Download Course Title - obrienprecal

Course: Pre-Calculus
Academic Year: 2012-2013
Faculty Name: Miss O'Brien
Contact Phone Number: 781-834-5050 x47791
Email Address:y'[email protected]
Room Number: 214
Website:
Course Description
Pre-Calculus is designed to prepare students to successfully enter calculus. Using
algebraic, numeric, graphic, and verbal methods, traditional topics of
advanced algebra, conic sections, and trigonometry are taught. Emphasis is
placed on understanding, skills mastery, problem solving, and independent
thought.
Key Prerequisite Knowledge/Skills for Success in this Course
Mastery of fundamental concepts that are essential for students’ mathematical
success are emphasized in Algebra I, II, and Geometry. Students need to
persevere, think critically, and use mathematics to model and solve problems
using: exponents, factoring, rational expressions, radicals, special right triangles,
and linear equations. See website for Review Packet of fundamental
concepts.
Learning Outcomes
Students analyze in increasingly wide range of functions, including polynomial,
trigonometric, logarithmic, rational, exponential, and other functions. Students
will explore and compare key features of these functions through modeling and
applications which includes using technology.
Textbooks & Reading Materials
 Books
Larson, Ron and Hostetler, Robert P.. (08 June, 2005). Precalculus With
Limits: A Graphing Approach. Houghton Mifflin Company.

Websites
Behavior Expectations & Classroom Conduct
Be on time and ready to learn: Tardiness will be treated in accordance to the
student handbook. There may be further consequences for frequent or extreme
tardiness. There will be warm-up activities at the beginning of most classes. You
will be expected to start the work on your own.
Come prepared to work: You are expected to arrive to class on time prepared
with a pencil, text book, notebook, and calculator. Materials will be addressed
below.
Respect your classmates and teacher: Respect and positive attitudes are
essential for an enriched learning environment. Students should raise their hands
when they have something to say, and listen attentively when someone else is
speaking Students should be kind and patient, especially when someone is
confused or makes a mistake. If you need to leave the room please ask me
before you go. Please do not ask to leave the room in the middle of a lesson or
presentation, unless it is an emergency.
Respect your classroom facility: Do not write on or vandalize the furniture in
anyway. There will be no food or drink allowed in the room, except water.
Academic honesty: Always submit your own work, but feel free to discuss
homework and class work with classmates. Copying someone elses work or
cheating is not allowed and will result in a zero on the assignment and
disciplinary action.
Absences/Make ups
If you are absent, you are responsible for any notes, homework, quiz/test you
may have missed. All make up work must be completed in no more than three
school days from the date of your return.
Materials
EVERYDAY you must bring your text book, binder/notebook, calculator, and
pencil. If you forget any of these you will not be allowed to go get them from
your locker.
Grading Policies
Your grade will be computed from your homework, class work, quiz/test, and
project grades.
Homework
You will be given homework every night, with the exception of the nights before
tests.
Homework will never be accepted late.
Homework is scored out of 3 points
3 = complete, all work shown
2 = not complete, some work
1 = not complete, no work
0 = nothing (If you do not have your homework you need to fill
out an excuse form.)
We will always go over homework. It is very important that you correct your
work.
Class work (1-30 points)
Class work scoring will vary with assignment.
Participation and completeness of the assignment is part of the grade.
Quiz/Test (30-100 points)
Quizzes will be given throughout the chapters (about every section).
Quizzes will generally take ½ a block.
There will be pop homework quizzes.
Tests will be given every 3-5 sections.
There will be no homework before a test. It is your responsibility to study for
exams.
Students who are successful in this course are prepared for
the following courses:
Calculus
Additional Comments
I am generally available after school on Tuesdays and Wednesdays. Please see
me to set up a time.
