Download SUMMER SCHOOL MATH I STUDENT SYLLABUS

Pre-Calculus
Course Syllabus
Mr. Tim Wicklund – Room 3
[email protected]
Classroom Phone: 423-6877
Conference Period: 1st Hour (8:05 – 9:09)
General Description: This course is designed to prepare students for college-level mathematical
courses such as Calculus. Topics covered in this class include analytical geometry, linear
algebra, trigonometry, functions, vectors, conic sections, limits, elementary calculus,
sequences and series, and probability. Throughout this course, technology will be used to
explore these topics, as well as find many ways to solve the same problems. Upon
completion of this class, students will have the necessary tools to be successful in
Calculus.
Course Standards:
Course standards consist of state standards and benchmarks for Mathematics in
accordance with the Michigan Curriculum Frameworks (MCF). Standards for each unit
are defined and outlined in the Decatur High School Mathematics Curriculum.
Methods:
This course will be taught primarily through the use of modeling and lots of practice.
The following methods and tools will also be used:
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Assessments:
Lecture
Videos
Cooperative Learning
Recitation
Assessments and evaluations will be based on course material and content. Students may
be evaluated in the following ways:
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The Internet
Document Camera
Student Presentations
Research
Comprehensive Semester Exam
Chapter and Unit Tests:
Multiple Choice
Matching
Constructed Response
Fill in the Blank
Classroom Participation
1
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Quizzes
Section Reviews
Group Projects
Class Presentations
Miscellaneous Assignments or
Projects
Algebra II
Grading:
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Marking Period Grades will be determined as follows:
Tests and Quizzes
Class Assignments
Class Participation
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Resources:
50 %
25%
25 %
Late assignments will be given half credit and will be accepted up until the final
Monday of the marking period. An assignment is considered to be late if it is
turned in after the instructor has collected other students’ assignments.
Extra Credit is available on a case-by-case basis and only after all missing work is
complete.
 Student Text Book: Advanced Mathematical Concepts: Glencoe/McGraw-Hill,
2004. http://www.glencoe.com/sec/math/precalculus/amc_04_index.php/mi
 Assorted Videos
 Alternate resources included in the Algebra II Teacher Materials
 High School Media Center
 Internet Sites including but not limited to the following:
o United Streaming
o ScoPE: An Internet Resource for Teachers
o Acellus
 TI-83/84 Calculator: A calculator of this type is mandatory for use in college-level
classes. It is recommended that each student get their own.
Discipline Code: Discipline is meted out on a case-by-case basis. Normally a warning will be given to a
student exhibiting a negative behavior. The second infraction may result in a lunch
detention in the classroom. The third infraction may result in an after school detention in
the detention room. Any further problems may result in time served in In House
Suspension. Major infractions could result in a snap-suspension and or Out of School
Suspension. A major infraction would also require a meeting with the Principal
Student Expectations:
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Turn in work on time
Participate in class discussion
Respect their classmates
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Respect the teacher
Participate in group projects
Algebra II
Course Outline:
The following topics will be covered in this course. The corresponding Michigan High
School Content Expectation is included.
Chapter 1:
1-1
1-2
1-3
1-4
1-5
1-6
1-7
1-8
Linear Relations and Functions (P1.1, P1.2, P1.3)
Relations and Functions
Composition of Functions
Graphing Linear Equations
Writing Linear Equations
Writing Equations of Parallel and Perpendicular Lines
Modeling Real-World Data with Linear Functions
Piecewise Functions
Graphing Linear Inequalities
Chapter 2:
2-1
2-2
2-3
2-4
2-5
2-6
2-7
Systems of Linear Equations and Inequalities (P7.1, P7.3, P7.5, P7.6, P7.7, P7.8)
Solving Systems of Equations in Two Variables
Solving Systems of Equations in Three Variables
Modeling Real-World Data with Matrices
