Colorado’s Best Pre-Calculus and Calculus Tutors

Denver Test Prep calculus tutors help students to master the fundamental principles of calculus including derivatives, limits, integrals, differential equations and infinite series.

Our Tutors

  • Graduated from a highly selective college or university.

  • Trained specifically to help students learn math in a one-on-one setting.

  • Available from 9am-10pm, 7 days per week to meet at your home or another location that is convenient for you.

Our Approach

  • Careful matching of each student with a tutor that fits his or her academic requirements and personality.

  • Customized study plans that are continually adapted to meet the evolving needs of the student.

  • Emphasis on teaching study techniques and organizational skills that position the student for long-term academic success.

What topics are covered in AP Calculus AB?

AP Calculus AB demands that students apply a wide-range of skills from previous math courses in the context of introductory level calculus. According to the College Board (https://apstudent.collegeboard.org/apcourse/ap-calculus-ab), AP Calculus AB students are expected to master the topics below.

Key Concepts in AP Calculus AB

  • Work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal.
  • Understand the meaning of the derivative in terms of a rate of change and local linear approximation and use derivatives to solve a variety of problems.
  • Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and use integrals to solve a variety of problems.
  • Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

Other Broader Math Goals in AP Calculus AB

  • Develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.
  • Model a written description of a physical situation with a function, a differential equation, or an integral.
  • Use technology to help solve problems, experiment, interpret results, and verify conclusions.
  • Communicate mathematics both orally and in well-written sentences and explain solutions to problems.
  • Determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

What topics are covered in AP Calculus BC?

According to the College Board (https://apstudent.collegeboard.org/apcourse/ap-calculus-bc#1), AP Calculus BC students are expected to master the topics below.

  • Limits
    • Students must be able to compute one-sided limits, limits at infinity, the limit of a sequence, and infinite limits.They should be able to apply limits to understand the behavior of a function near a point and understand how limits are used to determine continuity.
  • Derivatives
    • Students should be able to use different definitions of the derivative, estimate derivatives from tables and graphs, and apply various derivative rules and properties. Students should be familiar with a variety of real-world applications, including related rates, optimization, and growth and decay models.
  • Integrals
    • Students should be familiar with basic techniques of integration, including basic antiderivatives and substitution, and properties of integrals.
  • Fundamental Theorem of Calculus
    • Students must understand the relationship between integration and differentiation as expressed in the Fundamental Theorem of Calculus.
  • Series
    • Students should be familiar with various methods for determining convergence and divergence of a series, Maclaurin series for common functions, Taylor series representations, radius and interval of convergence, and operations on power series.

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