Pre-Calculus 11 Course Outline
Course Description
Pre-Calculus 11 is designed to provide students with the mathematical skills and understanding necessary for success in Pre-Calculus 12 and other mathematics programs at the post-secondary level. This course focuses on developing algebraic skills, graphical understanding, and problem-solving abilities. Students will explore functions, equations, and mathematical models that form the foundation for calculus and other advanced mathematics courses.
Course Objectives
Upon successful completion of Pre-Calculus 11, students will be able to:
- Solve linear, quadratic, and systems of equations using multiple methods
- Analyze and graph linear, quadratic, and absolute value functions
- Simplify and perform operations with rational expressions and functions
- Simplify and solve equations involving radicals
- Solve problems involving arithmetic and geometric sequences and series
- Apply trigonometric ratios to solve problems involving right and non-right triangles
- Analyze financial literacy skills, including personal budgeting and investments
Units of Study
Unit 1: Sequences and Series
- Arithmetic sequences and their properties
- Arithmetic series and their sums
- Geometric sequences and their properties
- Geometric series and their sums
- Applications of sequences and series in real-world contexts
Unit 2: Trigonometry
- Review of primary trigonometric ratios
- Solving problems involving right triangles
- The Law of Sines and Law of Cosines
- Applications to non-right triangles and real-world problems
- Standard position of angles
- Special angles and reference angles
Unit 3: Quadratic Functions and Equations
- Properties of quadratic functions
- Graphing quadratic functions in vertex and standard form
- Completing the square
- Solving quadratic equations by factoring, completing the square, and quadratic formula
- Applications of quadratic functions to optimization problems
Unit 4: Radical Expressions and Equations
- Simplifying radical expressions
- Performing operations with radicals
- Solving equations involving radicals
- Graphing radical functions
- Applications of radical expressions
Unit 5: Rational Expressions and Functions
- Simplifying rational expressions
- Operations with rational expressions (addition, subtraction, multiplication, division)
- Solving rational equations
- Graphing rational functions
- Applications of rational expressions and functions
Unit 6: Absolute Value Functions and Equations
- Properties of absolute value
- Graphing absolute value functions
- Solving absolute value equations
- Solving absolute value inequalities
- Applications of absolute value
Unit 7: Systems of Equations
- Solving linear systems by graphing, substitution, and elimination
- Solving linear-quadratic systems
- Solving quadratic-quadratic systems
- Applications of systems of equations to real-world problems
Assessment Methods
- Unit Tests: 40% - Comprehensive assessments at the end of each unit
- Quizzes: 15% - Short assessments to monitor progress on specific topics
- Assignments: 20% - Regular homework assignments and problem sets
- Projects: 15% - Applied problem-solving projects connecting mathematics to real-world scenarios
- Final Examination: 10% - Comprehensive final exam covering all course material
Required Materials
- Textbook: "Pre-Calculus 11" (specified edition according to school policy)
- Graphing calculator (approved model) - TI-83 or TI-84 recommended
- Scientific calculator as backup
- Binders or notebooks for notes and assignments
- Graph paper, rulers, protractors, and compasses
- Pencils, erasers, and pens
Expectations and Guidelines for Success
- Active participation in class discussions and activities
- Completion of all assigned work on time
- Regular review of class notes and textbook material
- Seeking help from the teacher when needed
- Working collaboratively with peers when appropriate
- Maintaining academic honesty on all assignments and assessments
- Developing problem-solving strategies and mathematical thinking skills
- Using technology appropriately to enhance mathematical understanding
Additional Resources
- Online math resources and video tutorials as provided by the teacher
- Math support center/tutoring services available at the school
- Additional practice materials and worksheets as distributed in class
- Review sessions offered before major assessments
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