# Mathematics and Statistics

## What is Mathematics and Statistics?

**Students are the heart of our mission. **

We promote an inclusive, student-centered learning community. We also provide open access to excellence in teaching and learning.

Mathematics and Statistics offer you a broad range of courses. Each course meets your varied needs in pursuit of your academic goals.

Courses range from basic arithmetic to college algebra, and include:

- Contemporary Mathematics
- Geometry
- Trigonometry
- Elementary Calculus
- Calculus

- Finite Mathematics
- Mathematics for Business
- Applied Mathematics
- Statistics

### Program Contact

**Jennifer Pevley**

Mathematics and Statistics Program Coordinator

Danville Campus 111-J

(859) 246-6872

jennifer.pevley@kctcs.edu

Contact Us (new window)

### Our Faculty

Mathematics and Statistics is home to many full-time and adjunct faculty members. Our dedicated educators & technical leaders have a genuine interest in helping you reach your full potential. We're committed to teaching in a way that is easy for students to understand. Helping students achieve educational growth & success is a top priority for us.

Our faculty go above and beyond to help students succeed. Instructors are not only available to students in the classroom. They're available for extra help, such as meeting one-on-one during office hours. They also help with advising during registration periods. We'll show unparalleled dedication to you.

We care about the success of our students and will do whatever it takes to help them achieve!

### Science to Success Scholarship

**The Science to Success Scholarship** awards $10,000 per year to eligible students for two years maximum.

To learn more about eligibility, requirements, and to apply, please visit the scholarship webpage (new window).

### Additional Information

**This form is for students who are not able to self-enroll in BCTC Mathematics or Statistics
courses in Peoplesoft.**

To prevent incidental drop for non-payment, requests placed on or immediately following payment deadlines (such as the Friday before classes start) will be processed in the order received once drops for non-payment are complete.

**This form cannot be used to switch to a different section of the same course.**

Drop backs are intended for students who are currently enrolled in one of the following math courses: MAT 011, MAT 075, MAT 085, MAT 150, MAT 150/100, MAT 171, MAT 170, MA 111, or MAT 175 and would like to drop back to a lower level course. Please see the Math Drop-back Policy for more information.

**Proctor Information**

The Mathematics and Statistics Division at Bluegrass Community and Technical College requires that students take proctored midterm or final exams. A proctor is a person, approved by the course instructor, who verifies the identification of students and serves as a monitor while the student takes the exam.

**To schedule your proctored exam,** please visit the BCTC Testing Center.

**Keep Calm and Get a Tutor!**

## What are my Career Choices?

Through this program, students acquire the ability to think logically and abstractly, as well as develop the problem-solving and computational skill necessary in all fields of study. Most of the courses within the mathematics curriculum fulfill general education and transfer requirements.

## What are my degree, diploma, or certificate options?

### Course Descriptions

Provides individualized, accelerated, mastery-level progression through entry-level college mathematics prerequisite competencies as defined by KY Council of Postsecondary Education. Note: A passing grade in this course does not necessarily indicate that all prerequisites for all entry-level college mathematics courses have been met.

**Prerequisite:** KCTCS Placement Exam

**Delivery Mode:** In-Person Computer Lab Setting and Remote Online

**Credit Hour Note:** This course may be repeated up to three (3) times for additional developmental credit
for a total of nine (9) credit hours.

**Type of Course:** Competency-based, mastery-learning, emporium course that provides individualized
instruction at a flexible-pace. Course allows for acceleration through developmental
math requirements. May require multiple enrollments to complete all developmental
math requirements based on studentâ€™s progress and program needs.

**Advising Note:**

For any student who was previously enrolled in MAT011, please look for STEP credit.

Placement scores and/or Special Credit by Exam received to verify college-level math prerequisites.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can demonstrate proficiency of at least 12 consecutive competencies from the list below.

- State and use properties of real numbers.
- Perform arithmetic operations on integers, fractions and decimals.
- Round whole numbers and decimals to an indicated place value.
- Evaluate whole number powers of integers, fractions and decimals.
- Evaluate square roots of perfect squares of integers, fractions and decimals.
- State and use the order of operations on integers, fractions and decimals.
- Simplify and evaluate algebraic expressions.
- Use both the addition and multiplication properties to solve basic linear equations in one variable.
- Solve problems involving ratios and proportions.
- Solve problems involving percents.
- Convert among fractions, decimals and percents.
- Calculate and solve applied problems using perimeter, circumference, area, volume, and surface area.
- Solve linear equations and applications in one variable.
- Solve and graph linear inequalities in one variable.
- Graph linear equations in two-variables using multiple methods.
- Determine the slope of a line given two points, its graph, or its equation.
- Determine an equation of a line given two points or a point and slope.
- Graph linear inequalities in two-variables.
- Solve systems of linear equations in two-variables using multiple methods.
- Use the properties of integer and basic rational (1/n) exponents to simplify algebraic expressions.
- Add, subtract, and multiply polynomials with one or more variables.
- Factor polynomials by finding the greatest common factor and factor simple trinomials.
- Solve quadratic equations and applications by factoring.
- Graph parabolas.
- Solve and graph compound inequalities and solve absolute value equations and inequalities.
- Write equations of lines, including parallel and perpendicular lines, from given data, verbal descriptions and graphs.
- Determine whether a given correspondence or graph represents a function.
- Evaluate and determine the domain of polynomial, rational and radical functions.
- Completely factor polynomial functions including finding the greatest common factor, using grouping, recognizing special products, and factoring general trinomials.
- Use properties of rational exponents to rewrite and simplify numeric and algebraic expressions.
- Add, subtract, multiply, and divide polynomial, rational, and radical expressions.
- Solve polynomial, rational and radical equations.
- Introduce complex numbers and simplify radicals of both positive and negative real numbers.
- Solve quadratic equations with complex solutions using factoring, completing the square, and the quadratic formula.
- Graph parabolas by finding the vertex and axis of symmetry and plotting points.
- Model and solve applications based on linear, quadratic, and exponential functions.

##### OFFICIAL COURSE OUTLINE

**Modules 1-4: Prealgebra MAT 055 STEP Credit**

- Whole Numbers
- Integers
- Square Roots
- Algebraic Expressions
- Properties of Real Numbers
- Fractions
- Order of Operations on Real Numbers
- Decimals
- Basic Linear Equations
- Ratios & Proportions
- Percentages
- Geometry
- Measurement

**Modules 5 â€“ 8: Mathematical Literacy MAT 075 STEP Credit***

- General Linear Equations in one-variable
- Linear Inequalities in one-variable & Interval Notation
- Linear Equation Applications
- Variation
- Scientific Notation
- Linear Equations in two-variables
- Slope
- Rules of Exponents
- Linear Inequalities in two-variables
- Systems of Linear Equations
- Square Roots and Rational Exponents
- Function Notation
- Polynomial Operations
- Factoring
- Quadratic Equations & Applications

*Topics A â€“ H above, Modules 5 â€“ 6: Intro to Workplace Mathematics MAT 062 STEP Credit

**Modules 9 â€“ 12: Intermediate Algebra MAT 085 STEP Credit**

- Absolute Value Equations and Inequalities
- Linear Equations in two-variables (including parallel & perpendicular)
- Functions
- Domain
- General Factoring
- Polynomial Functions and Equations
- Rational Functions and Equations (including rational exponents)
- Radical Functions and Equations
- Quadratic Equations with Complex Solutions
- Graphing Quadratic Functions
- Introduction to Exponential Functions

Prepares students to take College Algebra with College Algebra Workshop. Introduces operations on integers, decimals, and fractions; ratios, proportions, and percents; simplifying radicals and algebraic expressions; solving linear and quadratic equations; linear inequalities; solving formulas; factoring; slope and graphing lines.

**Prerequisite: **KCTCS Placement Policy.

**Components:** Lecture: 4.0 credits (60 contact hours)

**Implementation:** Fall 2024

**Attributes:** Remedial -Mathematics

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of MAT 061, the student can:

- Perform operations on integers and decimals.
- Find the prime factorization and least common multiple of whole numbers.
- Add, subtract, multiply, divide, and simplify fractions.
- Simplify ratios and rates and solve application problems involving proportions.
- Convert between decimals and percents and calculate percent change.
- Simplify radicals and find decimal approximations.
- Apply common units for length, area, volume, time, currency, or speed.
- Simplify numeric expressions using the order of operations.
- Simplify algebraic expressions.
- Solve linear equations in one variable.
- Solve a formula for a given variable.
- Solve linear inequalities in one variable. Write the solution set, including compound inequalities, interval notation and set builder notation.
- Identify and plot points in the Cartesian coordinate system.
- Find the slope of a line.
- Graph lines using a table of solutions, slope-intercept form, and intercepts.
- Add, subtract, and multiply polynomials.
- Factor polynomials by factoring common factors, grouping, and special products; and factor general trinomials.
- Simplify rational expressions.
- Solve quadratic equations by factoring.
- Identify and evaluate linear, polynomial, rational, and exponential functions.
- Solve application problems based on the above competencies.

##### OFFICIAL COURSE OUTLINE

- Pre-Algebra
- Operations on Integers, Decimals, and Fractions
- Simplifying Radicals
- Ratios, Rates, and Proportions
- Percents and Percent Change
- Measurement and Unit Conversion
- Order of Operations
- Translating Between Words and Algebraic Expressions

- Linear Equations and Linear Inequalities
- Checking Solutions of Equations
- Simplifying Algebraic Expressions
- Solving Linear Equations
- Solving Linear Inequalities
- Set-Builder and Interval Notation
- Solving Formulas
- Applications

- Polynomials and Quadratic Equations
- Polynomial Operations A300 23 2003-2004
- Factoring
- Simplifying Rational Expressions
- Solving Quadratic Equations
- Applications

- Graphing
- Identifying Functions
- Evaluating Functions
- Plotting Points
- Tables of Solutions
- Intercepts
- Slope
- Equation of a Line
- Graphing Lines

Designed to develop the mathematical thinking skills and understanding needed for non-math and non-science majors, this one-semester course integrates numeracy, proportional reasoning, algebraic reasoning, and functions. This course provides an alternate path to college-level math courses other than college algebra.

