LSU College Readiness Program
COURSE PROFILE
F15 (11-9-15)
COURSE NAME:
PRIMARY ONLINE
CONTENT SOURCE
COURSE/UNIT CREDIT:
GRADE(S):
PREREQUISITE(S):
High School Advanced Math – Precalculus paired with
LSU Math 1021 College Algebra (including CLEP Prep)
and LSU Math 1022 Trigonometry
Algebra and Trigonometry, 2e, MyMathLab
Kirk Trigsted
1 Carnegie Unit
10, 11, or 12
Successful Completion of Algebra II
CHAPTERS FOR MATH 1021 COLLEGE ALGEBRA
1 - Equations, Inequalities, and Applications 4 - Polynomial and Rational Functions
2 - The Rectangular Coordinate System,
5 - Exponential and Logarithmic
Lines, and Circles
Functions and Equations
3 - Functions
12 - Systems of Equations
SECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVES FOR
MATH 1021 COLLEGE ALGEBRA
CHAPTER 1: Equations, Inequalities, and Applications
1.1 Linear Equations (42)
Find the least common denominator of an expression
Recognize linear equations
Solve linear equations with integer coefficients
Solve linear equations involving fractions
Solve linear equations involving decimals
Solve equations that lead to linear equations
1.4 Quadratic Equations (39)
Simplify radical expressions
Factor trinomials
Solve quadratic equations by factoring
Solve quadratic equations using the square root property
Solve quadratic equations using the quadratic formula
Use the discriminant to determine the type of solutions of a quadratic equation
1.6 Other Types of Equations (34)
Simplify expressions
Solve higher-order polynomial equations
Solve equations that are quadratic in form
Solve equations involving single radicals
1.7 Linear Inequalities (19)
Solve linear inequalities
Solve three-part inequalities
1.8 Absolute Value Equations and Inequalities (29)
Solve an absolute value equation
Solve an absolute value “less than” inequality
Solve an absolute value “greater than” inequality
CHAPTER 2: The Rectangular Coordinate System, Lines, and Circles
2.1 The Rectangular Coordinate System (25)
Find the average of two numbers
Simplify radicals
Plot ordered pairs
Find the midpoint of a line segment using the midpoint formula
Find the distance between two points using the distance formula
2.2 Circles (32)
Complete the square to form perfect square trinomials
Write the standard form of an equation of a circle
Sketch the graph of a circle given its equation in general form
Find the center and radius of a circle given its equation in general form
2.3 Lines (56)
Solve a linear equation for the variable y
Determine the slope of a line through two given points
Sketch a line given a point and the slope
Find the equation of a line using the point-slope form
Find the equation of a line using the slope-intercept form
Write the equation of a line in standard form
Find the slope and the y-intercept of a line in standard form
Sketch lines by plotting intercepts
Sketch a line given its equation in standard form
Find the equation of a horizontal line and a vertical line
2.4 Parallel and Perpendicular Lines (38)
Determine whether two lines are parallel, perpendicular, or neither
Find the equations of parallel and perpendicular lines
CHAPTER 3: Functions
3.1 Relations and Functions (62)
Simplify algebraic expressions
Understand the definitions of relations and functions
Determine whether equations represent functions
Use function notation and evaluate functions
Use the vertical line test
Determine the domain of a function given the equation
3.2 Properties of a Function’s Graph (48)
Evaluate f(-x) given a function f(x)
Determine the intercepts of a function
Determine the domain and range of a function from its graph
Determine whether a function is increasing, decreasing, or constant
Determine relative maximum and relative minimum values of a function
Determine whether a function if even, odd, or neither
Determine information about a function from a graph
3.3 Graphs of Basic Functions; Piecewise Functions (28)
Sketch the graphs of the basic functions
Analyze piecewise-defined functions
3.4 Transformations of Functions (53)
Use vertical shifts to graph functions
Use horizontal shifts to graph functions
Use vertical stretches and compressions to graph functions
Use combinations of transformations to graph functions
3.5 Composite Functions (25)
Simplify fractional expressions
Form and evaluate composite functions
Determine the domain of composite functions
3.6 One-to-One Functions; Inverse Functions (43)
Understand the definition of a one-to-one function
