High Calculus

Segment 1:

• Review of Function Terminology and More
• Graphing Calculators
• Compositions and Transformations of Functions
• Some Common Functions
• Introduction to Limits
• Properties of Limits
• Limits Involving Infinity
• Continuity
• Applications of Limits
• The Derivative
• Rules of Differentiation
• Trigonometric Derivatives and the Chain Rule
• Inverse Functions
• Exponential and Logarithmic Functions
• Derivatives of Exponential, Logarithmic, and Inverse Trig Functions
• Implicit Differentiation
• Analyzing Functions Part I: Curve Sketching
• Analyzing Functions Part II: Maximums and Minimums
• Applied Maximum and Minimum Problems
• Distance, Velocity, Acceleration, and Rectilinear Motion
• Related Rates
• The Mean-Value Theorem and L'Hôpital's Rule
• Linearization

Segment 2:

• Area Approximation and Riemann Sums
• Introduction to the Definite Integral
• The Fundamental Theorem of Calculus
• Integrals and Antiderivatives
• Integration by Substitution
• The Definite Integral
• Finding the Area Under and Between Curves
• Volume by Discs (Slicing)
• Average Value of a Function and Rectilinear Motion Revisited
• Differential Equations – An Introduction
• Initial Value Problems and Slope Fields 
• Numerical Approximation Methods with Integrals
• Exploring the Graphs of f, f Prime, and f Double Prime
• Relative Rates of Growth
• Using Calculus with Data in a Table
• Functions Defined by Integrals

Study Forge - Provided within the course.

Besides engaging students in challenging curriculum, the course guides students to reflect on their learning and evaluate their progress through a variety of assessments. Assessments can be in the form of practice lessons, multiple choice questions, writing assignments, projects, research papers, oral assessments, and discussions. This course will use the state-approved grading scale. Each course contains a mandatory final exam or culminating project that will be weighted at 20% of the student’s overall grade.***

***Proctored exams can be requested by FLVS at any time and for any reason in an effort to ensure academic integrity. When taking the exam to assess a student’s integrity, the exam must be passed with at least a 59.5% in order to earn credit for the course.  

To achieve success, students are expected to submit work in each course weekly. Students can learn at their own pace; however, “any pace” still means that students must make progress in the course every week. To measure learning, students complete self-checks, practice lessons, multiple choice questions, projects, discussion-based assessments, and discussions. Students are expected to maintain regular contact with teachers; the minimum requirement is monthly. When teachers, students, and parents work together, students are successful.