Denver’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 calculus tutors are also experts at helping students to prepare for the Math I and Math II SAT Subject Tests.
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.
- 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.
- 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.
- 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.
- 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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