**Prerequisite:** MAT 055 or equivalent as determined by KCTCS placement examination.

Note: MAT 075 is equivalent to MAT 011 Modules 5 - 8.

**Components:** Lecture: 4.0 credits (60 contact hours)

**Implementation:** n/a

**Attributes:** Remedial -Mathematics

**Advising Note:** None

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Convert between units of measurement.
- Use significant digits to show the accuracy and precision of a measurement.
- Use and interpret scientific notation.
- Simplify algebraic expressions using the properties of algebra, including the distributive law and combining like terms.
- Solve linear equations in one variable.
- Translate verbal statements into algebraic expressions.
- Solve literal equations for a given variable.
- Solve variation problems with percentages, ratios, and proportions.
- Plot points on a rectangular coordinate system.
- Graph lines from their equation.
- Find the intercepts of a line from the graph or equation.
- Calculate the slope of a line from the graph, equation, or two given points.
- Interpret slope as a rate of change in applications.
- Simplify algebraic expressions using the rules of exponents.
- Use technology appropriately to solve application problems.
- Solve applied problems using the above competencies within appropriate contexts.

##### OFFICIAL COURSE OUTLINE

- Studying Mathematics

- Learning Styles
- Study Skills
- Test Taking
- Real Number Arithmetic Skills
- Effective Calculator Use
- Calculation with Basic Geometric Formulas

- Measurement

- Unit Conversion
- Significant Digits
- Scientific Notation
- Accuracy and Precision of Measurements

- Formulas

- Introduction to Formulas
- Writing Formulas from Verbal Information
- Formulas and Applications

- Properties of Algebra

- Basic Properties of Algebra
- Simplifying Algebraic Expressions
- Properties of Equality

- Equations

- Interpreting Equations
- Guidelines for Solving Equations
- Solving Linear Equations
- Solving Formulas for a Variable

- Ratios, Proportions, and
- Variation
- Ratios
- Proportions
- Percent
- Direct Variation
- Inverse Variation
- Joint Variation

- Graphing

- Plotting Points
- Graphing Lines
- Slope
- Rates of Change
- Intercepts of a Line

- Exponents

- Algebraic Rules of Exponents
- Integer Exponents
- Simplifying Algebraic Expressions with Exponents

Includes rational expressions, radical expressions, rational exponents, graphing parabolas, inequalities, equations of lines, functions and applications, with emphasis on solving quadratic, rational, and radical equations.

**Prerequisite:** MAT 065 or MAT 075 or equivalent as determined by KCTCS placement examination.

Note: MAT 085 is equivalent to MAT 011 Modules 9 - 12.

**Components:** Lecture: 3 credit hours (45 contact hours)

**Implementation:** Fall 2012

**Advising Note:** None

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student will:

- Write equations of lines from given data, verbal descriptions, and graphs.
- Write the equation of a line parallel or perpendicular to a given line.
- Solve absolute value equations.
- Solve compound inequalities.
- Solve and graph absolute value inequalities.
- Graph linear inequalities in two variables.
- Simplify rational expressions.
- Add, subtract, multiply, and divide rational expressions.
- Solve equations involving rational expressions.
- Convert between radical and rational exponent form.
- Simplify radicals.
- Add, subtract, multiply, and divide radicals.
- Solve equations involving radicals.
- Solve quadratic equations with complex solutions using completing the square and the quadratic formula.
- Parabolas by finding the vertex, finding the axis of symmetry, and plotting points.
- Evaluate a function using function notation.
- Determine whether a given correspondence or graph represents function.

Determine the domain of a function. - Identify the range of a function.
- Model and solve applications based on linear, quadratic, and exponential functions.

##### OFFICIAL COURSE OUTLINE

- Equations of Lines

- Writing Equations of Lines Given Data, Verbal Descriptions, and Graphs
- Writing Equations of Parallel or Perpendicular Lines

- Absolute Value and Inequalities

- Absolute Value Equations
- Compound Inequalities
- Absolute Value Inequalities
- Graphing Linear Inequalities in Two Variables

- Rational Expressions

- Simplifying Rational Expressions
- Basic Operations
- Solving Equations

- Radicals

- Converting Between Radical and Rational Exponent Form
- Simplifying Radicals
- Basic Operations
- Solving Equations

- Quadratics

- Completing the Square
- Quadratic Formula
- Complex Solutions
- Graphing Parabolas

- Functions

- Function Notation
- Evaluating Functions

Approved: March 2012 - Identifying Functions
- Domain and Range

##### LEARNING RESOURCES

Martin-Gay, E. (2009). *Intermediate Algebra* (5th ed.). Boston, MA: Pearson

Covers basic mathematical concepts as applied to finance. Includes percentages, simple and compound interest, annuities, sinking funds, depreciation, and consumer debt, including installment buying, credit cards, and mortgages.

**Prerequisite:** MAT 062 or MAT 065 or equivalent as determined by KCTCS placement examination. [AAS
degrees only]

##### OFFICIAL COURSE COMPETENCIES

Upon completion of this course, the student can:

- Solve for the unknown quantity in a percentage, rate, and base problem.
- Determine percent increase and decrease using markup and markdown applications.
- Apply use of annual percentage rate and annual percentage yield to problems in finance.
- Solve problems which involve the simple interest formula.
- Calculate compound interest and compound amount.
- Determine present and future values of an annuity.
- Calculate periodic payment for a sinking fund.
- Set up an amortization schedule and calculate the early payoff of a loan.
- Solve problems involving installment buying and credit card usage.
- Determine mortgage payment amount, closing costs, and total cost of a loan.
- Compute annual and accumulated depreciation and book value using various depreciation methods.
- Solve application problems involving the above competencies.

##### MAT 105 COURSE OUTLINE

- Percents

- Percentage, Base and Rate
- Percent Increase and Decrease
- Markup and Markdown

- Simple Interest

- Ordinary and Exact Methods
- Appropriate Use of Simple Interest Formula

- Compound Interest

- Annual Percentage Rate
- Annual Percentage Yield
- Present and Future Value of Money

- Consumer Savings

- Annuity
- Sinking Fund

- Fixed Installment Loans

- Amount of Periodic Payment, Finance Charge and Total Amount Paid
- Unearned Interest on Early Payoff

- Credit Cards

- Average Daily Balance Method
- Unpaid Balance Method

- Mortgages

- Closing Costs
- Truth in Lending Statements
- Amortization Schedule
- Total Cost of Loan

- Depreciation

- Straight-Line Method
- Declining-Balance Method
- Sum-of -the-Year's Digits Method
- Accelerated Cost Recovery System

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the
sciences and

mathematics, social sciences, humanities, histories, languages, and the arts. - Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment across general and specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

In MAT 105, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Determine percent increase and decrease using markup and markdown applications.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Set up an amortization schedule and calculate the early payoff of a loan.
- Compute annual and accumulated depreciation and book value using various depreciation methods.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Solve for the unknown quantity in a percentage, rate, and base problem
- Solve problems which involve the simple interest formula.
- Calculate compound interest and compound amount.
- Determine present and future values of an annuity.
- Calculate periodic payment for a sinking fund.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Solve application problems involving compound interest, annuities and sinking funds.
- Determine mortgage payment amount, closing costs, and total cost of a loan.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Apply use of annual percentage rate and annual percentage yield to problems in finance.

##### LEARNING RESOURCES

Miller, C. D. et al. (2008). Business mathematics (11th ed.). Boston, MA: Addison-Wesley, Inc.

##### MAT 105S Co-requisite Remediation for Business Mathematics (1)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 105. Covers content necessary for student success in MAT 105.

Note: Concurrent Enrollment in MAT 105 Required.

Includes the concepts of ratio and proportion, units and conversions, linear equations in two variables, inequalities, graphing and writing equation of a line, percents, interest, descriptive statistics, and logical symbolism. Emphasizes applications in the various technologies.

**Prerequisite:** MAT 062 or MAT 065 or equivalent as determined by KCTCS placement examination. [AAS
degrees only]

##### OFFICIAL COURSE COMPETENCIES

Upon completion of this course, the student can:

- Write the equation of a given line and graph linear equations in two variables;
- Solve systems of linear equations in two variables;
- Set up and solve ratios and proportions;
- Use and interpret scientific notation;
- Convert between various units of measure;
- Solve problems involving percents;
- Solve problems involving significant digits, and accuracy and precision of measurements;
- Solve problems involving simple and compound interest;
- Calculate and interpret basic descriptive statistical measures such as mean, median, mode, range, variance, and standard deviation and use the normal distribution.
- Use logic to determine the validity of arguments.
- Solve application problems involving the above competencies.

##### MAT 110 COURSE OUTLINE

- Number Theory and the Real Number System

- Prime Numbers and Divisibility
- Least Common Multiple and Greatest Common Divisor
- Rules of Exponents
- Scientific Notation
- Operations with Square Roots
- Applications

- Measurements and Units

- Significant Digits
- Precision and Accuracy
- Metric Units of Measurement
- Conversions to and from U.S. Customary ("Standard") System of Measurement
- Applications

- Algebra and Graphs

- Solving Linear Equations in One Variable
- Solving Proportions
- Graphing Lines
- Writing the Equation of a Given Line
- Applications

- Inequalities and Systems of Linear Equations

- Solving Systems of Linear Equations
- Solving Inequalities
- Applications

- Consumer Mathematics

Percents

Simple and Compound Interest

Applications - Statistics

- Sampling Techniques
- Statistical Graphs and Charts
- Measures of Central Tendency (Mean, Median, Mode)
- Measures of Dispersion (Range, Variance, Standard Deviation)
- Using the Normal Distribution Curve
- Applications

- Logic

- Conjunction, Disjunction, and Conditionals
- Truth Tables
- Categorical Propositions
- Fallacies and Valid
- Applications

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics, social sciences, humanities, histories, languages, and the arts.
- Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment
across general and

specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING

Approved Spring 2018

Upon completion of MAT 110, the student can:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Use and interpret scientific notation;

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Calculate and interpret basic descriptive statistical measures such as mean, median,
mode, range, variance,

and standard deviation and use the normal distribution.

