 4. 2x4 x3 12x2 25x 5 0a. 2 c. 4b. 3 d. 5

____ 5. Find all the real square roots of 916

.

a. no real root c. 34

and 34

b. 34

d. 81256

Find the real-number root.

____ 6. 125343

3

a. 2549

b. 125343

c. 1251029

d. 57

Name: ________________________ ID: A

2

What is a simpler form of the radical expression?

____ 7. 27x15 y243

a. 3x5 y8 b. 9x 15 y 24 c. 3x5 y8 d. 9 x15 y 24

Multiply and simplify if possible.

____ 8. 7x x 7 7

a. x 7 49 x c. x 7 x 49b. 7x 49x d. 42x

What is the simplest form of the product?

____ 9. 50x 7y 7 6xy 4

a. 2x 4 y 6 75y c. 5x4 y6 12

b. 10x 4y 5 3y d. 30x4 y5 y

____ 10. 270x203

5x3

a. 2x 3x63 b. 3x6 2x3 c. 135x 193 d. 3x6 135x

What is the simplest form of the expression?

____ 11. 20 45 5a. 4 5 c. 13 5b. 6 5 d. 5 5

What is the product of the radical expression?

____ 12. 7 2

8 2

a. 54 56 2 c. 13 15 2b. 54 2 d. 58 56 2

Name: ________________________ ID: A

3

How can you write the expression with rationalized denominator?

____ 13. 2 33

63

a.2 63 9 183

6c.

2 63 9 43

6

b.2 363 3 23

6d.

2 363 3 43

6

____ 14. Write the exponential expression 3x38 in radical form.

a. 3 x38 b. 3x38 c. 3 x83 d. 338 x 38

____ 15.

Write the radical expression 8x 157 in exponential form.

a. 8x

715 b. 8x

157 c. 8x

157 d. 8x

715

What is the simplest form of the number?

____ 16. 2 28

a. 1024 c. 285

b. 258 d. 2

110

____ 17. What is the solution of 5x 1 x 5?a. x = 0 c. x = 16b. x = 16 and x = 0 d. x = 16 and x = 1

____ 18. Let f(x) 3x 6 and g(x) x 2. Find fg and its domain.

a. 3; all real numbersb. 3; all real numbers except x 2c. 1; all real numbersd. –3; all real numbers except x 3

Name: ________________________ ID: A

4

____ 19. The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 361 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth.

a. y 361 12

32 x

; 0 kg c. y 2 1361

132

x

; 0.797 kg

b. y 361 12

132

x

; 323.945 kg d. y 12

1361

132

x

; 0.199 kg

____ 20. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years?a. $800.26 b. $6,701.28 c. $10,138.07 d. $1,923.23

____ 21. You open a savings account and deposit $1,000. After 1 year of earning continuously compounded interest, your balance is $1,018.16. After 2 years, the balance is $1,036.66. Assuming you make no deposits or withdrawals, find the equation for the best-fitting exponential function to represent the balance of the account after x years. How much money will be in the account after 10 years?

a. A 1000 e1.8 , $6,049.65 c. A 1000 e 0.018t , $1,197.22b. A 1000 e0.018t , $1,001.20 d. A 1000 e 1.8 * t , $1,001.20

Write the equation in logarithmic form.

____ 22. 25 32a. log 32 5 2 c. log 32 5b. log2 32 5 d. log5 32 2

Write the equation in exponential form.

____ 23. log(a b)c 16

a. (a b)16 c c. c16 (a b)b. 16(a b) c d. (a b)c 16

Evaluate the logarithm.

____ 24. log3 243a. 5 b. –5 c. 4 d. 3

Expand the logarithmic expression.

____ 25. log3 11p 3

a. log3 11 3 log3 p c. log3 11 3 log3 pb. log 3 11 3 log 3 p d. 11 log 3 p 3

Name: ________________________ ID: A

5

____ 26. Use the Change of Base Formula to evaluate log7 40. a. 0.527 c. 3.689b. 1.602 d. 1.896

Write the expression as a single natural logarithm.

____ 27. 3 ln a 12 (ln b ln c2 )

a. ln 3a0.5bc2 b. 3

2 ln abc2 c. ln a 3

bc d. ln a 3

c b

____ 28. Simplify ln e3 .

a. 3 b. 13e c. 3e d. 1

3

____ 29. Solve ln x ln 6 0.a. 6 b. 6e c. e6 d. ln 6

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it.

