Advanced Topics
Necessary Content Needed For College Algebra Success
Set & Interval Notation
Factoring
Graphs (picture, D/R, info)
Piecewise functions
Necessary Skills Needed for College Readiness
Self Motivated
Grading Categories
60% Tests
20% Quizzes
10% Homework
10% Final
Have the opportunity to
retake Quizzes and Tests.
Unit 1 Basic Concepts and Skills (2 WEEKS)
Standard A R3
Exponents, Scientific Notation, and Review of Polynomials
1. Apply properties of exponents
2. Perform operations in Sci Notation
3. Identify and classify polynomial expressions
4. Add/Subtract polynomials
5. Multiply polynomials
6. Special products (binomial conjugates, binomial squares)
Standard B R4
Factoring Polynomials
1. Factoring GCF
2. Common binomial factors and grouping
3. Factoring quadratic polynomial
4. Factoring special forms (sum/dif cubes) and quadratic forms
Standard C R5
Rational Expressions
1. Writing rational in simplest form
2. Mult/Div rational expressions
3. Add/Sub rational expressions
4. Simplify compound fractions
5. Rewrite formulas algebraic expressions
Standard D R6
Radicals and Rational Exponents
1.
2.
3.
4.
5.
6.
𝑛
Simplify radical expressions √𝑎𝑛
Rewrite and simplify radicals expressions using rational exponents
Use properties of rational exponents to simplify radical expressions
Add/Sub radical expressions
Mult/Div radical expressions; write a radical expression in simplest form
Evaluate formulas involving radicals
Unit 2 Equations and Inequalities (3 WEEKS)
Standard A 1.1
Linear Equations, Formulas, and Problems Solving
1. Solve linear equations using properties of equality
2. Recognize equations that are identities or contradictions
3. Solve for a specified variable in a formula or literal equation
4. Use the problem-solving guide to solve various problem types (modeling)
Standard B 1.2
Linear Inequalities in One Variable
1. Solve inequalities and state solution sets
2. Solve linear inequalities
3. Solve compound inequalities
4. Solve applications of inequalities
Standard C 1.3
Absolute Value Equations and Inequalities
1. Solve absolute value equations
2. Solve “less than” absolute value inequalities
3. Solve “greater than” absolute value inequalities
4. Solve application involving absolute value
Standard D 1.4
Complex Numbers
1. Identify and simplify complex numbers
2. Add/Sub complex numbers
3. Mult complex numbers and find powers of i
4. Div complex numbers
Standard E 1.5
Solving quadratic equations
1. Solve quadratic equations using ZPP
2. Solve quadratic equations using sqrt prop
3. Solve quadratic equations by CTS
4. Solve quadratic equations using QuadForm
5. Use discriminant to identify solutions
6. Solve applications of quadratic equations
Standard F 1.6
Solving Other Types of Equations
1. Solving polynomial equations of higher degree
2. Solving rational equations
3. Solving radical equations and equations with rational exponents
4. Solving equations in quadratic form
5. Solve application of various equation types
Unit 3A Relations, Functions, and Graphs (2 WEEKS)
Standard A 2.1
Rectangular Coordinates; Graphing Circles and Other Relations
1. Express a relation in mapping notation in ordered pair form
2. Graph a relation
3. Develop the equation of a circle using the distance and midpoint formulas
4. Graphing circles
Standard B 2.2
Graphs of Linear Equations
1. Graph linear equations using the intercept method
2. Find the slope of a line
3. Graph horiz/vert lines
4. Identify par/perp lines
5. Apply linear equations in context
*2.3 Linear Graphs and Rates of Change (OPTIONAL)
1. Write a linear equation in slope-intercept form
2. Use slope-intercept form to graph equations
3. Write a linear equation in point-slope form
4. Apply the slope-intercept and point-slope forms in context
Standard C 2.4
Functions, Function Notation, and the Graph of a Function
1. Distinguish the graph of a function from that of a relation
2. Determine the domain and range of a function
3. Use function notation and evaluate functions
4. Apply the rate of change concept to nonlinear functions
Standard D 2.8
The Algebra and Composition of Functions
1. Compute a sum/dif of functions and determine the domain of the result
2. Compute quotient of functions and determine the domain of the result
3. Compose two functions and determine the domain; decompose a function
4. Interprete operations on functions graphically