Determine whether a function is one-to-one using the horizontal line test
Understand and verify inverse functions
Sketch the graphs of inverse functions
Find the inverse of a one-to-one function
CHAPTER 4: Polynomial and Rational Functions
4.1 Quadratic Functions (35)
Determine whether the graph of a quadratic function opens up or down
Determine properties of quadratic function in standard form and graph
Determine properties of quadratic function using the vertex formula and graph
Determine the equation of a quadratic function given its graph
4.2 Applications of Quadratic Functions (10)
Find the maximum value for projectile motion functions
Find the maximum value for functions in economics
4.3 Graphs of Polynomial Functions (46)
Identify polynomial functions, degree, constant and leading coefficients
Sketch the graphs of power functions
Determine the end behavior of polynomial functions
Determine the intercepts of a polynomial function
Determine the real zeros of polynomial functions and their multiplicities
Sketch the graph of a polynomial function
Determine a possible equation of a polynomial function given its graph
4.6 Rational Functions and Their Graphs (35)
Find the domain and intercepts of rational functions
Identify vertical asymptotes
Identify horizontal asymptotes
Use transformations to sketch the graphs of rational functions
Sketch rational functions
CHAPTER 5: Exponential and Logarithmic Functions and Equations
5.1 Exponential Functions (53)
Rewrite expressions in exponential form
Evaluate exponential expressions
Sketch the graphs of exponential functions
Determine possible equations of exponential functions given their graphs
Sketch the graphs of exponential functions using transformations
Solve exponential equations by relating the bases
5.2 Logarithmic Functions (62)
Change equations between exponential form and logarithmic form
Evaluate logarithmic expressions
Use properties of logarithms to evaluate expressions
Use common and natural logarithms
Sketch the graphs of logarithmic functions
Find the domain of logarithmic functions
5.3 Properties of Logarithms (41)
Expand and evaluate logarithmic expressions
Condense and evaluate logarithmic expressions
Solve logarithmic equations using the logarithm property of equality
Use the change of base formula
5.4 Exponential and Logarithmic Equations (42)
Evaluate exponential and logarithmic expressions using a calculator
Solve exponential equations
Solve logarithmic equations
5.5 Applications of Exponential and Logarithmic Functions (27)
Solve applications involving exponential functions
Solve compound interest applications
Solve exponential growth and decay applications
CHAPTER 12: Systems of Equations
12.1 Systems of Linear Equations in Two Variables (23)
Verify solutions to a system of linear equations in two variables
Solve a system of linear equations using the substitution method
Solve a system of linear equations using the elimination method
Solve systems of linear equations in two variables using either method
Solve applied problems using a system of linear equation
CHAPTERS FOR MATH 1022 TRIGONOMETRY
6 - An Introduction to Trigonometric
9 - Applications of Trigonometry
Functions
7 - The Graphs of Trigonometric Functions 10 - Polar Equations, Complex Numbers,
and Vectors
8 - Trigonometric Identities, Formulas, and
Equations
SECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVES FOR
MATH 1022 TRIGONOMETRY
CHAPTER 6: An Introduction to Trigonometric Functions
6.1 An Introduction to Angles: Degree and Radian Measure (50)
Understand degree measure
Understand radian measure
Convert between degree measure and radian measure
Find coterminal angles using degree measure
Find coterminal angles using radian measure
6.2 Applications of Radian Measure (19)
Determine the area of a sector of a circle
Determine the arc length of a sector of a circle
6.3 Triangles (20)
Classify triangles
Use the Pythagorean Theorem
Understand similar triangles
Understand the special right triangles
6.4 Right Triangle Trigonometry (52)
Understand the right triangle definitions of the trigonometric functions
Use the special right triangles
Understand the fundamental trigonometric identities
Understand cofunctions
Evaluate trigonometric functions using a calculator
6.5 Trigonometric Functions of General Angles (84)
Understand the four families of special angles
Understand the definitions of the trigonometric functions of general angles
Find the values of the trigonometric functions of quadrantal angles
