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Math III_ Midterm Review 2013 Name __________________________ Multiple Choice Identify 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. b. ____ 2. Let c. d. be the reflection of in the x-axis. What is a function rule for a. b. ____ 3. The function function rule for a. b. ? c. d. . The graph of is translated to the left 7 units and up 8 units. What is the ? c. 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: –3 domain: all real numbers range: all real numbers c. maximum value: 3 domain: all real numbers range: all real numbers d. minimum value: –3 domain: 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: b. vertex: ( 2, –12) axis of symmetry: c. vertex: ( –2, –12) axis of symmetry: d. vertex: ( 2, –12) axis of symmetry: What is the vertex form of the equation? ____ 7. a. b. ____ c. 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. 1870 1871 1872 1873 1874 1875 1876 Year 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. b. c. d. ; 124 people ; 272 people ; 218 people ; 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 8 A.M. 10 A.M. 12 P.M. 2 P.M. 4 P.M. 6 P.M. Predicted Temperature (oF) 51.17 62.7 70.13 73.48 72.75 67.92 a. b. c. 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) 0 1 2 3 4 5 a. b. Height (in feet) 16 36.3 47.2 48.7 40.8 23.5 c. d. ____ 14. Factor. a. b. c. d. ____ 15. Factor. a. b. c. d. ____ 16. Factor. a. b. c. d. What are the solutions of the quadratic equation? ____ 17. =0 a. 7 1 , 3 2 b. 1 6, 2 c. –6, 3 d. –6, 7 3 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. b. 6 c. d. 6 Rewrite the equation in vertex form. Name the vertex and y-intercept. ____ 20. a. c. vertex: (6, – 2) y-intercept: (0, 34) b. vertex: (–12, –2) y-intercept: (0, –2) d. vertex: (–12, –2) y-intercept: (0, –2) vertex: (6, – 2) y-intercept: (0, 34) Use the Quadratic Formula to solve the equation. ____ 21. a. b. 5 2 c. 5 4 d. 4 5 5 4 What is the number of real solutions? ____ 22. a. one real solution b. two real solutions c. no real solutions d. cannot be determined Simplify the number using the imaginary unit i. ____ 23. a. b. c. d. Simplify the expression. ____ 24. a. b. c. d. a. b. c. d. a. b. c. d. a. c. b. d. ____ 25. ____ 26. ____ 27. What are the solutions? ____ 28. a. b. c. d. ____ 29. Classify –2x4 – x3 + 8x2 + 12 by degree. a. quartic b. quintic c. quadratic d. cubic Consider the leading term of each polynomial function. What is the end behavior of the graph? ____ 30. a. The leading term is up. b. The leading term is down. c. The leading term is d. The leading term is down. . Since n is even and a is positive, the end behavior is down and . Since n is even and a is positive, the end behavior is up and . Since n is even and a is positive, the end behavior is up and up. . Since n is even and a is positive, the end behavior is down and Write the polynomial in factored form. ____ 31. 