Name: ______________________ Class: _________________ Date: _________ ID: A

1

Sem 1 Final

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

____ 1. What is the result of (x2 + 9)(–x3 – 4x + 5)?

a. x6 + 36x4 + 5x2 + 45 c. x5 – 13x3 + 5x2 + 36x + 45b. –x5 – 13x3 + 5x2 – 36x + 45 d. x4 + 36x3 + 5x2

____ 2. Mina bought a plane ticket to New York City and used a coupon for 10% off the ticket price. The total cost of her ticket, with the discount, was $253.10. Which equation could she use to find the price of the ticket without the discount?

a. z = 253.10 + 0.10 c. z + 0.10(z) = 253.10b. 0.10z = 253.10 d. z – 0.10(z) = 253.10

____ 3. Sydney has a $75 mall gift card. She wants to buy a purse and a movie ticket. The movie ticket with tax costs $8.85. The sales tax on the purse will be 5%. How much can the ticketed price of the purse be?

a. less than or equal to $63.00 c. less than or equal to $44.10b. less than $63.00 d. less than $44.10

Name: ______________________ ID: A

2

____ 4. A ringtone company charges $9 a month for the service plus $1.25 for each ringtone downloaded. What is the graph of the equation that models the total fees per month?

a. c.

b. d.

____ 5. A town’s population increases at a rate of 1.4% every year. The current population is 7,500 people. What equation models this scenario?

a. y = 7,500(0.14)x c. y = 7,500(0.014)x

b. y = 7,500(1.14)x d. y = 7,500(1.014)x

____ 6. What is the y-intercept of the quadratic function g(x) = 2x2 – 4x – 6?

a. (3, 0) c. (0, –6)b. (1, –8) d. (–1, 0)

Name: ______________________ ID: A

3

____ 7. What is the standard form of the equation of the function graphed below?

a. f(x) = x2 − 112

x + 52

c. f(x) = –4x2 + 22x − 10

b. f(x) = −5x2 − 12

x − 10 d. none of the above

____ 8. What are the zeros of t(x) = (3x + 24)(x – 8)?

a. x = –8 or x = –8 c. x = 8b. x = –8 or x = 8 d. none of the above

____ 9. Solve x2 – 11x = –24 for x.

a. x = 8; x = 3 c. x = –3; x = –8b. x ≈ 0.89; x ≈ 10.11 d. x ≈ –10.11; x ≈ –0.89

Name: ______________________ ID: A

4

____ 10. What is the equation of a quadratic in standard form, given the zeros x = 4 and x = –2 and the point (–3, 7)?

a. f(x) = 4x2 – 2x – 8 c. f(x) = x2 – 2x – 8b. f(x) = 4x2 + 2x + 8 d. f(x) = x2 + 2x – 8

____ 11. The effectiveness of a dry-cleaning fluid decreases by 14

each time it is used. The fluid is given a

rating after each use, and when the rating drops below 1 the fluid is replaced. If the fluid has a rating of 18 after 2 uses, which of the following equations models this situation? Let n be the number of times the fluid is used and let r be the rating.

a. r = 32 • 34

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n

c. r = 2 • 4−n

b. r = 32 • 14

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃

n

d. r = 18 • 4−n

____ 12. What are the coefficients in the expression 7g3 – 4g2 – 10g + 9?

a. 7, –4, and –10 c. 7, 4, 10, and 9b. 7, 4, and 10 d. 7, –4, – 10, and 9

____ 13. What expression represents the factored form of 4x2− 16?

a. 4x + 4( ) x − 4( ) c. 4 x + 2( ) x − 2( )

b. 4 x + 2( )2 d. 4 x − 4( )

2

____ 14. What is the solution to the equation 3(3x + 5) = 2x – 20?

a. x = − 13

c. x =− 256

b. x = 5 d. x = –5

____ 15. What values of x make the expression x − 2( ) x + 8( ) negative?

a. −2 < x < 8 c. x < −8 or x > 2b. 2 < x < −8 d. −8 < x < 2

____ 16. What factored equation can be used to solve x2− 4x = 12?

a. x − 4( ) x − 12( ) = 0 c. x − 4( ) x + 12( ) = 0b. x − 2( ) x + 6( ) = 0 d. x − 6( ) x + 2( ) = 0

