Download LSU College Readiness Program COURSE

LSU College Readiness Program
COURSE PROFILE
11-16-15
COURSE NAME:
PRIMARY ONLINE
CONTENT SOURCE:
COURSE/UNIT CREDIT:
GRADE(S):
PREREQUISITE(S):
High School Algebra II
Algebra II in MyMathLab
Elayn Martin-Gay, with contributions from Robert Blitzer
1 Carnegie Unit
9, 10, or 11
Successful Completion of Geometry
CHAPTERS
1 – Real Numbers and Algebraic
8 – Rational Exponents, Radicals, and
Expressions
Complex Numbers
2 – Equations, Inequalities, and Problem
9 - Quadratic and Higher Degree
Solving
Equations and Functions
3 - Graphs and Functions
10 - Exponential and Logarithmic
Functions
4 – Systems of Equations
11 – Graphing Quadratic Functions,
Rational Functions, and Conic Sections
6 - Exponents, Polynomials, and Polynomial 13 - Counting Methods and Probability
Functions
7 - Rational Expressions
14 and 15 - Trigonometric Functions
X – Statistics (from another book)
SECTION NAMES (NUMBER OF EXERCISES), LEARNING OBJECTIVES, AND
LDoE MATHEMATICS STANDARDS CORRELATIONS
CHAPTER 1: Real Numbers and Algebraic Expressions
8.NS.A.1
*1.2 Algebraic Expressions and Sets of Numbers (50)
Identify and evaluate algebraic expressions
Identify natural numbers, whole numbers, integers, and rational and irrational
numbers
Find the absolute value of a number
Find the opposite of a number
Write phrases as algebraic expressions
8.EE.A.1
*1.3 Operations on Real Numbers (61)
Add and subtract real numbers
8.EE.A.2
Multiply and divide real numbers
Evaluate expressions containing exponents
Find roots of numbers
Use the order of operations
Evaluate algebraic expressions
A-SSE.A.2
*1.4 Properties of Real Numbers (60)
Use operation and order symbols to write mathematical sentences
Identify identity numbers and inverses
Identify and use the commutative, associative, and distributive properties
1
Write algebraic expressions
Simplify algebraic expressions
CHAPTER 2: Equations, Inequalities, and Problem Solving
*2.1 Linear Equations in One Variable (47)
Solve linear equations using properties of equality
Solve linear equations that can be simplified by combining like terms
Solve linear equations containing fractions or decimals
*2.2 An Introduction to Problem Solving (44)
Write algebraic expressions that can be simplified
Apply the steps for problem solving
*2.3 Formulas and Problem Solving (38)
Solve a formula for a specified variable
Use formulas to solve problems
*2.4 Linear Inequalities and Problem Solving (53)
Graph inequalities
Solve linear inequalities using the multiplication and addition property of
inequality
Solve problems that can be modeled by linear inequalities
*2.5 Compound Inequalities (49)
Find the union and the intersection of two sets
Solve compound inequalities involving “and” and “or”
*2.6 Absolute Value Equations (43)
Solve absolute value equations
*2.7 Absolute Value Inequalities (51)
Solve absolute value inequalities
CHAPTER 3: Graphs and Functions
*3.1 Graphing Equations (46)
Plot ordered pairs
Determine whether an ordered pair is a solution to an equation in two variables
Graph linear and nonlinear equations
*3.2 Introduction to Functions (56)
Define relation, domain, and range
Use the vertical line test for functions
Identify functions
Use function notation
*3.3 Graphing Linear Functions (39)
Graph linear functions
Graph linear functions using intercepts
Graph vertical and horizontal lines
*3.4 The Slope of a Line (50)
Find the slope of a line given two points on the line
Find the slope of a line given the equation of the line
Interpret the slope-intercept form in an application
Compare the slopes of parallel and perpendicular lines
Find the slope as a ratio of vertical change to horizontal change
2
A-REI.B.3
A-SSE.A.1a
A-CED.A.1
A-CED.A.4
A-REI.B.3
A-REI.B.3
A-REI.B.3
A-REI.B.3
A-REI.D.10
F-IF.A.1
F-IF.A.2
F-IF.C.7a
F-LE.A.2
F-LE.B.5
G-GPE.B.5
3.5 Equations of a Line (50)
