Our Courses
The Mathematics and Statistics Division at Bluegrass Community and Technical College offers a broad range of mathematics and statistics courses that meet the varied needs of students who are pursuing their academic goals.
Courses range from basic arithmetic to college algebra, contemporary mathematics, geometry, trigonometry, elementary calculus, calculus, finite mathematics, mathematics for business, applied mathematics, and statistics.
Through such coursework, students acquire the ability to think logically and abstractly, as well as develop the problemsolving and computational skill necessary in all fields of study. Most of the courses within the mathematics curriculum fulfill general education and transfer requirements.
Math & Stats Enrollment Request Form
BCTC Courses
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.
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
 DividerChooser Method
 Sealed Bids
 Proportional Division
 Quota Methods
 Hamilton
 Lowndes’
 Divisor Methods
 Jefferson
 Adams’
 Webster
 HuntingtonHill
 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 specializedskills.
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
A course in onevariable calculus, including topics from analytic geometry. Derivatives and integrals of elementary functions (including the trigonometric functions) with applications. Lecture, three hours; recitation, two hours per week. Students may not receive credit for MA 113 and MA 137.
Prerequisite: Math ACT of 27 or above, or math SAT of 620 or above, or MA 109 and MA 112, or MA 110, or consent of the department. Students who enroll in MA 113 based on their test scores should have completed a year of precalculus study in high school that includes the study of the trigonometric function.
Note: Math placement test recommended.
Official Course Description 
A course in onevariable calculus, including topics from analytic geometry. Derivatives and integrals of elementary functions (including the trigonometric functions) with applications. Lecture, three hours; recitation, two hours per week. Students may not receive credit for MA 113 and MA 137. Prerequisite: Math ACT of 27 or above, or math SAT of 620 or above, or a grade of C or better in MA 109 and in MA 112, or a grade of C or better in MA 110, or appropriate score on math placement test, or consent of the department. Students who enroll in MA 113 based on their test scores should have completed a year of precalculus study in high school that includes the study of the trigonometric function. Note: Math placement test recommended. 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES (Approved Fall 2017)
Upon completion of this course, the student can:
 Approximate limits graphically and numerically and evaluate limits analytically.
 Evaluate infinite limits, limits at infinity, and limits of indeterminate form including the use of L’Hospital’s Rule.
 Determine whethera function is continuous using the definition of continuity.
 Define the derivative of a function and evaluate the derivative using the definition.
 Determine the derivative of a function using differentiation rules for algebraic, trigonometric and transcendental functions.
 Use product rule, quotient rule,and chain rule techniques to determine derivatives of functions.
 Write the equation of a line tangent to a curve at a given point using derivatives.
 Use calculus to sketch graphs of functions.
 Determine derivatives using implicit differentiation.
 Define the integral of a function and evaluate using the definition of integration.
 Find indefinite and definite integrals of a function using integration rules for algebraic, trigonometric and transcendental functions.
 Use substitution techniques to determine the definite and indefinite integrals of functions.
 Analyze information to develop models for solving application problems involving related rates, optimization, area under curves and velocity/acceleration.
OFFICIALCOURSE OUTLINE (Approved Fall 2017)
 Functions
 Review
 Composition
 Inverses
 Trigonometric Functions
 Exponential Functions
 Definition
 Natural Exponential
 General Exponential
 Properties
 Graphs
 Definition
 Logarithmic Functions 1. Definition a. Natural Logarithm b. General Logarithm 2. Properties 3. Graphs
 Inverse Trig Functions 1. Definitions 2. Properties 3. Graphs
 Review
 Limits of a Function
 Definition
 Left and Right Handed Limits
 Graphical Limits
 Algebraic Limits
 Trigonometric Limits
 Infinite Limits
 Limits at Infinity
 Indeterminate Forms00,¥¥,¥¥,0×¥,00,¥0,1¥
 L’Hospital’s Rule
 Squeeze Theorem
 Continuity
 Definition
 Intermediate Value Theorem
 Derivatives
 Definition
 Differentiation Formulas
 Functions
 Polynomials
 Exponential
 Logarithmic
 Trigonometric
 Inverse Trig
 Power Rule
 Product Rule
 Quotient Rule
 Chain Rule
 Functions
 Higher Order Derivatives
 Implicit Differentiation
 Logarithmic Differentiation
 Applications of Derivatives
 Tangent Lines
 Rolle’s Theorem
 Mean Value Theorem
 Rates of Change
 Related Rates
 Linear Approximations and Differentials
 Optimization
 Graphing with Calculus
 Increasing and Decreasing Functions
 Relative Extrema
 Concavity
 Inflection Points
 Asymptotes
 Vertical
 Horizontal
 Oblique
 Curve Sketching
 Integration
 Riemann Sums
 Antiderivatives
 Fundamental Theorem of Calculus
 Definite Integrals
 Indefinite Integrals
 Substitution Integrals
 Applications of Integrals
 Area Under a Curve
 Net Change
 Velocity & Acceleration
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 specializedskills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
In MA 113, 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 using the definition.
