AB Midterm Review Topics
Unit 1: Functions, Limits, and Continuity
A.
B.
C.
The Cartesian Plane and Functions
 Absolute Value
 Symmetry
 Even and Odd Functions
 Domain and Range
Limits and Their Properties
 One and two-sided limits
 Calculate limits of polynomial and rational functions graphically, analytically, and by using a table of
values
 Infinite Limits and Limits at Infinity
 Horizontal and Vertical Asymptotes of a Function
Continuity
 Develop definition of continuity
 Continuous and Discontinuous Functions
o Removable, Non-removable, Infinite, Jump Discontinuity
 Intermediate Value Theorem
 Extreme Value Theorem (introduce and revisit in Unit 3)
Unit 2: Differentiation
A.
Rates of Change of a Function
 Average Rate of Change
 Tangent Line to a Curve
 Instantaneous Rate of Change
B. The Derivative
 Definition of the Derivative (difference quotient)
 Derivative at a Point
 One-sided derivatives
 Numerical Derivative of a Function (using nDeriv on the calculator)
 Graphing f`(x) using the graph of f(x)
 The Derivative as a Function
 Graphing the Derivative (explore using Y2 = nDeriv(Y1,X,X) on the calculator)
C. Differentiability
 Define differentiability
 Differentiability and Continuity
 Local Linearity
 Symmetric Difference Quotient
 Intermediate Value Theorem for Derivatives
D. Differentiation Rules
 Sum and Difference Rules
 Constant, Power, Product, and Quotient Rules
 Chain Rule
 Higher Order Derivatives
E. Applications of the Derivative
 Position, Velocity, Acceleration, and Jerk (show that vertical motion formulas from physics are
related through differentiation)
 Particle Motion
F. Implicit Differentiation
 y` notation
 Expressing derivatives in terms of x and y.
G. Related Rates
AB Midterm Review Topics
Unit 3: Applications of Differentiation
A. Extema and Related Theorems
 Absolute Extrema
 Extreme Value Theorem
 Relative Extrema
 Critical Values
 Rolle’s Theorem
 Mean Value Theorem
B. Determining Function Behavior
 Increasing and Decreasing Functions
 First Derivative Test to Locate Relative Extrema
 Concavity
 Using the Second Derivative to Locate Points of Inflection
 Second Derivative Test to Locate Relative Extrema
 The Relationship Between f(x), f`(x), and f``(x).
C. Optimization
D. Differentials
 Local Linearity
 Tangent Line Approximation
Unit 4: Integration
A. Antiderivatives
 Indefinite Integrals
 Initial Conditions and Particular Solutions
 Basic Integration Rules
B. Area Under a Curve
 RAM (Rectangle Approximation Method)
 Riemann Sums
 Left sums, right sums, midpoint sums
 Definite Integrals
C. The Fundamental Theorem of Calculus
 FTC Part 1
 Numerical Integral (using fnInt on the calculator)
 FTC Part 2
 Mean Value Theorem for Integrals
 Average Value of a Function
 Integration by Substitution
 Integrating with Respect to the x and y axes
D. Trapezoidal Rule
Unit 5: Transcendental Functions
A. Trigonometric Functions
 Differentiation
 Integration
B. Inverse Trigonometric Functions
 Differentiation
 Integration
 General Rule for Derivative of an Inverse Function
C. Exponential and Logarithmic Functions