Use the slope intercept form to write the equation of line
Graph a line using its slope and y-intercept
Use the point slope form to write the equation of line
Read a graph to find the function value
Write equations of vertical and horizontal lines
Find equations of parallel and perpendicular lines
3.6a Graph Piece-Wise-Defined (11)
Graph piecewise-defined functions
3.6b Shift and Reflect Graphs (18)
Graph functions using vertical and horizontal shifts
Reflect graphs
3.7 Graphing Linear Inequalities (33)
Graph linear inequalities
Graph the intersection or union of two linear inequalities
3.8 Stretching and Compressing Absolute Value Functions (12)
Graph the absolute value function
Find the equation of a graphed absolute value function
CHAPTER 4: Systems of Equations
4.1 Solving Systems of Equations in Two Variables (40)
Determine whether an ordered pair is solution of a system of two linear
equations
Solve a system by graphing
Solve a system by substitution
Solve a system by elimination
Solve applications
4.2 Solving Systems of Equations in Three Variables (22)
Determine whether an ordered triple is solution of system of three linear
equations
Solve a system of three linear equations in three variables
4.3 Systems Used in Problem Solving (30)
Solve problems that can be modeled by a system of two linear equations
Solve problems with cost and revenue functions
Solve problems that can be modeled by a system of three linear equations
CHAPTER 6: Exponents, Polynomials, and Polynomial Functions
6.1 Use the Product Rule for Exponents (69)
Use the product rule for exponents
Use the quotient rule for exponents
Evaluate expressions raised to the 0 power
Evaluate expressions raised to the negative nth power
Convert between scientific notation and standard notation
6.2 Use the Power Rule for Exponents (53)
Use the power rules for exponents
Use exponent rules and definitions to simplify exponential expressions
Compute, using scientific notation
3
A-CED.A.2
F-IF.A.1
A-CED.A.1
G-GPE.B.5
F-IF.C.7b
F-BF.B.3
A-REI.D.12
F-IF.C.7b
A-REI.C.6
A-REI.C.6
F-BF.A.1a
A-REI.C.6
A-SSE.A.2
8.EE.A.1
8.EE.A.4
8.EE.A.1
8.EE.A.4
6.3 Identify and Evaluate, Add and Subtract Polynomials (61)
Identify polynomials, parts of polynomials, and degree of term and of
polynomial
Evaluate polynomial functions
Review combining like terms
Add polynomials
Subtract polynomials
6.4 Multiplying Polynomials (45)
Multiply two polynomials
Multiply binomials
Square binomials
Multiply the sum and difference of two terms
Multiply three or more polynomials
Evaluate polynomial functions
6.5 The GCF and Factoring by Grouping Polynomials (43)
Identify the GCF
Factor out the GCF of a polynomial's terms
Factor polynomials by grouping
6.6 Factoring Trinomials (57)
Factor trinomials of the form x^2+bx+c
Factor trinomials of the form ax^2+bx+c by trial and check or by grouping
Factor by substitution
6.7 Factoring by Special Products (46)
Factor a perfect square trinomial
Factor the difference of two squares
Factor the sum or difference of two cubes
6.8 Solving Equations by Factoring and Problem Solving (52)
Solve polynomial equations by factoring
Solve problems that can be modeled by polynomial equations
Find the x-intercepts of a polynomial function
6.9 Even and Odd Power Functions and End Behavior (15)
Graph even and odd power functions
Describe the end behavior of a polynomial function
Graph even and odd power functions
CHAPTER 7: Rational Expressions
7.1 Rational Functions and Mult/Div Rational Expressions (49)
Find the domains of rational expressions
Simplify rational expressions
Multiply rational expressions
Divide rational expressions
Multiply and divide rational expressions
Use rational functions in applications
7.2 Adding and Subtracting Rational Expressions (46)
Add and subtract rational expressions with common denominators
Identify the least common denominator of two or more rational expressions
