Math III_ Midterm Review 2013 Name __________________________

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

____ 1. If a function, is shifted to the left one unit(s), what function represents the transformation?

a. c.b. d.

____ 2. Let be the reflection of in the x-axis. What is a function rule for ?

a. c.b. d.

____ 3. The function . The graph of is translated to the left 7 units and up 8 units. What is the function rule for ?

a. c.b. d.

____ 4. Identify the vertex and the axis of symmetry of the graph of the function .a. vertex: (–2, 4);

axis of symmetry: b. vertex: (2, –4);

axis of symmetry: c. vertex: (–2, –4);

axis of symmetry: d. vertex: (2, 4);

axis of symmetry:

____ 5. Identify the maximum or minimum value and the domain and range of the graph of the function

.a. minimum value: 3

domain: all real numbers range: all real numbers

b. maximum value: –3domain: all real numbers range: all real numbers

c. maximum value: 3domain: all real numbersrange: all real numbers

d. minimum value: –3domain: all real numbers

range: all real numbers

What are the vertex and the axis of symmetry of the equation?

____ 6.

a. vertex: ( –2, 12)axis of symmetry:

c. vertex: ( –2, –12)axis of symmetry:

b. vertex: ( 2, –12)axis of symmetry:

d. vertex: ( 2, –12)axis of symmetry:

What is the vertex form of the equation?

____ 7.

a. c.b. d.

____ 8. You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be

modeled with the function where x and y are in feet. How high above the river is the bridge (the top of the arch)? How long is the section of bridge above the arch?

a. The bridge is about 193.52 ft. above the river and the length of the bridge above the arch is about 625.25 ft.

b. The bridge is about 193.52 ft. above the river and the length of the bridge above the arch is about 1250.51 ft.

c. The bridge is about 1250.51 ft. above the river and the length of the bridge above the arch is about 193.52 ft.

d. The bridge is about 1250.51 ft. above the river and the length of the bridge above the arch is about 625.25 ft.

What is the equation, in standard form, of a parabola that contains the following points?

____ 9. (–2, –16), (0, –4), (4, –28)

a. c.b. d.

What is the equation, in standard form, of a parabola that models the values in the table?

____ 10.x –2 0 4

f(x) –7 3 –73

a. c.b. d.

____ 11. A historian took a count of the number of people in a Gold Rush town for six years in the 1870’s. Year 1870 1871 1872 1873 1874 1875 1876

Population 370 386 392 388 374 350 316

Find a quadratic function that models the data as a function of x, the number of years since 1870. Use the model to estimate the number of people in the town in 1888.

a. ; 124 peopleb. ; 272 peoplec. ; 218 peopled. ; 88 people

____ 12. The table shows a meteorologist's predicted temperatures for an April day in Washington D.C. Use quadratic regression to find a quadratic model for this data. (Use the 24-hour clock to represent times after noon.)

Time Predicted Temperature (oF)

8 A.M. 51.1710 A.M. 62.712 P.M. 70.132 P.M. 73.484 P.M. 72.756 P.M. 67.92

a. c.b. d.

____ 13. You threw a rock off the balcony overlooking your backyard. The table shows the height of the rock at different times. Use quadratic regression to find a quadratic model for this data.

Time(in seconds)

Height (in feet)

0 161 36.32 47.23 48.74 40.85 23.5

a. c.b. d.

____ 14. Factor.

a. c.b. d.

____ 15. Factor. a. c.b. d.

____ 16. Factor. a. c.b. d.

What are the solutions of the quadratic equation?

____ 17. = 0 a.

73 ,

12

c. –6, 3

b.6,

12

d.–6,

73

What is the solution of the equation?

____ 18.a. 7 c.

b. 7 , – 7 d.

Solve the quadratic equation by completing the square.

____ 19.a. 6 c. 6b. d.

Rewrite the equation in vertex form. Name the vertex and y-intercept.

____ 20. a.

vertex: (6, – 2)y-intercept: (0, 34)

c.vertex: (–12, –2)y-intercept: (0, –2)

b.vertex: (–12, –2)y-intercept: (0, –2)

d.vertex: (6, – 2) y-intercept: (0, 34)

Use the Quadratic Formula to solve the equation.

____ 21.a.

52

c. 4

5 b.

54

d. 5

4

What is the number of real solutions?