Name: ______________________ ID: A

5

____ 17. Find c so that x2 + 4x + c is a perfect square trinomial.

a. c = 16 c. c = 4b. c = 4 d. c = 2

____ 18. Solve 2x2− 13x + 15 = 0 for x.

a. x = –5 or x = 1.5 c. x = 1.5b. x = –5 d. x = 5 or x = 1.5

____ 19. Solve x2 = 81 for x.

a. x = ±9 c. x = 9b. x = ±40.5 d. x = –9

____ 20. Which expression is not a perfect square trinomial?

a. x2− 14x + 49 c. x2

− 2x + 49b. x2

+ 14x + 49 d. x2+ 2x + 1

____ 21. What is the vertex of the quadratic function f(x) = 6x2 + 12x – 18?

a. (0, –18) c. (–1, –24)b. (–3, 0) d. (1, 0)

____ 22. Given the quadratic function q(x) = 2(x – 3)2 – 2, identify the vertex and determine whether it is a minimum or maximum.

a. (–4, 96); maximum c. (–3, 70); minimumb. (6, 16); maximum d. (3, –2); minimum

____ 23. What is the equation of the axis of symmetry for the function f(x) = x2 + 12x + 26?

a. x = –6 c. x = 26b. x = –24 d. none of the above

____ 24. What is the vertex form of the function f(x) = –5x2 – 10?

a. f(x) = –5(x + 0)2 – 10 c. f(x) = (x – 10)2

b. f(x) = (x − 5)2 – 10 d. none of the above

Name: ______________________ ID: A

6

____ 25. If f(x) = 3x + 3, what is f(x – 2)?

a. undefined c. 3(x – 2) + 3b. 3x + 1 d. 3(x + 2) + 3

____ 26. What is the average rate of change of the function f(x) = –0.5x2 – 5x – 0.45 from x = 0 to x = 0.5?

a. –2.8 c. –2.6b. –5.3 d. –3.1

____ 27. What is the area of a rectangle with one side of length x and the other 5 more than six times x?

a. 6x + 5 c. 6x2+ 5x

b. 6(x + 5) d. 6x2+ 5

____ 28. Given f(x) = 5x2+ 3x − 7 and g(x) = −6x2

+ 4x − 3, find (f − g)(x).

a. 11x2+ 7x − 4 c. 11x2

− x − 4b. 11x2

− x − 10 d. 11x2+ 7x − 10

____ 29. Given f(x) = −2x − 2 and g(x) = 5x + 4, find (f • g)(x).

a. −10x2− 18x + 8 c. −10x2

+ 5x − 8b. −10x2

− 18x − 8 d. 3x2+ 5x − 8

____ 30. Given f(x) = x2+ 2x − 24 and g(x) = x − 4, find

fg

Ê

Ë

ÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃(x).

a. x + 7 c. x − 6b. x + 6 d. −2x + 6

____ 31. Given f(x) = x2− 6x − 5, what is the shift in the vertex of the graph of f x + 6( )?

a. The vertex shifts 6 units down. b. The vertex shifts 6 units up.c. The vertex shifts 6 units to the right.d. The vertex shifts 6 units to the left.

____ 32. The vertex of f(x) is (–1, –4). What is the vertex of f(x) − 9?

a. (–10, –4) c. (8, –4)b. (–1, 5) d. (–1, –13)

Name: ______________________ ID: A

7

____ 33. If f(x) = x2 , what is the equation of g(x) if f(x) is translated to the right 7 units and up 1 unit?

a. g(x) = x − 1( )2+ 7 c. g(x) = x + 7( )

2+ 1

b. g(x) = x + 1( )2− 7 d. g(x) = x − 7( )

2+ 1

____ 34. What is the inverse of f(x) = x + 14?

a. f−1 (x) = −x + 14 c. f−1 (x) = x + 14

b. f−1 (x) = −x − 14 d. f−1 (x) = x − 14

____ 35. What are the x-intercepts of the parabola with the equation g(x) = (x + 30)(x – 41)?

a. (0, 30) and (0, –41) c. (0, 41) and (0, 41)b. (–30, 0) and (41, 0) d. (30, 0) and (–41, 0)

____ 36. The graph below is the graph of which function?

a. y = x⎡⎢⎤⎥ + 2 c. y = − x⎡⎢

⎤⎥ + 2

b. y = x⎣ ⎦ − 2 d. y = x⎣ ⎦ + 2

Name: ______________________ ID: A

8

____ 37. What is the graph of y = x − 1, if x ≤ 0

−2x, if x > 0

Ï

Ì

Ó

ÔÔÔÔÔÔÔÔÔÔÔÔ

?

a. c.

b. d.

