Topics for Spring Final 2016 and 2017Name:
The six concept categories that will make up your second semester grade shown below. Use this as an outline to help guide your studying. Add notes, examples and insights to make this outline a more detailed tool to help you study for the final. The details in each of the six reorganized concept categories are a guide as to what is in that concept category, there might be some minor ideas that I didn’t put in the concept category details that could appear on the final. Make sure you look at units and understand what your answers mean in context of the problems and use proper notation!
1. Limits, Asymptotes, and Continuity
Algebraic Techniques for solving limits
a. As x approaches specific value,
b. Using a graph to find the limit.
The limit definition of Asymptotes
a. Horizontal Asymptotes and
b. Vertical Asymptotes
Definition of Continuity
a. Using a graph to determine continuity
b. Proving continuity algebraically with a function such as a polynomial or piecewise.
c. Focus on Notation to help justify conclusions.
d. IVT
Using L’Hopital’s Rule to solve indeterminate limits (using derivatives to solve certain types of limits that end up as or )
2. Slope, Rate of Change, Differentiability and Calculating Derivatives
Instantaneous versus Average Rate of Change
a. Approximation with data tables
Definition of Differentiability
a. Graphically
b. Using evidence from a graph or algebraically (ie. Piecewise functions) to support conditions to show whether or not a function is differentiable.
Derivative Rules
a. Basic Derivatives: Power, Exponential, Logarithmic, Trigonometric, and Constant
b. Intermediate Derivatives: Product, Quotient, and Chain
c. Implicit Derivative such as or
3. Curve Sketching (Derivatives and Graph Behavior)
Know relationship between
a. is positive then is increasing
is negative then is decreasing
ispositive then is increasing and is concave up
isnegative then is decreasing and is concave down
How to find Critical Points and Extrema (max and min) using derivatives
a. Algebraically given equations for
b. Graphically given graphs of
c. Definition of a critical point: is 0 or dne
d. Using the first derivative test for extrema
- Does change from positive to negative around critical point local max
- Does change from negative to positive around critical point local min
e. d. Using the second derivative test for extrema
- If 0 or dne (critical point) and then min (concave up)
- If 0 or dne (critical point) and then max (concave down)
How to find and test for points of inflection
a. Algebraically given equations for
b. Graphically given graphs of
c. Definition of a point of inflection: is 0 or dne, AND changes sign
4. Concept of an Integral
Riemann Sum and Area Approximation
a. Using data tables and graphs
b. Basic Understanding of Sigma Notation
FTC 1 and 2
a. Using notation to show the relationship between a derivative and integral
b. Using graphs with FTC to solve for unknown values.
Solving an integral and interpret what the integral means.
*For Part 2 and 3 look at FRQ practice that use integrals in the context of a story.
5. Integration techniques
Indefinite and definite integration
Separable Differential Equations
Slope Fields
6. Integral Applications
Finding the Area under a graph or between two graphs.
a. Using integrals
b. Using geometric formulas of common shapes
Volumes of Cross Sections
Volumes of Rotations
**********************Not Tested on the Final: Related Rates and Optimization*************************