____ 30. x 9 11 13 15

y –17 –1 6 27

a. inverse variation; y 153x

b. direct variation; y = 179 x

c. neither

____ 31. Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse variation.

a. y 2x c. y 80

x

b. y 18x d. y = 0.8x

____ 32. Suppose that y varies directly with x and inversely with z, and y = 28 when x = 32 and z = 8. Write the equation that models the relationship. Then find y when x = 12 and z = 3.

a. y 8zx ; 2 c. y 7z

x ; 74

b. y 7xz ; 28 d. y 8x

z ; 32

Name: ________________________ ID: A

6

____ 33. This graph of a function is a translation of y 4x . What is an equation for the function?

a. y 4x 3 4 c. y 4

x 4 3

b. y 4x 3 4 d. y 4

x 4 3

Find any points of discontinuity for the rational function.

____ 34. What are the points of discontinuity? Are they all removable?

y (x 7)(x 3)x 2 10x 21

a. x = 1, x = –8, x = –2; yes c. x = –7, x = –3; nob. x = 7, x = 3; yes d. x = –1, x = 8, x = 2; no

____ 35. Describe the vertical asymptote(s) and hole(s) for the graph of y (x 3)(x 1)(x 1)(x 5) .

a. asymptote: x = 5 and hole: x = 1b. asymptote: x = –5 and hole: x = –1c. asymptote: x = –3 and hole: x = 5d. asymptote: x = 5 and hole: x = –1

____ 36. Find the horizontal asymptote of the graph of y 2x 3 3x 22x 3 6x 2

.

a. y = 1 c. no horizontal asymptoteb. y = 1 d. y = 0

Name: ________________________ ID: A

7

Simplify the rational expression. State any restrictions on the variable.

____ 37. n 4 10n 2 24n 4 9n 2 18

a. n 2 4n 2 3

; n 6 , n 3 c. n 2 4n 2 3

; n 6, n 3

b. n 2 4n 2 3

; n 6, n 3 d.(n 2 4)

n 2 3; n 6 , n 3

What is the product in simplest form? State any restrictions on the variable.

____ 38. 3g 5

10h 2 h 5

10g 2

a.3g 3 h 3

100, g 0, h 0 c.

3g 7

100h 7 , g 0, h 0

b. 1003g 3 h 3 , g 0, h 0 d. 3

100g 7 h 7 , g 0, h 0

____ 39. y 2

y 3 y 2 y 6

y 2 1y

a.y2 2yy 1 , y 3, 1 c.

y 2y 1 , y 3, 0, 1

b.y2 2yy 1 , y 3, 0, 1 d.

y 2y 1 , y 3, 1

What is the quotient in simplified form? State any restrictions on the variable.

____ 40. a 2a 5 a 1

a 2 8a 15

a.(a 2)(a 3)

a 1 , a 5, 1, 3 c.(a 2)(a 3)

a 1 , a 3, 1

b.(a 2)(a 1)(a 5)2(a 3)

, a 5, 3, 1 d.(a 2)(a 1)(a 5)2 (a 3)

, a 5, 3

Name: ________________________ ID: A

8

Simplify the difference.

____ 41. z2 11z 30z2 z 20

z2 2z 24z2 9z 18

a. z 34(z 4)(z 3) c. 2z2 2

(z 4)(z 3)

b. 17z 2(z 4)(z 3) d. 2z2 8z 34

2z2 34

Simplify the complex fraction.

____ 42. x 4x

y73x

a. 15x2

7y b.7x(y 4)

3xy c.3x2 (y 4)

7y d.3(y 4)

7y

Name: ________________________ ID: A

9

____ 43. Graph 4x2 4y2 64. What are the domain and range?

a.

Domain: 4 x 4Range:4 y 4

c.

Domain: 16 x 16Range: 16 y 16

b.

Domain: all real numbersRange: 16 y 16

d.

Domain: all real numbersRange: 4 y 4

Name: ________________________ ID: A

10

Identify the center and intercepts of the conic section. Then find the domain and range.

____ 44.

a. The center of the ellipse is (0, 0). The x-intercepts are (0, 5) and (0, –5). The y-intercepts are (–3, 0) and (3, 0). The domain is {x | –3 x 3}. The range is {y | –5  y  5}.

c. The center of the ellipse is (0, 0). The x-intercepts are (0, 5) and (0, –5). The y-intercepts are (–3, 0) and (3, 0). The domain is {x | –5 y 5}. The range is {y | –3  x  3}.

b. The center of the ellipse is (0, 0). The x-intercepts are (–3, 0) and (3, 0). The y-intercepts are (0, 5) and (0, –5). The domain is {x | –3  x  3}. The range is {y | –5  y  5}.

d. The center of the ellipse is (0, 0). The x-intercepts are (–3, 0) and (3, 0). The y-intercepts are (0, 5) and (0, –5). The domain is {x | –5 y 5}. The range is {y | –3  x  3}.

