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
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 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 |
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Week 2 |
Properties of Exponents, Logarithms Solving Exponential and Logarithmic Equations |
|
Week 3 |
Graphs of Logarithms Models for Growth and Decay |
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Week 4 |
Complex Numbers Solving Equations with Complex Numbers |
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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 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 |
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Week 16 |
Inverse Trig Functions Domain, Range of Inverse Trig Functions |
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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 |
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Week 26
|
Continuity One-Sided Limits Infinite Limits |
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Week 27 |
Trigonometric Limits Squeeze Theorem |
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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 |
