This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ree basic trig functions
by hand
Identify and apply frequently used
identities, including reciprocal
functions and Pythagorean
relationships.
Utilize all associated terminology; i.e.
amplitude, period
Know the exact values of critical
points of each graph
Identify the significance of each
coefficient of the following general
function: D + A f(Bx + C)
Describe the transformations as a
vertical or horizontal stretch or shift
Sketch various transformations of
common functions NJ CCCS
4.1
4.2
4.3
4.5
4.1
4.2
4.3
4.5
4.1
4.2
4.3 Strands &
Indicators
A,B,C
A1,A3,C,D
A,B1,B2,B4,
C,D
B,C,D,E,F
A,B,C
A1,A3,C,D
A,B1,B2,B4,
C,D
B,C,D,E,F Suggested
Timeframe
(in blocks)
1 2 2 4.5 A,B,C
A1,A3,C,D
A,B1,B2,B4,
C,D
B,C,D,E,F 4.1
4.2
4.3
4.5 A,B,C)
A1,A3,C,D
A,B,C,D
B,C,D,E,F 1 UNIT 2 – Limits
Course Objective(s)
Define “limit” graphically,
analytically, and intuitively Student Objectives
• •
•
•
Evaluate limits algebraically •
•
•
• Explain the concept of a limit in nonmathematical terms as well as by the
formal definition: intended height of a
function, a value that can be reached
or is approached, etc.
Recall domain and range
Recognize when a limit exists or does
not exist when illustrated on a
coordinate plane
Identify lefthand versus righthand
limits
Apply properties of limits including
rules for constants, rational functions,
products and compositions
Evaluate a limit by substitution
Apply further methods of evaluation,
such as factoring, when substitution
results in “0/0”
Identify “special” limits and functions
with specific properties or ones that
result in an “exception to the rule” NJ CCCS Strands &
Indicators 4.1
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D,E,F 4.1
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D,E,F Suggested
Timeframe
(in blocks)
2 2 Course Objective(s)
Discuss characteristics of
continuous functions Student Objectives
•
• Interpret limits in terms of
discontinuities •
•
• Apply methods of evaluating
limits to remove a
discontinuity • Demonstrate the
Intermediate Value Theorem • *Optional (Calculus BC
topic)
Introduce the concept of the
derivative and apply
L’Hopital’s Rule to
evaluating limits • • Identify all types of discontinuities:
asymptotes, holes, jumps, breaks, etc.
Examine functions with
discontinuities both algebraically and
graphically
Examine limits that produce
horizontal and vertical asymptotes
Recognize when a hole is present in a
function both graphically and
algebraically
Analyze the discussion over limits
that “do not exist” versus “approach
infinity”
Recognize “holes” as a removable
discontinuity
Apply algebraic manipulation to
create an “extended function” to
create a piecewise function
Describe the Intermediate Value
Theorem and mathematical and nonmathematical terms
Use the algebraic form of the
derivative to simplify rational
functions before evaluating the limit NJ CCCS Strands &
Indicators Suggested
Timeframe
(in blocks)
1 4.1
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D,E,F 4.1
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D,E,F 2 4.1
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D,E,F 1 4.1
4.3
4.5
4.1
4.3
4.5 A,B,C
A,B,C,D
A,B,C,D,E,F
A,B,C
A,B,C,D
A,B,C,D,E,F ½
1 UNIT 3 – Derivatives
Course Objective(s)
Define “derivative” intuitively
and analytically while
presenting all associated
terminology and notation Student Objectives
• •
•
• •
Illustrate the definition of
“derivative” graphically • •
• Explain the concept of a
derivative as the slope of the line
tange...
View
Full
Document
This note was uploaded on 03/12/2010 for the course CALCULUS 1561234586 taught by Professor Zalla during the Spring '10 term at Air Force Institute of Technology, Ohio.
 Spring '10
 Zalla
 Calculus, AP Calculus

Click to edit the document details