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Penn Highlands Syllabus

PENN HIGHLANDS SYLLABUS

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**COURSE TITLE: College Algebra**

**NUMBER OF CREDITS: ** 3 credits

**REQUIRED TEXTS: **Blitzer, Robert. College Algebra, 5e. Upper Saddle River: Prentice Hall, 2010.** **

**REQUIRED COURSE MATERIALS:**

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Students need a scientific calculator. Graphing calculators are allowed and recommended as long as they follow the acceptable use policy such as the one located in the SAT booklet.

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**COURSE DESCRIPTION: **

Students enrolled in this course should have a strong background in basic and intermediate algebra. Topics include a more in-depth study of expressions, solving equations, solving inequalities, circles, and a detailed study of functions including polynomial, logarithmic, and exponential functions.

**PREREQUISITE**: Algebra II with a minimum of a B average

**COURSE METHODOLOGY:**

The instructor will choose the appropriate method to teach each topic including

(but not limited to):

- Lecture
- Class Discussion
- Question-Answer Periods
- Small Group Problem-Solving with limited guidance
- Whiteboard Examples
- Brainstorming - to allow students to learn to think for themselves when solving problems.
- Student Presentation of Solutions

Tutoring sessions are available at 7:00 each school day morning.

**ATTENDANCE POLICY: **

All students are expected to attend all classes. In the event of an unavoidable absence, the student is responsible for the material covered and the assignments given during the absence which will be due upon day of returning. In the event the absence is a quiz or test day, the student must have proof of an excused absence or receive a zero. Excused absences upon the instructors’ discretion would include, but not limited to, doctor excuses and immediate family tragedies.

**STUDENT EVALUATION:**

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Will involve, but not limited to: graded homework assignments, quizzes, a project, exams, a mid-term, and a final exam. Graphing calculators will be prohibited on certain sections of evaluations.

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**GRADING SCALE:**

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** A:*** Excellent..................................................... 90% - 100%*

* ***B: Above average........................................... 80% - 89%**

* ***C: Average...................................................... 70% - 79%**

* ***D: Below average............................................ 60% - 69%**

** F: Failure to meet competencies……………….. 0 – 59%**

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**Course Syllabus:**

The following is a tentative schedule for the course. Your instructor may deviate from the schedule as deemed necessary. Advance notice will be provided by your instructor if changes are made to this schedule. You instructor will assign appropriate assignments with the topics. Projects may be inserted at your instructors’ discretion. Topics requiring graphing calculators are dependent on their availability.

Chapter P: Prerequisites: Fundamental Concepts of Algebra I

- P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
- Evaluate algebraic expressions
- Use mathematical models
- Find the intersection of two sets
- Find the union of two sets
- Recognize subsets of the real numbers
- Use inequality symbols
- Evaluate absolute value
- Use absolute value to express distance
- Identify properties of the real numbers
- Simplify algebraic expressions

- P.2 Exponents and Scientific Notation
- Use the product rule
- Use the quotient rule
- Use the zero-exponent rule
- Use the negative-exponent rule
- Use the power rule
- Find the power of a product
- Find the power of a quotient
- Simplify exponential expressions
- Use scientific notation

- P.3 Radicals and Rational Exponents*
- Evaluate square roots
- Simplify expressions of the form the square root of
*a*squared - Use the product rule to simplify square roots
- Use the quotient rule to simplify square roots
- Add and subtract square roots
- Rationalize denominators
- Evaluate and perform operations with higher roots
- Understand and use rational exponents

- P.4 Polynomials
- Understand the vocabulary of polynomials
- Add and subtract polynomials
- Distribute polynomials
- Use special products in polynomial multiplication
- Perform operations with polynomials in several variables

- P.5 Factoring Polynomials
- Factor out the greatest common factor of a polynomial
- Factor by grouping
- Factor trinomials
- Factor the difference of squares
- Factor perfect square trinomials
- Factor the sum or difference of two cubes
- Use a general strategy for factoring polynomials
- Factor algebraic expressions containing fractional and negative exponents

- P.6 Rational Expressions*
- Specify numbers that must be excluded from the domain of rational expressions
- Simplify rational expressions
- Multiply rational expressions
- Divide rational expressions
- Add and subtract rational expressions
- Simplify complex rational expressions