6x3 – 60x2 + 144x a. 6x(x – 6)(x + 4) b. –4x(x – 6)(x + 6) c. –6x(x + 6)(x – 4) d. 6x(x – 4)(x – 6) ____ 32. What is a cubic polynomial function in standard form with zeros –4, –5, and 4? a. b. c. d. What are the zeros of the function? What are their multiplicities? ____ 33. a. b. c. d. the numbers 1, –4, and 0 are zeros of multiplicity 2 the numbers –1, 4, and 0 are zeros of multiplicity 2 the numbers –1, 4, and 0 are zeros of multiplicity 1 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 b. 4, –2 c. 4, –4 d. no solution What are the real or imaginary solutions of the polynomial equation? ____ 36. a. b. 2, ____ 37. Divide a. b. ____ 38. Is a. yes: c. 2, d. 2, and , and , and , and by x + 4. , R –232 c. d. , R 240 a factor of ? If it is, write c. yes: b. yes: d. as a product of two factors. is not a factor of Divide using synthetic division. ____ 39. Divide a. b. by ( , R –6 ____ 40. Use synthetic division to find P(–2) for a. –2 b. 0 ). c. d. , R 18 . 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, 8 b. –8, –4, –2, –1, 1, 2, 4, 8 d. no possible roots Find the roots of the polynomial equation. ____ 42. a. –3 ± 5i, –4 b. 3 ± 5i, –4 c. –3 ± i, 4 d. 3 ± i, 4 ____ 43. A polynomial equation with rational coefficients has the roots a. c. b. . Find two additional roots. 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 1908 1937 1959 1996 Pounds Consumed 3.255 9.053 17.837 58.395 Use a cubic model to estimate milk production in 1978. a. 30.4 b. 33.4 What is the equation of c. 36.4 d. 66.7 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. b. . c. and , , , and d. and What is a simpler form of the radical expression? ____ 50. a. b. c. d. c. d. Multiply and simplify if possible. ____ 51. a. 3 b. 11 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. b. c. d. not possible to simplify a. b. c. d. not possible to simplify ____ 55. What is the simplest form of the expression? ____ 56. a. b. c. d. ____ 57. a. ____ 58. What is b. 12 c. –8 d. in simplest form? a. c. b. d. What is the simplest form of the number? ____ 59. c. –28 d. –18 a. 9 b. 57 What is the solution of the equation? ____ 60. a. 4 b. –2 c. 12 d. –3 a. –5, 11 b. 5 c. 11 d. –11 a. –9 b. 9 and –4 c. –4 d. –9 and –4 ____ 61. ____ 62. ____ 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. ____ 64. Write an equation for the translation of d. y = 0.8x 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 b. x = 7, x = 3; yes c. x = –7, x = –3; no d. x = –1, x = 8, x = 2; no ____ 66. Describe the vertical asymptote(s) and hole(s) for the graph of a. b. c. d. . asymptotes: x = –4, –2 and hole: x = 1 asymptote: x = 1 and no holes asymptote: x = 1 and holes: x = –4, –2 asymptotes: x = –4, –2 and no holes Simplify the rational expression. State any restrictions on the variable. ____ 67. a. b. c. 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. 19 4 b. 1 3 c. 19 3 d. 2 ____ 75. a. –9 b. –6 c. –9 and –6 d. 6 Math III_ Midterm Review 2013 Answer Section MULTIPLE CHOICE 1. ANS: OBJ: TOP: DOK: 2. ANS: OBJ: TOP: DOK: 3. ANS: OBJ: TOP: DOK: 4. ANS: REF: OBJ: STA: KEY: 5. ANS: REF: OBJ: STA: KEY: 6. ANS: REF: OBJ: TOP: KEY: 7. ANS: REF: OBJ: TOP: KEY: 8. ANS: REF: OBJ: TOP: DOK: 9. ANS: REF: OBJ: STA: KEY: 10. ANS: REF: A PTS: 1 DIF: L2 REF: 2-6 Families of Functions 2-6.1 To analyze transformations of functions NAT: G.2.c| G.4.d| A.1.e| A.1.h| A.2.b 2-6 Problem 2 Horizontal Translation KEY: translation | transformation DOK 2 A PTS: 1 DIF: L3 REF: 2-6 Families of Functions 2-6.1 To analyze transformations of functions NAT: G.2.c| G.4.d| A.1.e| A.1.h| A.2.b 2-6 Problem 3 Reflecting a Function Algebraically KEY: transformation DOK 2 C PTS: 1 DIF: