Pre-Calculus 11 Course Outline

Course Description

Pre-Calculus 11 is designed to provide students with the mathematical knowledge and skills necessary for success in calculus and other advanced mathematics courses. This course builds on algebraic concepts from previous mathematics courses and introduces new topics that develop students' understanding of functions, equations, and mathematical reasoning.

Course Objectives

Upon completion of Pre-Calculus 11, students will be able to:

Solve and manipulate algebraic expressions and equations
Understand and analyze various types of functions
Apply mathematical concepts to solve real-world problems
Develop critical thinking and problem-solving skills
Use appropriate mathematical terminology and notation
Apply mathematical reasoning to justify solutions

Prerequisites

Students should have successfully completed Pre-Calculus 10 or an equivalent course with a strong understanding of algebraic concepts, including:

Linear equations and inequalities
Basic factoring and polynomial operations
Exponents and radicals
Graphing linear equations
Basic trigonometry

Course Units

Unit 1: Algebra and Number Operations

This unit focuses on advancing algebraic skills essential for the course. Topics include:

Operations with real numbers
Radicals and radical equations
Rational expressions and equations
Complex numbers
Polynomial operations and factorization

Unit 2: Functions

Students will explore different types of functions and their properties:

Domain and range
Function notation
Composition of functions
Inverse functions
Transformations of functions

Unit 3: Polynomial and Rational Functions

This unit examines specific types of functions in depth:

Quadratic functions and equations
Polynomial functions
Rational functions
Asymptotes and end behavior
Zeros of functions

Unit 4: Exponential and Logarithmic Functions

Students will study exponential growth and decay models:

Properties of exponents
Exponential functions
Logarithmic functions
Properties of logarithms
Exponential and logarithmic equations

Unit 5: Systems of Equations and Inequalities

This unit covers techniques for solving systems:

Solving systems of linear equations
Systems of nonlinear equations
Solving linear inequalities
Systems of inequalities
Linear programming

Unit 6: Sequences and Series

Students will examine patterns and summations:

Arithmetic sequences and series
Geometric sequences and series
Summation notation
Convergence and divergence of series
Mathematical induction (introduction)

Unit 7: Trigonometry

This unit extends trigonometric concepts:

Trigonometric functions of special angles
Trigonometric equations
Graphs of trigonometric functions
Trigonometric identities
Applications of trigonometry

Unit 8: Conic Sections

Students will study the properties of conics:

Circles
Parabolas
Ellipses
Hyperbolas
Applications of conic sections

Assessment Methods

Student understanding will be evaluated through various assessment methods:

Unit tests (30%)
Midterm examination (20%)
Final examination (30%)
Assignments and homework (10%)
Quizzes (10%)

Assessment Schedule

Unit tests will be conducted at the end of each unit. The midterm examination will cover Units 1-4, while the final examination will be comprehensive, covering all course material. Regular quizzes will be administered to monitor ongoing understanding.

Learning Resources

Students will have access to:

Textbook: "Pre-Calculus 11" by [Author Name]
Online learning platform with video tutorials and practice problems
Graphing calculators (required for certain units)
Supplementary worksheets and practice problems
Mathematics support center with tutoring services

Course Policies

Attendance

Regular attendance is crucial for success in this course. Students are expected to attend all classes and participate in classroom activities. Excessive absences may negatively impact performance and understanding of the material.

Make-up Tests

Make-up tests will only be granted in exceptional circumstances with appropriate documentation. Students must notify the instructor prior to the scheduled test when possible.

Homework

Homework assignments are designed to reinforce concepts taught in class and are due at the beginning of the following class period. Late assignments may receive a penalty of 10% per day.

Academic Integrity

Academic honesty is expected at all times. Cheating, plagiarism, or any form of academic dishonesty will result in a zero for the assignment or test and may lead to further disciplinary action.

Course Schedule

Semester 1

Weeks 1-3: Unit 1 - Algebra and Number Operations
Weeks 4-6: Unit 2 - Functions
Weeks 7-9: Unit 3 - Polynomial and Rational Functions
Week 10: Midterm Examination
Weeks 11-13: Unit 4 - Exponential and Logarithmic Functions
Weeks 14-15: Unit 5 - Systems of Equations and Inequalities

Semester 2

Weeks 1-3: Unit 6 - Sequences and Series
Weeks 4-6: Unit 7 - Trigonometry
Weeks 7-8: Unit 8 - Conic Sections
Week 9: Review and Preparation for Final Examination
Week 10: Final Examination

Tips for Success

            Complete all assigned homework on time
Actively participate in class discussions and activities
Ask questions when concepts are unclear
Form study groups with classmates
Review previous material regularly
Seek help early if experiencing difficulties
Utilize available resources, including tutoring services
Practice solving a variety of problems
        