5. Apply algebra and compositions of functions in context
FALL BREAK
Unit 3B Relations, Functions, and Graphs(2 WEEKS)
Standard E 2.5
Analyze the Graph of a Function
1. Determine even/odd/neither (symmetry)
2. Determine intervals of pos/neg
3. Determine increasing/decreasing
4. Identify max/min
5. Develop a formula to calculate rates of change for any function
Standard F 2.6
Parent Functions and Transformations (LFSU)
1
1. Basic characteristics of parent functions (x, 𝑥 2 , 𝑥 3 , √𝑥, |𝑥|,𝑥)
2. Vert/Horz shifts
3. Vert/Horz reflections
4. Vert stretch and compressions
5. Transform a function
Standard G 2.7
Piecewise Defined Functions
1. State the equation and domain of a piecewise function
2. Graph piecewise functions
3. Solve applications involving piecewise functions
Unit 4 Polynomial and Rational functions (3 WEEKS)
Standard A 3.1
Quadratic Functions and Applications
1. Graph using vertex form
2. Find the vertex first then graph the function (-b/2a,f(-b/2a))
3. Find the equation of a quadratic function from its graph
4. Solve applications involving extreme values
Standard B 3.2
Synthetic Division; Remainder and Factor Theorems
1. Divide polynomials using long division and synthetic division
2. Use the remainder theorem to evaluate polynomials
3. Use the factor theorem to factor and build polynomials
4. Solve applications using the remainder theorem
Standard C 3.3
The Zeros of Polynomial Functions
1. Apply the fundamental theorem of algebra and the linear factorization theorem
2. Locate zeros of a polynomial using the intermediate value theorem
3. Find rational zeros of a polynomial using the rational zeros theorem
4. Solve applications of polynomials
Standard D 3.4
Graphing Polynomial Functions
1. Identify the graph of a polynomial function and determine its degree
2. Describe the end behavior of a polynomial graph
3. Discuss the attributes of a polynomial graph with zeros of multiplicity
4. Graph polynomial functions in standard form
5. Solve applications of polynomials
Standard E 3.5
Graphing Rational Functions
1. Identify horizontal and vertical asymptotes
2. Find the domain of a rational function
3. Apply the concept of “multiplicity” to rational graphs
4. Find the horizontal asymptotes of a rational function
5. Graph general rational functions (using test points)
6. Solve applications of rational functions
Standard F 3.6
Additional Insights Into Rational Functions
1. Graph rational functions with removable discontinuities
2. Graph rational functions with oblique or non-linear asymptotes
3. Solve applications involving rational functions
Standard G 3.7
Polynomial and Rational Inequalities
1. Solve quadratic inequalities
2. Solve polynomial inequalities
3. Solve rational inequalities
4. Use interval tests to solve inequalities
5. Solve applications of inequalities
Standard H 3.8
Variation: Function Models in Action
1. Solved direct variations
2. Solve inverse variations
3. Solve joint variations
Unit 5 Exponential and Logarithmic Functions (2 WEEKS)
Standard A 4.1
One-to-One and Inverse Functions
1. Identify one to one functions
2. Explore inverse functions using ordered pairs
3. Find inverse functions using an algebraic method
4. Graph a function and its inverse
5. Solve applications of inverse functions
Standard B 4.2
Exponential Functions
1. Evaluate an exponential function
2. Graph general exponential functions
3. Graph base e exponential functions
4. Solve exponential equations and applications
Standard C 4.3
Logarithms and Logarithmic Functions
1. Write exponential equations in logarithmic form
2. Find common logarithms and natural logarithms
3. Graph logarithmic functions
4. Find the domain of a logarithmic function
5. Solve applications of logarithmic functions
Standard D 4.4
Properties of Logarithms; Solving Exponential / Logarithmic Equations
1. Solve logarithmic equations using the fundamental properties of logarithms
2. Apply the product quotient and power properties of logarithms
3. Solve general logarithmic and exponential equations
4. Solve applications involving logistic, exponential and logarithmic functions
Standard E 4.5
Applications from Business Finance and Science
1. Calculate simple interest and compound interest
2. Calculate interest compounded continuously
3. Solve applications of annuities and amortization
4. Solve applications of exponential growth and decay