- Calculate and interpret basic descriptive statistical measures such as mean, median,
mode, range, variance,
- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Solve problems involving percents;
- Solve problems involving simple and compound interest;

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Convert between various units of measure;
- Solve application problems involving the above competencies.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Use logic to determine the validity of arguments.

##### LEARNING RESOURCES

- Angel, A. and Porter, S. (2001). A Survey of Mathematics with Applications (6th ed.)
New York: Addison

Wesley Longman. - Aufmann, R.N. Lockwood, J.S., Nation, R.D., & Clegg, D.K. (2004). Mathematical Excursions
Boston, MA:

Houghton Mifflin Co. - Setek, Gallo (2002). Fundamentals of Mathematics (9th ed) New Jersey: Prentice Hall.
- Smith, R. D. (2002). Technical Mathematics (4th ed.). Albany, NY: Delmar-Thompson Learning.

##### MAT 110S Co-requisite Remediation for Applied Mathematics (1)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 110. Covers content necessary for student success in MAT 110.

Note: Concurrent Enrollment in MAT 110 Required.

Includes some mathematical concepts from algebra, geometry, and trigonometry and applications relevant to these topics. Includes unit conversions, variation, measurement of geometric figures, vectors, and solving right and oblique triangles using trigonometry. Emphasizes applications in the various technologies.

**Prerequisite:** MAT 062 or MAT 065 or equivalent as determined by KCTCS placement examination. [AAS
degrees only]

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Perform conversions using U. S. customary and SI (metric) measures.
- Apply basic plane geometric principles of lines, angles, triangles and other polygons, circles and arcs, congruency and similarity.
- Calculate surface area and volume of basic geometric solids.
- Solve problems involving significant digits and accuracy and precision of numbers.
- Solve problems involving ratio, proportion, direct, inverse and joint variation.
- Perform conversions between coordinate systems.
- Apply fundamentals of trigonometric functions and co-functions to right triangles.
- Apply the law of sines and the law of cosines to oblique triangles.
- Solve problems involving compound angles.
- Identify the vector concept, the components of vectors and add vectors.
- Use a scientific calculator.
- Solve application problems involving the above competencies.

##### OFFICIAL COURSE OUTLINE

- Measurement

- Precision
- Accuracy
- Significant Digits
- Conversion US customary - Metric

- Variation

- Ratio
- Proportion
- Direct Variation
- Inverse Variation
- Joint Variation

- Geometry

- Lines
- Angles
- Triangles and Other Polygons
- Circles and Arcs
- Congruency and Similarity
- Solids - Surface and Volume

- Trigonometry

- Trigonometric Functions for Right Triangles
- Law of Sines
- Law of Cosines
- Compound Angles
- Conversions between Coordinate Systems
- Vector Concepts, Components and Addition

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the
sciences and

mathematics, social sciences, humanities, histories, languages, and the arts. - Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment
across general and

specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING Approved Spring 2018

Upon completion of MAT 116, the student can:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Perform conversions using U. S. customary and SI (metric) measures.
- Identify the vector concept, the components of vectors and add vectors.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Calculate surface area and volume of basic geometric solids.
- Solve problems involving significant digits and accuracy and precision of numbers.
- Solve problems involving compound angles.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Perform conversions between coordinate systems.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Apply basic plane geometric principles of lines, angles, triangles and other polygons,
circles and arcs,

congruency and similarity. - Apply fundamentals of trigonometric functions and co-functions to right triangles.
- Apply the law of sines and the law of cosines to oblique triangles.

- Apply basic plane geometric principles of lines, angles, triangles and other polygons,
circles and arcs,
- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Solve application problems involving the course competencies.

##### LEARNING RESOURCES

- Tan, S.T. (2004). Applied Mathematics (3rd ed.). Belmont, CA: Wadsworth-Thomson Learning.
- Smith, Karl J. (2003). Mathematics Its Power and Utility (7th ed.). Pacific Grove,
CA: Brooks/Cole-Thomson

Learning. - Smith (2002). Technical Mathematics (4th ed.). Albany, NY: Delmar/Thomson Learning.
- Kramer, A. D. (2002). Mathematics for Electricity & Electronics (2nd ed.). Albany,
NY: Delmar-Thompson

Learning.

##### MAT 116S Co-requisite Remediation for Technical Mathematics (1)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 116. Covers content necessary for student success in MAT 116.

Note: Concurrent Enrollment in MAT 116 Required.

Examines mathematical concepts from algebra and trigonometry. Includes vectors, phasor algebra, variation, trigonometric functions, coordinate systems, system of linear equations, quadratic, rational, exponential and logarithmic equations.

**Prerequisite:** MAT 065 or equivalent as determined by KCTCS placement examination. [AAS degrees
only]

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Solve problems involving ratio, proportion, direct, inverse, and joint variation.
- Solve rational equations.
- Define trigonometric functions and use them to solve right triangles.
- Solve triangles using the law of sines and the law of cosines.
- Identify the vector concept and the components of vectors, and add vectors.
- Determine the solutions to simultaneous linear equations using determinants.
- Solve quadratic equations by the processes of factoring, completing the square, and the quadratic formula.
- Apply radians and radian measurements including their applications to rotating objects.
- Utilize Phasor algebra to perform basic operations on complex numbers.
- Utilize exponent and logarithmic equations such as population growth, time constants and pH scale.
- Perform conversions between number systems such as decimal, binary, octal, and hexadecimal.
- Use a scientific calculator.
- Solve occupation specific application problems using the above competencies.

##### OFFICIAL COURSE OUTLINE

- Algebra

- Variation
- Quadratic Equations

- Factoring
- Completing the square
- Quadratic formula

- Rational Equations
- Ratio and Proportion
- Rectangular Coordinate Plane
- Phasor Form
- Systems of Linear Equation Solution by Determinants
- Exponential Equations
- Logarithmic Equations
- Complex Numbers

- Trigonometry

- Basic Definitions of Functions
- Radians
- Law of Sines
- Law of Cosines
- Polar Coordinates

- Number systems

- Decimal
- Binary
- Octal
- Hexadecimal

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the
sciences and

mathematics, social sciences, humanities, histories, languages, and the arts. - Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment
across general and

specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

Upon completion of MAT 126, the student can:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Define trigonometric functions and use them to solve right triangles.
- Identify the vector concept and the components of vectors, and add vectors.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):

- Solve problems involving ratio, proportion, direct, inverse, and joint variation.
- Utilize Phasor algebra to perform basic operations on complex numbers.
- Solve triangles using the law of sines and the law of cosines.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Solve quadratic and rational equations.
- Perform conversions between number systems such as decimal, binary, octal, and hexadecimal.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Apply radians and radian measurements including their applications to rotating objects.
- Utilize exponent and logarithmic equations such as population growth, time constants and pH scale.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):

- Solve occupation specific application problems using course competencies.

##### LEARNING RESOURCES

- Cleaves and Hobbs (2004). College Mathematics for Technology (6rd ed.). Upper Saddle
River, NJ: Prentice

Hall - Deem, B. R., & Zannini, T. (2003). Electronics and Computer Math (7th ed.). Upper Saddle River, NJ: Prentice Hall

##### MAT 126S Co-requisite Remediation for Technical Algebra and Trigonometry (2)

Provides supplementary instruction for students who do not meet college readiness
standards for MAT 126. Covers content necessary for student success in MAT 126.

Note: Concurrent Enrollment in MAT 126 Required.

An introduction to concepts and applications of mathematics, with examples drawn from such areas as voting methods, apportionment, consumer finance, graph theory, tilings, polyhedra, number theory and game theory. This course is not available for credit to persons who have received credit in any mathematics course of a higher number with the exceptions of MA 112, 123, 162, 201 and 202. This course does not serve as a prerequisite for any calculus course. Credit not available on the basis of special examination.

**Prerequisite:** Two years of high school algebra and a Math ACTE score of 19 or above, or MA 108R,
or math placement test.

Note: Prerequisites may also be met by MAT 075 or MAT 011 Modules 5 - 8

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Read pictorial representations and charts to solve fair division problems and/or voting method problems
- Interpret apportionment information given in charts
- Organize information in preference schedules for use in discussing various voting methods and apportionment problems
- Create graphs to illustrate graph theory problems and/or geometric concepts
- Find appropriate modified divisors for different apportionment methods
- Solve equations involving consumer finance formulas
- Select the appropriate formula to use when solving problems involving consumer finance
- Use circuits and paths to model situations involving graph theory
- Compare advantages and disadvantages of different voting methods and different apportionment methods
- Estimate the relative error using an approximate algorithm to solve graph theory problems
- Compare results of consumer finance problems and evaluating assumptions applicable to different formulas

##### OFFICIAL COURSE OUTLINE(Approved February 2016)

Include parts I, II, III, and IV, plus at least one section from part V.

