What topics will I learn about in Calculus AB?

This course stresses the dual goals of conceptual understanding of calculus and fluency in the procedures that accompany the understanding of calculus concepts. The following major ideas will be introduced during the year: limits, derivatives, and integrals of polynomial, rational, exponential, and trigonometric functions and their inverses. Students will develop the skills necessary to apply calculus in solving a variety of practical problems. They will discover the importance of calculus to modern science and technology, and will learn to apply elementary calculus to the definition and solution of physical problems. Instruction is integrated with a biblical worldview to help students explore and discover God’s purpose in creating the beauty and precision of the mathematical sciences. The purpose of this course is to prepare students to take the Advanced Placement® Calculus AB examination given each spring, for which placement and/or credit may be awarded at the college level if a qualifying score is obtained. Content of this course corresponds to the College Board’s guidelines for Calculus AB. Course goals include:

  • Working with functions represented in a variety of ways—graphically, numerically, analytically, or verbally—and understanding the connections among these representations.
  • Understanding the meaning of the derivative in terms of a rate of change and local linear approximation, and using derivatives to solve a variety of problems.
  • Understanding the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change, and using integrals to solve a variety of problems.
  • Understanding the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.
  • Communicating mathematics both orally and in well-written sentences and to explain solutions to problems.
  • Modeling a written description of a physical situation with a function, a differential equation, or an integral.
  • Using technology to help solve problems, experiment, interpret results, and verify conclusions.
  • Determining the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.
  • Developing an appreciation for calculus as a coherent body of knowledge and as a beautifully elegant, yet eminently practical aspect of God’s creation.

Instruction will be given primarily through pre-recorded lectures. Reinforcement will take place through assigned practice, as well as a variety of opportunities for assistance and feedback, including weekly online class discussions.