AP Calculus

Announcements

NOTICE: AP Calculus BC has a mandatory class in period 5 on Choice Fridays during the first round of choice (up to Oct. 23)

Schedule

• Wednesday, Sep. 2: First day activities, summer homework review
• Friday, Sep. 4: Tuesday schedule (no class)

Homework

If you are consistently spending more than 1 hour per day on homework, please see me. Nearly every section has an AP Classroom homework with a deadline (usually the next class). Paper assignments from Flipped Math will also be assigned, also due for the next class. Any additional homework will be listed here.

Exams

Units 1-4 test

Scheduled for Monday, September 7 (in class). You should be proficient in all material contained in Units 1-4. More precisely, you should be able to:

• Compute limits of a function graphically.
• Compute limits of a composite function graphically.
• Interpret tabular information for finding limits.
• Use limit properties and arithmetic to find limits.
• Compute a limit of a function algebraically via 4 techniques:
  • Technique 0: rational-like function evaluation
  • Technique 1: factor and reduce
  • Technique 2: rationalize
  • Technique 3: Fundamental Trigonometric Limit
  • Technique 4: (for x approaching +/- infinity) divide by dominant terms in the denominator
    • Apply this technique for expressions involving radicals
• Compute a one-sided limit, including checking for signs in absolute values and values close to 0.
• Find a limit via one-sided limits.
• Determine where a function is continuous, or find values for constants which give continuity.
• Identify the type of a discontinuity.
• Find vertical and horizontal asymptotes of a function.
• Use Squeeze Theorem.
• Use Intermediate Value Theorem.
• Describe the relationship between continuity and differentiability.
• Calculate the average rate of change from a table, graph, or function.
• Compute a derivative from first principles.
• Identify a limit as a derivative and use derivative rules to find the limit.
• Approximate the value of a derivative from either a table or graph.
• Sketch the derivative of a function given a graph of the function and vice versa, the graph of a function given the derivative.
• Apply the various derivative rules: sum/difference rule, constant multiple rule, power rule, product rule, quotient rule (this is of course the vast majority of the test, either directly or indirectly)
  • Note: This is true both for given functions (involving powers, trigonometric functions, exponential functions, and logarithmic functions) as well as given a table of values for f(x), g(x), f'(x), g'(x).
• Use derivatives to find the equation of tangent/normal lines with a given slope and through a point or parallel/perpendicular to given lines.
• Apply chain rule
• Compute dy/dx implicitly, and find the slope of the tangent to an implicit curve at a point.
• Compute higher-order derivatives.
• Be able to compute higher-order implicit derivatives.
• Differentiate inverse functions, including the inverse trigonometric functions.
• Be able to compute derivatives via logarithmic differentiation.
• Determine the velocity and acceleration of a particle moving in a straight-line given its position/displacement function as well as compute the value of the velocity or acceleration at particular times.
• Determine when a particle is at rest as well as when it is moving in the positive or negative direction.
• Find the total distance travelled by a particle within a specified amount of time.
• Find rates of change in contexts other than motion including understanding the correct units
• Solve related rates problems (you should know standard formulas for area/volume and perimeter/surface area, and be able to use simple geometry such as similarity of triangles and Pythagorean Theorem)
• Approximate a function with local linearization and analyze a linearization
• Use l'Hôpital's rule appropriately

Unit 5 test

Scheduled for Wednesday, September 30 in-class. There will be a calculator portion and a non-calculator portion. You should be proficient in all material contained in Unit 5. More precisely, you should be able to:

• Apply the Mean Value Theorem
• Determine where a function satisfies the Mean Value Theorem
• Apply the Extreme Value Theorem
• Find and classify critical points
• Find local and global extrema
• Determine where a function is increasing or decreasing
• Use the First Derivative Test
• Determine the concavity of a function on an interval
• Use the Second Derivative Test
• Determine information about f, f', or f'' given information about another one of these functions
• Solve optimization problems
• Analyze an implicit function using derivatives and second derivatives

Exam weighting: 12.5

NOTE: any material from Units 1 to 4 is also fair game and may be useful/necessary.

Online Resources

• Shared Google Drive for AP Calculus BC
• RTC information
• Flipped Math – AP Calculus
• The Essence of Calculus (3Blue1Brown)
• Khan Academy: AP Calculus BC
• WolframAlpha – Online calculator
• Desmos – Graphing calculator
• Interactive Chain Rule
• Concavity visual: Curve, tangent, and f''
• Trig: Etymology of trig functions · Proofs of trig derivatives

Practice Problems

• Unit 1
  • Limits (graphical) (Answers)
• Units 2–4
  • Derivative practice (answers included)

Challenges

• Unit 1: A weird limit – limit at 0⁺ DNE example.
• Unit 1: Continuous nowhere
• Unit 1: Continuous on irrationals
• Unit 1: Continuous on rationals
• Unit 2: Continuous but not differentiable
• Unit 2: Differentiability for piecewise
• Unit 3: Continuous but nowhere differentiable

Logistics

• AP Calculus course at a glance
• Course outline
• Renert AP Policy