Add and subtract rational expressions with unlike denominators
Add and subtract rational expressions with common denominators
Mixed Practice
4
A-SSE.A.1
F-IF.A.2
A-SSE.A.2
A-APR.A.1
A-APR.A.1
F-IF.A.2
A-SSE.A.1
A-SSE.A.2
A-SSE.A.2
A-SSE.A.2
A-APR.B.3
A-REI.B.4b
F-BF.B.3
F-IF.C.7c
A-APR.D.7(+)
A-APR.D.7(+)
7.3 Simplifying Complex Fractions (37)
Simplify complex fractions by simplifying numerator/denominator and
dividing
Simplify complex fractions by multiplying by a common denominator
Simplify expressions with negative exponents
7.4 Dividing Polynomials: Long & Synthetic Division, Remainder
Theorem (54)
Divide a polynomial by a monomial
Divide by a polynomial
Use synthetic division to divide a polynomial by a binomial
Use the remainder theorem to evaluate polynomials
Use the factor theorem
7.5 Solving Equations Containing Rational Expressions (39)
Solve equations containing rational expressions
7.6 Rational Equations and Problem Solving (45)
Solve equations that contain radical expressions
Use the Pythagorean theorem to model problems
Solve application problems
7.7 Variation and Problem Solving (33)
Solve problems involving direct variation
Solve problems involving joint variation
Solve problems involving inverse variation
Solve problems involving combined variation
A-APR.D.7(+)
A-APR.B.2
A-APR.D.6
A-REI.A.2
A-REI.A.2
A-CED.A.1
A-CED.A.1
F-BF.A.1
CHAPTER 8: Rational Exponents, Radicals, and Complex Numbers
8.1 Radicals and Radical Functions (56)
Find square roots
Approximate roots
Find cube roots
Find nth roots
Find the nth root of a^n, where a is a real number
Find function values of square and cube roots
Graph square and cube root functions
8.2 Rational Exponents for Radicals (60)
Understand the meaning of a^(1/n)
Understand the meaning of a^(m/n)
Understand the meaning of a^(-m/n)
Use rules for exponents to simplify expressions that contain rational exponents
Use rational exponents to simplify radical expressions
8.3 Simplifying Radical Expressions (57)
Use the product rule for radicals
Use the quotient rule for radicals
Simplify radicals
Use the distance and midpoint formulas
8.4 Adding, Subtracting, and Multiplying Radical Expressions (43)
Add or subtract radical expressions
Multiply radical expressions
5
N-RN.A.1
N-RN.A.2
F-IF.B.2
F-IF.C.7b
F-BF.B.3
N-RN.A.1
N-RN.A.2
N-RN.A.1
8.G.B.8
A-SSE.A.2
8.5 Rationalizing Radical Denominators and Numerators (42)
Rationalize denominators
Rationalize denominators having two terms
Rationalize numerators
8.6 Radical Equations and Problem Solving (45)
Solve equations that contain radical expressions
Use the Pythagorean theorem to model problems
Solve application problems
8.7 Complex Numbers (58)
Write square roots of negative numbers in the form bi
Graph complex numbers on the complex plane
Add or subtract complex numbers
Divide complex numbers
Multiply complex numbers
Raise i to powers
CHAPTER 9: Quadratic and Higher Degree Equations and Functions
9.1 Solving Quadratics by Completing the Square (51)
Use the square root property to solve quadratic equations
Complete and factor the perfect square trinomial
Solve quadratic equations by completing the square
Use quadratic equations to solve problems
9.2 Solving Quadratics by Quadratic Formula (51)
Solve quadratic equations by using the quadratic formula
Determine number and type of solutions of quadratic equation using
discriminant
Solve geometric problems modeled by quadratic equations
9.3 Solving Quadratic by Quadratic Methods (42)
Solve quadratic equations by squaring both sides
Solve quadratic equations by multiplying by the lowest common denominator
Solve higher degree equations in quadratic form
Solve equations by converting to a quadratic with substitution
Solve various equations that are quadratic in form
Solve problems that lead to quadratic equations
9.4 Zeros of Polynomial Functions (19)
Use the rational zero theorem to find possible rational zeros