L3 REF: 2-6 Families of Functions 2-6.1 To analyze transformations of functions NAT: G.2.c| G.4.d| A.1.e| A.1.h| A.2.b 2-6 Problem 5 Combining Transformations KEY: transformation DOK 2 C PTS: 1 DIF: L3 4-1 Quadratic Functions and Transformations 4-1.1 To identify and graph quadratic functions NAT: G.2.c| A.2.d A.B.4.a TOP: 4-1 Problem 3 Interpreting Vertex Form parabola | vertex of a parabola | y-intercept DOK: DOK 2 D PTS: 1 DIF: L3 4-1 Quadratic Functions and Transformations 4-1.1 To identify and graph quadratic functions NAT: G.2.c| A.2.d A.B.4.a TOP: 4-1 Problem 3 Interpreting Vertex Form parabola | vertex of a parabola | y-intercept DOK: DOK 2 B PTS: 1 DIF: L3 4-2 Standard Form of a Quadratic Function 4-2.1 To graph quadratic functions written in standard form 4-2 Problem 1 Finding the Features of a Quadratic Function standard form DOK: DOK 2 B PTS: 1 DIF: L3 4-2 Standard Form of a Quadratic Function 4-2.1 To graph quadratic functions written in standard form 4-2 Problem 3 Converting Standard Form to Vertex Form standard form DOK: DOK 2 B PTS: 1 DIF: L4 4-2 Standard Form of a Quadratic Function 4-2.1 To graph quadratic functions written in standard form 4-2 Problem 4 Interpreting a Quadratic Graph KEY: standard form DOK 3 C PTS: 1 DIF: L3 4-3 Modeling With Quadratic Functions 4-3.1 To model data with quadratic functions NAT: A.2.f A.B.2.a| S.C.3.b TOP: 4-3 Problem 1 Writing an Equation of a Parabola quadratic function | quadratic model DOK: DOK 2 C PTS: 1 DIF: L2 4-3 Modeling With Quadratic Functions 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. OBJ: STA: KEY: ANS: REF: OBJ: STA: KEY: DOK: ANS: REF: OBJ: STA: DOK: ANS: REF: OBJ: STA: DOK: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: NAT: KEY: ANS: REF: OBJ: TOP: DOK: ANS: OBJ: STA: KEY: ANS: OBJ: STA: KEY: ANS: OBJ: STA: KEY: ANS: OBJ: STA: KEY: 4-3.1 To model data with quadratic functions NAT: A.2.f A.B.2.a| S.C.3.b TOP: 4-3 Problem 1 Writing an Equation of a Parabola quadratic function | quadratic model DOK: DOK 2 C PTS: 1 DIF: L3 4-3 Modeling With Quadratic Functions 4-3.1 To model data with quadratic functions NAT: A.2.f A.B.2.a| S.C.3.b TOP: 4-3 Problem 2 Using a Quadratic Model quadratic model | quadratic function | word problem | problem solving | multi-part question DOK 3 D PTS: 1 DIF: L3 4-3 Modeling With Quadratic Functions 4-3.1 To model data with quadratic functions NAT: A.2.f A.B.2.a| S.C.3.b TOP: 4-3 Problem 3 Using Quadratic Regression DOK 2 B PTS: 1 DIF: L3 4-3 Modeling With Quadratic Functions 4-3.1 To model data with quadratic functions NAT: A.2.f A.B.2.a| S.C.3.b TOP: 4-3 Problem 3 Using Quadratic Regression DOK 2 C PTS: 1 DIF: L2 4-4 Factoring Quadratic Expressions 4-4.1 To find common and binomial factors of quadratic expressions N.5.c| A.2.a TOP: 4-4 Problem 2 Finding Common Factors factoring | greatest common factor DOK: DOK 2 D PTS: 1 DIF: L3 4-4 Factoring Quadratic Expressions 4-4.1 To find common and binomial factors of quadratic expressions N.5.c| A.2.a TOP: 4-4 Problem 3 Factoring ax^2+bx+c when abs(a)<>1 factoring DOK: DOK 2 C PTS: 1 DIF: L2 4-4 Factoring Quadratic Expressions 4-4.2 To factor special quadratic expressions NAT: N.5.c| A.2.a 4-4 Problem 5 Factoring a Difference of Two Squares KEY: difference of two squares | factoring