____ 22.

a. one real solution c. no real solutionsb. two real solutions d. cannot be determined

Simplify the number using the imaginary unit i.

____ 23.a. c.b. d.

Simplify the expression.

____ 24.a. c.b. d.

____ 25.a. c.b. d.

____ 26.a. c.b. d.

____ 27.

a. c.

b. d.

What are the solutions?

____ 28.

a. c.b. d.

____ 29. Classify –2x4 – x3 + 8x2 + 12 by degree.a. quartic c. quadratic b. quintic d. cubic

Consider the leading term of each polynomial function. What is the end behavior of the graph?

____ 30.a. The leading term is . Since n is even and a is positive, the end behavior is down and

up.b. The leading term is . Since n is even and a is positive, the end behavior is up and

down.c. The leading term is . Since n is even and a is positive, the end behavior is up and up.d. The leading term is . Since n is even and a is positive, the end behavior is down and

down.

Write the polynomial in factored form.

____ 31. 6x3 – 60x2 + 144xa. 6x(x – 6)(x + 4) c. –6x(x + 6)(x – 4)b. –4x(x – 6)(x + 6) d. 6x(x – 4)(x – 6)

____ 32. What is a cubic polynomial function in standard form with zeros –4, –5, and 4?

a. c.b. d.

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

____ 33.a. the numbers 1, –4, and 0 are zeros of multiplicity 2 b. the numbers –1, 4, and 0 are zeros of multiplicity 2 c. the numbers –1, 4, and 0 are zeros of multiplicity 1 d. the numbers 1, –4, and 0 are zeros of multiplicity 1

What is the relative maximum and minimum of the function?

____ 34.a. The relative maximum is at (–1.53, 8.3) and the

relative minimum is at (1.2, –12.01).b. The relative maximum is at (–1.53, 12.01) and the

relative minimum is at (1.2, –8.3).c. The relative maximum is at (–1.2, 8.3) and the

relative minimum is at (1.53, –12.01).d. The relative maximum is at (–1.2, 12.01) and the

relative minimum is at (1.53, –8.3).

What are the real or imaginary solutions of each polynomial equation?

____ 35.a. 4, –4, 2, –2 c. 4, –4b. 4, –2 d. no solution

What are the real or imaginary solutions of the polynomial equation?

____ 36.a. and c. 2, , and b. 2, , and d. 2, , and

____ 37. Divide by x + 4.a. c. , R –232b. , R 240 d.

____ 38. Is a factor of ? If it is, write as a product of two factors.a. yes: c. yes:

b. yes: d. is not a factor of

Divide using synthetic division.

____ 39. Divide by ( ).

a. , R –6 c. , R 18b. d.

____ 40. Use synthetic division to find P(–2) for .

a. –2 b. 0 c. –36 d. 68

____ 41. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation . 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

Find the roots of the polynomial equation.

____ 42.a. –3 ± 5i, –4 c. –3 ± i, 4b. 3 ± 5i, –4 d. 3 ± i, 4

____ 43. A polynomial equation with rational coefficients has the roots . Find two additional roots.a. c.b. d.

____ 44. Find a quadratic equation with roots –1 + 4i and –1 – 4i.a. c.b. d.

Use Pascal’s Triangle to expand the binomial.

____ 45.a.b.c.d.

Use the Binomial Theorem to expand the binomial.

____ 46. What is the second term of ?a.b.c.d.

____ 47. The table shows the annual consumption of cheese per person in the U.S. for selected years in the 20th century.

Year Pounds Consumed

1908 3.2551937 9.0531959 17.8371996 58.395

Use a cubic model to estimate milk production in 1978.

a. 30.4 c. 36.4b. 33.4 d. 66.7

What is the equation of with the given transformations?____ 48. vertical stretch by a factor of 8, horizontal shift 2 units to the right, vertical shift 7 units down

a. c.b. d.

____ 49. Find all the real fourth roots of .a.

and c.

, , , and b.

and d.

What is a simpler form of the radical expression?

____ 50.a. b. c. d.

Multiply and simplify if possible.

____ 51.a. 3 b. 11 c. d.

What is the simplest form of the product?

____ 52.a. c.

b. d.

What is the simplest form of the quotient?

____ 53.a. b. c. d.

What is the simplest form of the radical expression?

