Williston School District 29 (AP) Calculus- ABPacing Guide

Chapter 1
Foundations of Geometry / Focus Questions / Overview / Focus
Indicators / Focus Indicators
90 Total Days
Day
1 / 2 / 3 / 4 / 5
1-1, Finding Limits Graphically, Numerically, and Analytically. / Using Technology, Tables of Values, and Rationalizing
Epsilon – Delta Proof using definition of a limit. / Define a limit with Rigour
Strategies for finding Limits using Squeeze Theorem. / Two Special trigonometric Limits
Discussing Continuity and One sided limits. / Removable Discontinuities, and open and closed intervals
Testing for Continuity / Intermediate Value Theorem
Determine Infinite Limits from left and right / Infinity and Negative Infinity
What are Vertical Asymptotes? / Look at Different Properties
Applications and AP Questions / Determine continuity and Limits from right and left
Find the slope of the tangent line to a curve at a point / Difference Quotient
What is a derivative? / Prove the Derivative at a Point.
How are Derivatives and Continuity related? / Differentiability implies Continuity
Find the Derivative using Rules / Power Rule, Sum and Difference, and Sine and Cosine
Finding Velocity of a Free Falling object. / Average and Instantaneous Velocity
Finding higher order Derivatives / Product and Quotient Rules
Finding Acceleration due to Gravity / 2nd Derivative
Finding Derivative of a Composite Function / Proving Chain Rule
What is the difference between Implicit and Explicit Differentiation? / Implicit differentation
Finding slope of a Graph Implicitly / Problem Solving Strategies
Finding related Rates to solve Real World Problems / Derivatives with respect to time.
Velocity vs. Speed / Scalars vs. Vector
AP Questions / Preparation for AP Test
Applications of Differentiation / Relative Extrema and Absolute Extrema
What are Critical Numbers? / Maximums and Minimums
How Many Max/Mins? / Rolle’s Theorem, and Mean Value Theorem
When is a Function increasing or decreasing? / 1st Derivative test
Applictions to real Life. / Path of a Projectile
What is Concavity? / 2nd Derivative Test
Find Points of Inflection. / Change in Concavity
Finding Limits at Infinity / Horizontal Asymptotes
Limits involving Trigonometric Functions. / Graphically and Numerically
Draw the Curve without Technology (Curve Sketching) / Review of Calculus Applications
Optimization Problems / Max./Min. Problems
Use Newton’s Method to approximate a zero. / Prove Newton’s Method
Tangent Line Approximation / Using differentials
Anti-derivatives and Indefinite Integration / General Solution of a differential equation
Applying Basic Integration Rules / Original integral- Rewrite-Integrate- Simplify
Finding Particular Solutions / Given Initial Conditions
Solving Vertical Motion Problems / Using Anti-Derivatives
Finding Area / Using Sigma Notation
Finding Upper and Lower Sums / Area Approximation
Finding Area using limit Definition / Apply limits to Sigma Notation
What are Riemann Sums? / Partitions of unequal width
What is a definite Integral? / Limit of a Riemann Sum
Find Area Between Curves / Top minus Bottom and Right minus left
What is the Fundamental Theorem of Calculus? / Mean Value for Integrals
What is Average Value? / Average Value formula
What is the 2nd Fundamental Theorem of Calculus? / Proof
Solving Particle Motion Problem / Integrate Velocity to get Position
Integration by U-Substitution / Pattern Recognition or Change Variable
Numerical Integration / Trapezoidal Rule
Logarithmic Function: differentiation and Integration / Natural log and Common Logs
Integration of Trig Functions / Proofs with Natural Logs
What are Inverse functions? / Changing Domains and Ranges
What are exponential functions? How to differentiate and Integrate / Properties of exponential functions
How to differentiate Bases other than “e” / Using logs and natural logs
Applications of Logarithmic and exponential functions. / Growth and Decay models
Differentiating and Integrating Inverse Trig Functions / Reversing Domains and Ranges
Solving Logistic Differential equations / Separation of Variables
Applications of Integration / Area, and Volume and Arc length.