- Voting Methods
- Methods
- Plurality
- Elimination
- Borda Count
- Pairwise Comparison

- Fairness Criteria

- Methods
- Fair Division
- Equal Division
- Fair Shares
- Divider-Chooser Method
- Sealed Bids

- Proportional Division
- Quota Methods
- Hamilton
- Lowndes'

- Divisor Methods
- Jefferson
- Adams'
- Webster
- Huntington-Hill

- Quota Methods

- Equal Division
- Financial Math
- Percent Increase/Decrease
- Simple Interest
- Compound Interest
- Systematic Savings Plans
- Amortized Loans

- Graph Theory
- Euler Paths and Circuits
- Euler's Theorems
- Graph Modelling
- Eulerization

- Hamilton Paths and Circuits
- Travelling Salesman Problem
- Approximate Algorithms
- Nearest Neighbor
- Cheapest Link

- Euler Paths and Circuits
- Additional Topics (Choose 1)
- Growth Modelling
- Geometry
- Scheduling
- Logic
- Number Theory
- Statistics

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics,social sciences, humanities, histories, languages, and the arts.
- Intellectual and practical skills, including
- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including
- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment across general and specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING(Approved Fall 2017)

Upon completion of this course, the student can:

- Interpret information presented in mathematical and/or statistical forms by:
- reading pictorial representations and charts to solve fair division problems and/or voting method problems
- interpreting apportionment information given in charts

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by:
- organizing information in preference schedules for use in discussing various voting methods and apportionment problems
- creating graphs to illustrate graph theory problems and/or geometric concepts

- Determine when computations are needed and execute the appropriate computations by:
- finding appropriate modified divisors for different apportionment methods
- solving equations involving consumer finance formulas

- Apply an appropriate model to the problem to be solved by:
- selecting the appropriate formula to use when solving problems involving consumer finance
- using circuits and paths to model situations involving graph theory
- comparing advantages and disadvantages of different voting methods and different apportionment methods

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by:
- estimating the relative error using an approximate algorithm to solve graph theory problems
- comparing results of consumer finance problems and evaluating assumptions applicable to different formulas

Includes selected topics in algebra and analytic geometry. Develops manipulative skills and concepts required for further study in mathematics. Includes linear, quadratic, polynomial, rational, exponential, logarithmic, and piecewise functions; systems of equations; and an introduction to analytic geometry. (Students may not receive credit for MAT 150 and any other College Algebra or Precalculus course. Credit not available on the basis of special exam.)

**Prerequisite:** 1. Math ACT score of 22 or above, 2. Math ACT score of 19-21 with concurrent MAT
100 workshop, 3. Successful completion of Intermediate Algebra, MAT 126, or equivalent,
or 4. KCTCS placement examination recommendation.

MAT 150 COLLEGE ALGEBRA (3 credit hours)

KCTCS Course Information

##### Official Course Description

Includes selected topics in algebra and analytic geometry. Develops manipulative skills and concepts required for further study in mathematics. Includes linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions; systems of equations; and an introduction to analytic geometry. (Students may not receive credit for both MAT150 and any other College Algebra or Pre-calculus course. Credit not available on the basis of special exam.)

Prerequisites: One of the following:

- Math ACT score of 22 or above;
- Math ACT score of 19 - 21 with concurrent MAT 100 workshop;
- Successful completion of Intermediate Algebra, MAT 126, or equivalent; or
- KCTCS placement exam recommendation.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Recognize functions and specify the domain and the range of a given function.
- Graph linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions.
- Write expressions from data, verbal descriptions or graph.
- Solve polynomial, rational, exponential and logarithmic equations.
- Solve application problems using linear, quadratic, exponential, and logarithmic functions.
- Perform operations with functions and find inverse functions.
- Solve linear and nonlinear systems of equations.
- Solve nonlinear inequalities

##### OFFICAL COURSE OUTLINE

- Functions
- Functions, relations, domain, and range
- Properties of functions
- Operations with functions
- Inverse functions

- Graphs and Applications
- Linear functions
- Quadratic functions
- Exponential functions
- Logarithmic functions
- Polynomial functions
- Rational Functions
- Piecewise-defined functions

- Equations and Inequalities
- Polynomial equations
- Rational equations
- Exponential equations
- Logarithmic equations
- Nonlinear inequalities
- Systems of linear equations
- Systems of nonlinear equations

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the
sciences and

mathematics, social sciences, humanities, histories, languages, and the arts. - Intellectual and practical skills, including
- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including
- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment
across general and

specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

In MAT 150, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
- Recognizing functions and specify the domain and the range of a given function

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by

(Gen Ed Comp A, B, C):- Graphing linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
- Solving polynomial, rational, exponential and logarithmic equations.
- Performing operations with functions and find inverse functions.
- Solving nonlinear inequalities.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
- Writing expressions from data, verbal descriptions or graph.
- Solving application problems using linear, quadratic, exponential, and logarithmic functions.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis

by (Gen Ed Comp A, D):- Solving linear and nonlinear systems of equations

##### LEARNING RESOURCES

Bittinger, M. L. et al. (2009). *Algebra & trigonometry: Graphs & models (4th ed.)*. Boston, MA: Pearson

Education, Inc.

Provides parallel and supplemental review of algebra skills needed for success in college algebra for students with a Math ACT of 19-21. (Credit not available by special exam; withdrawal from MAT 100 requires withdrawal from MAT 150; can be offered pass/fail or letter grade basis.) Lecture: 2.0 credits (30 contact hours).

**Prerequisite:** Concurrent enrollment in MAT 150.

Includes the trigonometric functions, identities, multiple analytic formulas, laws of sines and cosines, graphs of trigonometric functions in rectangular and polar coordinates, and solving trigonometric equations. Emphasizes applications in each topic. (Students may not receive credit for both MAT155 and any other trigonometry or precalculus course.)

**Prerequisite:** One of the following:

- Math ACT score of 22 or above,
- Math ACT score of 19-21 with concurrent MAT150,
- Successful completion of Intermediate Algebra, MAT 126, or equivalent, or
- KCTCS placement examination recommendation.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- State the definition of the six trigonometric functions in their multiple forms.
- Compute trigonometric function values using the definitions.
- State basic trigonometric identities.
- Apply the trigonometric function definitions to right triangles.
- Find trigonometric values of angles.
- Solve right triangle application problems.
- Solve problems involving vectors and right triangles.
- Use radian and degree measure.
- Solve application problems using radian measure.
- Graph the six trigonometric functions.
- Determine the amplitude and period of the trigonometric functions.
- Determine the inverse functions for the six trigonometric functions.
- Prove trigonometric identities.
- Solve problems using the sum and difference and double-angle formulas.
- Solve trigonometric equations.
- Solve general triangles using the Law of Sines and the Law of Cosines.
- Put complex numbers into trigonometric form.
- Calculate complex roots of numbers.
- Plot points in polar coordinates.
- Graph equations in polar coordinates.

##### OFFICIAL COURSE OUTLINE

- Six Trigonometric Functions

- Angles, Degrees, and Special Triangles
- The Rectangular System
- Definitions of the Trigonometric Functions
- Introduction to Identities

- Right Triangle Trigonometry

- Right Triangle Trigonometric Definitions
- Calculator and Trigonometric Functions of an Acute Angle
- Solving Right Triangles
- Applications
- Vectors

- Radian Measure

- Reference Angle
- Radians and Degrees
- Definitions of the Circular Functions
- Arc Length and Area of a Sector Formulas
- Linear and Angular Velocities

- Graphing and Inverse Functions

- Basic Graphs
- Amplitude and Period
- Phase Shift
- Inverse Trigonometric functions

- Identities and Formulas

- Proving Identities
- Sum and Difference Formulas
- Double-Angle Formulas
- Half-Angle Formulas
- Other Identities

- Trigonometric Equations

- Solving Trigonometric Equations
- Trigonometric Equations Involving Multiple Angles
- Parametric Equations and Further Graphing

- General Triangles

- Law of Sines
- Law of Cosines
- Area of a General Triangle

- Complex Numbers and Polar Coordinates

- Complex Numbers
- Trigonometric Form for Complex Numbers
- Products and Quotients in Trigonometric Form
- Roots of a Complex Number
- Polar Coordinates
- Equations in Polar Coordinates

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics, social sciences, humanities, histories, languages, and the arts.
- Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment across general and specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

In MAT 155, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Stating the definition of the six trigonometric functions in their multiple forms.
- Stating basic trigonometric identities.
- Using radian and degree measure.
- Determining the inverse functions for the six trigonometric functions.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):

- Solving problems involving vectors and right triangles.
- Graphing the six trigonometric functions.
- Determining the amplitude and period of the trigonometric functions.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Computing trigonometric function values using the definitions.
- Finding trigonometric values of angles.
- Solving trigonometric equations.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Applying the trigonometric function definitions to right triangles.
- Solving right triangle application problems.
- Solving application problems using radian measure.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):

- Proving trigonometric identities.
- Solving problems using the sum and difference and double-angle formulas.
- Solving general triangles using the Law of Sines and the Law of Cosines

Examines finite mathematics with applications to business, biology and the social sciences including linear functions and inequalities, matrix algebra, linear programming, probability with emphasis on setting up mathematical models from stated problems.

**Prerequisite:** MAT 150 or MAT 161 or equivalent.

**Attributes: **QR - Quantitative Reasoning

**Components:** Lecture 3.0 credits (45 contact hours)

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Solve linear systems of two or more variables by graphing, substitutions, elimination and Gauss-Jordan methods.
- Identify consistent, inconsistent, and dependent systems.
- Set up and solve applied problems involving systems of linear equations.
- Identify and be able to write coefficient matrices and augmented matrices.
- Define and identify square matrices, equal matrices, and dimensions of matrices.
- Add and subtract matrices.
- Perform scalar multiplication and matrix multiplication.
- Find inverses of matrices.
- Use inverses of matrices to solve systems of equations.
- Graph linear inequalities and systems of linear inequalities.
- Identify corner points and feasible solutions.
- Solve optimization problems by substituting corner points into objective functions.
- Identify standard maximization and minimization problems.
- Solve standard maximization simplex problems.
- Convert non-standard optimization problems to standard maximum problems, including i. problems with (greater than or equal) constraints; ii. problems with (equal) constraints; iii. problems with negative numbers on the right-hand side of constraints; iv. problems with an objective function to be minimized.
- Identify simplex problems without a single solution, such as problems with multiple solutions, unbounded solutions or no solutions.
- Solve applied optimization problems using simplex and/or graphing methods.
- Use, define, and identify set builder notation, empty or null set, universal set, equal sets, subsets, proper subsets, elements, union, intersection, complements and disjoint sets.
- Use and solve applied problems with Venn diagrams.
- Identify the number of elements in sets.
- Define and use the Multiplication Rule on applied counting problems.
- Define and use the Addition Rule on applied counting problems.
- Solve applied permutation problems.
- Solve applied combination problems.
- Identify and define experiment, outcome, trial, sample space, event, empirical probability, random outcomes.
- Find probabilities of equally likely events in applied problems.
- Find probabilities of compound events in applied problems using union, intersection, and complement.
- Define and identify mutually exclusive events and independent events.
- Solve applied conditional probability problems.