Transformation Matrices/ Modeling Motion with Matrices
Determinants and Multiplicative Inverses of Matrices
Solving Systems of Linear Inequalities
Linear Programming
Chapter 3:
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
The Nature of Graphs (P1.4, P1.5, P1.6, P1.8)
Symmetry and Coordinate Graphs
Families of Graphs
Graphs of Nonlinear Inequalities
Inverse Functions and Relations
Continuity and End Behavior
Critical Points and Extrema
Graphs of Rational Functions
Direct, Inverse, and Joint Variation
Chapter 4:
4-1
4-2
4-3
4-4
4-5
4-6
4-7
4-8
Polynomial and Rational Functions (P3.1, P3.2, P3.3, P4.1, P4.2, P4.3, P5.1, P5.2, P5.3)
Polynomial Functions
Quadratic Equations
The Remainder and Factor Theorems
The Rational Root Theorem
Locating Zeros of a Polynomial Equation
Rational Equations and Partial Fractions
Radical Equations and Inequalities
Modeling Real-World Data and Polynomial Functions
Chapter 5:
5-1
5-2
5-3
5-4
5-5
5-6
5-7
5-8
The Trigonometric Functions (P6.1)
Angles and Degree Measure
Trigonometric Ratios in Right Triangles
Trigonometric Functions on the Unit Circle
Applying Trigonometric Functions
Solving Right Triangles
The Law of Sines
The Ambiguous Case for the Law of Sines
The Law of Cosines
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Algebra II
Chapter 6:
6-1
6-2
6-3
6-4
6-5
6-6
6-7
6-8
Graphs of Trigonometric Functions (P6.2, P6.3, P6.7)
Angles and Radian Measure
Linear and Angular Velocity
Graphing Sine and Cosine Functions
Amplitude and Period of Sine and Cosine Functions
Translations of Sine and Cosine Functions
Modeling Real-World Data with Sinusoidal Functions
Graphing Other Trigonometric Functions
Trigonometric Inverses and Their Graphs
Chapter 7:
7-1
7-2
7-3
7-4
7-5
7-6
7-7
Trigonometric Identities and Equations (P6.4, P6.5, P6.7, P7.2, P7.4)
Basic Trig Identities
Verifying Trig Identities
Sum and Difference Identities
Double-Angle and Half-Angle Identities
Solving Trig Functions
Normal Form of a Linear Equation
Distance from a Point to a Line
Chapter 8:
8-1
8-2
8-3
8-4
8-5
8-6
8-7
8-8
Vectors and Parametric Equations (P9.3, P9.4, P9.5, P9.6)
Geometric Vectors
Algebraic Vectors
Vectors in Three-Dimensional Space
Perpendicular Vectors
Applications with Vectors
Vectors and Parametric Equations
Modeling Motion Using Parametric Equations
Transformational Matrices in Three-Dimensional Space
Chapter 9:
9-1
9-2
9-3
9-4
9-5
9-6
9-7
9-8
Polar Coordinates and Complex Numbers (P9.1, P9.2)
Polar Coordinates
Graphs of Polar Coordinates
Polar and Rectangular Coordinates
Polar-Form of a Linear Equation
Simplifying Complex Numbers
The Complex Plane and Polar Forma of Complex Numbers
Products and Quotients of Complex Numbers in Polar Form
Powers and Roots of Complex Numbers
Chapter 10:
10-1
10-2
10-3
10-4
10-5
10-6
10-7
10-8
Conics (P9.7, P9.8, P9.9, P9.10)
Introduction to Analytic Geometry
Circles
Ellipses
Hyperbolas
Parabolas
Rectangular and Parametric Forms of Conic Sections
Transformations of Conics
Systems of Second-Degree Equations and Inequalities
Chapter 11: Exponential and Logarithmic Functions (P2.1, P2.2, P2.3, P2.4, P2.5)
11-1 Real Exponents
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Algebra II
11-2
11-3
11-4
11-5
11-6
11-7
Exponential Functions
The Number e
Logarithmic Functions
Common Logarithms
Natural Logarithms
Modeling Real-World Data with Exponential and Logarithmic Functions
Chapter 12:
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
Sequences and Series (P8.1, P8.2, P8.3, P8.4, P8.5, P8.6)
Arithmetic Sequences and Series
Geometric Sequences and Series
Infinite Sequences and Series
Convergent and Divergent Series
Sigma Notation and the nth Term
The Binomial Theorem
Special Sequences and Series
Sequences and Iteration
Mathematical Induction
Chapter 13:
13-1
13-2
13-3
13-4
13-5
13-6
Combinatorics and Probability
Permutations and Combinations
Permutations with Repetitions and Circular Permutations
Probability and Odds
Probabilities and Compound Events
Conditional Probability
The Binomial Theorem and Probability
Chapter 14:
14-1
14-2
14-3
14-4
14-5
Statistics and Data Analysis
The Frequency Distribution
Measures of Central Tendency
Measures of Variability
The Normal Distribution
Sample Sets of Data
Chapter 15:
15-1
15-2
15-3
15-4
Introduction to Calculus (P1.7)
Limits
The Slope of a Curve/ Derivatives and Antiderivatives
Area Under a Curve
The Fundamental Theorem of Calculus
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Algebra II