Calculus
Syllabus First Semester
C: CK – 12 Calculus
T: Thompson, Calculus Made Easy
K: Kutasoftware Worksheets
Date
31 JUL
3 AUG
5 AUG
7 AUG
10 AUG
12 AUG
14 AUG
17 AUG
19 AUG
24 AUG
26 AUG
28 AUG
Title
Objective
Course Introduction
Readings
Homework
T: 1 – 9, T: 38
Equations and Graphs
Properties and solutions of graphs.
Relations and Functions
Function review.
Models and Data
Fit data to function models.
C: 1 – 8
Write a 200 word
paragraph reflecting on
what it means to be a
mathematical fool.
C: 1.1 1 - 10
C: 12 – 25, T: 10 – 17
C: 1.2 1 - 10
C: 28 – 32
C: 1.3 1 – 6
The Calculus
Introduction to differential calculus.
C: 39 – 44
C: 1.3 7 – 10
C: 1.4 1 – 4
Finding Limits
Find limits mathematically and graphically.
C: 47 – 51, T: 18 – 29
C: 1.4 5 – 8
C: 1.5 1 – 5
Evaluating Limits
Find limits for basic, polynomial, rational, radical,
composite and trigonometric functions.
C: 54 – 59,
C: 1.5 6 – 10
C: 1.6 1 – 5
Continuity
Continuity of functions.
Understand the properties of continuous functions.
C: 60 – 66
C: 1.6 6 – 10
C: 1.7 1 – 6
31 AUG
2 SEP
Indefinite Limits
Find and analyze infinite limits of functions.
C: 69 – 71
C: 1.7 7 – 10
C: 1.8 1 – 7
Test
C: 74 – 81, T: 103 – 115
C: 1.8 8 – 11
Study for test
No HW
C: 2.1 1 – 6
C: 82 – 87, T: 30 – 34
K: Tangent lines
C: 2.2 1 – 9
T: 41 – 44
C: 88 – 93, T: 45 – 50
K: Derivative at a value
C: 2.3 1 – 13
T: 51 – 64
C: 95 – 98, T: 175 – 183
T: Page 58 1 – 10
C: 2.4
C: 99 – 102 T: 94 – 101
T: Page 183 1 – 15
C: 2.5
C: 104 – 108
T: Page 100 1 – 9
Page 101 1 – 3
C: 2.6
C: 110 – 116
K: Implicit differentiation
C: 2.7
4 SEP
9 SEP
11 SEP
14 SEP
16 SEP
18 SEP
21 SEP
23 SEP
25 SEP
28 SEP
30 SEP
Test on Functions, Limits, Continuity
Tangent Lines and Rates of Change
Understand that slope is the tangent line of a graph.
Understand instantaneous rate of change.
The Derivative
Understand the derivative of a function of slope.
Understand the derivative as rate of change.
Techniques of Differentiation
Use various techniques to find derivatives of functions.
Derivatives of Trigonometric Functions
Compute derivatives of trigonometric functions.
The Chain Rule
Know the chain rule and its proof.
Use the chain rule to differentiate composite functions.
2 OCT
14 OCT
16 OCT
19 OCT
21 OCT
Implicit Differentiation
Find derivatives using implicit differentiation.
Newton’s Method
Approximate a function by method of linearization.
Newton’s Method for approximating roots of a function.
K: Newton’s Method
Study for test
23 OCT
26 OCT
28 OCT
30 OCT
2 NOV
4 NOV
6 NOV
9 NOV
13 NOV
16 NOV
18 NOV
20 NOV
23 NOV
Test on Derivatives
Related Rates
Solve problems that involve related rates.
Test
C: 119 – 123, T: 83 – 91
No HW
C: 3.1
Mean Value Theorem
Solve problems that involve extrema.
Study Rolle’s Theorem.
Use the Mean Value Theorem to solve problems.
Maxima and Minima
Find the local maxima and minima of functions.
Find the maximum volume of a given shape.
First Derivative Test
Find intervals where a function is increasing or
decreasing.
Apply the first derivative test to find extrema.
C: 125 – 128
T: Page 91 1 – 10
C: 3.2
T: 116 – 130
T: Page 130 1 – 11
C: 131 – 134
C: 3.3 1 – 6
Second Derivative Test
Find intervals where a function is concave upward or
downwards.
Apply the second derivative test to determine
concavity.
C: 137 – 140
C: 3.3 7 – 10
C: 3.4 1 – 5
Limits at Infinity
Examine end behavior of functions.
Determine Horizontal Asymptotes.
Apply L’Hopital’s Rule to find limits.
C: 142 – 146
C: 3.4 6 – 10
C: 3.5
C: 147 – 153
K: L’Hopital’s Rule
C: 3.6
Analyzing the Graph of a Function
Summarize the properties of a function.
Apply First and Second Derivatives to sketch graphs.
K: Curve Sketching
25 NOV
30 NOV
2 DEC
Optimization
Use First and Second Derivatives to find absolute
maxima and minima.
Use First and Second Derivatives to solve related
rates.
C: 157 – 161
C: 3.7
Approximation Errors
Extend the Mean Value Theorem to make linear and
quadratic approximations.
Analyze errors in linear and quadratic approximations.
C: 163 – 167
K: Optimization
C: 3.8
4 DEC
7 DEC
9 DEC
Test Review
Review Applications of Derivatives
Test on Applications of Derivatives
11 DEC
14 DEC
16 DEC
Semester Final Review
Semester Final Review
Semester Final Exam
Grading Policy:
Tests
Quizzes
Homework
Notebook
50%
25%
15%
10%
Semester Grading Quarter 1
Quarter 2
Final Exam
35%
35%
30%
Review Applications of
Derivatives
Study for Test
Test
Begin reviewing notes
and homework for
semester final
Study for semester final
Study for semester final