Understand the signs of the trigonometric functions
Determine reference angles
Evaluate trigonometric functions of angles belonging to π/3, π/4, and π/6 families
6.6 The Unit Circle (10)
Understand the definition of the unit circle
Understand the unit circle definitions of the trigonometric functions
CHAPTER 7: The Graphs of Trigonometric Functions
7.1 Graphs of Sine and Cosine Functions (31)
Perform operations on fractions containing π
Understand graph of the sine function and its properties
Understand graph of the cosine function and its properties
Determine properties and sketch graphs of form y=Asinx and y=Acosx
Determine properties and sketch graphs of form y=sinBx and y=cosBx
Determine properties and sketch graphs of form y=AsinBx and y=AcosBx
Determine eq. of a function of the form y=AsinBx and y=AcosBx given graph
7.2a Graphs of Sine and Cosine: Phase Shift (22)
Solve inequalities, factor expressions, perform operations on fractions containing π
Determine properties and sketch graphs of form y=sin(x-C) and y=cos(x-C)
Determine properties and sketch graphs of form y=Asin(Bx-C) and y=Acos(Bx-C)
7.2b Graphs of Sine and Cosine: Vertical Shift (14)
Determine properties, sketch graphs of y=Asin(Bx-C)+D and y=Acos(Bx-C)+D
7.3 Graphs of Secant, Cosecant, Tangent, and Cotangent (46)
Solve inequalities involving radian measure
Understand the graph of the tangent function and its properties
Sketch graphs of the form y=Atan(Bx-C)+D
Understand the graph of the cotangent function and its properties
Sketch graphs of the form y=Acot(Bx-C)+D
Understand the graph of the cosecant and secant functions and their properties
Sketch graphs of the form y=Asec(Bx-C)+D and y=Acsc(Bx-C)+D
7.4 Inverse Trigonometric Functions Part I (34)
Understand and find the exact and approximate values of inverse sine function
Understand and find the exact and approximate values of inverse cosine function
Understand and find the exact and approximate values of inverse tangent function
7.5 Inverse Trigonometric Functions Part II (54)
Evaluate composite functions of the form f(f^(-1)(x)) and f^(-1)(f(x))
Evaluate composite functions of the form f(g^(-1)(x)) and f^(-1)(g(x))
CHAPTER 8: Trigonometric Identities, Formulas, and Equations
8.1 Trigonometric Identities (36)
Review and use the fundamental identities
Verify trigonometric identities
8.2 The Sum and Difference Formulas (47)
Review simplifying radical expressions
Use the sum and difference formulas for the cosine function
Use the sum and difference formulas for the sine function
Use the sum and difference formulas for the tangent function
Use the sum and difference formulas to verify identities
Use sum and difference formulas to evaluate inverse trigonometric functions
8.3 The Double-Angle and Half-Angle Formulas (45)
Review simplifying radical expressions
Use the double-angle formulas
Use the half-angle formulas
Use the double-angle and half-angle formulas to verify identities
Use the double-angle and half-angle formulas to evaluate inverse trigonometric functions
8.5 Trigonometric Equations (47)
Solve quadratic equations
Solve trigonometric equations that are linear in form
Solve trigonometric equations that are quadratic in form
Solve trigonometric equations using identities
Solve other types of trigonometric equations
Solve trigonometric equations using a calculator
CHAPTER 9: Applications of Trigonometry
9.1 Right Triangle Applications (18)
Solve right triangles
Solve applied problems using right triangles
9.2 The Law of Sines (30)
Determine if the Law of Sines can be used to solve an oblique triangle
Use the Law of Sines to solve the SAA case or the ASA case
Use the Law of Sines to solve the SSA (ambiguous) case
9.3 The Law of Cosines (27)
Use a calculator to approximate trig and inverse trigonometric expressions
Determine whether Law of Sines or Cosines should be used to solve an oblique triangle
Use the Law of Cosines to solve the SAS case
Use the Law of Cosines to solve the SSS case
Use the Law of Cosines to solve applied problems involving oblique triangles
9.4 Area of Triangles (17)
Determine the area of oblique triangles
Use Heron’s Formula to determine the area of an SSS triangle
Solve applied problems involving the area of triangles
CHAPTER 10: Polar Equations, Complex Numbers, and Vectors
10.1 Polar Coordinates and Equations (62)
Plot points using polar coordinates
Determine different representations of a point (r, θ)
Convert from polar to rectangular coordinates