This course assists students in meeting the General Education Student Learning Outcomes in Quantitative Reasoning.

##### OFFICIAL COURSE OUTLINE

- Linear Systems
- Linear systems of two or more variables
- Consistent, inconsistent, and dependent systems
- Solutions in parametric form (optional)
- Applied problems

- Matrix Operations
- Coefficient matrices and augmented matrices
- Dimensions of matrices
- Addition and subtraction of matrices
- Scalar multiplication
- Matrix multiplication
- Inverses of matrices
- Matrix solution of a system of equations

- Linear Inequalities
- Graphs
- Systems of inequalities and their graphs
- Corner points and feasible regions
- Optimization problems
- Objective function
- Simplex method
- Duality problems
- Conversion of non-standard problems to standard optimization problems
- Simplex problems without a single solution
- Applied optimization problems

- Sets
- Basic concepts of sets
- Venn diagrams and applied problems
- The number of elements in a set

- Combinatorics
- The multiplication rule
- The addition rule
- Applied permutation problems
- Applied combination problems

- Probability
- Basic concepts of probability theory
- Equally likely events
- Compound events
- Mutually exclusive and independent events
- Conditional probability
- Bayes Rule (optional)

- Markov Chains (optional)
- State matrices, transition matrices, Markov chains, steady-state matrices
- Applications of Markov chains
- Steady-state matrices
- Regular matrices

- Bernoulli's Formula (optional)
- Theory
- Applications

Introduces problem solving, number and numeration systems, whole numbers, integers, rational and irrational numbers, and elementary number theory. Requires demonstration of basic skills in mathematics to receive credit in this course.

**Pre-requisite:** MA 111U or MAT 150 or equivalent with a minimum grade of "C".

**Components:** Lecture 3.0 credits (45 contact hours)

**Attributes:** Other

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Demonstrate interpretations, models, and applications of whole, integer, rational, and real number operations, the relationships among them, including division with remainders.
- Demonstrate place value, operations, exponentiation, and ordering of the base-ten number system.
- Explain multi-digit calculations in base-ten structure, including standard algorithms, "mental math," and non-standard methods commonly created by students.
- Organize and justify computations using the commutative, associative and distributive properties.
- Apply number sense and various strategies for mental computations, estimation, and rounding to whole, rational, and real numbers and their operations.
- Perform calculations using scientific notation including both positive and negative powers of ten.
- Demonstrate an understanding of rational numbers, their fractional and decimal representations, and their ordering.
- Demonstrate the underlying mathematics of algorithms for fraction and decimal operations.
- Solve application problems using appropriate whole, integer, rational, and real number operations.
- Demonstrate an understanding of various representations of a percentage.
- Explain and provide justification for conjectures involving fundamental ideas of number theory, including divisibility, odd and even numbers, composite and prime numbers, and prime factorization.
- Apply various problem solving strategies to different situations.
- Explain and justify generalizations using a variety of representations including conventional algebraic notation.
- Apply algebraic identities and properties.
- Solve applications via algebraic manipulation.
- Devise and use both inductive and deductive arguments.
- Explain concepts and demonstrate notations of functions.
- Create and use tables, recursive formulas, and closed formulas.

This course assists students in meeting the General Education Student Learning Outcomes in Quantitative Reasoning.

##### OFFICIAL COURSE OUTLINE

- Basic Operations with Whole Numbers
- Mathematical models of whole numbers.
- Various interpretations and visualizations of addition, subtraction, multiplication, and division with whole numbers.
- Number properties to organize and justify computation.
- Mental math computation and flexibility.

- Base-Ten Number System
- Efficient representation of numbers and magnitude of numbers compared to other number systems.
- Implications for ordering, estimating and approximating numbers.
- Explanations for addition, subtraction, multiplication and division algorithms for whole and rational numbers.
- Multi-digit calculations using standard and non-standard algorithms and "mental math".
- Explanations for scientific notation.

- Basic Operations with Rational Numbers
- Mathematical models of fractions and decimals.
- Various interpretations and visualizations of addition, subtraction, multiplication and division algorithms with rational numbers.
- Finite, repeating and non-repeating decimals and their relationship with fractions. Specifically, demonstrate how and why whole number decimal arithmetic extends to finite decimals and, in particular, how place value extends to decimal fractions.
- Demonstrate how any number represented by a finite or repeating decimal is rational, and how the convers is true.
- Relationships among fractions, decimals, percents and ratios.
- Appropriate applications of rational numbers.
- Demonstrate number sense and explain when proposed solutions to rational number problems are unreasonable.

- Basic Operations with Integers
- Mathematical models of integers.
- Magnitude and meaning of integers.
- Addition, subtraction, multiplication and division of integers.
- Demonstrate the concepts of integer and operations on integers, including the meanings of sign and magnitude, interpretations and applications, and how whole number arithmetic extends to integers.
- Appropriate applications of integers.

- Real Number System
- Number line as a representation of real numbers.
- Relationships among the whole, rational, irrational, and real numbers, and the integers.

- Number Theory
- Prime Factorization Theorem and relationship to algebra.
- Justifications of conjectures made about odd, even, composite and prime numbers.
- Justification and use of Euclidean Algorithm. (optional)

- Mathematical Conventions
- Knowledge and interpretation of results from different calculators.
- Proper use of a calculator.
- Problem solving strategies.
- Order of operations.
- Venn Diagrams. (optional)

- Algebra and Functions
- Algebraic and function concept and notation.
- Algebraic expressions as notations for describing math computation.
- Algebraic identities as statements of equivalence expressions.
- Formulas created from tables, closed and recursive.
- Word problems using algebraic manipulation.
- Different roles algebra plays through patterns, symbolic language, problem solving, quantitative reasoning, arithmetic, and modeling physical situations.

Introduces probability and statistics; geometric concepts including congruence and similarity; and measurement. Required demonstration of basic skills in mathematics to receive credit in this course.

**Pre-requisite:** MA 111U or MAT 150 or equivalent with a minimum grade of "C".

**Attributes:** QR - Quantitative Reasoning

**Components:** Lecture 3.0 credits (45 contact hours)

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Decompose common two- and three-dimensional figures.
- Identify and determine cross-sections of three-dimensional objects, represent three-dimensional shapes in two dimensions, and construct three-dimensional objects from two-dimensional representations.
- Determine the rotational and line symmetries for two-dimensional shapes.
- Demonstrate an understanding of fundamental objects of geometry, including point, ray, line, and line segment.
- Demonstrate concepts of angles and how they are measured.
- Identify plane isometries - reflections (flips), rotations (turns), and translations (slides).
- Demonstrate an understanding of congruence and similarity.
- Draw conclusions about basic shapes and their properties using formal definitions.
- Select the appropriate unit of measurement for length, area, and volume.
- Compare units and relate measurements within each of the two common systems of measure: U.S. Customary and the International System (SI-metric).
- Apply the Pythagorean Theorem to problem solving.
- Demonstrate an understanding of the effect of dilations on length, area, and volume.
- Apply and justify area formulas for triangles, parallelograms, trapezoids, and circles.
- Apply and justify volume and surface area formulas for prisms, cylinders, and other three-dimensional objects.
- Find areas and volumes of irregular (compound) regions and figures.
- Demonstrate an understanding of the relationship between perimeter and area, and between surface area and volume.
- Apply measures of dispersion (range and outliers) and measures of central tendency (mean, median, and mode) to interpret data.
- Construct, interpret, and make appropriate inferences from different forms of graphical data representation (line plots, histograms, line graphs, bar graphs, box plots, pie charts, stem-and-leaf plots) and distinguish when one graphical data representation is more appropriate than others for a given data set.
- Communicate some of the difficulties that arise in collecting data, including random sampling, and recognize some of the ways that statistics and graphical displays of data can be misleading.
- Determine and list the total number of outcomes for single-stage and multi-stage events.
- Calculate, interpret, and apply fundamental and conditional probabilities.
- Develop empirical probabilities through simulations; relate them to theoretical probability.
- Calculate and apply expected value.

This course assists students in meeting the General Education Student Learning Outcomes in Quantitative Reasoning.

##### OFFICIAL COURSE OUTLINE

- Geometry.
- Visualization Skills.
- Projections, cross-sections and decomposition of two- and three-dimensional figures.
- Rotational and line symmetries for two-dimensional figures.
- Representation of three-dimensional figures from two-dimensional representations.
- Demonstrate the ability to mentally manipulate physical representations of two- and three-dimensional shapes.

- Basic Geometry Figures and their Properties.
- Definitions and recognition of fundamental two- and three-dimensional figures of geometry.
- Definitions of point, ray, line and line segment.
- Angles and angle measurement.
- Reflections, rotations, and translations.
- Congruence and similarity.
- Demonstrate an understanding of congruence and similarity and their relationship to proportional reasoning.

- Length, area and volume of fundamental two-and three-dimensional geometry figures.
- Area and Perimeter formulas for basic figures.
- Volume formulas for basic figures.
- Behavior of measure under uniform dilations.

- Identify and use appropriate technology or manipulatives to build an understanding of shapes, congruence, angle construction, bisectors, etc.