____ 54.a. c.b. d. not possible to simplify

____ 55.a. c.b. d. not possible to simplify

What is the simplest form of the expression?

____ 56.a. c.b. d.

____ 57.a. b. 12 c. –8 d.

____ 58. What is in simplest form? a. c.

b. d.

What is the simplest form of the number?

____ 59.a. 9 c. –28b. 57 d. –18

What is the solution of the equation?

____ 60.a. 4 b. –2 c. 12 d. –3

____ 61.a. –5, 11 b. 5 c. 11 d. –11

____ 62.a. –9 b. 9 and –4 c. –4 d. –9 and –4

____ 63. Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse variation.a. c.

b. d. y = 0.8x

____ 64. Write an equation for the translation of that has the asymptotes x = 7 and y = 6.a. c.

b. d.

Find any points of discontinuity for the rational function.

____ 65. What are the points of discontinuity? Are they all removable?

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

____ 66. Describe the vertical asymptote(s) and hole(s) for the graph of .a. asymptotes: x = –4, –2 and hole: x = 1b. asymptote: x = 1 and no holesc. asymptote: x = 1 and holes: x = –4, –2d. asymptotes: x = –4, –2 and no holes

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

____ 67.a. c.b. d.

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

____ 68.a. c.

b. d.

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

____ 69.a. c.

b. d.

____ 70.a.

b.

c.

d.

Simplify the sum.

____ 71.a. c.

b. d.

Simplify the difference.

____ 72.a. c.

b. d.

Simplify the complex fraction.

____ 73.a. c.

b. d. not here

Solve the equation. Check the solution.

____ 74.a.

194

b. 13

c. 19

3d. 2

____ 75. a. –9 b. –6 c. –9 and –6 d. 6

Math III_ Midterm Review 2013Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: L2 REF: 2-6 Families of FunctionsOBJ: 2-6.1 To analyze transformations of functions NAT: G.2.c| G.4.d| A.1.e| A.1.h| A.2.bTOP: 2-6 Problem 2 Horizontal Translation KEY: translation | transformationDOK: DOK 2

2. ANS: A PTS: 1 DIF: L3 REF: 2-6 Families of FunctionsOBJ: 2-6.1 To analyze transformations of functions NAT: G.2.c| G.4.d| A.1.e| A.1.h| A.2.bTOP: 2-6 Problem 3 Reflecting a Function Algebraically KEY: transformationDOK: DOK 2

3. ANS: C PTS: 1 DIF: L3 REF: 2-6 Families of FunctionsOBJ: 2-6.1 To analyze transformations of functions NAT: G.2.c| G.4.d| A.1.e| A.1.h| A.2.bTOP: 2-6 Problem 5 Combining Transformations KEY: transformationDOK: DOK 2

4. ANS: C PTS: 1 DIF: L3REF: 4-1 Quadratic Functions and TransformationsOBJ: 4-1.1 To identify and graph quadratic functions NAT: G.2.c| A.2.dSTA: A.B.4.a TOP: 4-1 Problem 3 Interpreting Vertex FormKEY: parabola | vertex of a parabola | y-intercept DOK: DOK 2

5. ANS: D PTS: 1 DIF: L3REF: 4-1 Quadratic Functions and TransformationsOBJ: 4-1.1 To identify and graph quadratic functions NAT: G.2.c| A.2.dSTA: A.B.4.a TOP: 4-1 Problem 3 Interpreting Vertex FormKEY: parabola | vertex of a parabola | y-intercept DOK: DOK 2

6. ANS: B PTS: 1 DIF: L3REF: 4-2 Standard Form of a Quadratic FunctionOBJ: 4-2.1 To graph quadratic functions written in standard formTOP: 4-2 Problem 1 Finding the Features of a Quadratic FunctionKEY: standard form DOK: DOK 2

7. ANS: B PTS: 1 DIF: L3REF: 4-2 Standard Form of a Quadratic FunctionOBJ: 4-2.1 To graph quadratic functions written in standard formTOP: 4-2 Problem 3 Converting Standard Form to Vertex FormKEY: standard form DOK: DOK 2

8. ANS: B PTS: 1 DIF: L4REF: 4-2 Standard Form of a Quadratic FunctionOBJ: 4-2.1 To graph quadratic functions written in standard formTOP: 4-2 Problem 4 Interpreting a Quadratic Graph KEY: standard formDOK: DOK 3

