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MATH 2 —PreCalculus

Course Syllabus—Summer 2022

Prerequisite: Math 32 and Math 20

Required Text:

Textbook: Precalculus: Unit Circle Approach To Trigonometry

On-line access code:  Please see the handout for registration instructions. You may register for a 14 day trial for free, after that you will need to pay with a credit card or purchase an access code or use the one that came with your textbook. Registration within MyMathlab is required within the first 2 weeks of class. If you have not registered by this date, you WILL not be able to do the homework and will be sacrificing part of your grade. Since registration is free for 14 days, there is no excuse for not registering. To access the online portion of our class you will need a MyMathLab/MyStatLab student access code, but you must enter through your SMC Canvas account. THE ACCESS CODE COMES WITH AN E-VERSION OF THE TEXTBOOK. YOU DO NOT NEED TO BUY THE PHYSICAL TEXTBOOK.

Course Description (Math 2):  Intensive preparation for calculus. This course is intended for computer science, engineering, mathematics, and natural science majors. Topics include algebraic, exponential, logarithmic and trigonometric functions and their inverses and identities, conic sections, sequences, series, the binomial theorem, and mathematical induction.

Course Objectives: Upon completion of the course students will be able to:                        

1.) Simplify, evaluate, factor or manipulate a numerical or algebraic expression.

2.) Solve linear, quadratic, radical, rational and absolute valueequations,and systems of          linear equations(in two or three variables) and representtheir solutionsusing set notation. 3.) Solve linear, quadratic, rational, absolute value,and compound inequalities.  Graph the solution set and express it in set notation and interval notation.

4.) Perform operations on complex numbers and apply them to solve quadratic equationswith negative discriminant.

5.) Use coordinate plane geometry to describe the location of a point in the plane.

6.) Use the distance formula to find the distance between two points in the plane.  Use the midpoint formula to find the coordinates of the midpoint of theline segment joining two distinct points.

7.) Defineand represent a relation in four different ways: verbally, numerically, symbolicallyand graphically, if possible; find thedomain and rangeof the relationand determine whether it is a function.

8.) Evaluate a relation or function at a specific point and determine whether an ordered pair is on its graph.

9.) Write the equation of a linein slope-intercept form (if applicable) given two distinct points orslopeand a point.

10.) Given a linear, quadratic, radical, orabsolute valuefunction, find its intercepts and graph it.

11.) Identifyand write theequation of a circle in standard form, find its center and radius, and graph it.

 12.) Determine whether a function is one to one and, if so, find its inverse. Sketch the graph of the inverse function and find its domain and range.

13.) Identify and use the rules ofexponents to simplifyexpressions involving exponents.

14.) Evaluate elementaryexponential and elementarylogarithmic expressions.

15.) Solve elementary exponential equations.

16.) Use the definition of logarithms to solve elementarylogarithmic equations.

17.) Recognize basic geometric Euclidean shapes. Find the perimeter and area of two-dimensional figures and the volume of three-dimensional figures.

18.) Recognize special right triangles and apply their properties in problem solving. Use properties of similar triangles in applications.

19.) Use algebraic expressions, equations and inequalities to model real world application problems.

20.)Consistently apply effective learning strategies for success in college.  Students will demonstratethat they can apply effective learning strategies if they:

          a.Attend class regularly  

          b.Turn in assignments on time

          c.Work productively with peers on group assignments

          d.Seek help from their peers, teacher, and other resources when necessarye.Set up          and maintain their math notebook

Student Learning Outcomes (SLOs):

1.) Students will develop success skills and academic behaviors including use of class notes and required text, regular attendance, timeliness, participation in class activities, and adherence to the College Honor Code and other codes of conduct.

2.) Students will apply the laws of exponents, factoring techniques, and properties of real numbers to a given algebraic expression to rewrite itin its simplest form.

3.) Students will solve a given linear, quadratic, absolute value, simple rational or simple radical equation and express the solution(s) in set notation.

 4.) Given the graph of a relation, students will determine whether it is a function, find its domain and range, and any intercepts.