Find zeros of a polynomial function
9.5 Fundamental Theorem of Algebra (18)
Solve polynomial equations
Find polynomials with given zeros
9.6 Nonlinear Inequalities in One Variable (33)
Solve polynomial inequalities of degree 2 or higher
Solve inequalities that contain rational expressions with variables in
denominator
Solve polynomial inequalities of degree 2 or higher
Solve inequalities that contain rational expressions with variables in
denominator
6
A-SSE.A.2
A-REI.A.2
N-CN.A.1
N-CN.A.2
N-CN.B.4(+)
A-REI.B.4b
A-CED.A.1
N-CN.C.7
A-REI.B.4b
N-CN.C.7
A-REI.B.4b
N-CN.C.7
F-IF.C.7c
A-APR.B.2
A-APR.B.3
N-CN.C.9(+)
A-APR.B.2
A-APR.B.3
A-CED.A.1
CHAPTER 10: Exponential and Logarithmic Functions
F-BF.A.1b
10.1 The Algebra of Functions; Composite Functions (26)
Add, subtract, multiply, and divide functions
F-BF.A.1c(+)
Construct composite functions
F-BF.B.4a
10.2 Inverse Functions (34)
Determine whether a function is a one-to-one function
F-BF.B.4b(+)
Find the inverse of a function
F-BF.B.4c(+)
Use the horizontal line test to decide whether a function is a one-to-one
F-BF.B.4d(+)
function
Find the equation of the inverse of a function
Graph functions and their inverses
Determine whether two functions are inverses of each other
F-IF.C.7e
10.3 Exponential Functions (36)
Graph exponential functions
F-BF.B.3
Solve equations of the form b^x = b^y
A-CED.A.1
Solve problems modeled by exponential equations
A-CED.A.1
10.4 Logarithmic Functions (49)
Convert between logarithmic and exponential notation
F-IF.C.7e
Find the value of logarithmic expressions
F-BF.B.3
Solve logarithmic equations by using exponential notation
Simplify using the properties of logarithms
Identify and graph logarithmic functions
A-SSE.A.2
10.5 Properties of Logarithms (38)
Use the product property of logarithms
Use the quotient property of logarithms
Use the power property of logarithms
Use the properties of logarithms together.
A-CED.A.1
10.6 Common and Natural Logs and Change of Base (45)
Identify and approximate natural logarithms
Identify and approximate common logarithms
Evaluate common logarithms of powers of 10
Evaluate natural logarithms of powers of e
Solve logarithmic equations
Use the change of base formula
Solve applications
A-CED.A.1
10.7 Exponential and Log Equations and Applications (40)
Solve exponential equations
F-LE.A.4
Solve logarithmic equations
Solve problems that can be modeled by exponential and logarithmic equations
CHAPTER 11: Graphing Quadratic Functions, Rational Functions, and Conic Sections
F-BF.A.3
11.1 Quadratic Functions and Their Graphs (38)
Graph quadratic functions of the form f(x) = x^2 + k
F-IF.C.7a
Graph quadratic functions of the form f(x) = (x - h)^2 + k
Graph quadratic functions of the form f(x) = ax^2
Graph quadratic functions of the form f(x) = a(x - h)^2 + k
7
11.2 Further Graphing of Quadratic Functions (40)
Write quadratic functions in the form of a(x-h)^2+k
Derive a formula for finding the vertex of a parabola
Find the minimum or maximum value of a quadratic function
11.3 Graphing Rational Functions by Transformations (23)
Find the domains of rational functions
Identify vertical asymptotes
Identify horizontal asymptotes
Use transformations to graph rational functions
Graph f(x)=1/x and f(x)=1/x^2
11.4 Further Graphing of Rational Functions (22)
Graph rational functions
Identify slant asymptotes
Solve applied problems involving rational functions
*11.5 The Parabola and the Circle (68)
Graph parabolas of the form x=a(y-k)^2+k and y=a(x-h)^2+k
Graph circles of the form (x-h)^2+(y-k)^2=r^2
Write the equation of a circle given its center and radius
Find the centers and radii of circles or vertices of parabolas, given the equation
*11.6 The Ellipse and the Hyperbola (53)
Define and graph an ellipse
Define and graph a hyperbola
Identify and graph conic sections
CHAPTER 13: Counting Methods and Probability
13.4 Fundamentals of Probability ( 26)