What are the vertex, focus, and directrix of the parabola with the given equation?

____ 45. 8y x2 8x 16a. vertex (–4, –4); focus (4, –2); directrix y = –6b. vertex (4, 4); focus (0, –2); directrix y = –2c. vertex (4, –4); focus (4, –2); directrix y = –6d. vertex (–4, 4); focus (0, 2); directrix y = 2

Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics.

____ 46. vertex at (3, 0) and co-vertex at (0, 5)

a. x2

5

y2

3 1 c. x2

9

y2

25 1

b. x2

25

y2

9 1 d. x2

3

y2

5 1

Name: ________________________ ID: A

11

____ 47. Write an equation of the ellipse with foci at (0, 11) and vertices at (0, 12).

a. x 2

265

y 2

144 1 c. x2

144

y2

23 1

b. x 2

265

y 2

144 1 d. x2

23

y2

144 1

____ 48. A hyperbola has vertices 5,0

and one focus 6,0

. What is the standard-form equation of the hyperbola?

a. x2

11 y2

25 1 c.y2

11 x2

25 1

b.y2

25 x2

11 1 d. x2

25 y2

11 1

Identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci.

____ 49. y2 4x 10y 33 0a. parabola; vertex (–2, 5) c. parabola; vertex (2, 4)b. parabola; vertex (4, 5) d. parabola; vertex (2, –5)

____ 50. x2 y2 8x 8y 17a. circle; center (–4, –4); radius = 49 c. circle; center (4, 4); radius = 49b. circle; center (–4, –4); radius = 7 d. circle; center (4, 4); radius = 7

Short Answer

51. Use synthetic division to find P(–2) for P(x) x4 6x3 2x2 7x 10.

52. Find a third-degree polynomial equation with rational coefficients that has roots –4 and 2 + i.

Find all the zeros of the equation.

53. 2x4 5x3 53x2 125x 75 0

What is a simpler form of the radical expression?

54. 36g 6

What is the simplest form of the radical expression?

55. 2 2x4 6 2x4

Name: ________________________ ID: A

12

How can you write the expression with rationalized denominator?

56. 3 63 6

What is the solution of the equation?

57. 2 (x 6)35 3 19

58. 4(3 x)43 5 59

What is the solution of the equation? Eliminate any extraneous solutions.

59. 2x 6 15 8 10x

15

60. Let f(x) 4x 5 and g(x) 6x 3. Find f(x) g(x).

61. Let f(x) 2x 7 and g(x) 4x 3. Find (f g)(5).

62. For the function f(x) (8 2x)2 , find f 1 . Determine whether f 1 is a function.

63. y 7 6 x 2 1

Write the expression as a single logarithm.

64. 4 log x 6 log (x 2)

Solve the exponential equation.

65. 116 644x 3

Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.

66. Solve log(4x 10) 3.

Use natural logarithms to solve the equation. Round to the nearest thousandth.

67. 8e4x 8 15

Name: ________________________ ID: A

13

Solve the equation. Check the solution.

68. 4x 1 1

x 5

69. 6x2 9

1x 3 1

70. Write an equation of a parabola with a vertex at the origin and a directrix at y = 5.

71. Write an equation for the translation of x2 y2 49 by 3 units left and 4 units up.

Write an equation in standard form for the circle.

72.

73. Divide 4x3 2x2 3x 4 by x + 4.

74. Write –2x2(–5x2 + 4x3) in standard form.

Find the roots of the polynomial equation.

75. x3 2x2 10x 136 0

76. A polynomial equation with rational coefficients has the roots 3 6, 2 5 . Find two additional roots.

What is the simplest form of the expression?

77. 128a 13 b 63

Multiply and simplify if possible.

78. 114 34

Name: ________________________ ID: A

14

Simplify.

79. 313 9

13

80. For the function f(x) x 9, find (f f 1)(5).

ID: A

1

Algebra 2 - Spring Final 2013 ReviewAnswer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: L2 REF: 5-1 Polynomial FunctionsOBJ: 5-1.1 To classify polynomials NAT: CC A.SSE.1.a| CC F.IF.4| CC F.IF.7| CC F.IF.7.cTOP: 5-1 Problem 1 Classifying Polynomials KEY: degree of a polynomial | polynomial function | standard form of a polynomial function

2. ANS: B PTS: 1 DIF: L3 REF: 5-2 Polynomials, Linear Factors, and Zeros OBJ: 5-2.2 To write a polynomial function from its zeros NAT: CC A.SSE.1| CC A.APR.3| CC F.IF.7| CC F.IF.7.c| CC F.BF.1 TOP: 5-2 Problem 4 Finding the Multiplicity of a Zero KEY: multiple zero | multiplicity

