ELEANOR ROOSEVELT HIGH SCHOOL AP CALCULUS AB



ELEANOR ROOSEVELT HIGH SCHOOL ADV. ALGEBRA/TRIGONOMETRY

DIMITRI SALIANI, PRINCIPAL LAIRD JONAS, TEACHER

Course Description

In Advanced Algebra/Trigonometry, the real number system becomes the basis for a more in depth study of Algebra. This allows us to explore the relationships between two quantities and it leads to definition of a Function. We will then study the properties of functions and explore how specific function such the Exponential Function, The Logarithmic Function and the Trigonometric Function are used to represent real world phenomena.

My goal is to provide students with the guidance and support that will help them to develop a deeper understanding of how mathematics works. We will develop problem solving strategies that will allow us to analyze and interpret information given to draw conclusions beyond what was given.

Essential Questions:

1. How do the rules and properties of numbers shape the language of mathematics?

2. How are functions used to describe real world phenomena?

Course Requirements

• Two notebooks for notes and homework

• Pens, Pencils, and Ruler

• TI-83+ graphing calculator

Students are expected to come to class prepared with their notebook, pens, pencils, rulers and graphing calculator. Failure to do so will affect your grade.

Criteria for Success

Criteria for Success

i. Homework

Homework serves two main purposes. It allows you to practice what was taught in class and to determine whether you understand the material. Homework is assigned on a daily basis. You will be selected to present problems from the previous homework assignment. There will be homework pop quizzes that are based on past homework assignments. From time to time, I will come around to check that the homework was done. Failure to do the homework will result in a point taken off your homework grade. I will collect specific homework assignments. Late Homework is not accepted.

ii. Homework of the Week (HOW)

After the third unit you will be given a weekly homework assignment (HOW) in addition to your regular homework assignments. These questions will be taken from past AP Statistics Exams. The grades from the HOW will go towards your test grades.

iii. Test/Project

Tests and Quizzes are given on a regular basis. Review sessions for test will be scheduled before or after school. Projects are assigned to provide deeper insights into the topics that are covered and to develop problem solving skills. The format and rubric for projects are discussed when the projects are assigned.

iv. Notes

Good note-taking is essential to success. In addition to class notes, you will be given reading assignments from the textbook. These reading assignments will be collected and graded. There will be notes pop quizzes that assess the terms and concepts from your notes that were taken in previous classes.

v. Participation/Presentation

Participation and presentations in class is also critical to success. You are expected to share your ideas and pay attention when others are speaking. This is an integral part of class discussions and group work. You are also expected to present problems on the board. Your grades for presentation and participation reflect your contribution to the learning process.

Grading Policy

Test/Quiz/Project 60%

Homework 15%

Classwork

- Notes 10%

- Participation/Presentation (Including Group Work) 15%

100%

vi. Reflection

Your thoughts about what we do in class allow us to create and maintain an environment that is conducive to learning.

Please sign below confirming that you understand and are in agreement with everything that is stated above.

Student:__________________________ Parent:_________________________

Course Outline

Textbook:

Edward P Keenan, Ann Xavier Gantert, Isodore Dressler. Amsco’s Mathematics B. Amsco School Publication 2002

|Unit |Time |Topic |

|1 |3 days |Rational Numbers |

| | |Properties of Rational Numbers |

| | |Equation and Inequalities |

| | |Polynomials |

|2 |2 weeks |Rational Expressions |

| | |Reducing Rational Expressions |

| | |Multiplying and Dividing Rational Expressions |

| | |Adding and Subtracting Rational Expressions |

| | |Complex Fractions |

| | |Solving ration Equations |

|3 |3 weeks |The Real Numbers |

| | |Completing the Real Number Line |

| | |Absolute Value Equations and Inequalities |

| | |Simplifying Radicals |

| | |Adding and Subtracting Radicals |

| | |Multiplying Radicals |

| | |Dividing Radicals |

| | |Rationalizing Denominators |

| | |Quadratic Equation |

| | |Solving equations with rdaicals |

|4 |3 weeks |Relations and Functions |

| | |Defining Functions |

| | |Graphing Functions |

| | |Function Notations |

| | |Types of Functions |

| | |The Parabola |

| | |Ellipse and Circles |

| | |The Conic Sections |

| | |Inverse Variations |

| | |Composite Functions |

| | |Inverse Functions |

|5 |1 week |Transformation of Functions |

| | |Transformations and Functions |

| | |Transformations and Coordinate Geometry |

|6 |2 weeks |Exponential Functions |

| | |Laws of Exponents |

| | |Scientific Notation |

| | |Fractional Exponnets |

| | |Exponential Functions |

| | |Equations with Fractional Exponents |

| | |Exponential Equations |

|7 |2 weeks |Logarithmic Functions |

| | |The Inverse of Exponential Functions |

| | |Logarithmic Forms of Equations |

| | |Logarithmic Relationships |

| | |Using Logarithms to Solve Exponential Equations |

| | |Logarithmic Equations |

|8 |3 weeks |Trigonometric Functions |

| | |The Right Triangle |

| | |Sine and Cosine as Coordinates |

| | |Sine and Cosine as Functions |

| | |The Tangent Function |

| | |Special Angles |

| | |Finding Reference Angles |

| | |Radian Measure |

| | |Trigonometric Functions in Radian Measure |

| | |The Reciprocal Trigonometric Functions |

| | |The Pythagorean Identities |

| | |Cofunctions |

|9 |2 weeks |Trigonometric Graphs |

| | |The Wrapping Function |

| | |Graphing the Sine and the Cosine Function |

| | |Amplitude and Period |

| | |Sketching the Sine and Cosine Curve |

| | |Graphing the Tangent Function |

| | |Graphing Reciprocal Functions |

| | |Reflections over the Line y = x |

| | |Inverse Trigonometric Functions |

|10 |2 weeks |Trigonometric Applications |

| | |The Law of Cosine |

| | |Area of a Triangle |

| | |The Law of Sine |

| | |The Ambiguous Case |

| | |Forces |

| | |Solving Triangles |

|11 |2 weeks |Trigonometric Identities and Equations |

| | |Trigonometric Identities |

| | |Trigonometric Sum and Difference of Angles |

| | |Double and Half Angles |

| | |First and Second Degree Trigonometric Equations |

|11 |2 weeks |The Complex Numbers |

| | |Imaginary Numbers |

| | |Defining Complex Numbers |

| | |Addition and Subtraction of Complex Numbers |

| | |Multiplication of Complex Numbers |

| | |Multiplicative Inverses and Division of Complex Numbers |

| | |Solving Quadratic Equations with Imaginary Roots |

| | |The Nature Of Roots |

| | |Writing Quadratic Equations |

| | |Solving Systems of Equations |

| | |Quadratic Inequalities |

|12 |2 weeks |Statistics |

| | |The Summation Symbol |

| | |Measures of Central Tendency |

| | |Measure of Dispersion |

| | |Normal Distribution |

| | |Two-valued Statistics |

|13 |2 weeks |Probability, Sequences and the Binomial Theorem |

| | |Permutations and Combinations |

| | |Probability |

| | |Binomial Probability |

| | |Arithmetic Sequences and Series |

| | |Geometric Sequences and Series |

| | |The Binomial Theorem |

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