____ 38. What is the minimum of the graph of y = 3 x − 9| |?

a. (0, 9) c. (0, 0) b. (–9, 0) d. (9, 0)

Name: ______________________ ID: A

9

____ 39. What function is shown in the graph below?

a. y = x + 1⎡⎢

⎤⎥ c. y = x + 1

b. y = x − 1⎣ ⎦ d. y = x⎡⎢⎤⎥ − 1

Name: ______________________ ID: A

10

____ 40. What is the graph of the function y = 3 x + 3| |?

a. c.

b. d.

____ 41. What is the maximum of the graph of y = −9 x + 8| | + 1?

a. (–1, 8) c. (0, –1) b. (8, 1) d. (–8, 1)

____ 42. If y = 43 1.13( )x, what is the percent rate of change of y for each unit of x?

a. 1.3% c. 1.13%b. 13% d. 113%

____ 43. If y = 56 1.22( )2x, what is the percent rate of change of y for each unit of x?

a. 22% increase c. 56% increaseb. 1.22% increase d. 49% increase

Name: ______________________ ID: A

11

____ 44. Which expression is equal to 61219

?

a. 619 c. 61912

b. 612

d. 61219

____ 45. What is the value of 932

?

a. 91 c. 2b. 3 d. 27

____ 46. Which expression is equal to 294

?

a. 24 c. 294

b. 24

d. 249

____ 47. Let x23= 4. What is the value of x?

a. 1.59 c. 2b. 4 d. 8

____ 48. Which expression is equal to g13x?

a. g13x

c. g1x

b. gx

13d. 13

g

x

____ 49. What is the result of (–2 – 6i) + (–37 – 19i)?

a. –39 + 25i c. –21 – 31ib. –25 – 39i d. –39 – 25i

____ 50. What is the result of (–2 + i)(8 + 2i)?

a. 6 + 3i c. –18 + 4ib. –14 + 4i d. –14

Name: ______________________ ID: A

12

____ 51. What is the result of (–6 + 6i)(9 – 2i)?

a. –42 + 66i c. 3b. –66 + 66i d. 3 + 4i

____ 52. What is the imaginary part of the complex number 8 − 10i?

a. 8 c. ib. –10i d. −8

____ 53. What value is equal to i18?

a. −1 c. −ib. 1 d. i

____ 54. What is the result of (–11 + 23i) – (21 + 26i)?

a. 49 + 32i c. –32 + 3ib. –32 + 49i d. –32 – 3i

____ 55. What is the result of (6 + 5i)(6 – 7i)?

a. 12 – 2i c. 1 – 72ib. 71 – 12i d. 36 – 35i

Name: ______________________ ID: A

13

Short Answer

Use the given information and the diagram that follows to answer the questions.

56. The perimeter of a rectangle is the sum of the side lengths: perimeter = 2l + 2w, where l is the rectangle’s length and w is the rectangle’s width. The area of a rectangle is the product of the side lengths: area = lw.

(5x + 7)

(4x – 9)

a

(4x – 9)

(5x + 7)

a. What is the perimeter of the rectangle in simplest form?

b. What is the area of the rectangle in simplest form?

Use your knowledge of polynomials, rational numbers, and complex numbers to answer the following questions.

57. The perimeter of a rectangle is the sum of the lengths of its sides. The area of a rectangle is the product of the rectangle’s length and width. If l is the length of a rectangle and w is the width, then its perimeter = 2l + 2w and its area = lw. Use the rectangle below to answer the questions that follow.

