Download Math III_ Midterm Review 2013 Answer Section

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
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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.
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15.
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17.
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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
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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
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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
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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
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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
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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
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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
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DIF: L3
5-2 Polynomials, Linear Factors, and Zeros
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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