Calculus BC

  • Basic Integration Rules
  • Trigonometric Integrals
  • Trigonometric Substitutions
  • L’Hospital’s Rule
  • Integration by Partial Fractions
  • Integration by Parts
  • Improper Integrals
  • Slope Field
  • Separable Differential Equations
  • Exponential Growth and Decay
  • Logistic Equations
  • Euler’s Method
  • Slopes and Tangents to the Parametric Curves
  • Arc Length (Distance Traveled Along a Curve) in Parametric Form
  • Vector Valued Functions
  • Polar Coordinates and Slopes of Curves
  • Areas in Polar Coordinates
  • Sequences and Series
  • The Integral Test and p-Series
  • The Comparison Test
  • Alternating Series and Error Bound
  • The Ratio Test
  • Convergence of Power Series
  • Representations of Functions as Power Series
  • Taylor Polynomial and Lagrange Error Bound
  • Taylor Series and Maclaurin Series

At Refresh Kid tutoring sessions, we offer a comprehensive Calculus BC course curriculum designed to provide students with an in-depth understanding of advanced calculus concepts and prepare them for success in the AP Calculus BC exam. Our goal is to help students develop strong problem-solving skills and a solid foundation for future math and science courses. Here is an overview of our Calculus BC course curriculum:

  1. Review of Calculus AB Concepts:
  • Reinforcing fundamental concepts from Calculus AB, including limits, derivatives, and integrals.
  • Strengthening problem-solving skills through the application of Calculus AB topics in more complex scenarios.
  1. Techniques of Integration:
  • Exploring advanced integration techniques, such as integration by parts, trigonometric substitution, and partial fractions.
  • Applying integration methods to evaluate improper integrals and solve challenging integration problems.
  1. Applications of Integration:
  • Solving problems involving area between curves, volume of solids with known cross-sections, and length of curves.
  • Investigating applications of integration in physics, engineering, and economics.
  1. Sequences and Series:
  • Understanding the concepts of sequences and series, including convergence and divergence.
  • Analyzing arithmetic and geometric sequences and series.
  • Exploring tests for convergence, such as the ratio test, comparison test, and integral test.
  1. Parametric, Polar, and Vector Functions:
  • Investigating parametric equations and their applications in describing motion and curves.
  • Understanding polar coordinates and equations, including graphing polar functions and finding area bounded by polar curves.
  • Introducing vector functions, operations with vectors, and their applications.
  1. Differential Equations:
  • Understanding the basics of differential equations and their applications.
  • Solving first-order differential equations, including separable equations and linear equations.
  • Exploring second-order linear homogeneous and nonhomogeneous differential equations.
  1. Advanced Topics:
  • Exploring additional calculus topics, such as L'Hôpital's rule, improper integrals, and Taylor series.
  • Investigating numerical methods, such as Euler's method and Simpson's rule.
  • Introducing concepts of multivariable calculus, including partial derivatives and double integrals (time permitting).

Throughout the course, students will engage in practice problems, concept discussions, and real-world applications to reinforce their understanding of the concepts covered. Our tutors provide individualized attention, clear explanations, and step-by-step guidance to help students master each topic.

We are committed to supporting students' progress and offer additional resources, practice materials, and ongoing support to ensure their success in Calculus BC and the AP exam.

At Refresh Kid, we believe that a solid foundation in Calculus BC is crucial for students' future success in advanced mathematics and STEM-related fields. Enroll in our tutoring program today and empower your child with the skills and knowledge needed to excel in Calculus BC and beyond.

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