9x + 5

6x – 6

a

6x – 6

9x + 5

a. What is the rectangle’s perimeter?

b. What is the rectangle’s area?

Name: ______________________ ID: A

14

Use what you have learned about operating with polynomials to solve the problem that follows.

58. Gina is designing a page for a yearbook ad. The figure below represents the layout she’s using for her design. Use the figure to answer the questions that follow. All units are in centimeters.

The perimeter of a rectangle is the sum of its sides. The area of a rectangle is length • width.

a. What is the perimeter of the shaded rectangle?

b. What is the area of the shaded rectangle?

ID: A

1

Sem 1 FinalAnswer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 REF: MII 1.2 NAT: A-APR.1TOP: Operating with Polynomials KEY: polynomial | like termsMSC: Pre-Assessment

2. ANS: D PTS: 1 REF: MI 1.2 NAT: A-CED.1TOP: Creating Equations and Inequalities in One Variable KEY: linear equation | variableMSC: Pre-Assessment

3. ANS: A PTS: 1 REF: MI 1.2 NAT: A-CED.1TOP: Creating Equations and Inequalities in One Variable KEY: inequality | rate | solution | variable MSC: Pre-Assessment

4. ANS: A PTS: 1 REF: MI 1.3 NAT: A-CED.2TOP: Creating and Graphing Equations in Two Variables KEY: independent variable | dependent variable | coordinate plane | linear equationMSC: Pre-Assessment

5. ANS: D PTS: 1 REF: MI 1.3 NAT: A-CED.2TOP: Creating and Graphing Equations in Two Variables KEY: independent variable | dependent variable | exponential growth | exponential equationMSC: Pre-Assessment

6. ANS: C PTS: 1 REF: MII 3.3 NAT: A-CED.4TOP: Creating Quadratic Equations in Two or More Variables KEY: key features of a quadratic | standard form of a quadratic function | y-interceptMSC: Pre-Assessment

7. ANS: C PTS: 1 REF: MII 3.3 NAT: A-CED.2TOP: Creating Quadratic Equations in Two or More Variables KEY: intercept form | standard form of a quadratic function | x-intercept MSC: Progress Assessment

8. ANS: B PTS: 1 REF: MII 3.3 NAT: A-CED.2TOP: Creating Quadratic Equations in Two or More Variables KEY: intercept form | x-intercept MSC: Progress Assessment

9. ANS: A PTS: 1 REF: MII 3 NAT: A-CED.1TOP: Expressions and Equations KEY: quadratic equation | factorMSC: Unit Assessment

10. ANS: C PTS: 1 REF: MII 3 NAT: A-CED.2TOP: Expressions and Equations KEY: standard form of a quadratic function | zerosMSC: Unit Assessment

ID: A

2

11. ANS: A PTS: 1 REF: MIII 4B NAT: A-CED.1TOP: Mathematical Modeling and Choosing a Model KEY: exponential function | rate of decrease MSC: Unit Assessment

12. ANS: A PTS: 1 REF: MI 1.1 NAT: A-SSE.1aTOP: Interpreting Structure in Expressions KEY: coefficient | algebraic expression MSC: Progress Assessment

13. ANS: C PTS: 1 REF: MIII 2A.2 NAT: A-SSE.2TOP: Proving Identities KEY: factor | factoring binomials | factored formMSC: Pre-Assessment

14. ANS: D PTS: 1 REF: MI 3.1 NAT: A-REI.3TOP: Solving Equations and Inequalities KEY: properties of equality | equationMSC: Pre-Assessment

15. ANS: D PTS: 1 REF: MII 3.1 NAT: A-SSE.1bTOP: Interpreting Structure in Expressions KEY: quadratic expression MSC: Progress Assessment

16. ANS: D PTS: 1 REF: MII 3.2 NAT: A-SSE.2TOP: Creating and Solving Quadratic Equations in One Variable KEY: factor | quadratic equation MSC: Pre-Assessment

17. ANS: B PTS: 1 REF: MII 3.2 NAT: A-REI.4aTOP: Creating and Solving Quadratic Equations in One Variable KEY: perfect square trinomial | quadratic expression MSC: Pre-Assessment

