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, 
Onetoone 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 4^{th}
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 7^{th} Edition Larson, Hostetler, Edwards (Houghton Mifflin) 2002
Required Supplement(s): TI83 or TI84 graphing calculator or comparable
graphing calculator (NCTM Technology Standard).
Course Objectives: Students will develop problemsolving
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
derivative.
Students will:
• Apply a graphical approach to problem solving. (NCTM Representation
Standard)
• Investigate the nature of graphs. (NCTM Geometry Standard)
• Perform operations with logarithmic and exponential equations. (NYS Algebra
Strands)
• Develop curvesketching 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 Transformations 
Week 7  Quadratic Functions, Parabolas, and Problem Solving 
Week 8

Algebra of Functions Composite Functions OnetoOne 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 DoubleAngle 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 Vectors 
Week 19  20 
Review Midterm 
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

Continuity OneSided 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 