3. ANS: B PTS: 1 DIF: L2 REF: 5-5 Theorems About Roots of Polynomial Equations OBJ: 5-5.1 To solve equations using the Rational Root Theorem NAT: CC N.CN.7| CC N.CN.8 TOP: 5-5 Problem 1 Finding a Rational RootKEY: Rational Root Theorem

4. ANS: C PTS: 1 DIF: L3 REF: 5-6 The Fundamental Theorem of Algebra OBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3TOP: 5-6 Problem 1 Finding All the Roots of a Polynomial Function KEY: Fundamental Theorem of Algebra | roots

5. ANS: A PTS: 1 DIF: L2 REF: 6-1 Roots and Radical ExpressionsOBJ: 6-1.1 To find nth roots NAT: CC A.SSE.2| A.3.e TOP: 6-1 Problem 1 Finding All Real Roots KEY: nth root

6. ANS: D PTS: 1 DIF: L3 REF: 6-1 Roots and Radical ExpressionsOBJ: 6-1.1 To find nth roots NAT: CC A.SSE.2| A.3.e TOP: 6-1 Problem 2 Finding Roots KEY: radicand | index | nth root

7. ANS: C PTS: 1 DIF: L3 REF: 6-1 Roots and Radical ExpressionsOBJ: 6-1.1 To find nth roots NAT: CC A.SSE.2| A.3.e TOP: 6-1 Problem 3 Simplifying Radical Expressions KEY: radicand | index | nth root

8. ANS: A PTS: 1 DIF: L4 REF: 6-2 Multiplying and Dividing Radical Expressions OBJ: 6-2.1 To multiply and divide radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 1 Multiplying Radical Expressions

9. ANS: B PTS: 1 DIF: L3 REF: 6-2 Multiplying and Dividing Radical Expressions OBJ: 6-2.1 To multiply and divide radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 3 Simplifying a Product KEY: simplest form of a radical

10. ANS: B PTS: 1 DIF: L3 REF: 6-2 Multiplying and Dividing Radical Expressions OBJ: 6-2.1 To multiply and divide radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 4 Dividing Radical Expressions KEY: simplest form of a radical

ID: A

2

11. ANS: A PTS: 1 DIF: L3 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 3 Simplifying Before Adding or Subtracting KEY: like radicals

12. ANS: B PTS: 1 DIF: L2 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 4 Multiplying Binomial Radical Expressions KEY: like radicals

13. ANS: D PTS: 1 DIF: L2 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 6 Rationalizing the Denominator KEY: like radicals

14. ANS: A PTS: 1 DIF: L2 REF: 6-4 Rational ExponentsOBJ: 6-4.1 To simplify expressions with rational exponents NAT: CC N.RN.1| CC N.RN.2TOP: 6-4 Problem 2 Converting Between Exponential and Radical FormKEY: rational exponents

15. ANS: C PTS: 1 DIF: L4 REF: 6-4 Rational ExponentsOBJ: 6-4.1 To simplify expressions with rational exponents NAT: CC N.RN.1| CC N.RN.2TOP: 6-4 Problem 2 Converting Between Exponential and Radical FormKEY: rational exponents

16. ANS: B PTS: 1 DIF: L3 REF: 6-4 Rational ExponentsOBJ: 6-4.1 To simplify expressions with rational exponents NAT: CC N.RN.1| CC N.RN.2TOP: 6-4 Problem 4 Combining Radical Expressions KEY: rational exponent

17. ANS: C PTS: 1 DIF: L3 REF: 6-5 Solving Square Root and Other Radical Equations OBJ: 6-5.1 To solve square root and other radical equations NAT: CC A.CED.4| CC A.REI.2| A.2.aTOP: 6-5 Problem 5 Solving an Equation With Two Radicals KEY: radical equation | extraneous solution

18. ANS: B PTS: 1 DIF: L3 REF: 6-6 Function OperationsOBJ: 6-6.1 To add, subtract, multiply, and divide functions NAT: CC F.BF.1| CC F.BF.1.b| A.3.fTOP: 6-6 Problem 2 Multiplying and Dividing Functions

19. ANS: B PTS: 1 DIF: L3 REF: 7-2 Properties of Exponential Functions OBJ: 7-2.1 To explore the properties of functions of the form y = ab^x NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f| G.2.c| A.1.b| A.2.d| A.2.h TOP: 7-2 Problem 3 Using an Exponential Model KEY: exponential function

20. ANS: D PTS: 1 DIF: L2 REF: 7-2 Properties of Exponential Functions OBJ: 7-2.2 To graph exponential functions that have base e NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f| G.2.c| A.1.b| A.2.d| A.2.h TOP: 7-2 Problem 5 Continuously Compounded InterestKEY: continuously compounded interest

