Syllabus - Quia



Pre-Calculus

Syllabus

Mrs. C. Cook

[pic]Course Objectives

❖ Students will master the concepts of manipulating and solving linear, quadratic, and polynomial functions. They will be able to factor quadratic and polynomial functions with ease.

❖ Students will be able to recognize and graph polynomial, rational, algebraic, and absolute value functions; understand the concepts of domain, range, zeros, asymptotes, and discontinuity; and define and find inverse functions.

❖ Students will be able to manipulate and solve problems (including word problems) involving logarithmic and exponential functions.

❖ Students will fully understand how trigonometry relates to all types of triangles, be able to solve various types of problems using trigonometry, and be able to model real life applications using trigonometry.

❖ Students will be able to use trigonometric identities to simplify and solve equations.

❖ Students will be able to define and use polar coordinates and complex numbers.

❖ Students will be able to prove and use the formulas for sums of arithmetic and geometric sequences, fully understanding the concept of summation notation.

❖ Students will be able to apply basic and advanced problem solving techniques to solve word problems, explain reasoning, and prove results.

[pic]Course Themes

❖ Advanced Algebra

❖ Functions and Their Graphs

❖ Polynomial and Rational Functions

❖ Logarithms

❖ Trigonometric Functions

❖ Analytical Trigonometry/Using Trigonometric Identities

❖ Sequences, Series, and Probability

❖ Conic Sections and Analytical Geometry

❖ Reasoning and Problem Solving

❖ Limits

[pic]Course Organization

Grades will be determined by the following:

❖ Chapter Tests - 35 %

❖ Homework Completion - 25 %

❖ Weekly Quizzes - 20 %

❖ Course Notebook - 10%

❖ Participation and Preparation - 10%

Chapter Tests

Tests will be administered at the end of each chapter with the exception of two times when multiple chapters will be combined for the test. Tests can be anticipated roughly every two to three weeks.

Homework Policy

Homework assignments will be assigned daily with the exception of Friday. Late assignments will be accepted one day after the due date for 75% credit and two days after the due date for 50% credit. After that, the student will receive no credit for the assignment. If a student is absent, it is his/her responsibility to obtain the missed assignments and notes. I will not track a student down to make sure that he/she knows what the missing assignment was.

Homework will be graded based on timely completion with reasonable answers. This means, if you do the work and it makes some sense, you will get full credit for that assignment. Students are required to complete homework in the format presented at the beginning of the course. Homework completed in any other format WILL NOT be accepted.

Weekly Quizzes

Quizzes will be administered at the beginning of class every Friday in which a test is not given. Quizzes will cover all the material that was covered in the homework that week. The purpose of the weekly quizzes is to ensure that students understand the material and that homework is being completely accurately and students are seeking out help when needed.

Course Notebook

Each student will be required to keep an up-to-date, organized course notebook consisting of all class notes, homework, quizzes, tests, and projects. The notebook will be checked on Friday during the weekly quiz.

Participation

Participation includes class preparation, completion of the daily questions, and participation in guided practice during lessons. This also includes student accountability to seek out assignments, notes, quizzes and tests missed due to illnesses.

[pic]Course Materials

❖ Textbook:

Larson, Ron and Hostetler, Robert. PreCalculus with Limits. Massachusetts: Houghton Mifflin Company. 2007.

❖ Calculator:

Each student is required to purchase a scientific calculator (similar to a TI-30). Students may wish to purchase a graphing calculator (TI – 83 or higher). These are not required for this course but may prove to be helpful.

❖ Helpful Websites:

Textbook Site - limits/1e/student_home.html

Quia Site –

Other Helpful Sites -

[pic]Expectations

I expect all of my students to come to class on time and prepared with your book, your notebook, a pencil, and a calculator. I will not tolerate lack of preparation including missing assignments. I expect each student to be accountable for his/her own academics including seeking out help when needed. I expect students to come to me with questions; I should not have to come to you! I expect students to respect each person in the classroom and his/her right to learn. I expect that each student will maintain a willingness to learn and will have fun while doing so. I expect a great year!