DOK 2 D PTS: 1 DIF: L3 REF: 4-5 Quadratic Equations 4-5.1 To solve quadratic equations by factoring NAT: A.2.a| A.4.a| A.4.c A.B.2.b| A.C.3.a TOP: 4-5 Problem 1 Solving a Quadratic Equation by Factoring DOK: DOK 2 B PTS: 1 DIF: L2 REF: 4-6 Completing the Square 4-6.1 To solve equations by completing the square NAT: A.2.a| A.4.c| A.4.g A.B.2.b| A.C.3.a TOP: 4-6 Problem 1 Solving by Finding Square Roots DOK: DOK 2 NOT: D PTS: 1 DIF: L3 REF: 4-6 Completing the Square 4-6.1 To solve equations by completing the square NAT: A.2.a| A.4.c| A.4.g A.B.2.b| A.C.3.a TOP: 4-6 Problem 5 Solving by Completing the Square completing the square DOK: DOK 2 A PTS: 1 DIF: L3 REF: 4-6 Completing the Square 4-6.2 To rewrite functions by completing the square NAT: A.2.a| A.4.c| A.4.g A.B.2.b| A.C.3.a TOP: 4-6 Problem 6 Writing in Vertex Form DOK: DOK 2 21. ANS: OBJ: NAT: TOP: DOK: 22. ANS: OBJ: NAT: TOP: DOK: 23. ANS: OBJ: NAT: KEY: 24. ANS: OBJ: NAT: KEY: 25. ANS: OBJ: NAT: KEY: 26. ANS: OBJ: NAT: KEY: 27. ANS: OBJ: NAT: KEY: 28. ANS: OBJ: NAT: KEY: 29. ANS: OBJ: TOP: KEY: DOK: 30. ANS: OBJ: STA: KEY: 31. ANS: REF: OBJ: TOP: DOK: 32. ANS: REF: D PTS: 1 DIF: L3 REF: 4-7 The Quadratic Formula 4-7.1 To solve quadratic equations using the Quadratic Formula A.2.a| A.4.c| A.4.e| A.4.f STA: A.B.2.b| A.C.3.a 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula DOK 2 B PTS: 1 DIF: L2 REF: 4-7 The Quadratic Formula 4-7.2 To determine the number of solutions by using the discriminant A.2.a| A.4.c| A.4.e| A.4.f STA: A.B.2.b| A.C.3.a 4-7 Problem 3 Using the Discriminant KEY: discriminant | Quadratic Formula DOK 2 B PTS: 1 DIF: L2 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers N.5.f| A.4.g TOP: 4-8 Problem 1 Simplifying a Number using i imaginary number | imaginary unit DOK: DOK 2 C PTS: 1 DIF: L2 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers N.5.f| A.4.g TOP: 4-8 Problem 3 Adding and Subtracting Complex Numbers complex number DOK: DOK 2 B PTS: 1 DIF: L3 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers N.5.f| A.4.g TOP: 4-8 Problem 3 Adding and Subtracting Complex Numbers complex number DOK: DOK 2 B PTS: 1 DIF: L3 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers N.5.f| A.4.g TOP: 4-8 Problem 4 Multiplying Complex Numbers complex number DOK: DOK 2 D PTS: 1 DIF: L3 REF: 4-8 Complex Numbers 4-8.1 To identify, graph, and perform operations with complex numbers N.5.f| A.4.g TOP: 4-8 Problem 5 Dividing Complex Numbers complex number | complex conjugates DOK: DOK 2 A PTS: 1 DIF: L3 REF: 4-8 Complex Numbers 4-8.2 To find complex number solutions of quadratic equations N.5.f| A.4.g TOP: 4-8 Problem 7 Finding Imaginary Solutions complex number | imaginary number DOK: DOK 2 A PTS: 1 DIF: L2 REF: 5-1 Polynomial Functions 5-1.1 To classify polynomials STA: A.C.7 5-1 Problem 1 Classifying Polynomials degree of a polynomial | polynomial function | standard form of a polynomial function DOK 1 C PTS: 1 DIF: L2 REF: 5-1 Polynomial Functions 5-1.2 To graph polynomial functions and describe end behavior A.C.7 TOP: 5-1 Problem 2 Describing End Behavior of Polynomial Functions polynomial | end behavior DOK: DOK 1 D PTS: 1 DIF: L3 5-2 Polynomials, Linear Factors, and Zeros 5-2.1 To analyze the factored form of a polynomial STA: A.C.5.b 5-2 Problem 1 Writing