9. ANS: C PTS: 1 DIF: L3REF: 4-3 Modeling With Quadratic FunctionsOBJ: 4-3.1 To model data with quadratic functions NAT: A.2.fSTA: A.B.2.a| S.C.3.b TOP: 4-3 Problem 1 Writing an Equation of a ParabolaKEY: quadratic function | quadratic model DOK: DOK 2

10. ANS: C PTS: 1 DIF: L2REF: 4-3 Modeling With Quadratic Functions

OBJ: 4-3.1 To model data with quadratic functions NAT: A.2.fSTA: A.B.2.a| S.C.3.b TOP: 4-3 Problem 1 Writing an Equation of a ParabolaKEY: quadratic function | quadratic model DOK: DOK 2

11. ANS: C PTS: 1 DIF: L3REF: 4-3 Modeling With Quadratic FunctionsOBJ: 4-3.1 To model data with quadratic functions NAT: A.2.fSTA: A.B.2.a| S.C.3.b TOP: 4-3 Problem 2 Using a Quadratic ModelKEY: quadratic model | quadratic function | word problem | problem solving | multi-part questionDOK: DOK 3

12. ANS: D PTS: 1 DIF: L3REF: 4-3 Modeling With Quadratic FunctionsOBJ: 4-3.1 To model data with quadratic functions NAT: A.2.fSTA: A.B.2.a| S.C.3.b TOP: 4-3 Problem 3 Using Quadratic Regression DOK: DOK 2

13. ANS: B PTS: 1 DIF: L3REF: 4-3 Modeling With Quadratic FunctionsOBJ: 4-3.1 To model data with quadratic functions NAT: A.2.fSTA: A.B.2.a| S.C.3.b TOP: 4-3 Problem 3 Using Quadratic Regression DOK: DOK 2

14. ANS: C PTS: 1 DIF: L2REF: 4-4 Factoring Quadratic ExpressionsOBJ: 4-4.1 To find common and binomial factors of quadratic expressionsNAT: N.5.c| A.2.a TOP: 4-4 Problem 2 Finding Common FactorsKEY: factoring | greatest common factor DOK: DOK 2

15. ANS: D PTS: 1 DIF: L3REF: 4-4 Factoring Quadratic ExpressionsOBJ: 4-4.1 To find common and binomial factors of quadratic expressionsNAT: N.5.c| A.2.a TOP: 4-4 Problem 3 Factoring ax^2+bx+c when abs(a)<>1KEY: factoring DOK: DOK 2

16. ANS: C PTS: 1 DIF: L2REF: 4-4 Factoring Quadratic ExpressionsOBJ: 4-4.2 To factor special quadratic expressions NAT: N.5.c| A.2.aTOP: 4-4 Problem 5 Factoring a Difference of Two Squares KEY: difference of two squares | factoringDOK: DOK 2

17. ANS: D PTS: 1 DIF: L3 REF: 4-5 Quadratic EquationsOBJ: 4-5.1 To solve quadratic equations by factoring NAT: A.2.a| A.4.a| A.4.cSTA: A.B.2.b| A.C.3.a TOP: 4-5 Problem 1 Solving a Quadratic Equation by FactoringKEY: DOK: DOK 2

18. ANS: B PTS: 1 DIF: L2 REF: 4-6 Completing the SquareOBJ: 4-6.1 To solve equations by completing the square NAT: A.2.a| A.4.c| A.4.gSTA: A.B.2.b| A.C.3.a TOP: 4-6 Problem 1 Solving by Finding Square RootsKEY: DOK: DOK 2 NOT:

19. ANS: D PTS: 1 DIF: L3 REF: 4-6 Completing the SquareOBJ: 4-6.1 To solve equations by completing the square NAT: A.2.a| A.4.c| A.4.gSTA: A.B.2.b| A.C.3.a TOP: 4-6 Problem 5 Solving by Completing the SquareKEY: completing the square DOK: DOK 2

20. ANS: A PTS: 1 DIF: L3 REF: 4-6 Completing the SquareOBJ: 4-6.2 To rewrite functions by completing the square NAT: A.2.a| A.4.c| A.4.gSTA: A.B.2.b| A.C.3.a TOP: 4-6 Problem 6 Writing in Vertex FormKEY: DOK: DOK 2