Compute empirical probability
Compute theoretical probability
13.8 The Normal Distribution (15)
Find scores at a specified standard deviation from the mean
Use the 68-95-99.7 rule
CHAPTER 14 and 15: Trigonometric Functions and Identities
14.1 Angles and Radian Measure (54)
Recognize and use the vocabulary of angles
Use radian measure
Convert between degrees and radians
Draw angles in standard position
Find coterminal angles
Find the length of a circular arc
Use linear and angular speed to describe motion on a circular path
14.2 Right Triangle Trigonometry (43)
Use right triangles to evaluate trigonometric functions
Find function values for 30 degrees (pi/6), 45 degrees (pi/4), and 60 degrees
(pi/3)
Recognize and use fundamental identities
Use equal cofunctions of complements
Evaluate trigonometric functions with a calculator
Use right triangle trigonometry to solve applied problems
8
F-IF.C.7a
F-IF.C.8a
F-IF.A.1
F-IF.C.7d(+)
F-BF.B.3
F-IF.C.7d(+)
G-GPE-A.1
S-CP.A.1
S-ID.A.4
G-CO.A.1
F-TF.A.1
F-TF.A.2
G-C.B.5
F-TF.A.3(+)
F-TF.C.8
G-SRT.C.6
G-SRT.C.7
G-SRT.C.8
14.3 Trigonometric Functions of Any Angle (54)
Use the definitions of trigonometric functions of any angle
Use the signs of the trigonometric functions
Find reference angles
Use reference angles to evaluate trigonometric functions
14.4 Trig Functions of Real Numbers; Periodic (25)
Use a unit circle to define trigonometric functions of real numbers
Use even and odd trigonometric functions
Use periodic properties
Solve Application problems
14.5 Graphs of Sine and Cosine Functions (45)
Understand the graph of y=sin(x)
Graph variations of y=sin(x)
Understand the graph of y=cos(x)
Graph variations of y=cos(x)
Use vertical shifts of sine and cosine curves
Solve Application problems
Solve Technology Exercises
14.6 Graph of the Tangent Function (11)
Understand the graph of y=tan(x)
Graph variations of y=tan(x)
Solve Application problems
Solve Technology Exercises
14.8 Applications of Trigonometric Functions (11)
Solve a right triangle
Solve Application problems
15.1 Verifying Trigonometric Identities (15)
Use the fundamental trigonometric identities to verify identities
CHAPTER X: Statistics
X.1 Measures of Central Tendency (21)
Identify characteristics of the design of an experimental study
Find the mean
Find the median
Find the mode
Solve application problems involving mean, median, and mode
Read a histogram
Determine the arithmetic mean of a variable from raw data
Determine the median and mode of a variable from raw data
Use the mean and the median to help identify the shape of a distribution
X.2 Data Gathering (18)
Describe effects of an experimental study design on its outcome
Understand the process of statistics
Explain the sources of bias in sampling
Find the margin of error
Identify methods of data collection
Identify bias or any potential problems
Identify subject, sample and population, and type of analysis
9
F-TF.A.2
F-TF.A.3(+)
F-TF.A.2
F-TF.A.3(+)
F-TF.A.4
F-TF.B.5
F-TF.B.5
G-SRT.C.8
F-TF.C.8
S-IC.A.1
S-ID.A.1
S-ID.A.2
S-ID.A.4
S-IC.B.3
S-IC.B.4
S-IC.B.6
S-IC.B.4
S-ID.A.2
X.3 Standard Deviation (18)
Determine the standard deviation for a data set
Convert a data item to a z-score
Understand percentiles and quartiles
X.4 Normal Distribution (22)
Use and interpret margins of error
Find scores at a specified standard deviation from the mean
Use the 68–95–99.7 Rule
Solve applied problems involving normal distributions
Understand percentiles and quartiles
Convert a data item to a z-score
S-ID.A.4
S-IC.B.4
*Optional or considered to be for individual students needing review
LDoE Mathematics Standards for Algebra II that are not reflected in MyMathLab course
exercises:
Standard # Standard Description
Comment
N-Q.A.2
A-SSE.B.3c
A-SSE.B.4
A-APR.C.4
A-REI.A.1
A-REI.C.7
A-REI.D.11
F-IF.A.3
F-IF.B.6
F-IF.C.8b
Define appropriate quantities for the purpose of
descriptive modeling.