a Polynomial in Factored Form KEY: DOK 2 D PTS: 1 DIF: L3 5-2 Polynomials, Linear Factors, and Zeros 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. OBJ: TOP: DOK: ANS: REF: OBJ: TOP: ANS: REF: OBJ: TOP: KEY: ANS: OBJ: STA: KEY: ANS: OBJ: STA: KEY: ANS: OBJ: TOP: DOK: ANS: OBJ: TOP: ANS: OBJ: TOP: DOK: ANS: OBJ: TOP: DOK: ANS: REF: OBJ: TOP: DOK: ANS: REF: OBJ: TOP: DOK: ANS: REF: OBJ: TOP: KEY: 5-2.2 To write a polynomial function from its zeros STA: A.C.5.b 5-2 Problem 3 Writing a polynomial function from its zeros DOK 2 C PTS: 1 DIF: L3 5-2 Polynomials, Linear Factors, and Zeros 5-2.2 To write a polynomial function from its zeros STA: A.C.5.b 5-2 Problem 4 Finding the Multiplicity of a Zero DOK: DOK 2 B PTS: 1 DIF: L3 5-2 Polynomials, Linear Factors, and Zeros 5-2.1 To analyze the factored form of a polynomial STA: A.C.5.b 5-2 Problem 5 Identifying a Relative Maximum and Minimum relative maximum | relative minimum DOK: DOK 2 A PTS: 1 DIF: L3 REF: 5-3 Solving Polynomial Equations 5-3.1 To solve polynomial equations by factoring NAT: A.2.a A.B.2.b TOP: 5-3 Problem 1 Solving Polynomial Equations Using Factors DOK: DOK 2 B PTS: 1 DIF: L2 REF: 5-3 Solving Polynomial Equations 5-3.1 To solve polynomial equations by factoring NAT: A.2.a A.B.2.b TOP: 5-3 Problem 2 Solving Polynomial Equations by Factoring sum of cubes | difference of cubes DOK: DOK 2 C PTS: 1 DIF: L2 REF: 5-4 Dividing Polynomials 5-4.1 To divide polynomials using long division NAT: N.1.d| A.3.c| A.3.e 5-4 Problem 1 Using Polynomial Long Division KEY: DOK 2 B PTS: 1 DIF: L4 REF: 5-4 Dividing Polynomials 5-4.1 To divide polynomials using long division NAT: N.1.d| A.3.c| A.3.e 5-4 Problem 2 Checking Factors KEY: DOK: DOK 3 A PTS: 1 DIF: L3 REF: 5-4 Dividing Polynomials 5-4.2 To divide polynomials using synthetic division NAT: N.1.d| A.3.c| A.3.e 5-4 Problem 3 Using Synthetic Division KEY: synthetic division DOK 2 C PTS: 1 DIF: L3 REF: 5-4 Dividing Polynomials 5-4.2 To divide polynomials using synthetic division NAT: N.1.d| A.3.c| A.3.e 5-4 Problem 5 Evaluating a Polynomial KEY: synthetic division DOK 2 B PTS: 1 DIF: L2 5-5 Theorems About Roots of Polynomial Equations 5-5.1 To solve equations using the Rational Root Theorem 5-5 Problem 1 Finding a Rational Root KEY: Rational Root Theorem DOK 1 B PTS: 1 DIF: L2 5-5 Theorems About Roots of Polynomial Equations 5-5.1 To solve equations using the Rational Root Theorem 5-5 Problem 2 Using the Rational Root Theorem KEY: Rational Root Theorem DOK 2 C PTS: 1 DIF: L2 5-5 Theorems About Roots of Polynomial Equations 5-5.2 To use the Conjugate Root Theorem 5-5 Problem 3 Using the Conjugate Root Theorem to Identify Roots Conjugate Root Theorem DOK: DOK 1 44. ANS: REF: OBJ: TOP: KEY: 45. ANS: OBJ: TOP: DOK: 46. ANS: OBJ: TOP: DOK: 47. ANS: REF: OBJ: TOP: 48. ANS: REF: OBJ: STA: DOK: 49. ANS: OBJ: TOP: DOK: 50. ANS: OBJ: TOP: DOK: 51. ANS: REF: OBJ: TOP: 52. ANS: REF: OBJ: TOP: DOK: 53. ANS: REF: OBJ: TOP: DOK: 54. ANS: OBJ: TOP: KEY: 55. ANS: OBJ: C PTS: 1 DIF: L4 5-5 Theorems About Roots of Polynomial Equations 5-5.2 To use the Conjugate Root Theorem 5-5 Problem 4 Using Conjugates to Construct a Polynomial Conjugate Root Theorem DOK: DOK 2 D PTS: 1 DIF: L2 REF: 5-7.1 To expand a binomial using Pascal's Triangle NAT: 5-7 Problem 1 Using