[pic]Content Outline

Attached you will find a week-by-week breakdown of the content to be taught this school year. This outline is tentative and may need to be adjusted slightly throughout the year. Any major adjustments to this outline (elimination of an entire chapter or subject) will be presented to the students and sent home for parents to review. We have a lot to cover this school year and we will be hitting the ground running.

NOTE – The first four weeks of the course are an extensive review of Algebra. Due to the need for mastery of these topics, the organization of the course for this review period will slightly differ from what is outlined above.

PreCalculus Content Outline

|SEMESTER 1 |

|Week |Subject |Content |Chapter |

|1 |Advanced Algebra |Rules of Algebra |A.1 – A.2 |

| | |Properties of Fractions | |

| | |Properties of Exponents | |

| | |Scientific Notation | |

| | |Properties of Roots | |

|2 |Advanced Algebra |Polynomials |A.3 – A.4 |

| | |Factoring | |

| | |Simplifying, Multiplying, and Dividing Rational | |

| | |Expressions | |

|3 |Advanced Algebra |No School Monday |A.4 – A.6 |

| | |Adding Rational Expressions | |

| | |Solving Linear Equations | |

| | |Inequalities | |

|4 |Advanced Algebra |Solving Quadratic Equations |A.5, A.7 |

| | |Common Errors | |

| | |The Algebra of Calculus | |

| | |Review Advanced Algebra | |

| | |Test Advanced Algebra | |

|5 |Functions and Their Graphs |Intercepts |1.1 – 1.3 |

| | |Symmetry | |

| | |Equations for lines, circles | |

| | |Parallel and Perpendicular Line Properties | |

|6 |Functions and Their Graphs |Functions, Domain, and Range |1.4 – 1. 5 |

| | |Evaluating Functions | |

| | |Piecewise Functions | |

| | |Difference Quotients | |

| | |Analyzing Graphs of Functions (even, odd | |

| | |functions; maxima, minima) | |

|7 |Functions and Their Graphs |Parent Functions |1.6 – 1.9 |

| | |Transformations of Functions | |

| | |Composition of Functions | |

| | |Inverse Functions | |

|8 |Functions and Their Graphs |No School Friday |1.10 |

| |Review Chapter 1 |Mathematical Modeling and Variation | |

| | |Chapter 1 Review | |

| | |Chapter 1 test | |

|9 |Catch Up |No Class Wednesday | |

| | |Grades Close Friday | |

| | |Catch Up Week | |

|10 |Polynomial and Rational Functions |Quadratic Functions and Graphs |2.1 – 2.4 |

| | |Polynomial Functions | |

| | |Zeros | |

| | |Complex Numbers | |

|11 |Polynomial and Rational Functions |Early Release Friday |2.5 – 2.7 |

| | |Zeros of Polynomial Functions | |

| | |Rational Functions | |

| | |Non-Linear Inequalities | |

|12 |Review Chapter 2 |Review Chapter 2 |4.1 – 4.2 |

| |Logarithms |Test Chapter 2 | |

| | |Exponential Functions | |

| | |Logarithmic Functions | |

| | |Properties of Logs | |

|13 |Logarithms |Expanding and Condensing |4.3 – 4.4, 4.8 |

| |Review Chapter 3 |Solving Log Equations | |

| | |Chapter 3 Review | |

| | |Chapter 3 Test | |

|14 |Trigonometric Functions |Thanksgiving No School Wednesday - Friday |4.1 – 4.2 |