18. ANS: D PTS: 1 REF: MII 3.2 NAT: A-REI.4bTOP: Creating and Solving Quadratic Equations in One Variable KEY: factor | quadratic equation | quadratic formula MSC: Pre-Assessment

19. ANS: A PTS: 1 REF: MII 3.2 NAT: A-REI.4bTOP: Creating and Solving Quadratic Equations in One Variable KEY: square root | quadratic formula | quadratic equation MSC: Progress Assessment

20. ANS: C PTS: 1 REF: MII 3.2 NAT: A-SSE.2TOP: Creating and Solving Quadratic Equations in One Variable KEY: perfect square trinomial | quadratic expression MSC: Progress Assessment

21. ANS: C PTS: 1 REF: MII 3.3 NAT: A-SSE.3TOP: Creating Quadratic Equations in Two or More Variables KEY: quadratic function | vertex of a parabola MSC: Pre-Assessment

22. ANS: D PTS: 1 REF: MII 3.3 NAT: A-SSE.3TOP: Creating Quadratic Equations in Two or More Variables KEY: maximum | minimum | vertex form | vertex of a parabola MSC: Pre-Assessment

23. ANS: A PTS: 1 REF: MII 3.3 NAT: A-SSE.3TOP: Creating Quadratic Equations in Two or More Variables KEY: axis of symmetry of a parabola | standard form of a quadratic functionMSC: Progress Assessment

ID: A

3

24. ANS: A PTS: 1 REF: MII 3.3 NAT: A-SSE.3TOP: Creating Quadratic Equations in Two or More Variables KEY: standard form of a quadratic function | vertex form | vertex of a parabolaMSC: Progress Assessment

25. ANS: C PTS: 1 REF: MI 2.1 NAT: F-IF.2TOP: Graphs As Solution Sets and Function Notation KEY: linear equation | function | function notation MSC: Pre-Assessment

26. ANS: B PTS: 1 REF: MII 2.2 NAT: F-IF.6TOP: Interpreting Quadratic Functions KEY: average rate of change | domainMSC: Pre-Assessment

27. ANS: C PTS: 1 REF: MII 2.3 NAT: F-BF.1aTOP: Building Functions KEY: function | area MSC: Pre-Assessment

28. ANS: C PTS: 1 REF: MII 2.3 NAT: F-BF.1bTOP: Building Functions KEY: function MSC: Pre-Assessment

29. ANS: B PTS: 1 REF: MII 2.3 NAT: F-BF.1bTOP: Building Functions KEY: function MSC: Pre-Assessment

30. ANS: B PTS: 1 REF: MII 2.3 NAT: F-BF.1bTOP: Building Functions KEY: function MSC: Pre-Assessment

31. ANS: D PTS: 1 REF: MII 2.6 NAT: F-BF.3TOP: Transforming Functions KEY: translation MSC: Pre-Assessment

32. ANS: D PTS: 1 REF: MII 2.6 NAT: F-BF.3TOP: Transforming Functions KEY: translation MSC: Pre-Assessment

33. ANS: D PTS: 1 REF: MII 2.6 NAT: F-BF.3TOP: Transforming Functions KEY: translation MSC: Progress Assessment

34. ANS: D PTS: 1 REF: MII 2.7 NAT: F-BF.4aTOP: Finding Inverse Functions KEY: inverse MSC: Pre-Assessment

35. ANS: B PTS: 1 REF: MII 2.1 NAT: F-IF.8aTOP: Analyzing Quadratic Functions KEY: quadratic function | x-intercept | factored form of a quadratic function MSC: Pre-Assessment

36. ANS: D PTS: 1 REF: MII 2.4 NAT: F-IF.7bTOP: Graphing Other Functions KEY: step function MSC: Pre-Assessment

37. ANS: A PTS: 1 REF: MII 2.4 NAT: F-IF.7bTOP: Graphing Other Functions KEY: piecewise function MSC: Pre-Assessment

38. ANS: D PTS: 1 REF: MII 2.4 NAT: F-IF.7bTOP: Graphing Other Functions KEY: absolute value | minimum | maximumMSC: Progress Assessment