- Visualization Skills.
- Measurement and measurement techniques.
- U.S. Customary and International System (SI-metric) of unit conversion.
- Appropriate use of measurement tools.
- Show that measurements are approximate and that different units affect precision.
- Role of pi in measurement.
- Pythagorean Theorem.
- Estimate with common units of measurement.

- Data Analysis.
- Types of questions addressed and decisions made using data.
- Designing surveys and statistical experiments.
- Random Sampling.

- Statistics.
- Symmetric and skewed distributions.
- Measures of data spread.
- Measures of central tendency.
- Graphical data representations.
- Comparing data and drawing conclusions from data.
- Misuses of data.
- Standard deviation.

- Probability.
- Single-stage and multi-stage events.
- Use tree diagrams and factorials to determine the number of outcomes of events.
- Conditional probability and its applications.
- Randomness.
- Empirical and theoretical probabilities.
- Expected value and fairness.
- Use expected value in real world applications such as gambling, insurance, etc.

Provides an introduction to differential and integral calculus with applications in biological sciences, social sciences, physical sciences, or business with an analysis of algebraic, exponential, and logarithmic functions. (Students may not receive credit for both MAT 170 and MAT 175.)

**Prerequisite: **1. Math ACT score of 27 or above or 2. Successful completion of College Algebra, MAT
150, or equivalent.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Approximate limits graphically and numerically and evaluate limits analytically.
- List the conditions for the continuity of a function at a point and determine if a function is continuous or discontinuous at a point.
- Determine the intervals of continuity of a function.
- Evaluate infinite limits and limits at infinity.
- Define the derivative of a function and evaluate the derivative of a function using the definition.
- Evaluate the derivative of a function using differentiation rules for algebraic functions as well as product, quotient, and chain rules.
- Use the derivative of a function to find the equation of the line tangent to the graph of the function at a given point.
- Sketch the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph.
- Perform implicit differentiation.
- Use derivatives to solve application problems including problems involving related rates and optimization for biological sciences, social sciences, physical sciences, or business.
- Define the differential and use differentials to approximate function values.
- Find indefinite and definite integrals of a function using integration rules for algebraic functions.
- Find definite and indefinite integrals using substitution.
- Find the average value of a function on an interval.
- Use definite integrals to find the area under a curve and the area between two curves.
- Determine if a function is differentiable or non-differentiable at a point.
- Find the derivative and integral of functions including polynomial, rational, root, exponential, and logarithmic functions.
- Solve application problems using integrals for biological sciences, social sciences, physical sciences, or business.

##### OFFICIAL COURSE OUTLINE

- Limits

- Finding limits graphically
- Approximating limits numerically
- Finding limits analytically
- One-sided limits
- Continuity
- Infinite limits (f(x)â†’Â±âˆž)
- Limits as xâ†’Â±âˆž
- Horizontal asymptotes
- Vertical asymptotes

- Differentiation

- Definition of the derivative
- Finding derivatives using the definition
- Finding the tangent line to the graph of a function
- Basic differentiation rules for algebraic functions, product and quotient rules, chain rule
- Finding the tangent line to a graph
- Implicit Differentiation

- Applications of Differentiation

- Related rate applications
- Finding critical numbers
- First derivative test/increasing/decreasing
- Finding relative maxima and minima
- Concavity and inflection points
- Second derivative test
- Curve sketching
- Optimization applications
- Differentials

- Integration

- Fundamental theorem of calculus
- Finding the average value of a function
- Properties of definite integrals
- Integration using substitution

- Applications of Integration

- Area under curve
- Area between two curves

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the
sciences and

mathematics, social sciences, humanities, histories, languages, and the arts. - Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment
across general and

specialized skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

In MAT 170, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):

- Approximating limits graphically and numerically and evaluating limits analytically.
- Defining the derivative of a function and evaluating the derivative of a function using the definition.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):

- Listing the conditions for the continuity of a function at a point and determining if a function is continuous or discontinuous at a point.
- Determining the intervals of continuity of a function.
- Sketching the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Evaluating infinite limits and limits at infinity.
- Evaluating the derivative of a function using differentiation rules for algebraic functions as well as product, quotient, and chain rules.
- Performing implicit differentiation.
- Finding indefinite and definite integrals of a function using integration rules for algebraic functions.
- Finding definite and indefinite integrals using substitution.
- Determining if a function is differentiable or non-differentiable at a point.
- Finding the derivative and integral of functions including polynomial, rational, root, exponential, and logarithmic functions.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Using the derivative of a function to find the equation of the line tangent to the
graph of the function at a given

point.

Make inferences, evaluate assumptions, and assess limitations in estimation modeling and/or statistical analysis

by (Gen Ed Comp A, D): - Using derivatives to solve application problems including problems involving related
rates and optimization for biological sciences, social sciences, physical sciences,
or business.

Using definite integrals to find the area under a curve and the area between two curves. - Solving application problems using integrals for biological sciences, social sciences, physical sciences, or business.

- Using the derivative of a function to find the equation of the line tangent to the
graph of the function at a given

##### LEARNING RESOURCES

- Berresford, G. & Rockett, A. (2004). Brief applied calculus (3rd ed.). Boston, MA: Houghton/Mifflin
- Lial, M. L., Greenwell, R. N., & Ritchey, N. P. (2005). Calculus with applications, brief version (8th ed.). Boston, MA: Pearson/Addison Wesley.

Serves as the entry-level mathematics class for students in STEM fields. Prepares students for success in Calculus I. Develops fluency in the manipulation of polynomial, rational, radical, exponential, logarithmic, and trigonometric functions in order to solve equations, inequalities, and application problems. Familiarizes students with the graphs of the aforementioned functions. Includes linear and nonlinear systems of equations. Students may not receive credit for both MAT 171 and any other College Algebra, Trigonometry, or Precalculus course. Credit not available on the basis of special examination.

**Prerequisite:** ACT Math of 23 or equivalent

##### OFFICIAL COURSE OUTLINE

- Relations and Functions
- Definition of relation, function, domain, and range
- Determining the domain of a function
- Piecewise functions
- Adding, subtracting, multiplying, and dividing functions
- Composition and inverses
- Graphing using transformations

- Polynomial and Rational Functions
- Linear functions and their graphs
- Quadratic functions, their graphs, and completing the square
- Polynomial functions and their graphs
- Solving polynomial equations and inequalities
- Rational functions and their graphs
- Performing operations on rational functions
- Solving rational equations and inequalities

- Radical Functions
- Radical functions and their graphs
- Solving radical equations and inequalities

- Exponential and Logarithmic Functions
- Definition of exponential and logarithmic functions and their graphs
- Converting between exponential and logarithmic forms
- Performing operations on logarithmic functions
- Solving exponential and logarithmic equations and inequalities
- Applications of exponential and logarithmic functions

- Systems of Equations
- Solving systems of 3 or more linear equations
- Solving systems of 2 nonlinear equations

- Introduction to Trigonometric Functions
- Angle measure in radians and degrees
- Arc length and sector area
- Definition of the six trigonometric functions and their inverses
- Basic trigonometric identities
- Finding exact trigonometric function values for common angles
- Applications of trigonometry to right triangles

- Analysis of Trigonometric Functions
- Graphs of trigonometric and inverse trigonometric functions
- Performing operations on trigonometric functions
- Solving trigonometric equations and inequalities
- Establishing the validity of trigonometric identities
- Laws of Sines and Cosines
- General applications of trigonometry

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the sciences and mathematics, social sciences, humanities, histories, languages, and the arts.
- Intellectual and practical skills, including
- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including
- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING

In MAT 171, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
- Stating the definition of the six trigonometric functions in their multiple forms.
- Stating basic trigonometric identities.
- Using radian and degree measure.
- Determining the inverse functions for the six trigonometric functions.
- Recognizing functions and specifying the domain and the range of a given function

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):
- Solving problems involving right triangles.
- Determining the amplitude and period of the trigonometric functions.
- Graphing linear, quadratic, polynomial, rational, exponential, logarithmic, piecewise, inverse and trigonometric functions

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Computing trigonometric function values using the definitions.
- Finding trigonometric values of angles using right triangle and unit circle trigonometry.
- Solving polynomial, rational, exponential, logarithmic and trigonometric equations.
- Performing operations with functions and finding inverse functions.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Applying the trigonometric function definitions to right triangles.
- Solving application problems using radian measure.
- Writing expressions from data, verbal descriptions or graphs.
- Solving application problems using linear, quadratic, exponential, logarithmic and trigonometric functions.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):

- Proving trigonometric identities.
- Solving problems using the sum and difference and double-angle formulas.
- Solving general triangles using the Law of Sines and the Law of Cosines.
- Solving linear and nonlinear systems of equations.

Examines one-variable calculus including limits, differentiation and integration of algebraic, trigonometric, exponential, logarithmic, hyperbolic, and inverse trigonometric functions with applications.

**Prerequisite:**

- College Algebra and Trigonometry, or equivalent, with grades of "C" or higher;
- Math ACT 27 or above;
- Placement exam recommendation; or
- Consent of instructor.

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Approximate limits graphically and numerically and evaluate limits analytically.
- List the conditions for the continuity of a function at a point and determine the intervals of continuity of a function.
- Evaluate infinite limits and limits at infinity.
- Define the derivative of a function and evaluate the derivative of a function using the definition.
- Evaluate the derivative of a function using differentiation rules for algebraic and trigonometric functions as well as product, quotient, and chain rules.
- Use the derivative of a function to find the equation of the line tangent to the graph of the function at a given point.
- Sketch the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph.
- Use implicit differentiation to find the equation of the line tangent to the graph of an equation at a given point.
- Use derivatives to solve application problems including problems involving related rates and optimization.
- Define the differential and use differentials to approximate function values.
- Use Riemann sums to find the area under a curve.
- Find indefinite and definite integrals of a function using integration rules for algebraic and trigonometric functions.
- Find definite and indefinite integrals using substitution.
- Find the average value of a function on an interval.
- Use definite integrals to find the area under a curve and the area between two curves.
- Find derivatives of exponential, logarithmic, inverse trigonometric, hyperbolic, and inverse hyperbolic functions.
- Find integrals of exponential and logarithmic functions.
- Find integrals using inverse trigonometric and inverse hyperbolic functions.