Pascal's Triangle KEY: DOK 2 B PTS: 1 DIF: L2 REF: 5-7.2 To use the Binomial Theorem NAT: 5-7 Problem 2 Expanding a Binomial KEY: DOK 2 B PTS: 1 DIF: L3 5-8 Polynomial Models in the Real World 5-8.1 To fit data to linear, quadratic, cubic, or quartic models 5-8 Problem 4 Using Interpolation and Extrapolation DOK: B PTS: 1 DIF: L3 5-9 Transforming Polynomial Functions 5-9.1 To apply transformations to graphs of polynomials NAT: A.C.9.a TOP: 5-9 Problem 1 Transforming y = x^3 DOK 2 B PTS: 1 DIF: L4 REF: 6-1.1 To find nth roots NAT: A.3.e 6-1 Problem 1 Finding All Real Roots KEY: DOK 1 A PTS: 1 DIF: L3 REF: 6-1.1 To find nth roots NAT: A.3.e 6-1 Problem 3 Simplifying Radical Expressions KEY: DOK 1 D PTS: 1 DIF: L2 6-2 Multiplying and Dividing Radical Expressions 6-2.1 To multiply and divide radical expressions NAT: 6-2 Problem 1 Multiplying Radical Expressions DOK: B PTS: 1 DIF: L3 6-2 Multiplying and Dividing Radical Expressions 6-2.1 To multiply and divide radical expressions NAT: 6-2 Problem 3 Simplifying a Product KEY: DOK 2 A PTS: 1 DIF: L2 6-2 Multiplying and Dividing Radical Expressions 6-2.1 To multiply and divide radical expressions NAT: 6-2 Problem 4 Dividing Radical Expressions KEY: DOK 1 C PTS: 1 DIF: L2 REF: 6-3.1 To add and subtract radical expressions NAT: 6-3 Problem 1 Adding and Subtracting Radical Expressions like radicals DOK: DOK 1 C PTS: 1 DIF: L2 REF: 6-3.1 To add and subtract radical expressions NAT: 5-7 The Binomial Theorem D.4.k Pascal's Triangle | expand 5-7 The Binomial Theorem D.4.k Pascal's Triangle | expand DOK 3 G.2.c 6-1 Roots and Radical Expressions nth root 6-1 Roots and Radical Expressions radicand | index | nth root N.5.e| A.3.c| A.3.e DOK 1 N.5.e| A.3.c| A.3.e simplest form of a radical N.5.e| A.3.c| A.3.e simplest form of a radical 6-3 Binomial Radical Expressions N.5.e| A.3.c| A.3.e 6-3 Binomial Radical Expressions N.5.e| A.3.c| A.3.e 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. TOP: 6-3 Problem 1 Adding and Subtracting Radical Expressions KEY: like radicals DOK: DOK 1 ANS: A PTS: 1 DIF: L4 REF: 6-3 Binomial Radical Expressions OBJ: 6-3.1 To add and subtract radical expressions NAT: N.5.e| A.3.c| A.3.e TOP: 6-3 Problem 3 Simplifying Before Adding or Subtracting DOK: DOK 2 ANS: C PTS: 1 DIF: L3 REF: 6-3 Binomial Radical Expressions OBJ: 6-3.1 To add and subtract radical expressions NAT: N.5.e| A.3.c| A.3.e TOP: 6-3 Problem 5 Multiplying Conjugates DOK: DOK 1 ANS: A PTS: 1 DIF: L3 REF: 6-4 Rational Exponents OBJ: 6-4.1 To simplify expressions with rational exponents STA: A.B.1.a| A.B.1.b| A.B.1.c TOP: 6-4 Problem 4 Combining Radical Expressions KEY: rational exponent DOK: DOK 1 ANS: A PTS: 1 DIF: L3 REF: 6-4 Rational Exponents OBJ: 6-4.1 To simplify expressions with rational exponents STA: A.B.1.a| A.B.1.b| A.B.1.c TOP: 6-4 Problem 5 Simplifying Numbers With Rational Exponents KEY: rational exponent DOK: DOK 1 ANS: B PTS: 1 DIF: L2 REF: 6-5 Solving Square Root and Other Radical Equations OBJ: 6-5.1 To solve square root and other radical equations NAT: A.2.a STA: A.B.1.c| A.B.2.b TOP: 6-5 Problem 1 Solving a Square Root Equation KEY: square root equation DOK: DOK 2 ANS: A PTS: 1 DIF: L4 REF: 6-5 Solving Square Root and Other Radical Equations OBJ: 6-5.1 To solve square root and other radical