Acc. Precalculus Syllabus
Texts
Precalculus (1st semester and part of 2nd)
Precalculus with Limits: A Graphing Approach (3rd edition) Larson, Hostetler, and Edwards.
Calculus (most of 2nd semester)
Calculus: Concepts and Contexts (2nd edition) James Stewart
Sequence and Content
Quarter 1
Trigonometric Functions (Chapter 4)
Radian and Degree Measure
Trigonometric Functions: The Unit Circle
Right Triangle Trigonometry
Trigonometric Functions of Any Angle
Graphs of the Six Trigonometric Functions
Inverse Trigonometric Functions
Applications and Models
Analytic Trigonometry (Chapter 5)
Using Fundamental Identities
Verifying Trigonometric Identities
Solving Trigonometric Equations
Multiple-Angle and Product-Sum Formulas
Additional Topics in Trigonometry (Chapter 6)
Law of Sines
Law of Cosines
Vectors in the Plane
Vectors and Dot Products
Trigonometric Form of a Complex Number
Quarter 2
Topics in Analytic Geometry (Chapter 10)
Review of Parabolas, Circles, Ellipses, and Hyperbolas
Parametric Equations
Polar Coordinates
Graphs of Polar Equations
Polar Equations of Conics
Analytic Geometry in Three Dimensions (Chapter 11)
3D Rectangular Coordinates
Vectors in Space
Cross Product of Vectors
Lines and Planes in Space
Surfaces (not in text)
Cylindrical and Spherical Coordinates (not in text)
Quarter 3
Topics in Problem Solving
Sequences and Series
Logarithms
Inequalities
Rational Functions
Probability and Combinatorics
Limits and Derivatives (Chapter 2)
The Limit of a Function
Techniques for Calculating Limits
Continuity
Limits involving Infinity
Tangents, Velocities, and Other Rates of Change
The Derivative
Relationships between f and f'
Linear Approximation
Quarter 4
Differentiation (Chapter 3)
Derivatives of Polynomials and Exponential Functions
The Product and Quotient Rules
Derivatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
The Chain Rule
Implicit Differentiation
Derivatives of Logarithmic Functions
Linear Approximations and Differentials
Applications of Derivatives (Chapter 4)
Related Rates
Maximum and Minimum Values
Derivatives and the Shapes of Curves
Indeterminate Forms and l'Hospital's Rule
Optimization Problems
Newton's Method
Antiderivatives
Materials
A graphing calculator is required for this course. No particular model is required, but theTI-89 and/or TI-83 will be used for demonstrations.
It is advisable to have a notebook in which to keep homework assignments, class notes, handouts, and returned quizzes.
A pencil is the preferred writing instrument. You may take class notes and do homework with an instrument of your choosing, but it is expected that you will do all tests and quizzes in pencil.
Classwork & Homework
In order to master most mathematical concepts or processes, practice is required. Homework is assigned almost every night to give you opportunities to practice. You should do the homework with the idea of engaging the concepts and doing the assignment well, not just to get it done. You should keep your homework and class notes in a notebook of some kind. Organization is one of the keys to success for a student.
You will be divided into groups, and your first task each day is to check homework within your group. We will discuss any problems that cannot be done by anyone in a group. While you are checking your homework within your group, I will visit each group to see that you have done your work. Each time you haven't completed your assignment, a zero (0) will be recorded. Beginning with the third zero and for every zero thereafter, one (1) point will be deducted from your quarter average.
At times, I may take up your homework and grade it. I sometimes take a grade on your homework by giving a short quiz asking you to copy your solutions to three or four problems from the assignment.
Grading
Daily work and major tests are factors used in computing a grade for each quarter. Class work, homework, quizzes, and other types of daily (or short term) activities are used to determine the daily average for the quarter. Two to four major tests will be given during the quarter, and each will weigh equally in determining a test average for the quarter. The quarter grade is computed using the formula:
Qtr Grade = (2/3)*(test average) + (1/3)*(daily average)
Students are required to take a comprehensive examination at the end of each semester. The semester grade is computed from the quarter grades and the examination grade using the formula:
Semester = 0.375*Qtr1 + 0.375*Qtr2 + 0.25*Exam