Homework:  The homework exercises are online; available from any computer, any time, as long as the MathXL plugin is installed.  The homework is interactive, meaning you can get help, view an example, and see the solution worked out in detail, step by step.  There are also instructional videos available of an instructor giving lectures and working out problems from all topics we cover in the class.  It’s like having “a professor in your computer.”  The work you need to do to complete your online homework should be neatly written in your notebook together with the title, section and the grade you earn.  Absolutely no late homework will be accepted.

You are expected to do homework after every class. Homework can be time consuming, so plan accordingly and do no wait until the night before and exam to start, such behavior will result in a poor exam grade.  It is an important part of this class and crucial to your success. The pace of the course is quite rapid, so it is in your best interests to be caught up with the schedule of assignments.  You should plan on completing each assignment before the next section of material is covered.  To be successful in the course, I strongly suggest keeping up with the homework and seeking help as soon as you need help.  The students who do well in this course will have consistently done the homework.  Doing and practicing the homework for this class is the key to success, mathematics is much like playing an instrument or a sport, you need to practice!

Course Content:

% of course     Topic

16%                 Algebraic factoring and simplification

28%                 Function concepts

16%                 Graphing concepts

10%                 Geometric concepts

20%                 Equation andinequality solving strategies

5%                   System solving strategies

5%                   Learning Skills   

     1.Study skills: organization and time management, test preparation and test-taking skills. 2.Sell-assessment: using performance criteria to judge and improve one’s own work analyzing and correcting errors on one’s test.

           Use of resources: strategies identifying utilizing, and evaluating the effectiveness of            resources in improving one’s own learning, e.g. peer study groups, computer resources, lab resources, tutoring resources.

100%                 Total  

Grading Policy:

Homework        15%

Quizzes             10%

Tests                 60%

Final                 15%

Students with Disabilities:  Santa Monica College accommodates students with disabilities.  If you qualify for any special accommodations due to a disability, you need to officially process your request through the Disabled Students Programs and Services (DSPS) office as close to the beginning of the semester as possible.  If you believe you have a learning disability that has not yet been documented, please see me and make an appointment at the DSPS office for assistance.  The DSPS office is located in the Admissions/Student Services Complex, Room 101, and the phone numbers are (310) 434-4265 and (310) 434-4273 (TDD). Scheduling of accommodated exams will be arranged on a case-by-case basis.

Academic Honesty:  Honest and ethical students are protected in this class.  It is your responsibility to familiarize yourself with The Code of Academic Conduct, which is printed in the General Catalog. Other guidance is also available online:

Student responsibilities:
http://www.smc.edu/StudentServices/StudentJudicialAffairs/Pages/What-you-should-know.aspx

Honor Council website:  
http://www.smc.edu/StudentServices/HonorCouncil/Pages/Honor-Code.aspx

Administrative Regulation 4412 :
http://www.smc.edu/ACG/AcademicSenate/Documents/AR%204412.pdf

Please be extremely careful that you do not engage in any behavior that could even be construed as cheating.  Violations could result in failing grades, reports to the Campus Disciplinarian, and subsequent academic disciplinary action.  Examples of behaviors that are not permitted include but are not limited to: Copying another student's homework, inappropriate language or physicality in the classroom, and inappropriate behaviors during an exam (talking with another student, looking at or copying from another student's paper, using a disallowed PDA or calculator, using disallowed notes, leaving the room without prior permission, removing exam materials from the classroom).

Extra Credit Policy:  Extra Credit is not available for this class.

Tutoring and Addition Help:  Monday to Friday: 8 am – 10 pm

Saturday: 10 am – 6:30 pm

MATH LAB ZOOM

https://cccconfer.zoom.us/s/731566134#success

Comments:

• Ask questions. No teacher expects students to understand every problem right away. When questions come up please ask them.

• Do your homework and do it on time. It is very difficult to succeed in a class when you are constantly trying to catch up on homework.

• Form study groups with other students. The best way to learn a subject is to teach it.

