PREREQUISITE: MAT105-Technical Mathematics I, equivalent, or placement; placement into ENG101 and college-level reading, or completion of ENG101S and RDG095

COREQUISITE: None

REQUIRED ACCESS CODE:

MyMathLab with Pearson eText - Standalone Access Card – for Basic Technical Mathematics, 11th/E, Pearson; Washington & Evans.

ISBN# 9780134764702

The MyMathLab (MML) card provides you access to the MML online learning system, which includes an e-text, video lectures, practice problems, and online homework assignments. A hardcopy of the textbook is not required for this course.

Students who purchased an MML access code for CCC’s MAT105 course do not need to purchase a new access code for this course. 

REQUIRED MATERIALS:

 A graphing calculator (the TI-83, TI-83 Plus, or TI-84 Plus)

COURSE OBJECTIVES:

As the result of instructional activities, students will be able to:

1. Simplify radical expressions
2. Convert back and forth between rational exponents and radical notation
3. Perform operations on radical expressions
4. Solve equations involving radical expressions
5. Solve linear inequalities
6. Solve equations and inequalities involving absolute value
7. Solve quadratic and rational inequalities
8. Solve problems involving ratio and proportion
9. Solve problems involving direct, inverse, and joint variation
10. Demonstrate the use of common logarithms and natural logarithms
11. Solve exponential and logarithmic equations
12. Graph exponential and power functions using log-log and semi-log paper
13. Convert back and forth between degrees and radians
14. Evaluate trigonometric functions and their inverses for angles measured in degrees and radians
15. Solve oblique triangles using the Law of Sines and/or Law of Cosines
16. Graphically add vectors
17. Resolve vectors into vertical and horizontal components
18. Solve vector problems using rectangular and polar forms
19. Sketch and interpret the graphs of sinusoidal, exponential, and logarithmic functions
20. Convert among rectangular, polar, exponential form of complex numbers
21. Perform the fundamental operations (addition, subtraction, multiplication, division) using the rectangular form of complex numbers
22. Perform multiplication and division of complex numbers in polar and exponential form
23. Using DeMoivre’s Theorem, find powers and roots of complex numbers
24. (Optional) Find an equation/model for data approximated by exponential, logarithmic, or trigonometric functions
25. (Optional) Summarize and interpret data using frequency distribution, measures of central tendency, and measures of dispersion
26. (Optional) Apply process control and quality assurance
27. (Optional, time permitting) Develop a brief intuitive feel for the concepts of limit, derivative (instantaneous rate of change), and integral (area under a curve)

SUNY GENERAL EDUCATION LEARNING OUTCOMES:

Students will demonstrate the ability to:

1. interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics;
2. represent mathematical information symbolically, visually, numerically and verbally;
3. use arithmetical, algebraic, geometric and statistical methods to solve problems;
4. estimate and check mathematical results for reasonableness; and
5. recognize the limits of mathematical and statistical methods

GENERAL TOPICS OUTLINE:

1. Right Triangle Trigonometry Review (textbook chapter 4)- including a review of the definitions of the trigonometric functions and applications of right triangles
2. Trigonometric Functions of Any Angle (textbook chapter 8)- including definitions of trig functions, radian measure, applications
3. Vectors and Oblique Triangles (textbook chapter 9)- including graphical addition of vectors, resolving vectors into vertical and horizontal components, applications of vectors, oblique triangles, law of sines, law of cosines, applications
4. Graphs of Trigonometric Functions (textbook chapter 10)- including graphing basic sine and cosine functions, finding amplitude, period, phase shifts and graphs of sinusoidal functions y = a sin (bx + c) and y = a cos (bx + c), (optional) curve fitting with data approximated by trigonometric functions
5. Exponents and Radicals (textbook chapter 11)- including integral exponents, rational exponents, simplification of radicals, basic operations with radicals, solving equations with radicals
6. Complex Numbers (textbook chapter 12)- including a review of basic definitions, operations on complex numbers in rectangular form, polar and exponential form of complex numbers, multiplication and division in polar and exponential form, powers and roots using DeMoivre’s Theorem
7. Exponential and Logarithmic Functions (textbook chapter 13)- including exponential functions, logarithmic functions, common and natural logarithms, properties of logarithms, solving exponential and logarithmic equations, (optional) curve fitting with data approximated by exponential and logarithmic functions, graphing on log and semi-log paper
8. Inequalities and Absolute Value (textbook chapter 17)- including solving linear inequalities, solving equations and inequalities involving absolute value, solving quadratic and rational inequalities
9. Ratio, Proportion and Variation (textbook chapter 18)- including solving problems involving ratio and proportion, finding equations involving direct, inverse, and joint variation, solving applications involving variation
10. Statistics (Optional) (textbook chapter 22)- including definitions and terminology, frequency distributions, measures of central tendency, measures of dispersion, the normal distribution, standard error, fitting curves to data, Statistical Process Control
11. Intuitive Approach to Calculus (Optional) (supplemental materials provided by instructor)- including limits, average rate of change, instantaneous rate of change, area under a curve

The Math Department at CCC recommends that you review the following prerequisite topics to prepare for MAT205:

1. Operations with real numbers, including fractions and decimals
   Significant digits and unit conversions
2. Applying basic geometric formulas
3. Factoring polynomials
4. Simplifying expressions involving algebraic fractions, complex fractions, and integral exponents
5. Solving linear and quadratic equations
6. Families of functions and transformations
7. Right triangle trigonometry.
   (If you have the textbook listed above, you should review chapters 1- 7.) 

You can do this from home by selecting any of the aforementioned topics on the math-tutorial websites listed below; there you will find mini-lectures, worked problems, practice problems and helpful tips.

Multiplying and Dividing Fractions
Adding and Subtracting Fractions
Order of Operations
Significant Digits & Rounding
Unit Conversions
Metric & US System Conversions
Metric Conversions
Area & Perimeter
Volume & Surface Area
Solving Linear Equations
Factoring
Factoring Polynomials
Special Factoring Formulas
Solving Quadratic Equations
Quadratic Formula
Solving Quadratic Equations
Simplifying Expressions Involving Algebraic Fractions
Multiplying Expressions Involving Algebraic Fractions
Adding & Subtracting Expressions Involving Algebraic Fractions
Complex Fractions
Simplifying Expressions With Integral Exponents
Functions
Function Transformations
Pythagorean Theorem
Right Triangle Trigonometry

Feel free to contact a member of the Math Department or the Math Department Chair.