AP/Advanced Calculus Part 1 teaches a balanced approach to problem solving, using analytical, algebraic, numerical, graphical, and verbal/written methods of representing problems. This course begins with a brief review of linear, polynomial, exponential, parametric, logarithmic, and trigonometric functions. Students will study all topics associated with limits and continuity. Student will also study derivatives of a variety of functions (i.e., polynomial, trigonometric and inverse trigonometric, exponential, and logarithmic), as well as learn how to apply the chain rule and implicit differentiation. The course closes with a study of extreme values and the Mean Value Theorem.
This course meets the Advanced Placement criteria required by the College Board.
*Note: AP/Advanced Calculus Parts 1 and 2 are required for the AP Calculus AB exam.
It is recommended that students successfully complete Pre-Calculus or equivalent course work before enrolling in this course. Successful completion of both Part 1 and Part 2 of this course is required for students to earn the AP designation.
Unit 1: Essential Content and Skills
- Identify the relationships between parallel lines, perpendicular lines, and slopes.
- Analyze exponential growth and decay, parametric equations, logarithms, and trigonometric functions.
- Estimate a limit and identify different ways that a limit can fail to exist.
- Locate and verify end behavior models for various functions.
- Identify vertical and horizontal asymptotes.
- State the intervals upon which a given function is continuous.
- Apply the Intermediate Value Theorem.
Unit 2: Essential Content and Skills
- Discover derivatives and how f’(a) might fail to exist.
- Analyze how differentiability implies local linearity.
- Discover rules for differentiation: positive integer powers, multiples, sums and differences, products and quotients, and negative integer powers of x.
- Calculate higher order derivatives.
- Examine instantaneous rate of change.
Unit 3: Essential Content and Skills
- Find the derivatives of trigonometric functions.
- Discover simple harmonic motion.
- Analyze jerk, a sudden change in acceleration.
- Examine the derivative of a composite function.
- Apply the chain rule.
- Use implicit differentiation to find derivatives of higher order.
- Find derivatives by using the Power Rule for rational powers of x.
Unit 4: Essential Content and Skills
- Find derivatives of the inverse trigonometric functions.
- Discover the derivatives of ex, ax, ln x, and loga x.
- Locate absolute (global) values of functions.
- Find local (relative) extreme values.
- Examine the Mean Value Theorem.
- Analyze increasing and decreasing functions.
- Calculus Graphical, Numerical, Algebraic (textbook, practice book, and CD)