equations NAT: A.2.a STA: A.B.1.c| A.B.2.b TOP: 6-5 Problem 2 Solving Other Radical Equations KEY: radical equation DOK: DOK 2 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: A.2.a STA: A.B.1.c| A.B.2.b TOP: 6-5 Problem 4 Checking for Extraneous Solutions KEY: radical equation DOK: DOK 2 ANS: C PTS: 1 DIF: L2 REF: 8-1 Inverse Variation OBJ: 8-1.1 To recognize and use inverse variation TOP: 8-1 Problem 2 Determining an Inverse Variation KEY: inverse variation DOK: DOK 1 ANS: C PTS: 1 DIF: L2 REF: 8-2 The Reciprocal Function Family OBJ: 8-2.2 To graph translations of reciprocal functions NAT: G.2.c STA: A.C.9.a TOP: 8-2 Problem 4 Writing the Equation of a Transformation KEY: reciprocal function DOK: DOK 2 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: A.2.h STA: A.C.6.a| A.C.6.b TOP: 8-3 Problem 1 Finding Points of Discontinuity KEY: rational function | point of discontinuity | removable discontinuity | non-removable points of discontinuity DOK: DOK 2 ANS: D PTS: 1 DIF: L2 REF: 8-3 Rational Functions and Their Graphs OBJ: 8-3.1 To identify properties of rational functions NAT: A.2.h STA: A.C.6.a| A.C.6.b TOP: 8-3 Problem 2 Finding Vertical Asymptotes KEY: 67. ANS: OBJ: STA: KEY: 68. ANS: OBJ: STA: KEY: 69. ANS: OBJ: STA: KEY: 70. ANS: OBJ: STA: KEY: 71. ANS: REF: OBJ: STA: DOK: 72. ANS: REF: OBJ: STA: DOK: 73. ANS: REF: OBJ: STA: KEY: 74. ANS: OBJ: TOP: DOK: 75. ANS: OBJ: TOP: DOK: rational function DOK: DOK 2 B PTS: 1 DIF: L2 REF: 8-4 Rational Expressions 8-4.1 To simplify rational expressions NAT: A.3.e A.C.1.b TOP: 8-4 Problem 1 Simplifying a Rational Expression rational expression | simplest form DOK: DOK 2 B PTS: 1 DIF: L3 REF: 8-4 Rational Expressions 8-4.2 To multiply and divide rational expressions NAT: A.3.e A.C.1.b TOP: 8-4 Problem 2 Multiplying Rational Expressions rational expression | simplest form DOK: DOK 2 A PTS: 1 DIF: L3 REF: 8-4 Rational Expressions 8-4.2 To multiply and divide rational expressions NAT: A.3.e A.C.1.b TOP: 8-4 Problem 3 Dividing Rational Expressions rational expression | simplest form DOK: DOK 2 C PTS: 1 DIF: L4 REF: 8-4 Rational Expressions 8-4.2 To multiply and divide rational expressions NAT: A.3.e A.C.1.b TOP: 8-4 Problem 3 Dividing Rational Expressions rational expression | simplest form DOK: DOK 2 C PTS: 1 DIF: L2 8-5 Adding and Subtracting Rational Expressions 8-5.1 To add and subtract rational expressions NAT: N.5.e| A.3.c| A.3.e A.C.1.a| A.C.1.c TOP: 8-5 Problem 2 Adding Rational Expressions DOK 2 A PTS: 1 DIF: L3 8-5 Adding and Subtracting Rational Expressions 8-5.1 To add and subtract rational expressions NAT: N.5.e| A.3.c| A.3.e A.C.1.a| A.C.1.c TOP: 8-5 Problem 3 Subtracting Rational Expressions DOK 2 C PTS: 1 DIF: L3 8-5 Adding and Subtracting Rational Expressions 8-5.1 To add and subtract rational expressions NAT: N.5.e| A.3.c| A.3.e A.C.1.a| A.C.1.c TOP: 8-5 Problem 4 Simplifying a Complex Fraction complex fraction DOK: DOK 2 C PTS: 1 DIF: L2 REF: 8-6 Solving Rational Equations 8-6.1 To solve rational equations STA: A.B.2.b| A.C.3.b 8-6 Problem 1 Solving a Rational Equation KEY: rational equation DOK 2 A PTS: 1 DIF: L4 REF: 8-6 Solving Rational Equations 8-6.1 To solve rational equations STA: A.B.2.b| A.C.3.b 8-6 Problem 1 Solving a Rational Equation KEY: rational equation DOK 2