Chapter 1: Equations and Inequalities

- 1.1 Graphs*
- Plot points in the rectangular coordinate system
- Graph equations in the rectangular coordinate system
- Interpret information about a graphing utility’s viewing rectangle or table
- Use a graph to determine intercepts
- Interpret information given by graphs

- 1.2 Linear Equations and Rational Equations*
- Solve linear equations in one variable
- Solve linear equations containing fractions
- Solve rational equations with variables in the denominators
- Recognize identities, conditional equations, and inconsistent equations
- Solve applied problems using mathematical models

- 1.3 Models and Applications*
- Use linear equations to solve problems
- Solve a formula for a variable

- 1.4 Complex Numbers*
- Add and subtract complex numbers
- Multiply complex numbers
- Divide complex numbers
- Perform operations with square roots of negative numbers

- 1.5 Quadratic Equations*
- Solve quadratic equations by factoring
- Solve quadratic equations by the square root property
- Solve quadratic equations by completing the square
- Solve quadratic equations using the quadratic formula
- Use the discriminant to determine the number and type of solutions
- Determine the most efficient method to use when solving a quadratic equations
- Solve problems modeled by quadratic equations

- 1.6 Other Types of Equations*
- Solve polynomial equations by factoring
- Solve radical equations
- Solve equations with rational exponents
- Solve equations that are quadratic in form
- Solve equations involving absolute value
- Solve equations modeled by equations

- 1.7 Linear Inequalities and Absolute Value Inequalities*
- Use interval notation
- Find intersections and unions of interval
- Solve linear inequalities
- Recognize inequalities with no solution or all real numbers as solutions
- Solve compound inequalities
- Solve absolute value inequalities

Chapter 2: Functions and Graphs

- 2.1 Basics of Functions and Their Graphs*
- Find the domain and range of a relation
- Determine whether a relation is a function
- Determine whether an equation represents a function
- Evaluate a function
- Graph functions by plotting points
- Use the vertical line test to identify functions
- Obtain information about a function from its graph
- Identify the domain and the range of a function from its graph
- Identify intercepts from a function’s graph

- 2.2 More on Functions and Their Graphs*
- Identify intervals on which a function increases, decreases, or is constant
- Use graphs to locate relative maxima or minima
- Identify even or odd functions and recognize their symmetries
- Understand and use piecewise functions
- Find and simplify a function’s difference quotient

- 2.3 Linear Functions and Slope*
- Calculate a line’s slope
- Write the point-slope form of the equation of a line
- Write and graph the slope-intercept form of the equation of a line
- Graph horizontal and vertical lines
- Recognize and use the general form of a line’s equations
- Use intercepts to graph the general form of a line’s equation
- Model data with linear functions and make predictions

- 2.4 More on Slope*
- Find slopes and equations of parallel and perpendicular lines
- Interpret slope as rate of change
- Find a function’s average rate of change

- 2.5 Transformations of Functions*
- Recognize graphs of common functions
- Use vertical shifts to graph functions
- Use horizontal shifts to graph functions
- Use reflections to graph functions
- Use vertical stretching and shrinking to graph functions
- Use horizontal stretching and shrinking to graph functions
- Graph functions involving a sequence of transformations

- 2.6 Combinations of Functions; Composite Functions*
- Find the domain of a function
- Combine functions using the algebra of functions, specifying domains
- Form composite functions
- Determine domains for composite functions
- Write functions as compositions

- 2.7 Inverse Functions*
- Verify inverse functions
- Find the inverse of a function
- Use the horizontal line test to determine if a function has an inverse function
- Use the graph of a one-to-one function to graph its inverse function
- Find the inverse function and graph both functions on the same axes

- 2.8 Distance and Midpoint Formulas; Circles*
- Find the distance between two points
- Find the midpoint of a line segment
- Write the standard form of a circle’s equation
- Give the center and radius of a circle whose equation is in standard form
- Convert the general form of a circle’s equation to standard form

Chapter 3: Polynomial and Rational Functions

- 3.1 Quadratic Functions*
- Recognize characteristics of parabolas
- Graph parabolas
- Determine a quadratic function’s minimum or maximum value
- Solve problems involving a quadratic function’s minimum or maximum value