ID: A

4

39. ANS: A PTS: 1 REF: MII 2.4 NAT: F-IF.7bTOP: Graphing Other Functions KEY: step function MSC: Progress Assessment

40. ANS: A PTS: 1 REF: MII 2.4 NAT: F-IF.7bTOP: Graphing Other Functions KEY: absolute value | translationMSC: Progress Assessment

41. ANS: D PTS: 1 REF: MII 2.4 NAT: F-IF.7bTOP: Graphing Other Functions KEY: absolute value | minimum | maximumMSC: Progress Assessment

42. ANS: B PTS: 1 REF: MII 2.5 NAT: F-IF.8bTOP: Analyzing Functions KEY: exponential equation | rate of changeMSC: Pre-Assessment

43. ANS: D PTS: 1 REF: MII 2.5 NAT: F-IF.8bTOP: Analyzing Functions KEY: exponential equation | rate of changeMSC: Progress Assessment

44. ANS: D PTS: 1 REF: MII 1.1 NAT: N-RN.2TOP: Working with the Number System KEY: base | exponent | exponential expression | power | radical expression | rootMSC: Pre-Assessment

45. ANS: D PTS: 1 REF: MII 1.1 NAT: N-RN.1TOP: Working with the Number System KEY: base | exponent | exponential expression | power | radical expression | root | rational numberMSC: Pre-Assessment

46. ANS: C PTS: 1 REF: MII 1.1 NAT: N-RN.2TOP: Working with the Number System KEY: base | exponent | exponential expression | power | radical expressionMSC: Progress Assessment

47. ANS: D PTS: 1 REF: MII 1.1 NAT: N-RN.2TOP: Working with the Number System KEY: base | exponent | exponential expression | power | exponential equationMSC: Progress Assessment

48. ANS: A PTS: 1 REF: MII 1.1 NAT: N-RN.2TOP: Working with the Number System KEY: base | exponent | exponential expression | power | radical expressionMSC: Progress Assessment

49. ANS: D PTS: 1 REF: MII 1.3 NAT: N-CN.2TOP: Operating with Complex Numbers KEY: complex numbers MSC: Pre-Assessment

50. ANS: C PTS: 1 REF: MII 1.3 NAT: N-CN.2TOP: Operating with Complex Numbers KEY: complex numbers MSC: Pre-Assessment

ID: A

5

51. ANS: A PTS: 1 REF: MII 1.3 NAT: N-CN.2TOP: Operating with Complex Numbers KEY: complex numbers MSC: Pre-Assessment

52. ANS: B PTS: 1 REF: MII 1.3 NAT: N-CN.1TOP: Operating with Complex Numbers KEY: complex numbers | complex number system | imaginary unit MSC: Progress Assessment

53. ANS: A PTS: 1 REF: MII 1.3 NAT: N-CN.2TOP: Operating with Complex Numbers KEY: complex numbers | complex number system | imaginary unit MSC: Progress Assessment

54. ANS: D PTS: 1 REF: MII 1.3 NAT: N-CN.2TOP: Operating with Complex Numbers KEY: complex numbers | complex number system | imaginary unit MSC: Progress Assessment

55. ANS: B PTS: 1 REF: MII 1.3 NAT: N-CN.2TOP: Operating with Complex Numbers KEY: complex numbers | complex number system | imaginary unit MSC: Progress Assessment

SHORT ANSWER

56. ANS: a. (18x – 4) unitsb. (20x2 – 17x – 63) units2

PTS: 3 REF: MII 1.2 NAT: A-APR.1 TOP: Operating with Polynomials KEY: like terms | polynomialMSC: Progress Assessment

57. ANS: a. 30x – 2 unitsb. 54x2 – 24x – 30 units2

PTS: 3 REF: MII 1 NAT: A-APR.1 TOP: Extending the Number System KEY: like terms | polynomialMSC: Unit Assessment

ID: A

6

58. ANS: a. 2(−3x + 18) + 2(18) = −6x + 72 cmb. (−3x + 18) • (18) = −54x + 324 cm2

PTS: 3 REF: MIII 2A.1 NAT: A-APR.1 TOP: Polynomial Structures and Operating with Polynomials KEY: polynomial | adding polynomials | multiplying polynomials | applying polynomialsMSC: Progress Assessment