21. ANS: C PTS: 1 DIF: L4 REF: 7-2 Properties of Exponential Functions OBJ: 7-2.2 To graph exponential functions that have base e NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f| G.2.c| A.1.b| A.2.d| A.2.h TOP: 7-2 Problem 5 Continuously Compounded InterestKEY: compare properties of two functions | continuously compounded interest

ID: A

3

22. ANS: B PTS: 1 DIF: L2 REF: 7-3 Logarithmic Functions as Inverses OBJ: 7-3.1 To write and evaluate logarithmic expressions NAT: CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.hTOP: 7-3 Problem 1 Writing Exponential Equations in Logarithmic FormKEY: write a function in different but equivalent forms

23. ANS: A PTS: 1 DIF: L4 REF: 7-3 Logarithmic Functions as Inverses OBJ: 7-3.1 To write and evaluate logarithmic expressions NAT: CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.hTOP: 7-3 Problem 1 Writing Exponential Equations in Logarithmic FormKEY: write a function in different but equivalent forms

24. ANS: A PTS: 1 DIF: L2 REF: 7-3 Logarithmic Functions as Inverses OBJ: 7-3.1 To write and evaluate logarithmic expressions NAT: CC A.SSE.1.b| CC F.IF.7.e| CC F.IF.8| CC F.IF.9| CC F.BF.4.a| G.2.c| A.2.h| A.3.hTOP: 7-3 Problem 2 Evaluating a Logarithm KEY: logarithm

25. ANS: C PTS: 1 DIF: L3 REF: 7-4 Properties of LogarithmsOBJ: 7-4.1 To use the properties of logarithms NAT: CC F.LE.4| N.1.d| A.3.hTOP: 7-4 Problem 2 Expanding Logarithms

26. ANS: D PTS: 1 DIF: L3 REF: 7-4 Properties of LogarithmsOBJ: 7-4.1 To use the properties of logarithms NAT: CC F.LE.4| N.1.d| A.3.hTOP: 7-4 Problem 3 Using the Change of Base Formula KEY: Change of Base Formula

27. ANS: D PTS: 1 DIF: L4 REF: 7-6 Natural LogarithmsOBJ: 7-6.1 To evaluate and simplify natural logarithmic expressions NAT: CC F.LE.4| A.3.h TOP: 7-6 Problem 1 Simplifying a Natural Logarithmic Expression KEY: natural logarithmic function

28. ANS: A PTS: 1 DIF: L2 REF: 7-6 Natural LogarithmsOBJ: 7-6.1 To evaluate and simplify natural logarithmic expressions NAT: CC F.LE.4| A.3.h TOP: 7-6 Problem 1 Simplifying a Natural Logarithmic Expression KEY: natural logarithmic function

29. ANS: A PTS: 1 DIF: L4 REF: 7-6 Natural LogarithmsOBJ: 7-6.2 To solve equations using natural logarithms NAT: CC F.LE.4| A.3.hTOP: 7-6 Problem 2 Solving a Natural Logarithmic Equation KEY: natural logarithmic function

30. ANS: C PTS: 1 DIF: L3 REF: 8-1 Inverse VariationOBJ: 8-1.1 To recognize and use inverse variation NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 1 Identifying Direct and Inverse Variations KEY: inverse variation

31. ANS: C PTS: 1 DIF: L2 REF: 8-1 Inverse VariationOBJ: 8-1.1 To recognize and use inverse variation NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 2 Determining an Inverse Variation KEY: inverse variation

32. ANS: B PTS: 1 DIF: L3 REF: 8-1 Inverse VariationOBJ: 8-1.2 To use joint and other variations NAT: CC A.CED.2| CC A.CED.4TOP: 8-1 Problem 4 Using Combined Variation KEY: inverse variation | combined variation

ID: A

4

33. ANS: D PTS: 1 DIF: L3 REF: 8-2 The Reciprocal Function Family OBJ: 8-2.2 To graph translations of reciprocal functions NAT: CC A.CED.2| CC F.BF.1| CC F.BF.3| G.2.c TOP: 8-2 Problem 4 Writing the Equation of a Transformation KEY: reciprocal function

34. ANS: B PTS: 1 DIF: L2 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 1 Finding Points of Discontinuity KEY: rational function | point of discontinuity | removable discontinuity | non-removable points of discontinuity

35. ANS: A PTS: 1 DIF: L3 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 2 Finding Vertical Asymptotes KEY: rational function

36. ANS: B PTS: 1 DIF: L3 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: CC A.CED.2| CC F.IF.7| CC F.BF.1| CC F.BF.1.b| A.2.h TOP: 8-3 Problem 3 Finding Horizontal Asymptotes KEY: rational function