21. ANS: D PTS: 1 DIF: L3 REF: 4-7 The Quadratic FormulaOBJ: 4-7.1 To solve quadratic equations using the Quadratic FormulaNAT: A.2.a| A.4.c| A.4.e| A.4.f STA: A.B.2.b| A.C.3.aTOP: 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic FormulaDOK: DOK 2

22. ANS: B PTS: 1 DIF: L2 REF: 4-7 The Quadratic FormulaOBJ: 4-7.2 To determine the number of solutions by using the discriminantNAT: A.2.a| A.4.c| A.4.e| A.4.f STA: A.B.2.b| A.C.3.aTOP: 4-7 Problem 3 Using the Discriminant KEY: discriminant | Quadratic FormulaDOK: DOK 2

23. ANS: B PTS: 1 DIF: L2 REF: 4-8 Complex NumbersOBJ: 4-8.1 To identify, graph, and perform operations with complex numbersNAT: N.5.f| A.4.g TOP: 4-8 Problem 1 Simplifying a Number using iKEY: imaginary number | imaginary unit DOK: DOK 2

24. ANS: C PTS: 1 DIF: L2 REF: 4-8 Complex NumbersOBJ: 4-8.1 To identify, graph, and perform operations with complex numbersNAT: N.5.f| A.4.g TOP: 4-8 Problem 3 Adding and Subtracting Complex NumbersKEY: complex number DOK: DOK 2

25. ANS: B PTS: 1 DIF: L3 REF: 4-8 Complex NumbersOBJ: 4-8.1 To identify, graph, and perform operations with complex numbersNAT: N.5.f| A.4.g TOP: 4-8 Problem 3 Adding and Subtracting Complex NumbersKEY: complex number DOK: DOK 2

26. ANS: B PTS: 1 DIF: L3 REF: 4-8 Complex NumbersOBJ: 4-8.1 To identify, graph, and perform operations with complex numbersNAT: N.5.f| A.4.g TOP: 4-8 Problem 4 Multiplying Complex NumbersKEY: complex number DOK: DOK 2

27. ANS: D PTS: 1 DIF: L3 REF: 4-8 Complex NumbersOBJ: 4-8.1 To identify, graph, and perform operations with complex numbersNAT: N.5.f| A.4.g TOP: 4-8 Problem 5 Dividing Complex NumbersKEY: complex number | complex conjugates DOK: DOK 2

28. ANS: A PTS: 1 DIF: L3 REF: 4-8 Complex NumbersOBJ: 4-8.2 To find complex number solutions of quadratic equationsNAT: N.5.f| A.4.g TOP: 4-8 Problem 7 Finding Imaginary SolutionsKEY: complex number | imaginary number DOK: DOK 2

29. ANS: A PTS: 1 DIF: L2 REF: 5-1 Polynomial FunctionsOBJ: 5-1.1 To classify polynomials STA: A.C.7TOP: 5-1 Problem 1 Classifying PolynomialsKEY: degree of a polynomial | polynomial function | standard form of a polynomial functionDOK: DOK 1

30. ANS: C PTS: 1 DIF: L2 REF: 5-1 Polynomial FunctionsOBJ: 5-1.2 To graph polynomial functions and describe end behaviorSTA: A.C.7 TOP: 5-1 Problem 2 Describing End Behavior of Polynomial FunctionsKEY: polynomial | end behavior DOK: DOK 1

31. ANS: D PTS: 1 DIF: L3REF: 5-2 Polynomials, Linear Factors, and ZerosOBJ: 5-2.1 To analyze the factored form of a polynomial STA: A.C.5.bTOP: 5-2 Problem 1 Writing a Polynomial in Factored Form KEY: DOK: DOK 2

32. ANS: D PTS: 1 DIF: L3REF: 5-2 Polynomials, Linear Factors, and Zeros

OBJ: 5-2.2 To write a polynomial function from its zeros STA: A.C.5.bTOP: 5-2 Problem 3 Writing a polynomial function from its zerosDOK: DOK 2

33. ANS: C PTS: 1 DIF: L3REF: 5-2 Polynomials, Linear Factors, and ZerosOBJ: 5-2.2 To write a polynomial function from its zeros STA: A.C.5.bTOP: 5-2 Problem 4 Finding the Multiplicity of a Zero DOK: DOK 2