| | |Radians and Degrees | |

| | |The Unit Circle and Evaluating Trig Functions | |

|15 |Right Triangle Trigonometry |Sine and Cosine Graphs |4.3 – 4.7 |

| | |Other Trig Graphs Right Triangle Trig | |

| | |Trig Functions at Any Angle | |

| | |Inverse Trig Functions | |

|16 |All Triangle |Law of Sines |4.8; 6.1 – 6.2 |

| |Trigonometry |Law of Cosines | |

| | |Trig Applications and Models | |

|17 |Chapter 4, 6 Review |Trig Form of Complex Numbers |6.5 |

| | |Review Chapter 4, 6 | |

| | |Test Chapter 4, 6 | |

|18 |Catch Up |Winter Break Starts Friday | |

| | |Catch Up/Trig Project | |

|19 |Review |Review Week | |

|20 |Midterm Exams |

|Semester 2 |

|Week |Subject |Content |Chapter |

|1 |Analytical Trig/ Using Trig |No School Monday |5.1 – 5.2 |

| |Identities |Fundamental Identities | |

| | |Verifying Trig Identities | |

|2 |Analytical Trig/ Using Trig |Sum and Difference Formulas |5.4- 5.5 |

| |Identities |Double and Half Angle Formulas | |

|3 |Analytical Trig/ Using Trig |Solving Trigonometric Equations |5.3 |

| |Identities | | |

|4 |Review Chapter 5 |Early Release Friday |9.1 – 9.2 |

| |Sequences and Series |Chapter 5 Review | |

| | |Chapter 5 Test | |

| | |Sequences | |

| | |Summation Notation | |

| | |Arithmetic Sequences | |

|5 |Sequences and Series |No School Monday |9.3, 9.5 – 9.6 |

| | |Geometric Sequences | |

| | |Binomial Theorem | |

| | |Counting Principles | |

|6 |Probability |Independence |9.7 |

| |Review Chapter 9 |Probability of an Event | |

| | |Chapter 9 Review | |

| | |Chapter 9 Test | |

|7 |Conic Sections |Lines |10.1 – 10.3 |

| | |Conics | |

| | |Circles | |

| | |Parabolas | |

| | |Ellipses | |

|8 |Conic Sections |Hyperbolas |10.4 |

| |Review Chapter 10 |Chapter 10 Review | |

| | |Chapter 10 Test | |

|Spring Break |

|9 |Polar Coordinates |Grades Close Friday |10.5 – 10.9 |

| | |Polar Coordinates | |

| | |Coordinate Conversion | |

| | |Graphs of Polar Coordinates | |

| | |Polar Equations of Conics | |

|10 |Reasoning and Problem Solving |Problem Solving Strategies |Handouts/Notes |

| | |Drawing diagrams | |

| | |Guess and Check | |

| | |Solving a Simpler Problem | |

| | |Working Backwards | |

| | |Solution Reasonability | |

|11 |Reasoning and Problem Solving |No School Friday |Handouts/Notes |

| | |Truth Statements | |

| | |Justifying Algebraic Steps | |

| | |Solutions Sets | |

| | |Proof by Contradiction | |

|12 |Reasoning and Problem Solving |Problem Solving Review | |

| | |Problem Solving Test | |

| | |Final Project | |

|13 |Reasoning and Problem Solving |Final Project | |

|14 |Senior Final Review |Senior Final Review |12.1 – 12.2 |

| |Calculus Introduction |Introduction to Calculus | |

| | |Limits | |

|15 |Senior Final |Senior Final Exam Week |12.3 – 12.5 |

| |Calculus Introduction |Limits | |

| | |The Area Problem | |

| | |The Tangent Line Problem | |

|16 |Class Trips |

|17 |Review |Final Exam Review |Chapter A–2, 4-6, 9, 10, 12 |

|18 |Final Exam |

Homework Assignment Outline

Every homework assignment will be completed in the following format. Assignments completed in any other format WILL NOT be accepted for credit. Absolutely NO assignments will be accepted if the holes are torn and not reinforced.

| |Student Name Assignment Due Date |

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| |Assignment (page number and problem numbers) |

|Problem Number 1 |Question |

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| |Solution (MUST write out the word solution) |

| |Worked out solution |

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| |Answer is circled with line to right margin with the work answer written |

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| |A line is drawn before beginning the next problem |

|Problem Number 2 |Question |

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| | |

| |Solution (MUST write out the word solution) |

| |Worked out solution |

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| | |

| | |

| |Answer is circled with line to right margin with the work answer written |

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| |A line is drawn before beginning the next problem |

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