Course Schedule
Week #/
Dates:
Major Topics
Assessment(s)
(Quizzes/Exams)
Semester 1
o
Homework
Classroom work
Quizzes
Tests
o
o
o
Radian and Degree Measure
o Sketching and finding
conterminal (14.1)
o Complementary and
Supplementary angles (14.1)
o Converting degrees to radians
and visa versa (16.1)
o Finding arc length (16.2)
o Finding linear / angular speed
(16.4)
Trig functions: Unit Circle
o The unit circle (16.3)
o Def of trig functions (14.3)
o Evaluating trig functions (14.3,
15.3 and 16.3)
o Period and Domain of sin/cos
(17.1)
o Even and Odd (17.1)
Right Triangle Trigonometry
o Right triangle definitions (SOH
CAH TOA) (15.4)
o Evaluating trig functions in
special right triangles (use
section 4.3 of level 1 text)
o Fundamental Trig identities
(14.4 and 18.1)
o Angel of depression/elevation
(15.4)
Trigonometric Functions of Any
Angle
o Evaluating trig functions
(15.2, 15.3)
o Finding reference angles
(15.2)
o Trig functions of non-acute
angles (15.2)
o Using trigonometric identities
o
o
o
o
o
o
o
(14.4 and use section 4.4 of
level 1 text)
Graph of Sine and Cosine functions
o Using Key points to Sketch a
Sine Curve (17.1)
o Scaling: Vertical and
Horizontal
stretching/shrinking (17.1 and
17.2)
o Finding an equation of a
graph (17.1 and 17.2)
o Finding a trig model (17.1 and
17.2)
Graphs of other Four trig functions
o Sketching the graph of
tangent, cotangent, cosecant,
secant function (17.3 and
17.4)
Applications and Models (15.4 for right
triangles, use section 4.8 of level 1 text
for further examples)
Inverse trig functions
o Def of inverse trig function
(19.1)
o Evaluating inverse trig
functions (19.1)
o Graphing Arcsin/Arccos (19.1)
o Domain and Range of inverse
trig functions ((19.1)
o Compositions of trig functions
(19.1)
Applications and Models
o Solving Right Triangles (15.4)
o Finding an angle of
depression/elevation (15.4)
o Harmonic Motion (Level 1 text
section 4.8)
Using Fundamental Identities
o Fundamental Trig Identities
(18.1)
o Simplifying a trig expression
(18.1)
o Verifying a trig identity (18.2)
o Factoring trig expressions
(19.2)
o Rewriting trig expressions
(18.1)
Verifying Trigonometric Identities
o Verifying trig identities (18.2)
o Converting to sine and cosine
(18.1)
o
o
o
Solving Trigonometric Equations
o Solving trig equations (19.2
and 19.3)
 Collecting like terms
 Extracting square roots
 Factoring
 Rewriting with a single
trig function
 Squaring and
converting to quadratic
type
o Functions with Multiple Angles
(19.3)
o Using inverse functions (19.1)
o Surface area of a Honeycomb
(use level 1 text section 5.3)
Sum and Difference Formula
o Sum and difference formulas
(18.3 and 18.4)
o Evaluating trig functions and
expressions (19.2 and 19.3)
o Applications (19.3)
o Solving a trig equation (19.2
and 19.3)
Law of Sines
o Law of sines (20.1)
 Given two angles and
one side (AAS)
 Given two angles and
one side (ASA)
o Ambiguous Case (SSA) (20.2)
 Single Solution, No
Solution, Two
solutions
o
o
Area of an Oblique Triangle
(20.1 and Heron’s formula in
20.3)
o Applications (20.1 and 20.2)
Law of Cosines
o Law of cosines (20.3)
 Given three sides (SSS)
 Given two sides and
their included angle
(SAS)
o Applications (20.3)
Semester 2
o
o
o
o
o
o
1.5: Combinations of Functions
o Finding the sum and difference
of two functions
o Finding the product and
quotient of two functions
o Forming the composite of
functions
o Finding the domain of a
composite function
o Identifying a composite
function
1.6: Inverse Functions
o Finding the inverse function
o Verifying Inverse Functions
Algebraically
o Verifying Inverse Functions
Graphically
o Testing for One-to-One
Functions
2.3: Real Zeros of Polynomial Functions
o Using Synthetic Division
o Using the Remainder Theorem
o Factoring a Polynomial
o Rational Zero Test with Leading
Coefficient of 1.