34. ANS: B PTS: 1 DIF: L3REF: 5-2 Polynomials, Linear Factors, and ZerosOBJ: 5-2.1 To analyze the factored form of a polynomial STA: A.C.5.bTOP: 5-2 Problem 5 Identifying a Relative Maximum and MinimumKEY: relative maximum | relative minimum DOK: DOK 2

35. ANS: A PTS: 1 DIF: L3 REF: 5-3 Solving Polynomial EquationsOBJ: 5-3.1 To solve polynomial equations by factoring NAT: A.2.aSTA: A.B.2.b TOP: 5-3 Problem 1 Solving Polynomial Equations Using FactorsKEY: DOK: DOK 2

36. ANS: B PTS: 1 DIF: L2 REF: 5-3 Solving Polynomial EquationsOBJ: 5-3.1 To solve polynomial equations by factoring NAT: A.2.aSTA: A.B.2.b TOP: 5-3 Problem 2 Solving Polynomial Equations by FactoringKEY: sum of cubes | difference of cubes DOK: DOK 2

37. ANS: C PTS: 1 DIF: L2 REF: 5-4 Dividing PolynomialsOBJ: 5-4.1 To divide polynomials using long division NAT: N.1.d| A.3.c| A.3.eTOP: 5-4 Problem 1 Using Polynomial Long Division KEY: DOK: DOK 2

38. ANS: B PTS: 1 DIF: L4 REF: 5-4 Dividing PolynomialsOBJ: 5-4.1 To divide polynomials using long division NAT: N.1.d| A.3.c| A.3.eTOP: 5-4 Problem 2 Checking Factors KEY: DOK: DOK 3

39. ANS: A PTS: 1 DIF: L3 REF: 5-4 Dividing PolynomialsOBJ: 5-4.2 To divide polynomials using synthetic division NAT: N.1.d| A.3.c| A.3.eTOP: 5-4 Problem 3 Using Synthetic Division KEY: synthetic divisionDOK: DOK 2

40. ANS: C PTS: 1 DIF: L3 REF: 5-4 Dividing PolynomialsOBJ: 5-4.2 To divide polynomials using synthetic division NAT: N.1.d| A.3.c| A.3.eTOP: 5-4 Problem 5 Evaluating a Polynomial KEY: synthetic divisionDOK: DOK 2

41. ANS: B PTS: 1 DIF: L2REF: 5-5 Theorems About Roots of Polynomial EquationsOBJ: 5-5.1 To solve equations using the Rational Root TheoremTOP: 5-5 Problem 1 Finding a Rational Root KEY: Rational Root TheoremDOK: DOK 1

42. ANS: B PTS: 1 DIF: L2REF: 5-5 Theorems About Roots of Polynomial EquationsOBJ: 5-5.1 To solve equations using the Rational Root TheoremTOP: 5-5 Problem 2 Using the Rational Root Theorem KEY: Rational Root TheoremDOK: DOK 2

43. ANS: C PTS: 1 DIF: L2REF: 5-5 Theorems About Roots of Polynomial EquationsOBJ: 5-5.2 To use the Conjugate Root TheoremTOP: 5-5 Problem 3 Using the Conjugate Root Theorem to Identify RootsKEY: Conjugate Root Theorem DOK: DOK 1

44. ANS: C PTS: 1 DIF: L4REF: 5-5 Theorems About Roots of Polynomial EquationsOBJ: 5-5.2 To use the Conjugate Root TheoremTOP: 5-5 Problem 4 Using Conjugates to Construct a PolynomialKEY: Conjugate Root Theorem DOK: DOK 2

45. ANS: D PTS: 1 DIF: L2 REF: 5-7 The Binomial TheoremOBJ: 5-7.1 To expand a binomial using Pascal's Triangle NAT: D.4.kTOP: 5-7 Problem 1 Using Pascal's Triangle KEY: Pascal's Triangle | expandDOK: DOK 2

46. ANS: B PTS: 1 DIF: L2 REF: 5-7 The Binomial TheoremOBJ: 5-7.2 To use the Binomial Theorem NAT: D.4.kTOP: 5-7 Problem 2 Expanding a Binomial KEY: Pascal's Triangle | expandDOK: DOK 2

47. ANS: B PTS: 1 DIF: L3REF: 5-8 Polynomial Models in the Real WorldOBJ: 5-8.1 To fit data to linear, quadratic, cubic, or quartic modelsTOP: 5-8 Problem 4 Using Interpolation and Extrapolation DOK: DOK 3