• Try not to miss class.  If you miss class make sure to get the notes from that day from a fellow student.

• Don’t wait until the last minute to study for an exam.

• Have a positive attitude, math can be hard, but that does not mean you cannot do it, it just means it might take more effort.

• Review your notes when doing your homework.  DO YOUR HOMEWORK, practice is the key to success.

Sections Covered:

 Introduction-Syllabus-Affective Domain

Useful Arithmetic for Precalculus-

AR 1.2 Number Systems-

Other Suggested Topicsonth roots; GCF and LCM; Rationalize Denominator/Numerator-

Handout: Order of Operations with integers and FractionsTEvaluating and Introductory Algebraic Expressions-

             AR 1.8 Constants and Variables-

             AR 1.1 Translating Verbal Expressions-

             AR 2.2 Monomials; Polynomials-

            AR 2.3 Addition and Subtraction of Polynomials-

         AR 2.4 Multiplication of Polynomials-Handout: Evaluating and Simplifying       AR 2.6 Factoring Polynomials; GCF; Factoring by Grouping-

AR 2.7 Factoring Second Degree Trinomials-

AR 2.8 Factoring Trinomials-Handout: Factoring Techniques-

A8 –Objective 1 –Solving Linear Equations-Handout: Solving Linear Equations-

2.8 –Objective 1 –Absolute Value Equations-Handout: Absolute Value Equations

Handout: Solving Quadratic Equations with Real Solution(s) using Factoring Completing the Square Square Root Property Quadratic Formula

Rational Expressionsand Equations-

AR 3.2 Reducing Rational Expressions to Lowest Terms-

AR 3.3 Multiplyingand Dividing Rational Expressions-

Handout: Finding the LCM of Polynomials

Rational Expressionsand Equations-

AR 3.4 Addition and Subtraction of Rational Expressions-

A.8 –Objective 2 –Solving Rational Equations-

Handout: Solving Rational EquationsRadical Equations-

A.8 –Objective 4 –SolvingRadical Equations-

Handout: Solving Radical Equations

A.2 –Objective 2 –Know Geometry Formulas-

Handout: Basic Geometric Shapes, Perimeter, Area

F.3 –Lines-Handout: Graphs and Equations of a Line (Standard Form, Point Slope Form, Slope-Intercept formW-

10.1 –Objectives 1, 2, and 3 –Solving Systems of Linear Equations in Two Variables-Handout: Solving Systems of Linear Equations in Two Variables-

Handout: Review Exam

Section 10.1 is the last section covered on Exam 1-

A.10 –Interval Notation; Solving Inequalities-Handout: Set Notation, Interval Notation, and Graphs-

Handout: Compound Inequalities

Exam 1

2. 8 –Absolute Value InequalitiesHandout: Absolute Value Inequalities-

2.5 –Solving Quadratic Inequalities-

Handout: Solving Quadratic Inequalities

1.1 Functions: Domain, Range-Handout: Domains of Different Functions-

Continue Handout: Domain of Different Functions-

1.2–Graph of a Function-

1.3 –Properties of Functions-

1.4 –Library of Functions; Piecewise-Defined Functions-

Handout: Evaluating and Graphing Piecewise Defined Functions-

1.5 Graphing Techniques; Transformations

Handout: Transformation of Quadratic and Absolute Value Functions-

2.3  –Finding Points of Intersection of Two Functions Algebraically and Graphically-Handout: Finding Points of Intersection of Two Functions Algebraically and Graphically-

1.6–Mathematical Models; Building Functions-

2.1–Properties of Linea Functions and Linear Models-

2.4 –Graphing Quadratic Functions-

2.6 –Modeling with Quadratic Functions-

3.6 –Polynomial and Rational Inequalities

Handout: Review for Exam 2

Section 2.6 is the last section included on Exam 2

Exam 2

Continue 3.6 –Polynomial and Rational Inequalities -

Handout: Solving Polynomial and Rational Inequalities Algebraically and Graphically, given the Graph-

3.1 –Polynomial Functions-Handout: Polynomial Functions, Properties and Graphs-Continue Handout: Polynomial Functions, Properties and Graphs-