o Using the Rational Zero Test
o Finding Real Zeros of a
Polynomial Functions
o Using Descarte’s Rule of Signs
o Finding the zeros of a
Polynomial Function
2.6: Rational Functions and
Asymptotes
o Finding the Domain of a
Rational Function
o Finding the Horizontal and
Vertical Asymptotes
2.7: Graphs of Rational Functions
o Sketching graphs of rational
functions
o Slant Asymptotes
3.1: Exponential Functions and Their
Graphs
o Evaluating exponential
functions
o Graphs of exponential
functions
 Transformations of
Homework
Classroom work
Quizzes
Tests
exponential function
o Natural Base exponential
functions
o Applications
 Compound Interest
 Population Growth
 Decay
o 3.2: Logarithmic Functions and Their
Graphs
o Evaluating logarithms
o Evaluating common logs on
the calculator
o Properties of logs
o Graphs of log functions
 Transformations of log
functions
o Natural Base log functions
o Domain of log functions
o Applications
o 3.3: Properties of Logarithms
o Change of base
o Properties of logs
 Expanding logs
 Condensing logs
o 3.4: Solving Exponential and
Logarithmic Equations
o Solving exponential and log
equations using 1-to-1
property
o Solving exponential and log
equations using the inverse
properties
o Applications
o 3.5: Exponential and Logarithmic
Models
o Exponential growth and decay
o Carbon Dating
o Gaussian Models
o Logistic Growth
o Logarithmic Models
o 8.5: The Binomial Theorem
o Binomial coefficients
o Binomial Theorem
o Pascal’s Triangle
o Binomial Expansion
Complex Numbers
o 2.4 Complex Numbers
o Equality of
o
o
o
complex numbers
o Operations with
complex numbers
o Complex
conjugates
o Plotting complex
numbers
2.5 The Fundamental
Theorem of Algebra
o The fundamental
theorem of algebra
o Linear
Factorization
o Complex zeros
o Writing a
polynomial given
the zeros
o Factoring
polynomials
9.6 Polar Coordinates
o Plotting points in
the polar
coordinate system
o Multiple
representation of
points
o Coordinate
conversion (polar <
--> rectangular)
o Equation
conversion (polar <
--> rectangular)
6.5 Trigonometric Form of
a Complex Number
o Absolute value of a
complex number
o Trigonometric
form of a complex
number
o Standard form
o Multiplication and
division of complex
numbers
o DeMoivre’s
Theorem
o Powers and Roots
of complex
numbers
Vector/Matrix
o 6.3 Vectors in the Plane
o Equivalent directed
line segments
o Component form
of a vector
o Vector operations
o Properties of
vector addition
and scalar
multiplication
o Unit vectors
o Direction angles
o Applications
o 7.4 Matrices and Systems
of Equations
o Definition of
matrix
o Order of matrices
o Writing matrices
o Elementary row
operations
o Gaussian
Elimination with
back- substitution
o Row-Echelon Form
o Reduced RowEchelon Form
o Guass-Jordan
Elimination
o 7.5 Operations with
Matrices
o Representation of
matrices
o Matrix addition
and scalar
multiplication
o Matrix
multiplication and
their properties
o Solving a matrix
equation
o Identity matrix
o Solving a system of
linear equations
o 7.6 The Inverse of a Square
Matrix
o
o
o
Inverse of a square
matrix
o Finding inverse
matrices
o Systems of linear
equations (unique
solutions)
7.7 The Determinate of a
Square Matrix
o Determinant of a
2x2 matrix
o Minors and
cofactors of a
matrix
o Determinant of a
square matrix
10.3 The Cross Product of
Two Vectors
o Cross product of
two vectors is
space
o Finding cross
products
o Algebraic
properties of the
cross product
o Geometric
properties of the
cross product
o Triple scalar
product
o Geometric
property of triple
scalar product
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