48. ANS: B PTS: 1 DIF: L3 REF: 5-9 Transforming Polynomial FunctionsOBJ: 5-9.1 To apply transformations to graphs of polynomials NAT: G.2.cSTA: A.C.9.a TOP: 5-9 Problem 1 Transforming y = x^3DOK: DOK 2

49. ANS: B PTS: 1 DIF: L4 REF: 6-1 Roots and Radical ExpressionsOBJ: 6-1.1 To find nth roots NAT: A.3.eTOP: 6-1 Problem 1 Finding All Real Roots KEY: nth rootDOK: DOK 1

50. ANS: A PTS: 1 DIF: L3 REF: 6-1 Roots and Radical ExpressionsOBJ: 6-1.1 To find nth roots NAT: A.3.eTOP: 6-1 Problem 3 Simplifying Radical Expressions KEY: radicand | index | nth rootDOK: DOK 1

51. ANS: D PTS: 1 DIF: L2REF: 6-2 Multiplying and Dividing Radical ExpressionsOBJ: 6-2.1 To multiply and divide radical expressions NAT: N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 1 Multiplying Radical Expressions DOK: DOK 1

52. ANS: B PTS: 1 DIF: L3REF: 6-2 Multiplying and Dividing Radical ExpressionsOBJ: 6-2.1 To multiply and divide radical expressions NAT: N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 3 Simplifying a Product KEY: simplest form of a radicalDOK: DOK 2

53. ANS: A PTS: 1 DIF: L2REF: 6-2 Multiplying and Dividing Radical ExpressionsOBJ: 6-2.1 To multiply and divide radical expressions NAT: N.5.e| A.3.c| A.3.eTOP: 6-2 Problem 4 Dividing Radical Expressions KEY: simplest form of a radicalDOK: DOK 1

54. ANS: C PTS: 1 DIF: L2 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 1 Adding and Subtracting Radical ExpressionsKEY: like radicals DOK: DOK 1

55. ANS: C PTS: 1 DIF: L2 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: N.5.e| A.3.c| A.3.e

TOP: 6-3 Problem 1 Adding and Subtracting Radical ExpressionsKEY: like radicals DOK: DOK 1

56. ANS: A PTS: 1 DIF: L4 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 3 Simplifying Before Adding or Subtracting DOK: DOK 2

57. ANS: C PTS: 1 DIF: L3 REF: 6-3 Binomial Radical ExpressionsOBJ: 6-3.1 To add and subtract radical expressions NAT: N.5.e| A.3.c| A.3.eTOP: 6-3 Problem 5 Multiplying Conjugates DOK: DOK 1

58. ANS: A PTS: 1 DIF: L3 REF: 6-4 Rational ExponentsOBJ: 6-4.1 To simplify expressions with rational exponents STA: A.B.1.a| A.B.1.b| A.B.1.cTOP: 6-4 Problem 4 Combining Radical Expressions KEY: rational exponentDOK: DOK 1

59. ANS: A PTS: 1 DIF: L3 REF: 6-4 Rational ExponentsOBJ: 6-4.1 To simplify expressions with rational exponents STA: A.B.1.a| A.B.1.b| A.B.1.cTOP: 6-4 Problem 5 Simplifying Numbers With Rational ExponentsKEY: rational exponent DOK: DOK 1

60. ANS: B PTS: 1 DIF: L2REF: 6-5 Solving Square Root and Other Radical EquationsOBJ: 6-5.1 To solve square root and other radical equations NAT: A.2.aSTA: A.B.1.c| A.B.2.b TOP: 6-5 Problem 1 Solving a Square Root EquationKEY: square root equation DOK: DOK 2

61. ANS: A PTS: 1 DIF: L4REF: 6-5 Solving Square Root and Other Radical EquationsOBJ: 6-5.1 To solve square root and other radical equations NAT: A.2.aSTA: A.B.1.c| A.B.2.b TOP: 6-5 Problem 2 Solving Other Radical EquationsKEY: radical equation DOK: DOK 2

62. ANS: C PTS: 1 DIF: L3REF: 6-5 Solving Square Root and Other Radical EquationsOBJ: 6-5.1 To solve square root and other radical equations NAT: A.2.aSTA: A.B.1.c| A.B.2.b TOP: 6-5 Problem 4 Checking for Extraneous SolutionsKEY: radical equation DOK: DOK 2