Convert from rectangular to polar coordinates
Convert equations from rectangular to polar form
Convert equations from polar to rectangular form
10.2 Graphing Polar Equations (65)
Simplify expressions for given value of k
Sketch equations of the form rcosθ = a, rsinθ = a, arcosθ + brsinθ = c, and θ = α
Sketch equations of the form r = a, r = asinθ, and r = acosθ
Sketch equations of the form r = a + bsinθ and r = a + bcosθ
Sketch equations of the form r = asin(nθ) and r = acos(nθ)
Sketch equations of the form r^2 = a^2sin(2θ) and r^2 = a^2cos(2θ)
Identify types of graphs of polar equations
10.4 Vectors (31)
Determine magnitudes of vectors that are represented geometrically
Perform operations on vectors that are represented geometrically
Determine components and magnitudes of vectors
Write vectors in terms of i and j
Perform operations on vectors written in ai+bj form and find magnitudes
Find unit vectors
Determine direction angles of vectors
Write vectors in the form v=ai+bj given magnitudes and direction angles
Solve applied problems involving velocity using vectors
COLLEGE ALGEBRA CLEP PREPARATION
SECTION NAMES (NUMBER OF EXERCISES) AND LEARNING OBJECTIVES
CLEP 1: Factoring and Expanding Polynomials (38)
Multiply polynomials
Factor out a greatest common factor
Factor by grouping
Factor trinomials with a leading coefficient equal to one
Factor using special factoring formulas
CLEP 2: Operations with Algebraic Expressions (13)
Use the order of operations to simplify numeric and algebraic expressions
CLEP 3: Operations with Exponents (52)
Simplify exponential expressions involving integer exponents
Simplify radical expressions
Simplify exponential expressions involving rational exponents
CLEP 4: Quadratic Inequalities (16)
Solve polynomial inequalities
CLEP 5: Systems of Non-linear Equations (16)
Determine the number of solutions to a system of nonlinear equations
Solve systems of nonlinear equations using substitution, elimination, or graphing
Solve applied problems using systems of nonlinear equations
CLEP 6: Inequalities in Two Variables (18)
Determine whether ordered pairs are solutions to inequalities in two variables
Graph linear inequalities in two variables
CLEP 7: Systems of Inequalities in Two Variables (21)
Determine if ordered pairs are solutions to systems of inequalities in two variables
Graph systems of linear inequalities in two variables
CLEP 8: Algebra of Functions (25)
Evaluate a combined function
Find combined functions and their domains
CLEP 9: Real Numbers (12)
Understand and classify real numbers
Understand absolute value and use it to find distance
CLEP 10: Complex Numbers (37)
Simplify powers of i
Add and subtract complex numbers
Multiply complex numbers
Find the quotient of complex numbers
Simplify radicals with negative radicands
Solve quadratic equations using the quadratic formula
CLEP 11: Sequences and Series (42)
Write the terms of a sequence
Write the terms of a recursive sequence
Write a formula for the general terms of a sequence
Compute partial sums of a series
Determine the sums of a finite series written in summation notation
Write a series using summation notation
Solve applications involving sequences and series
CLEP 12: Arithmetic Sequences and Series (35)
Determine if a sequence is arithmetic
Find the general term of an arithmetic sequence
Find a specific term of an arithmetic sequence
Compute the nth partial sum of an arithmetic series
Solve applications of arithmetic sequences and series
CLEP 13: Geometric Sequences and Series (38)
Write the terms of a geometric sequence
Determine whether a sequence is geometric and find its common ratio
Find the general term of a geometric sequence
Find a specific term of a geometric sequence
Compute the nth partial sum of a geometric series
Determine if an infinite geometric series converges or diverges and find its sum
Solve applications of geometric sequences and series
CLEP 14: Binomial Theorem (25)
Expand binomials raised to a power using Pascal's triangle
Evaluate binomial coefficients
Expand binomials raised to a power using the Binomial Theorem
Find a particular term of a binomial expansion
Find a particular coefficient of a binomial expansion
CLEP 15: Determinants of 2 by 2 Matrices (14)
Determine the size of matrices and their types
Evaluate second-order determinants
Evaluate determinants of 2x2 matrices
Solve equations involving determinants
Write systems of linear equations given determinants and solve equations