Novato Unified School District
Course Description
PRE-CALCULUS
Course Title
Pre Calculus
School
Novato High School, San Marin High School,
Marin Oaks High School, NOVA
District
Novato Unified School District
City
Novato, California 94945
Name of School Contact
Curriculum and Instruction
Phone: 415-897-4269
Fax: 415-892-1622
E-mail:
Department or Discipline
History/Social Studies
English/Language Arts
Mathematics
Laboratory Science
Language other than English
Visual & Performing Arts (for 2003)
College Preparatory Elective:
Subject Area: __________________
Grade Level(s) for which course is
intended
10, 11, 12
Length of Course
Semester
Year
courseoutline@nusd.org
Other
Unit Value
0.5 (half year equivalent)
1.0 (one year equivalent)
2.0 (two year equivalent)
Other: _____________________
Date of School Board Approval
Seeking “Honors” distinction?
October 15, 2002
Yes
No
Was this course previously approved by UC?
Yes
No
If so, in what year?
Under what course title?
Pre-Requisites
Algebra 2 with a grade of “A’ or “B” (“C” with recommendation).
Adopted Textbook
Pre-Calculus with Limits, Houghton Mifflin
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Novato Unified School District
Course Description
PRE-CALCULUS
Brief Course Description
Students in this course are preparing for the world of calculus. In order to become a student of
calculus, pupils must understand coordinate geometry, graphing techniques, circular and
trigonometric functions. Students must be able to use functions such as exponential and
logarithmic, and polynomial and rational. They must understand sequences and series, vectors,
limit functions, and be ready for an introduction to differential calculus.
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Novato Unified School District
Course Description
PRE-CALCULUS
COURSE CONTENT
A.
Course goals and/or major student outcomes
Provide the student with the trigonometric, geometric, and algebraic techniques
needed for the preparation of the study of calculus.
Provide the student with an understanding of the main functions used in the study
of calculus, emphasize these functions from a graphical stand point, making
extensive use of a graphing utility.
B.
Course Objectives-specific student learning objectives
Objectives
Standards
Students will graph polynomial functions with an
emphasis on the zeros
Math Analysis 4.0
Students will graph rational functions with an
emphasis on asymptotic behavior
Math Analysis 6.0
Students will use exponential and logarithmic
functions to analyze exponential growth models
Algebra 2 12.0
Students will engage in an intensive study of the trig
functions, gaining a facility with these functions as
well as the ability to prove basic identities regarding
them
Trig-2.0, 4.0, 8.0, 9.0, 10.0,
11.0, 13.0, 14.0, 19.0
Students will be familiar with conic sections, both
analytically and geometrically
Math Analysis 5.1, 5.2
Students will find the limit of certain sequences and
find limits for various functions
Math Analysis 8.0
Students will use vectors and vector diagrams to solve
various physical problems
Linear algebra 7.0, 12.0,
Math Analysis 1.0
Students will apply polar coordinates in the plane and
graph polar equations
Math Analysis 1.0
Trig 15.0, 16.0
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Novato Unified School District
Course Description
PRE-CALCULUS
C.
Course Outline
Topics/Units/Themes
Object 1
Key Activities/Assignments
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Object 2
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Object 3
Object 4
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Object 5
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Object 6
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Graph nth degree polynomial functions, understanding
the behavior as the variable approaches positive or
negative infinity ± ∞
Approximate the zeros of polynomial functions
Apply the fundamental theorem of algebra, the factor
theorem, and the rational root test in the factoring and
finding of the zeros of polynomial functions
Find complex zeros and understand that they appear as
conjugate pairs
Graph rational functions, understanding how to identify
vertical asymptotic behavior
Graph rational functions, understanding how to identify
horizontal asymptotic behavior
Study exponential growth models
Log function as the inverse of the exponential function
Solve exponential and logarithmic equations
Understand the role of the irrational number e in
exponential growth models
Natural logarithms
Circular and right triangle definitions of the six
trigonometric-circular functions
Graphs of 6 trig functions
Graphs of functions of the form y =A sin B(x-c) + D
Proofs of trigonometric identities
Sum and difference formulas
Multiple-angle and product-sum formulas
Solving problems involving triangles using the law of
sines and the law of cosines
Know the geometric definitions of the four conic
sections
Derive the second degree equation associated with each
conic section
Take a quadratic equation in two variables and put it in
standard form, identifying the type of conic section the
equation represents
Know and work with the formulas associated with
arithmetic and geometric sequences
Work with summation notation
Binomial theorem
Limit of a sequence as n approaches infinity
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Novato Unified School District
Course Description
PRE-CALCULUS
Object 7
Objective 8
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Vector quantities-magnitude and direction
Vectors as arrows and as ordered pairs
Vector addition and scalar multiplication
Vector diagrams
Dot product
Plotting points in polar coordinates
Graphing functions given in polar form
Translating from polar form to rectangular form and
visa-versa
D.
Texts and supplemental instructional materials
Pre-Calculus with Limits—Houghton Mifflin
E.
Instructional methods and strategies
 Lecture
 Teacher facilitated discussion
 Graphical analysis using a graphing calculator (example-TI83)
 Student practice problems
F.
Assessment methods and/or tools
 Teacher designed tests
 Publisher tests
 Portfolio/notebook
 Final semester exams
 Homework
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