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Course Curriculum and Syllabus for Mathematics

Course Description:
This course provides the numerical and graphical foundation for a college
calculus. An outline of the topics includes:

Relations and Functions,
Domain, Range, interval notation,
Complex Numbers, Vectors
The Nature of Graphs,
Trigonometric Graphs,
Rational functions,
Limits, Continuity of functions,
One-to-one and Inverse Functions,
Properties of logarithms and exponents,
Amplitude, Period, and Phase shift,
Graphs of Inverses,
Vertical and horizontal asymptotes,
The First Derivative
Rational, radical expressions and equations.

Prerequisites: Three years of NYS regent’s Mathematics (or equivalent high
school Mathematics).

Required Text(s): PRECALCULUS WITH LIMITS – A graphing approach 4th
Edition Larson, Hostetler, Edwards (McDougal Littel),2005

Supplemental Text(s): Intermediate Algebra with Applications 6th Edition
Aufmann, Barker, Lockwood (Houghton Mifflin) 2004, Calculus of a Single
Variable 7th Edition Larson, Hostetler, Edwards (Houghton Mifflin) 2002

Required Supplement(s): TI-83 or TI-84 graphing calculator or comparable
graphing calculator (NCTM Technology Standard).

Course Objectives: Students will develop problem-solving techniques using
equations, functions, and graphs. Students will perform operations including
logarithmic and exponential properties, and analyze graphs of various functions.
Students will also find vertical and horizontal asymptotes of functions, and
investigate limits and continuity. Students will be introduced to the first

Students will:

• Apply a graphical approach to problem solving. (NCTM Representation

• Investigate the nature of graphs. (NCTM Geometry Standard)

• Perform operations with logarithmic and exponential equations. (NYS Algebra

• Develop curve-sketching techniques. (NCTM Geometry Standard)

• Identify areas of discontinuity caused by holes, asymptotes, gaps and jumps.
(NYS Representation Strands)

• Be introduced to limits, continuity, and the first derivative.

Attendance Policy: Attendance is required. Students are responsible for missed
class work, notes, and assignments.

Grading Scale: Tests: 45%, Quizzes: 30%, Homework and class work: 25%.
Final Grade Determined by (include percentages): The 4 – 10 week marking
periods are averaged and weighted 75% and the final exam is 25%.

Week 1 Real Number Properties
Week 2
Properties of Exponents, Logarithms
Solving Exponential and Logarithmic Equations
Week 3
Graphs of Logarithms
Models for Growth and Decay
Week 4
Complex Numbers
Solving Equations with Complex Numbers
Week 5
Relations and Functions
Domain and Range
Week 6


Graphs of Functions, Analyzing Graphs of Functions
Horizontal, Vertical shifts, Reflecting and Stretching Graphs
Week 7 Quadratic Functions, Parabolas, and Problem Solving
Week 8


Algebra of Functions
Composite Functions
One-to-One and Inverse Functions
Week 9 Mathematical Modeling
Week 10 Bernoulli’s Theorem
Binomial Theorem, Binomial Coefficients
Week 11 – 12


Trigonometric Functions
Angles and their measure
Radian and Degree Measure
Right Triangle Trigonometry
Week 13
Using Trig Identities
Verifying Trig Identities
Week 14
Sum, Difference, and Double-Angle Identities
Solving Trig Equations
Week 15
Graphs of Trig Functions
Amplitude, Period, and Phase Shift
Week 16
Inverse Trig Functions
Domain, Range of Inverse Trig Functions
Week 17
Right Triangle Trig
Solving Inverse Trig Equations
Week 18
Trigonometry and Complex Numbers
Week 19 - 20
Week 21


Polynomial Functions
Locating Zeroes of Functions
Synthetic Division
Week 22 - 23
Rational Functions
Vertical Asymptotes, holes in functions
Week 24 - 25


Limits and Discontinuity
Finding Limits Graphically
Finding Limits Numerically
Week 26


One-Sided Limits
Infinite Limits
Week 27
Trigonometric Limits
Squeeze Theorem
Week 28


Average Rate of Change
Tangent Line Problem
Limit Definition of the Derivative
Week 29 - 30


Differentiation Rules
Sum and Difference, Constant Multiple
Product Rule
Week 31 - 32
Quotient Rule
Chain Rule
Week 33 Trig Derivatives
Week 34 Implicit Differentiation
Week 35
Extrema on an Interval
Absolute extrema
Week 36 Local Extrema
Week 37 Optimization Problems
Week 38 Review
Week 39 Final