63. ANS: C PTS: 1 DIF: L2 REF: 8-1 Inverse VariationOBJ: 8-1.1 To recognize and use inverse variationTOP: 8-1 Problem 2 Determining an Inverse Variation KEY: inverse variationDOK: DOK 1

64. ANS: C PTS: 1 DIF: L2REF: 8-2 The Reciprocal Function FamilyOBJ: 8-2.2 To graph translations of reciprocal functions NAT: G.2.cSTA: A.C.9.a TOP: 8-2 Problem 4 Writing the Equation of a TransformationKEY: reciprocal function DOK: DOK 2

65. ANS: B PTS: 1 DIF: L2REF: 8-3 Rational Functions and Their GraphsOBJ: 8-3.1 To identify properties of rational functions NAT: A.2.hSTA: A.C.6.a| A.C.6.b TOP: 8-3 Problem 1 Finding Points of DiscontinuityKEY: rational function | point of discontinuity | removable discontinuity | non-removable points of discontinuity DOK: DOK 2

66. ANS: D PTS: 1 DIF: L2REF: 8-3 Rational Functions and Their GraphsOBJ: 8-3.1 To identify properties of rational functions NAT: A.2.hSTA: A.C.6.a| A.C.6.b TOP: 8-3 Problem 2 Finding Vertical Asymptotes

KEY: rational function DOK: DOK 267. ANS: B PTS: 1 DIF: L2 REF: 8-4 Rational Expressions

OBJ: 8-4.1 To simplify rational expressions NAT: A.3.eSTA: A.C.1.b TOP: 8-4 Problem 1 Simplifying a Rational ExpressionKEY: rational expression | simplest form DOK: DOK 2

68. ANS: B PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: A.3.eSTA: A.C.1.b TOP: 8-4 Problem 2 Multiplying Rational ExpressionsKEY: rational expression | simplest form DOK: DOK 2

69. ANS: A PTS: 1 DIF: L3 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: A.3.eSTA: A.C.1.b TOP: 8-4 Problem 3 Dividing Rational ExpressionsKEY: rational expression | simplest form DOK: DOK 2

70. ANS: C PTS: 1 DIF: L4 REF: 8-4 Rational ExpressionsOBJ: 8-4.2 To multiply and divide rational expressions NAT: A.3.eSTA: A.C.1.b TOP: 8-4 Problem 3 Dividing Rational ExpressionsKEY: rational expression | simplest form DOK: DOK 2

71. ANS: C PTS: 1 DIF: L2REF: 8-5 Adding and Subtracting Rational ExpressionsOBJ: 8-5.1 To add and subtract rational expressions NAT: N.5.e| A.3.c| A.3.eSTA: A.C.1.a| A.C.1.c TOP: 8-5 Problem 2 Adding Rational ExpressionsDOK: DOK 2

72. ANS: A PTS: 1 DIF: L3REF: 8-5 Adding and Subtracting Rational ExpressionsOBJ: 8-5.1 To add and subtract rational expressions NAT: N.5.e| A.3.c| A.3.eSTA: A.C.1.a| A.C.1.c TOP: 8-5 Problem 3 Subtracting Rational ExpressionsDOK: DOK 2

73. ANS: C PTS: 1 DIF: L3REF: 8-5 Adding and Subtracting Rational ExpressionsOBJ: 8-5.1 To add and subtract rational expressions NAT: N.5.e| A.3.c| A.3.eSTA: A.C.1.a| A.C.1.c TOP: 8-5 Problem 4 Simplifying a Complex FractionKEY: complex fraction DOK: DOK 2

74. ANS: C PTS: 1 DIF: L2 REF: 8-6 Solving Rational EquationsOBJ: 8-6.1 To solve rational equations STA: A.B.2.b| A.C.3.bTOP: 8-6 Problem 1 Solving a Rational Equation KEY: rational equationDOK: DOK 2

75. ANS: A PTS: 1 DIF: L4 REF: 8-6 Solving Rational EquationsOBJ: 8-6.1 To solve rational equations STA: A.B.2.b| A.C.3.bTOP: 8-6 Problem 1 Solving a Rational Equation KEY: rational equationDOK: DOK 2