- 3.2 Polynomial Functions and Their Graphs*
- Identify polynomial functions
- Recognize the characteristics of graphs of polynomial functions
- Determine end behavior
- Use factoring to find zeros of polynomial functions
- Identify zeros and their multiplicities
- Use the Intermediate Value Theorem
- Understand the relationship between degree and turning points
- Graph polynomial functions

- 3.3 Dividing Polynomials; Remainder and Factor Theorems*
- Use long division to divide polynomials
- Use synthetic division to divide polynomials
- Evaluate a polynomial using the Remainder Theorem
- Use the Factor Theorem to solve a polynomial equation

- 3.4 Zeros of Polynomial Functions*
- Use the Rational Zero Theorem to find possible rational zeros
- Find zeros of a polynomial function
- Solve polynomial equations
- Use the Linear Factorization Theorem to find polynomial with given zeros
- Use Descartes’s Rule of Sings

- 3.5 Rational Functions and Their Graphs*
- Find the domain of rational functions
- Use arrow notation
- Identify vertical asymptotes
- Identify horizontal asymptotes
- Use transformations to graph rational functions
- Graph rational functions
- Identify slant asymptotes
- Solve applied problems involving rational functions

- 3.6 Polynomial and Rational Inequalities*
- Solve polynomial inequalities
- Solve rational inequalities
- Solve problems modeled by polynomial or rational inequalities

- 3.7 Modeling Using Variation*
- Solve direct variation problems
- Solve inverse variation problems
- Solve combined variation problems
- Solve problems involving joint variation

Chapter 4: Exponential and Logarithmic Functions

- 4.1 Exponential Functions*
- Evaluate exponential functions
- Graph exponential functions
- Evaluate functions with base
*e* - Use exponential interest formulas

- 4.2 Logarithmic Functions*
- Change from logarithmic to exponential form
- Change from exponential to logarithmic form
- Evaluate logarithms
- Use basic logarithmic properties
- Graph logarithmic functions
- Find the domain of a logarithmic function
- Use common logarithms
- Use natural logarithms

- 4.3 Properties of Logarithms*
- Use the product rule
- Use the quotient rule
- Use the power rule
- Expand logarithmic expressions
- Condense logarithmic expressions
- Use the change-of-base property

- 4.4 Exponential and Logarithmic Equations*
- Use like bases to solve exponential equations
- Use logarithms to solve exponential equations
- Use the definition of a logarithm to solve logarithmic equations
- Use the one-to-one property of logarithms to solve logarithmic equations
- Solve applied problems involving exponential and logarithmic equations

- 4.5 Exponential Growth and Decay*
- Model exponential growth and decay
- Use logistic growth models
- Choose and appropriate model for data
- Express an exponential model in base
*e*

Chapter 5-6: Systems of Equations and Inequalities and Matrices

- 5.1 Systems of Linear Equations in Two Variables*
- Decide whether an ordered pair is a solution of a linear system
- Solve linear systems by substitution
- Solve linear systems by addition
- Identify systems that do not have exactly one ordered-pair solution
- Solve problems using systems of linear equations

- 5.2 Systems of Linear Equations in Three Variables
- Verify the solution of a system of linear equations in three variable
- Solve systems of linear equations in three variables
- Solve problems using systems in three variables

- 6.1 Matrix Solutions to Linear Systems
- Write the augmented matrix for a linear system
- Perform matrix row operations
- Use matrices and Gaussian elimination to solve systems
- Use matrices and Gauss-Jordan elimination to solve systems

- 5.4 Systems of Nonlinear Equations in Two Variables*
- Recognize systems of nonlinear equations in two variables
- Solve nonlinear systems by substitution
- Solve nonlinear systems by addition
- Solve problems using systems of nonlinear equations

- 5.6 Linear Programming
- Write an objective function describing a quantity that must be maximized or minimized
- Use inequalities to describe limitations in a situation
- Use linear programming to solve problems

Chapter 8: Sequences, Induction, and Probability

- 8.1 Sequences and Summation Notation
- Find particular terms of a sequence from the general term
- Use recursion formulas
- Use factorial notation
- Use summation notation

Review for Final Exam*

*Penn Highlands requirement for course credit

Bibliography:

Blitzer, Robert. College Algebra. Upper Saddle River, New Jersey: Prentice Hall, 2010.

Alg II