##### COURSE OUTLINE

- Limits
- Finding limits graphically
- Approximating limits numerically
- Finding limits analytically
- Î´-Îµ proofs
- One-sided limits
- Continuity
- Removable/non-removable discontinuities
- Infinite limits (f(x)â†’Â±âˆž)
- Limits as xâ†’Â±âˆž
- Horizontal asymptotes
- Indeterminate forms
- Vertical asymptotes

- Differentiation

- Definition of the derivative
- Finding derivatives using the definition
- Finding the tangent line to the graph of a function
- Basic differentiation rules for algebraic and trigonometric functions, product and quotient rules, chain rule
- Implicit differentiation
- Finding the tangent line to a graph

- Applications of Differentiation
- Related rate applications
- Rolle's Theorem
- Mean Value Theorem
- Finding critical numbers
- First derivative test/increasing/decreasing
- Finding relative maxima and minima
- Concavity and inflection points
- Second derivative test
- Curve sketching
- Optimization applications
- Differentials
- Newton's method for approximating zeros

- Integration
- Riemann sums/finding area using a limit
- Fundamental theorem of calculus
- Finding the average value of a function
- Properties of definite integrals
- Integration using substitution
- Area between two curves

- Transcendental Functions

- Differentiation of ln x
- Differentiation using ex
- Differentiation using ax and logax
- Differentiation of inverse trigonometric functions, hyperbolic functions, and inverse hyperbolic functions
- Integration using ln x
- Integration using ex
- Integration using ax and logax
- Integration using inverse trigonometric functions
- Integration using hyperbolic functions
- Integration using inverse hyperbolic function

**GENERAL EDUCATION COMPETENCIES**

- Intellectual and practical skills, including
- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

**STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING**

In MAT175, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
- Approximate limits graphically and numerically and evaluate limits analytically.
- Define the derivative of a function and evaluate the derivative of a function using the definition.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):
- List the conditions for the continuity of a function at a point and determine the intervals of continuity of a function.
- Sketch the graph of a function using the first and second derivatives to determine the critical points, intervals on which the function is either increasing or decreasing, relative extrema, intervals on which the graph is either concave up or concave down, and inflection points of the graph.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Evaluate infinite limits and limits at infinity.
- Evaluate the derivative of a function using differentiation rules for algebraic and trigonometric functions as well as product, quotient, and chain rules.
- Use implicit differentiation to find the equation of the line tangent to the graph of an equation at a given point.
- Find indefinite and definite integrals of a function using integration rules for algebraic and trigonometric functions.
- Find definite and indefinite integrals using substitution.
- Find derivatives of exponential, logarithmic, inverse trigonometric, hyperbolic, and inverse hyperbolic functions.
- Find integrals of exponential and logarithmic functions.
- Find integrals using inverse trigonometric and inverse hyperbolic functions.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Use the derivative of a function to find the equation of the line tangent to the graph of the function at a given point.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
- Use derivatives to solve application problems including problems involving related rates and optimization.
- Use definite integrals to find the area under a curve and the area between two curves.

Includes applications of integration, advanced integration techniques, sequences and infinite series, and parametric and polar equations.

**Prerequisite:** Calculus I, or equivalent, with grade of "C" or higher, or consent of instructor.

**OFFICIAL COURSE** OUTLINE

- Applications of Integration
- Volume using the disk/washer method
- Volume using the shell method
- Arc length
- Area of a surface of revolution
- Work applications
- Moments/center of mass
- Fluid force

- Advanced Integration Techniques
- Integration by parts
- Trigonometric integrals
- Integration using trigonometric substitution
- Integration using the method of partial fractions
- Integration using tables and other techniques
- L'HÃ´pital's Rule
- Improper integrals

- Sequences and Infinite Series
- Sequences
- Series
- nth term test
- Integral test
- p-series test
- Direct comparison test
- Limit comparison test
- Alternating series test/absolute convergence
- Ratio test
- Root test

- Power Series
- Taylor/Maclaurin polynomials
- Taylor/Maclaurin series

- Nonrectangular Coordinates
- Parametric curves (plane)
- Arc length and surface area (parametric)
- Polar coordinates
- Area and volume using polar coordinates

**GENERAL EDUCATION COMPETENCIES**

- Intellectual and practical skills, including
- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

**STUDENT LEARNING OUTCOMES FOR QUANTITATIVE** REASONING

In MAT 185, students will learn to:

- Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
- Determine whether a given sequence converges, and find the limit of a convergent sequence.
- Determine whether infinite series converge by using tests such as the nth term test, the integral test, the p-series test, the direct comparison test, the limit comparison test, the alternating series test, the ratio test, and the root test.
- Determine whether the convergence of a series is absolute.
- Find Taylor and Maclaurin polynomials for a given function.
- Find power series and Taylor and Maclaurin series representations of a given function and determine their intervals of convergence.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):
- Convert between parametric equations and rectangular equations.
- Convert between polar coordinates and rectangular coordinates.

- Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):

- Use L'HÃ´pital's Rule.
- Find integrals using integration by parts, trigonometric substitution, the method of partial fractions, and by using tables.
- Evaluate improper integrals.
- Determine the slope of a tangent line to a parametric graph, and determine the arc length of a parametric graph.

- Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):

- Use integration to solve application problems involving work, center of mass, and fluid force.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
- Use integration to find the volume of a solid of revolution and the area of a surface of revolution, and the arc length of the graph of a function.
- Calculate the slope of a tangent line to a polar graph; determine the arc length of a polar graph; and determine the volume and surface area of solids formed by revolving regions bound by polar graphs.

Examines multivariate calculus including parametric equations; rectangular, cylindrical, and spherical coordinate systems; vectors and vector-valued functions; limits and derivatives of functions of several variables; multiple integration; and line and surface integrals.

**Pre-requisite: **MAT 185 or equivalent, or Consent of instructor

**Attributes:** QR - Quantitative Reasoning

**Components:** Lecture 4.0 credits (60 contact hours)

##### OFFICIAL COURSE COMPENTENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Perform the operations of addition, subtraction, dot product, and cross product on vectors.
- Identify various surfaces, including quadric surfaces, by their equations and their graphs.
- Convert between rectangular, cylindrical, and spherical coordinates.
- Determine velocity and acceleration functions from a vector-valued position function.
- Determine arc length of a vector-valued function.
- Determine the unit tangent vector, principal unit normal vector, and curvature of a vector-valued function.
- Solve application problems involving projectile motion.
- Find partial derivatives and total differentials of functions of several variables.
- Find directional derivatives and the gradient of functions of several variables.
- Find relative extrema of functions of several variables and solve constrained optimization problems using Lagrange multipliers.
- Evaluate double and triple integrals, and use multiple integration to solve problems involving volume, surface area, and center of mass.
- Evaluate line integrals within vector fields.
- Use Green's Theorem and the principle of path independence to evaluate line integrals within conservative vector fields.
- Evaluate surface integrals and flux integrals.
- Use the Divergence Theorem to evaluate flux integrals.
- Use Stokes' Theorem to evaluate line integrals along a surface.

OFFICIAL COURSE OUTLINE

- Vectors
- Addition, subtraction, and scalar multiples
- Dot and cross products
- Three-dimensional graphs including quadric surfaces
- Rectangular, cylindrical, and spherical coordinates

- Vector-valued functions
- Position, velocity, and acceleration
- Unit tangent vector and principal unit normal vector
- Curvature

- Functions of several variables
- Limits and derivatives
- Directional derivatives and the gradient
- Relative extrema and Lagrange's Theorem

- Multiple integration
- Double and triple integrals
- Volume and surface area
- Center of mass and moments

- Vector fields
- Line integrals
- Green's Theorem
- Surface and flux integrals
- Divergence Theorem and Stokes's Theorem

Examines ordinary differential equations emphasizing first and second order equations and applications. Includes series solutions of second order equations and Laplace transform methods.

**Pre-requisite:** MAT 275 or Consent of instructor

**Attributes:** QR - Quantitative Reasoning

**Components:** Lecture 3.0 credits (45 contact hours)

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Identify and Classify Differential Equation.
- Solve differential equations by separation of variables.
- Solve homogeneous, exact, and linear differential equations.
- Solve differential equations with constant coefficients.
- Solve differential equations using reduction of order and variation of parameters.
- Solve application problems using differential equations of first order.
- Solve application problems using differential equations involving simple and damped harmonic motion.
- Find the Laplace transforms of common functions, and use Laplace Transforms to solve differential equations.
- Find series solutions to differential equations.
- Solve linear systems of differential equations.

OFFICIAL COURSE OUTLINE

- First-Order Differential Equations
- Separable variables
- Homogeneous equations
- Exact equations
- Linear equations
- Bernoulli's equations

- Applications of First Order Differential Equations
- Applications of linear equations
- Applications of non-linear equations

- Linear Differential Equations of Higher Order
- Equations with constant coefficients
- Undetermined coefficients
- Differential operators and the annihilator approach
- Variation of parameters

- Applications of Second Order Differential Equations
- Simple harmonic motion
- Damped harmonic motion

- Differential Equations with Variable Coefficients
- Cauchy-Euler equations
- Power series solution around ordinary and singular points

- Laplace Transforms
- Laplace transforms of common functions
- Using Laplace Transforms to solve equations

- Systems of Linear Differential Equations
- Laplace transform method
- Matrices

The goal of this course is to help students develop or refine their statistical literacy skills. Both the informal activity of human inference arising from statistical constructs, as well as the more formal perspectives on statistical inference found in confidence intervals and hypothesis tests are studied. Throughout, the emphasis is on understanding what distinguishes good and bad inferential reasoning in the practical world around us.