37. ANS: A PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.1 To simplify rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 1 Simplifying a Rational Expression KEY: rational expression | simplest form

38. ANS: A PTS: 1 DIF: L2 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 2 Multiplying Rational Expressions KEY: rational expression | simplest form

39. ANS: B PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 2 Multiplying Rational Expressions KEY: rational expression | simplest form

40. ANS: A PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: CC A.SSE.1| CC A.SSE.1.a| CC A.SSE.1.b| CC A.SSE.2| A.3.e TOP: 8-4 Problem 3 Dividing Rational Expressions KEY: rational expression | simplest form

41. ANS: B PTS: 1 DIF: L4 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 3 Subtracting Rational Expressions

42. ANS: C PTS: 1 DIF: L3 REF: 8-5 Adding and Subtracting Rational Expressions OBJ: 8-5.1 To add and subtract rational expressions NAT: CC A.APR.7| N.5.e| A.3.c| A.3.eTOP: 8-5 Problem 4 Simplifying a Complex Fraction KEY: complex fraction

ID: A

5

43. ANS: A PTS: 1 DIF: L4 REF: 10-1 Exploring Conic SectionsOBJ: 10-1.1 To graph and identify conic sections NAT: CC G.GPE.1| CC G.GPE.2| CC G.GPE.3| G.4.c TOP: 10-1 Problem 1 Graphing a CircleKEY: conic sections

44. ANS: B PTS: 1 DIF: L2 REF: 10-1 Exploring Conic SectionsOBJ: 10-1.1 To graph and identify conic sections NAT: CC G.GPE.1| CC G.GPE.2| CC G.GPE.3| G.4.c TOP: 10-1 Problem 4 Identifying Graphs of Conic Sections KEY: conic sections

45. ANS: C PTS: 1 DIF: L3 REF: 10-2 ParabolasOBJ: 10-2.1 To write the equation of a parabola and to graph parabolas NAT: CC G.GPE.2 TOP: 10-2 Problem 4 Analyzing a Parabola KEY: directrix | focus of a parabola

46. ANS: C PTS: 1 DIF: L3 REF: 10-4 EllipsesOBJ: 10-4.1 To write the equation of an ellipse NAT: CC G.GPE.3| G.4.gTOP: 10-4 Problem 1 Writing an Equation of an Ellipse KEY: ellipse | vertices of an ellipse | co-vertices of an ellipse | center of an ellipse

47. ANS: D PTS: 1 DIF: L2 REF: 10-4 EllipsesOBJ: 10-4.1 To write the equation of an ellipse NAT: CC G.GPE.3| G.4.gTOP: 10-4 Problem 4 Using the Foci of an Ellipse KEY: ellipse | focus of an ellipse | major axis | center of an ellipse | minor axis | vertices of an ellipse | co-vertices of an ellipse

48. ANS: D PTS: 1 DIF: L3 REF: 10-5 HyperbolasOBJ: 10-5.1 To graph hyperbolas NAT: CC G.GPE.3| G.4.g TOP: 10-5 Problem 1 Writing and Graphing the Equation of a HyperbolaKEY: hyperbola | focus of the hyperbola | vertex | transverse axis | axis of symmetry | conjugate axis

49. ANS: D PTS: 1 DIF: L2 REF: 10-6 Translating Conic SectionsOBJ: 10-6.2 To identify a translated conic section from an equation NAT: CC G.GPE.1| CC G.GPE.2| G.2.c TOP: 10-6 Problem 3 Identifying a translated conic section

50. ANS: B PTS: 1 DIF: L3 REF: 10-6 Translating Conic SectionsOBJ: 10-6.2 To identify a translated conic section from an equation NAT: CC G.GPE.1| CC G.GPE.2| G.2.c TOP: 10-6 Problem 3 Identifying a translated conic section

SHORT ANSWER

51. ANS: 52

PTS: 1 DIF: L3 REF: 5-4 Dividing PolynomialsOBJ: 5-4.2 To divide polynomials using synthetic division NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e TOP: 5-4 Problem 5 Evaluating a Polynomial KEY: synthetic division | remainder theorem

ID: A

6

52. ANS: x3 11x 20 0

PTS: 1 DIF: L3 REF: 5-5 Theorems About Roots of Polynomial EquationsOBJ: 5-5.2 To use the Conjugate Root Theorem NAT: CC N.CN.7| CC N.CN.8TOP: 5-5 Problem 4 Using Conjugates to Construct a Polynomial KEY: Conjugate Root Theorem