Use the properties of exponents to transform
expressions for exponential functions.
Derive the formula for the sum of a finite
geometric series (when the common ratio is not 1),
and use the formula to solve problems.
Prove polynomial identities and use them to
describe numerical relationships.
Explain each step in solving a simple equation as
following from the equality of numbers asserted at
the previous step, starting from the assumption that
the original equation has a solution. Construct a
viable argument to justify a solution method.
Solve a simple system consisting of a linear
equation and a quadratic equation in two variables
algebraically and graphically.
Explain why the x-coordinates of the points where
the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) =
g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of
values, or find successive approximations.
Recognize that sequences are functions, sometimes
defined recursively, whose domain is a subset of
the integers.
Calculate and interpret the average rate of change
of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of
change from a graph.
Use the properties of exponents to interpret
expressions for exponential functions.
10
Requires paper and pencil work.
Requires paper and pencil work.
Included in the CLEP prep portion
of the College Algebra course.
Requires paper and pencil work.
Requires paper and pencil work.
Included in the CLEP prep portion
of the College Algebra course.
Requires paper and pencil work.
Included in the CLEP prep portion
of the College Algebra course.
Requires paper and pencil work.
Requires paper and pencil work.
F-IF.C.9
F-BF.A.2
G-GPE.A.2
S-ID.B.6a
S-IC.A.2
S-IC.B.5
S-CP.A.2
S-CP.A.3
S-CP.A.4
S-CP.A.5
S-CP.B.6
S-CP.B.7
Compare properties of two functions each
represented in a different way (algebraically,
graphically, numerically in tables, or by verbal
descriptions).
Write arithmetic and geometric sequences both
recursively and with an explicit formula, use them
to model situations, and translate between the two
forms
Derive the equation of a parabola given a focus and
directrix.
Fit a function to the data; use functions fitted to
data to solve problems in the context of the data.
Decide if a specified model is consistent with
results from a given data-generating process, e.g.,
using simulation.
Use data from a randomized experiment to
compare two treatments; use simulations to decide
if differences between parameters are significant.
Understand that two events A and B are
independent if the probability of A and B occurring
together is the product of their probabilities, and
use this characterization to determine if they are
independent.
Understand the conditional probability of A given
B as P(A and B)/P(B), and interpret independence
of A and B as saying that the conditional
probability of A given B is the same as the
probability of A, and the conditional probability of
B given A is the same as the probability of B.
Construct and interpret two-way frequency tables
of data when two categories are associated with
each object being classified. Use the two-way table
as a sample space to decide if events are
independent and to approximate conditional
probabilities.
Recognize and explain the concepts of conditional
probability and independence in everyday language
and everyday situations.
Find the conditional probability of A given B as the
fraction of B's outcomes that also belong to A, and
interpret the answer in terms of the model.
Apply the Addition Rule, P(A or B) = P(A) + P(B)
- P(A and B), and interpret the answer in terms of
the model.
11
Requires paper and pencil work.
Included in the CLEP prep portion
of the College Algebra course.
Requires paper and pencil work.
Requires paper and pencil work.
Requires paper and pencil work.
Requires paper and pencil work.
Not included in the course.
Not included in the course.
Not included in the course.
Not included in the course.
Not included in the course.
Not included in the course.