Pre-Calculus

Precalculus, at its core, bridges and refines concepts acquired in Algebra 2 and Geometry courses in order to prepare students for future calculus-based endeavors. This requires a wide variety of topics to be covered that take elements from every piece of students' previous journeys in mathematics. It is almost unanimously regarded as the most difficult math course that students take throughout their entire K-12 careers—including calculus. Though the topics appear similar to those listed in Algebra 2, this course entails a widening and deepening of perspective on all fronts. One should expect their work ethic and critical thinking skills to be both challenged and grown throughout the year.

Students will complete portfolio projects that deepen their understanding of the concepts, appreciate the role of mathematics in God’s creation, and lead them to explore real-world applications of mathematics. Throughout the course, students will be led to see mathematics as a tool to solve real-world problems and will practice problem-solving strategies on HOT (Higher-Order-Thinking) Problems. 

Experience
The teaching of a new concept opens with a brief review of previously covered content. This review connects the previous lesson to the current lesson. The premise of the current lesson is presented via a question or idea. The students now have a puzzle or idea that they want to explore. As we delve deeper into answering the question at hand, we begin to discover the new mathematical concept. We use our prior knowledge and intuition to uncover a new truth about mathematics. Once this truth has been uncovered, we begin to work examples; first as a class and then as individuals or in groups. As our understanding of the concept deepens, we extend our knowledge base to include specific cases or situations that lead to minor adjustments in the truth that we have uncovered – thus expanding the truth. We use a variety of methods to uncover new truths. The most frequent method is a Socratic-style discussion that the entire class participates in. A discussion takes place that reveals the relevance of this truth in our mathematical studies or our daily lives (real-life application). 

Delivery
Each teacher has a unique presentation style in delivering the aforementioned experience. Sometimes the teacher leads the discussion using questions; following the example set by Socrates.. Sometimes a problem is presented and the students take the lead in finding a solution based on extending previous knowledge. Sometimes students participate in a hands-on activity to discover new truths. Sometimes a short lecture or presentation is required, however, we aim to minimize lecturing, especially before high school. 

Methodology
Students continue to study the new truth and deepen their understanding of it via homework, classwork, projects, and assessments. Since our classes do not meet 5 days per week, students must spend time studying the concepts outside of class. This also helps students grow in their ability to think and work math concepts independently which is required for future math classes. For this reason, we ask that parents minimize the assistance that students are given on assignments. If a student receives an A on an assignment, it should be a true indication of their independent ability as the teacher interprets this A as independent mastery. 

Review assignments or classroom review activities are utilized to assist students with opportunities to retain or improve their mastery. Assessments are directly or indirectly cumulative and serve as an opportunity to deepen their learning. Assessments are not meant to be a regurgitation of previous homework assignments.

Preparedness
Students who are adequately prepared to take this course will have mastered (can work independently without prompting):

• Completed a comparable Algebra 2 with Trigonometry Course
• Solve Polynomial Equations with degrees higher than 3
• Synthetic Division, Remainder Theorem, Complex Conjugate Theorem
• Understand Complex Numbers and can include them in calculations
• Prove Polynomial and Trigonometric Identities
• Determine Inverse Function Algebraically and Graphically
• Mastered Properties of Logarithms and Exponential Functions with base e
• Add, Subtract, Multiply, and Divide Rational Functions
• Understand and Utilize the Normal Distribution
• Understand Circular and Periodic Functions
• Solve Trigonometric Equations