53. ANS:

1, 32

, 5i

PTS: 1 DIF: L3 REF: 5-6 The Fundamental Theorem of AlgebraOBJ: 5-6.1 To use the Fundamental Theorem of Algebra to solve polynomial equations with complex solutions NAT: CC N.CN.7| CC N.CN.8| CC N.CN.9| CC A.APR.3TOP: 5-6 Problem 2 Finding All the Zeros of a Polynomial Function KEY: Fundamental Theorem of Algebra

54. ANS: 6 g 3

PTS: 1 DIF: L2 REF: 6-1 Roots and Radical ExpressionsOBJ: 6-1.1 To find nth roots NAT: CC A.SSE.2| A.3.e TOP: 6-1 Problem 3 Simplifying Radical Expressions KEY: radicand | index | nth root

55. ANS: 8 2x4

PTS: 1 DIF: L2 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 1 Adding and Subtracting Radical Expressions KEY: like radicals

56. ANS: 3 2 2

PTS: 1 DIF: L3 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 6 Rationalizing the Denominator KEY: like radicals

57. ANS: 26

PTS: 1 DIF: L3 REF: 6-5 Solving Square Root and Other Radical EquationsOBJ: 6-5.1 To solve square root and other radical equations NAT: CC A.CED.4| CC A.REI.2| A.2.aTOP: 6-5 Problem 2 Solving Other Radical Equations KEY: radical equation

58. ANS: –5, 11

PTS: 1 DIF: L4 REF: 6-5 Solving Square Root and Other Radical EquationsOBJ: 6-5.1 To solve square root and other radical equations NAT: CC A.CED.4| CC A.REI.2| A.2.aTOP: 6-5 Problem 2 Solving Other Radical Equations KEY: radical equation

ID: A

7

59. ANS: 76

PTS: 1 DIF: L4 REF: 6-5 Solving Square Root and Other Radical EquationsOBJ: 6-5.1 To solve square root and other radical equations NAT: CC A.CED.4| CC A.REI.2| A.2.aTOP: 6-5 Problem 4 Checking for Extraneous Solutions KEY: radical equation | extraneous solution

60. ANS: –2x – 2

PTS: 1 DIF: L3 REF: 6-6 Function OperationsOBJ: 6-6.1 To add, subtract, multiply, and divide functions NAT: CC F.BF.1| CC F.BF.1.b| A.3.fTOP: 6-6 Problem 1 Adding and Subtracting Functions

61. ANS: –53

PTS: 1 DIF: L3 REF: 6-6 Function OperationsOBJ: 6-6.2 To find the composite of two functions NAT: CC F.BF.1| CC F.BF.1.b| A.3.fTOP: 6-6 Problem 3 Composing Functions KEY: composite function

62. ANS:

f 1(x) 8 x

2; f 1 is not a function.

PTS: 1 DIF: L3 REF: 6-7 Inverse Relations and FunctionsOBJ: 6-7.1 To find the inverse of a relation or function NAT: CC F.BF.4.a| CC F.BF.4.c| A.1.jTOP: 6-7 Problem 4 Finding an Inverse Function KEY: inverse function

63. ANS:

PTS: 1 DIF: L4 REF: 7-2 Properties of Exponential FunctionsOBJ: 7-2.1 To explore the properties of functions of the form y = ab^x NAT: CC A.SSE.1.b| CC A.CED.2| CC F.IF.7| CC F.IF.7.e| CC F.IF.8| CC F.BF.1| CC F.BF.1.b| N.3.f| G.2.c| A.1.b| A.2.d| A.2.h TOP: 7-2 Problem 2 Translating y = ab^x KEY: exponential function

ID: A

8

64. ANS: none of these

PTS: 1 DIF: L4 REF: 7-4 Properties of LogarithmsOBJ: 7-4.1 To use the properties of logarithms NAT: CC F.LE.4| N.1.d| A.3.hTOP: 7-4 Problem 1 Simplifying Logarithms

65. ANS: 712

PTS: 1 DIF: L4 REF: 7-5 Exponential and Logarithmic EquationsOBJ: 7-5.1 To solve exponential and logarithmic equations NAT: CC A.REI.11| CC F.LE.4| A.3.h| A.4.c TOP: 7-5 Problem 1 Solving an Exponential Equation-Common Base KEY: exponential equation

66. ANS: 4952

PTS: 1 DIF: L3 REF: 7-5 Exponential and Logarithmic EquationsOBJ: 7-5.1 To solve exponential and logarithmic equations NAT: CC A.REI.11| CC F.LE.4| A.3.h| A.4.c TOP: 7-5 Problem 5 Solving a Logarithmic Equation KEY: logarithmic equation