A.3 –Objective 6 –Dividing Polynomials using Long DivisionHandout: Long Division of Polynomials-

3.4 –Properties of Rational Functions-Handout: Rational Functions: Domain and Asymptotes-3.5 –Graphing Rational FunctionsT-

Continue 3.5 –Graphing Rational Functions-

Handout: Graphing Rational Functions

A.5 –Synthetic Division-

3.2 –Real Zeros of Polynomial Functions

 3.2 –Real Zeros of Polynomial Functions-

A.11 –Complex Numbers-2.7 –Complex Zeros of Quadratic Functions-

Handout: Solving Quadratic Equations with a Negative Discriminant-

Handout Review for Exam 3

Section 3.3 is the last section included on Exam 3-

3.3 –Complex Zeros, Fundamental Theorem of AlgebraT-

Exam 3-

4.1 –Composite Functions

Handout: Composite Functions and their Domains-

Continue 4.1 and Handout: Composite Functions and their Domains-

4.2 –One-to-one Functions and Their Inverses-

AR 4.1 –Negative Exponents-

AR 4.4 –Rational Exponents -Handout: Rules of Exponents

-4.3 –Exponential FunctionsHandout: Properties and Graphs of Exponential Functions-

4.4 Logarithmic Functions-

Handout: Graphing Exponential and Logarithmic Functions-

4.5 –Properties of Logarithms-

Continue 4.5 –Properties of Logarithms-

Handout: Properties of Logarithms-

4.6 –Exponential and Logarithmic Equations-

Handout: Exponential and Logarithmic Equations-

Handout: Review for Exam 4

Section 4.7 and 4.8 are the last Sections included on Exam 4

4.7 and 4.8 –Applications of Exponential and Logarithmic Functions-

Handout: Types of Angeles, Similar Triangles, Special Right Triangles-Handout:Equations of a Circle, Finding its Center and Radius, Graphing a Circle-

5.1 –Angles and Radian Measure-

5.2 –Definitions and Values of Trigonometric Functions-

Handout: Evaluating Trigonometric Functions-

Continue Handout: Evaluating Trigonometric Functions-

5.3 –Properties of Trigonometric Functions-

Handout: Properties of Trigonometric Functions-

5.4 –Graphs of the Sine and Cosine Functions-

Handout: Graphs of Sine and Cosine

5.5 –Graphs of Tangent, Cotangent, Cosecant, and Secant-

Handout: Graphs of Tangent, Cotangent, Cosecant, and Secant-

5.6 –Graphs of Transformed  Trigonometric Functions-

Handout: Restricting a Domain to make an Invertible Function-

6.1 –The inverse of Sine, Cosine, and Tangent Functions-

6.2 –The inverse Trigonometric Functions (Continued)-

Handout: Determining the Value of an Inverse Trigonometric Function, if it exists

6.4 –Trigonometric Identities-Handout: Trigonometric Identities-

6.5 –Sum and Difference Identities-

Continue 6.5-Handout: Sum and Difference Identities-

6.6 –Double-Angle and Half-Angle Identities-

Handout: Double-Angle and Half-Angle Identities-

Handout: Review for Exam 5

Section 6.3 is the last section to be included on Exam 5-

6.3 –Trigonometric Equations-

Handout: Trigonometric Equations-

7.1 –Right Triangle Trigonometry-

7.2 –Law of Sines-

Handout: Law Of Sines-

Exam 5-

Law of Cosines-

Handout Law of Cosines-

7.4 –Area Formulas-

Handout: Sigma Notation-

11.1 –Sequences and Summation Notation

Handout Getting Started on the Idea of Mathematical Induction-

11.4 –Mathematical Induction-

Continue 11.4 –Mathematical Induction-

11.5 –Binomial Theorem-

9.2 –Parabolas-

9.3 –Ellipses-9.4 –Hyperbolas-

Handout: Review for Exam 6-

Exam 6  

L-Handout Final Exam Review

Fianl Exam