Below are syllabi for various courses:
PreCalculus 11
PreCalculus 12
Calculus 12
I have the following expectations in all my courses:
Politeness towards other students
Effortful practice in class
Some intellectual curiosity
Honesty during tests
PreCalculus 11
Topics
Absolute Value and Radicals
Absolute Value
Radical Operations
Simplifying Radicals
Adding and Subtracting Radical Expressions
Multiplying and Dividing Radical Expressions
Radical Equations
Rational Expressions
Properties of Rational Expressions
Multiplication and Division of Rational Expressions
Sums and Differences of Rational Expressions
Mixed Operations
Rational Equations
Applications of Rational Equations
Trigonometry
Angles and Their Measure
The Three Trigonometric Functions
Special Angles
Oblique Triangles
Law of Sines
Law of Cosines
Factoring and Functions
Factoring x^2 + bx + c
Factoring ax^2 + bx + c
Absolute Value Functions
Solving Absolute Value Equations
Rational Functions
Reciprocal Functions
Quadratic Functions
Properties of Quadratic Functions
The Standard Form of a Quadratic Function
Finding the Equation of a Parabola
General Form to Standard Form
Vertex of a Parabola
Applications of Quadratic Functions
Quadratic Equations
Solving Quadratic Equations by Factoring
Completing the Square and Square Root Property
The Quadratic Formula
Graphing Calculator and the Discriminant
Applications of Quadratic Equations
Systems of Equations
Graphing Non-Linear Systems of Equations
Solving Non-Linear Systems Algebraically
Graphing Linear Inequalities
Graphing Non-Linear Inequalities in Two Variables
Sequence and Series
Arithmetic Sequences
Arithmetic Series
Geometric Sequences
Geometric Series
Infinite Geometric Series
Applied-Math Computer Labs
Introduction to geogebra.org / Introduction to JavaScript
Interactive Applets using GeoGebra
other specific topics TBD
Random Simulations: or How to Be Approximately Right
Interactive Data Visualizations
Final Project (based on individual studentsâ€™ interests)
Grading
Q1
Q2
Q3
Q4
Projects
15%
20%
15%
30%
20%
PreCalculus 12
Topics
Transformations
Functions and Relations
Arithmetic Combinations of Functions
Composite Functions
Transformations of Graphs
Inverse Functions
Combined Transformations
Polynomials
Polynomials
Graphing Polynomial Functions
Division of Polynomials
The Remainder and Factor Theorems
Polynomial Applications
Radicals and Rational Functions
Radicals
Graphing and Solving Radical Equations
Rational Functions
Graphing Rational Functions
Logarithms
Exponents
Logarithmic Functions and Their Graphs
Properties of Logarithms
Exponential and Logarithmic Equations
Applications of Exponential and Logarithmic Equations
Trigonometry, Part I
Angles and Their Measure
Trigonometric Functions of Acute Angles
Trigonometric Functions - General and Special Angles
Graphing Basic Trigonometric Functions
Applications of Periodic Functions
Trigonometry, Part II
Trigonometric Identities and Equations
Verifying Trigonometric Identities
Trigonometric Equations
Sum and Difference Identities
Double Angle Identities
Combinatorics
Fundamental Counting Principle
Permutations
Combinations
Binomial Theorem
Pathway Problems
Applied-Math Computer Labs
Introduction to geogebra.org / Introduction to JavaScript
Interactive Applets using GeoGebra
other specific topics TBD
Series Approximation / Handling Polynomials
Random Simulations: or How to Be Approximately Right
Interactive Data Visualizations
Final Project (based on individual studentsâ€™ interests)
Grading
Q1
Q2
Q3
Q4
Projects
15%
20%
15%
30%
20%
Calculus 12
Topics
Limits and Rates of Change
One-sided limits
Full (two-sided) limits
Tangent lines
Sequences and Series
Derivatives
Definition
Sum rule and difference rule
Power rule
Product rule
Chain rule
Implicit differentiation
Higher-order derivatives
Applications of Derivatives
Velocity and acceleration
Related-rates problems
Physical settings
Extrema
Monotonicity
Minimum and maximum values (both local and global)
First derivative test
Sketching Curves
Asymptotes
Inflection points and curve concavity/convexity
Second derivative test
Review of Trigonometry & their Derivatives
Review of Exponentials and Logarithms & their Derivatives
Differential Equations
Antidifferentiation
Initial conditions
2nd-order differential equations
Integration
Area calculations
Substitution rule
Integration by parts
Trigonometric substitutions
Partial fractions
Volumes of revolution
Grading
Q1
Q2
Q3
Q4
20%
30%
15%
35%