**Prerequisites:** Quantitative Reasoning College Readiness Indicators as defined by CPE (ACT 19 or
higher, or equivalent as determined by placement examination)

##### OFFICIAL COURSE COMPETENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Begin to absorb common statistical information appropriately and form associated human inferences carefully.
- Develop an evolved sense of what statistical confidence means and doesn't mean by involving students in real surveys they will enjoy discussing.
- Juxtapose the concepts and language of hypothesis testing with the more easily accessible ideas of sensitivity and specificity

##### OFFICIAL COURSE OUTLINE

- Begin to absorb common statistical information appropriately and form associated human
inferences carefully.

- Identify categorically good or bad statistical summaries, charts and graphs, and explain the reasons they are so categorized.
- Identify categorically good or bad statistical arguments based on statistical summaries, charts, and graphs, and explain the reasons they are so categorized.
- Distinguish the concepts of correlation and causation and explain how they offer different types of evidence.
- Identify hidden or confounding variables in studies reported by the media or in the literature.
- Explain if and how hidden or confounding variables can or did affect the associated common-sense inferences.
- Define what is meant by Simpson's Paradox.
- Explain how a misinterpretation of randomness leads to poor human inferences.
- Explain how not having enough or the right information leads to poor human inference.
- Present examples relative to each of parts E, F, G, and H.
- Identify and present at least one argument from psychology or neuroscience that supports the contention that poor human inferences are common.

- Develop an evolved sense of what statistical confidence means and doesn't mean by
involving students in real surveys they will enjoy discussing.

- Identify categorically good or bad surveys and explain the reasons they are so categorized.
- Identify a push poll from the news and explain the reasons such a poll is likely not a source of useful information.
- Explain the difference between sampling variability and non-sampling variability.
- Identify strategies for understanding non-sampling variability.
- Identify a margin of error that is in the news, but not discussed in class, from the associated confidence interval and use statistical language to explain the sort of confidence that is being offered, and the type of risk that is being quantified.
- Compare and contrast the information contained in a Cosmopolitan on-line poll, a CBS Evening News call-in poll, a Gallup random-dialing poll, and a door-to-door political campaign poll.
- Define sampling variability and explain the role it plays in the construction of a confidence interval.
- Define sampling distribution and demonstrate the Central Limit Theorem by hands-on repeated sampling.
- Produce a non-95% confidence interval for a proportion or mean, based on data from a simple random sample.
- Explain what happens to a confidence interval as the confidence level changes and/or the sample size changes.

- Juxtapose the concepts and language of hypothesis testing with the more easily accessible
ideas of sensitivity and specificity in an effort to demystify these more difficult
ideas and facilitate a discussion of the related statistical Issues.

- Define sensitivity and specificity.
- Read about a dichotomous decision process that is in the news, not discussed in class, and explain the roles for sensitivity and specificity in assessing the integrity of that process.
- Identify the structure of a test of hypothesis and explain the purpose of the null and the alternative hypotheses, and the way in which the evidence that is gathered is used.
- Define significance and power and explain the roles each play in assessing the integrity of dichotomous significance test.
- Read about a test of significance associated with an experiment that is in the news,
but not discussed in class,

and use the language of statistics to explain and evaluate the nature of the evidence that is presented. - Explain the role of modeled error in a simple test of hypothesis for a simple experimental design.
- Define the Prosecutor's Fallacy.
- Explain the importance of the Prosecutor's Fallacy to interpreting specificity and sensitivity.
- Explain the importance of the Prosecutor's Fallacy to describing the results of null hypothesis testing.
- Read a news story and identify and demonstrate the difference between various conditional
events and

unconditional events discussed in that story.

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the
sciences and mathematics,

social sciences, humanities, histories, languages, and the arts. - Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

- Integrative and applied learning, including synthesis and advanced accomplishment
across general and specialized

skills.

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

- Interpret information presented in mathematical and/or statistical forms. (B)

- Explain if and how hidden or confounding variables can or did affect the associated
common-sense inferences.

Explain the difference between sampling variability and non-sampling variability. - Define significance and power and explain the roles each play in assessing the integrity
of dichotomous significance

test.

- Explain if and how hidden or confounding variables can or did affect the associated
common-sense inferences.
- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically. (A, B and C)

- Identify categorically good or bad statistical summaries, charts and graphs, and explain
the reasons they are so

categorized. - Identify categorically good or bad statistical arguments based on statistical summaries,
charts, and graphs, and

explain the reasons they are so categorized.

- Identify categorically good or bad statistical summaries, charts and graphs, and explain
the reasons they are so
- Determine when computations are needed and to execute the appropriate computations.
(B)

- Define sampling distribution and demonstrate the Central Limit Theorem by hands-on repeated sampling.
- Define sensitivity and specificity.

- Apply an appropriate model to the problem to be solved. (A, C and D)

- Distinguish the concepts of correlation and causation and explain how they offer different types of evidence.
- Identify the structure of a test of hypothesis and explain the purpose of the null
and the alternative hypotheses, and

the way in which the evidence that is gathered is used.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis. (B, C and D)

- Produce a non-95% confidence interval for a proportion or mean, based on data from a simple random sample.
- Explain what happens to a confidence interval as the confidence level changes and/or the sample size changes.
- Explain the role of modeled error in a simple test of hypothesis for a simple experimental design.

##### LEARNING RESOURCES

*Beyond the Numbers: Student-Centered Activities for Learning Statistical Reasoning*, current edition, by William Rayens,

Van-Griner Publishers

*StatCrunch* Student 6-Month Access Code

STA 220 Statistics (3) - Course Information

Examines statistical description of sample data including frequency distributions,
measures of central tendency, and measures of dispersion. Includes theoretical distributions,
statistical estimation, and hypothesis testing. Introduces simple linear regression
and correlation.

**Prerequisite:** MAT 150 or equivalent.

**Official Course Description**

Introduction to principles of statistics with emphasis on conceptual understanding.
Students will articulate results of statistical description of sample data (including
bivariate), application of probability distributions, confidence interval estimation
and hypothesis testing to demonstrate properly contextualized analysis of real-world
data.**Prerequisites:** MA 113, MA 123, MA 137 or equivalent.

##### OFFICAL COURSE COMPENTENCIES/OBJECTIVES

Upon completion of this course, the student can:

- Demonstrate understanding of p-value, margins of error and confidence intervals, formal hypothesis tests through their creation or evaluation.
- Generate and/or analyze critically quantitative and graphic data summaries in their real-world contexts.
- Integrate knowledge from huge reservoir of available data and illustrate their comprehension of that knowledge through individual summarization.

##### OFFICIAL COURSE OUTLINE (Approved Fall 2014)

- Data

- Data Collection
- Sample Designs
- Categorical vs.
- Quantitative Data

- Descriptive Statistics

- Summarizing Categorical Data
- Summarizing Quantitative Data
- Measures of Center
- Measures of Spread
- Standard Deviation
- Sensitivity and Specificity

- Probability

- Probability Rules
- Joint Probability and Contingency Tables
- Conditional Probability

- Random Variables

- Discrete Random Variables
- Binomial Probability Distributions
- Continuous Probability Distributions
- Normal Distributions
- t-Distributions

- Sampling Distributions

- Sampling Distribution for Proportions
- Central Limit Theorem
- Sampling Distribution for Means

- Confidence Intervals

- Confidence Intervals for Proportions
- Confidence Intervals for Means
- Margin of Error
- Assumptions
- Sample Size

- Hypothesis Testing

- Hypotheses
- P-values
- Reasoning
- Testing Hypotheses about the Mean
- Testing Hypotheses about the Proportion

- Comparing Means

- Difference between Two Means - Dependent Samples
- Difference between Two Means - Independent Samples

- Comparing Proportions

- Goodness of Fit Tests
- Chi-Square Interpretation
- Chi-Square Test of Homogeneity
- Chi-Square Test of Independence

- Linear Regression

- Correlation
- Linear Model
- Assumptions
- Test for the Regression Slope

##### GENERAL EDUCATION COMPETENCIES

- Knowledge of human cultures and the physical and natural worlds through study in the
sciences and

mathematics, social sciences, humanities, histories, languages, and the arts. - Intellectual and practical skills, including

- inquiry and analysis
- critical and creative thinking
- written and oral communication
- quantitative literacy
- information literacy
- teamwork and problem solving

- Personal and social responsibility, including

- civic knowledge and engagement (local and global)
- intercultural knowledge and competence
- ethical reasoning and action
- foundations and skills for lifelong learning

##### STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)

- Interpret Information presented in mathematical and/or statistical forms. (B)

- Summarize data with measures of center and measures of spread.
- Identify and explain sensitivity and specificity.

- Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically.

(A, B and C)

- Summarize categorical data in graphical form.
- Summarize quantitative data in graphical form.

- Determine when computations are needed and execute the appropriate computations. (B)

- Properly apply rules of probability.
- Calculate joint and conditional probability.
- Find the probability, mean and standard deviation for discrete and continuous probability distributions.

- Apply an appropriate model to the problem to be solved. (A, C and D)

- Construct a linear model for a regression problem.
- Predict an outcome within the range of a linear model.

- Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis.

(B, C and D)

- Construct and interpret confidence intervals for a mean and proportion.
- Conduct hypothesis testing for a mean and proportion.
- Construct and interpret confidence intervals for the difference between two means.
- Conduct hypothesis testing for the difference between two means.

##### LEARNING RESOURCES

- Rayens, William (2013 or latest edition). Making Sense of Uncertainty: Activities
for Teaching Statistical

Reasoning. Van-Griner Publishing. ISBN-13: 978-1-61740-106-0 - My Stat Lab

## Length of Program

You can earn an associate in applied science degree in two years if you maintain full-time status.

This information should not be considered a substitute for the KCTCS Catalog. You should always choose classes in cooperation with your faculty advisor to ensure that you meet all degree requirements.