AP Calculus AB tutor

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About AP Calculus AB

The College Board AP Calculus AB course covers fundamentals of limits and differential and integral calculus. It is equivalent to a first-semester calculus college course. Students usually take this course after studying precalculus. A school that can organize the material for students with advanced math skills can offer the Calculus AB syllabus.

 Is AP Calculus AB hard?

According to collegevine.com, AP Calculus AB had a passing rate of about 60% in 2020. It has above-average difficulty and is one of the longer ones. For having a good chance of scoring well, students shall practice thoroughly and familiarize themselves with the test. An AP Calculus AB score calculator is available at https://www.albert.io/blog/ap-calculus-ab-score-calculator/.

AP Calculus AB prerequisites

Geometry, trigonometry, algebra, analytic geometry, and elementary functions are prerequisites for AB Calculus AB. The students should understand the properties of linear, rational, exponential, polynomial, trigonometric, inverse trigonometric, logarithmic, and piecewise-defined functions. They should know how to draw graphs and solve equations for these functions. A student should also be familiar with combinations, compositions, and inverses for general functions and algebraic transformations.

Is there an equation sheet for AP Calculus AB?

Unlike some other AP subjects, the AP Calculus AB exam doesn’t include an equation sheet while taking the test. Students should memorize the formulas and equations useful in the exam. They can bring a maximum of two approved calculators to the exam.

Is AP Calculus AB worth taking?

Definitely! It pays dividends in financial and academic terms to complete AP Calculus AB. Students can save the tuition fees for the first-semester calculus college course instead of AP Calculus AB. AP courses demonstrate the student’s readiness and willingness for the academic rigor involved in higher studies. It also increases a student’s confidence while entering college.

AP Calculus AB topics

Here is the list outlining the AP Calculus AB units.

 Part 1: Limits and Continuity (10 – 12% of the total score)

Learn how to solve problems that involve change using limits. Develop an understanding of functions.

Topics:

Using limits to measure instantaneous change

Defining limits and understanding their properties in different settings

Studying a function’s continuity at a given point or over a domain

Understanding asymptotes

Studying limits at infinity

Using the intermediate value theorem and the squeeze theorem for reasoning

Part 2: Differentiation and its fundamental properties (10 – 12% of the total score)

Learn to use limits to define and determine derivatives

Topics:

Defining the function derivatives

Understanding the relationship between differentiability and continuity

Calculating derivatives for elementary functions

Learning to use differentiation rules

Part 3: Differentiation of implicit, composite, and inverse functions (9 – 13% of the total score)

Learn about higher-order derivatives and advanced differentiation techniques with the chain rule. 

Topics:

Implicit differentiation

Differentiating composite functions with the chain rule

Deriving higher-order derivatives of functions

Differentiation of inverse functions

Part 4: Applying differentiation in various contexts (10 – 15% of the total score)

Learn to define and solve real-world problems that involve instantaneous rates of change by applying derivatives. Use mathematical reasoning to derive the limits of some indeterminate forms.

Topics:

Extracting relevant mathematical information of real-world problems involving rates of change from verbal descriptions

Solve motion equations with differentiation

Extending knowledge of motion problems to other rates of change situations

L’Hospital’s rule

Local linearity and approximation

Part 5: Analysis using differentiation (15 – 18% of the total score)

Study how graphs of a function relate to its derivatives. Learn how to use calculus for optimization problems.

Topics:

Properties of functions and their derivatives

Mean Value Theorem

Extreme Value Theorem

First and second derivative tests

Candidates test

Drawing graphs of functions and derivatives

Implicit relations’ behavior

Solve optimization problems

Part 6: Accumulation of change and integration (17 – 20% of the total score)

Learn to define definite integrals by using limits. Study how the fundamental theorem links differentiation and integration. Practice various integration techniques and understand how to apply properties of integrals for it.

Topics:

Use Riemann Sums to approximate integrals

Determine accumulated change over an interval with definite integrals

Indefinite integrals

Antiderivatives

The Fundamental Theorem of Calculus

Accumulation functions and definite integrals

Integration techniques

Properties of integrals

Part 7: Differential equations (6 – 12% of the total score)

Learn to solve differential equations. Understand exponential growth and decay.

Topics:

Derive separable differential equations by interpreting verbal descriptions of change

Solving separable differential equations for general and particular solutions

Drawing fields enclosed by slopes

Sketching curves with families of solution

Derivation and application for exponential growth and decay model

Part 8: Applications of integration (10 – 15% of the total score)

Learn to solve for net change over time. Find areas of and volumes using functions.

Topics:

Modeling particle motion

The average value of functions using definite integrals

Area between curves

Solving accumulation problems

Deriving volume with the disc method, cross-sections, and the washer method

(Note: The up-to-date AP Calculus AB curriculum is available on the official College Board AP Calculus AB web page.)

Recommended resources for preparing for the AP Calculus AB exam

Here is a list of the resources, including textbooks, to prepare for the AP Calculus AB exam.

The College Board AP Calculus AB questions webpage has the official database of past AP Calculus AB free-response exam questions.

You can also get AP Calculus AB multiple-choice and free-response questions on the Albert.io AP Calculus page to help you practice for the exam.

Khan Academy: The Khan Academy AP Calculus AB page provides free resources for preparing for the AP Calculus AB curriculum. It has online lessons, video quizzes, and AP Calculus sample questions.

My Engineering Buddy is an excellent destination for you to get online AP Calculus AB tutoring at affordable fees. If you want a private AP Calculus AB tutor to help you, book a session at www.myengineeringbuddy.com. Learn vital problem-solving concepts and techniques based on the AP Calculus AB course.

AP Calculus AB textbooks

• Here is a broad list of AP Calculus AB books for understanding the subject and exam prep:
• Calculus – A Complete Course 7th Edition by Robert Adams, Christopher Essex. Publisher – Pearson Education
• Calculus, AP Edition – AP Calculus AB 11th edition by Howard Anton, Irl C Bivens. Publisher – Wiley
• Calculus – Graphical, Numerical, Algebraic AP Edition 6th Edition by Ross L Finney, Franklin D Demana, Bert K Waits, Daniel Kennedy. Publisher – Savvas Learning Co
• Calculus – AP Calculus AB 3rd Edition by Leslie Dietiker, Judy Kysh, Tom Sallee, Brian Hoey. Publisher – CPM Educational Program
• Calculus – Single and Multivariable AP Edition 7th Edition by Deborah Hughes-Hallett, William G McCallum et al. Publisher – Wiley
• Calculus for AP 1st edition by Ron Larson, Paul Battaglia. Publisher – Cengage Learning
• Rogawski s Calculus for AP – Early Transcendentals Second Edition by Jon Rogawski, Ray Cannon. Publisher – W. H. Freeman
• Calculus for AP – A Complete Course 1st edition by Stephen Kokoska, James Stewart. Publisher – Cengage Learning
• Calculus for the AP Course Third Edition by Michael Sullivan, Kathleen Miranda. Publisher – W. H. Freeman