67. ANS: –1.843

PTS: 1 DIF: L3 REF: 7-6 Natural LogarithmsOBJ: 7-6.2 To solve equations using natural logarithms NAT: CC F.LE.4| A.3.hTOP: 7-6 Problem 3 Solving an Exponential Equation KEY: natural logarithmic function

68. ANS:

193

PTS: 1 DIF: L2 REF: 8-6 Solving Rational EquationsOBJ: 8-6.1 To solve rational equations NAT: CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11TOP: 8-6 Problem 1 Solving a Rational Equation KEY: rational equation

69. ANS: 4

PTS: 1 DIF: L3 REF: 8-6 Solving Rational EquationsOBJ: 8-6.1 To solve rational equations NAT: CC A.APR.6| CC A.APR.7| CC A.CED.1| CC A.REI.2| CC A.REI.11TOP: 8-6 Problem 1 Solving a Rational Equation KEY: rational equation

ID: A

9

70. ANS:

y 120

x 2

PTS: 1 DIF: L3 REF: 10-2 Parabolas OBJ: 10-2.1 To write the equation of a parabola and to graph parabolas NAT: CC G.GPE.2 TOP: 10-2 Problem 1 Parabolas with Equation y = ax^2KEY: directrix

71. ANS: x 3 2 y 4

2 49

PTS: 1 DIF: L2 REF: 10-3 Circles OBJ: 10-3.1 To write and graph the equation of a circle NAT: CC G.GPE.1| G.2.c| G.4.fTOP: 10-3 Problem 2 Using Translations to Write an Equation KEY: circle | center of a circle | radius | standard form of the equation of a circle

72. ANS: x 3 2 y 6

2 16

PTS: 1 DIF: L3 REF: 10-3 Circles OBJ: 10-3.1 To write and graph the equation of a circle NAT: CC G.GPE.1| G.2.c| G.4.fTOP: 10-3 Problem 3 Using a Graph to Write an Equation KEY: circle | center of a circle | radius | standard form of the equation of a circle

73. ANS: 4x2 14x 59, R –232

PTS: 1 DIF: L2 REF: 5-4 Dividing PolynomialsOBJ: 5-4.1 To divide polynomials using long division NAT: CC A.APR.1| CC A.APR.2| CC A.APR.6| N.1.d| A.3.c| A.3.e TOP: 5-4 Problem 1 Using Polynomial Long Division

74. ANS: –8x5 + 10x4

PTS: 1 DIF: L3 REF: 5-1 Polynomial FunctionsOBJ: 5-1.1 To classify polynomials NAT: CC A.SSE.1.a| CC F.IF.4| CC F.IF.7| CC F.IF.7.cTOP: 5-1 Problem 1 Classifying Polynomials KEY: degree of a polynomial | polynomial function | standard form of a polynomial

75. ANS: 3 ± 5i, –4

PTS: 1 DIF: L2 REF: 5-5 Theorems About Roots of Polynomial EquationsOBJ: 5-5.1 To solve equations using the Rational Root Theorem NAT: CC N.CN.7| CC N.CN.8 TOP: 5-5 Problem 2 Using the Rational Root TheoremKEY: Rational Root Theorem

ID: A

10

76. ANS: 3 6, 2 5

PTS: 1 DIF: L2 REF: 5-5 Theorems About Roots of Polynomial EquationsOBJ: 5-5.2 To use the Conjugate Root Theorem NAT: CC N.CN.7| CC N.CN.8TOP: 5-5 Problem 3 Using the Conjugate Root Theorem to Identify RootsKEY: Conjugate Root Theorem

77. ANS: 4a 4 b 2 2a3

PTS: 1 DIF: L3 REF: 6-2 Multiplying and Dividing Radical ExpressionsOBJ: 6-2.1 To multiply and divide radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 2 Simplifying a Radical Expression KEY: simplest form of a radical

78. ANS: 334

PTS: 1 DIF: L2 REF: 6-2 Multiplying and Dividing Radical ExpressionsOBJ: 6-2.1 To multiply and divide radical expressions NAT: CC A.SSE.2| N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 1 Multiplying Radical Expressions

79. ANS: 3

PTS: 1 DIF: L3 REF: 6-4 Rational ExponentsOBJ: 6-4.1 To simplify expressions with rational exponents NAT: CC N.RN.1| CC N.RN.2TOP: 6-4 Problem 1 Simplifying Expressions with Rational Exponents KEY: rational exponents

80. ANS: 5

PTS: 1 DIF: L2 REF: 6-7 Inverse Relations and FunctionsOBJ: 6-7.1 To find the inverse of a relation or function NAT: CC F.BF.4.a| CC F.BF.4.c| A.1.jTOP: 6-7 Problem 6 Composing Inverse Functions KEY: rearrange formulas to highlight a quantity | composition of functions | inverse relations and functions