 Defining the integral of a function and evaluating using the definition of integration.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by(Gen Ed Comp A, B, C):
 Determining whether a function is continuous using the definition of continuity.
 Using calculus to sketch graphs of functions.
 Determine when computations are needed and execute theappropriate computations by
(Gen Ed Comp A, B):
 Evaluating infinite limits, limits at infinity, and limits of indeterminate form including the use of L’Hospital’s Rule.
 Determining the derivative of a function using differentiation rules for algebraic, trigonometric and transcendental functions.
 Using product rule, quotient rule,and chain rule techniques to determine derivatives of functions.
 Determining derivatives using implicit differentiation.
 Finding indefinite and definite integrals of a function using integration rules for algebraic, trigonometric and transcendental functions.
 Using substitution techniques to determine the definite and indefinite integrals of functions.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Writing the equation of a line tangent to a curve at a given point using derivatives.
 Make inferences, evaluate assumptions, and assesslimitations in estimation modeling
and/or statistical analysisby (Gen Ed Comp A, D):
 Analyzing information to developmodels for solving applicationproblems involving related rates, optimization, area under curves and velocity/acceleration
A second course in Calculus. Applications of the integral, techniques of integration, convergence of sequence and series, Taylor series, polar coordinates. Lecture, three hours; recitation, two hours per week.
Prerequisite: A grade of C or better in MA 113, MA 137, or MA 132.
MA 114 CALCULUS II (UK Course) (4 credit hours)
Official Course Description  A second course in Calculus. Applications of the integral, techniques of integration,
convergence of sequence and series, Taylor series, polar coordinates. Lecture, three hours; recitation, two hours per week. Prerequisite: A grade of C or better in MA113, MA137, or MA132. 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES (Approved Fall 2017)
Upon completion of this course, the student can:
1. Use integration to find the area between curves, volume of solids of revolution, and the arc length of graphs of a function. 2. Use integration to solve application problems involving average value and work. 3. Compute integrals using various techniques including the methods of substitution, integration by parts, trigonometric substitution, partial fractions, and tables. 4. Evaluate improper integrals. 5. Determine and compute convergence/divergence of sequences and series. 
6. Find power series and Taylor and Maclaurin series 7. Represent curves by parametric equations, and 8. Determine the slope of a tangent line to and the 9. Calculate the slope of a tangent line to and the arc 
OFFICIAL COURSE OUTLINE (Approved Fall 2017)
 Applications of Integrals
 Area Between Curves
 Volumes of Revolution
 Disks
 Washers
 Shells
 Average Value
 Work
 Arc Length
 Integration Techniques/Strategies
 Integration by Parts
 Trigonometric Integrals
 Powers of sin(x), cos(x), sec(x) & tan(x)
 Products of sin(x) & cos(x)
 Products of sec(x) & tan(x)
 Arbitrary Combinations of Trigonometric Functions
 Trigonometric Substitution
 Partial Fractions
 Long Division
 Completing the Square
 Rationalizing Substitutions
 Tables
 Improper Integrals
 Infinite Intervals
 Discontinuous Integrands
 Sequences
 Definition
 Convergent
 Divergent
 Definition
 Series
 Definition
 Convergence
 Divergence
 Absolute Convergence
 Conditional Convergence
 Geometric Series
 PSeries
 Alternating Series
 Tests
 Test for Divergence
 Integral Test
 Comparison Tests
 Direct Comparison Test
 Limit Comparison Test
 Alternating Series Test
 Ratio Test
 Root Test
 Power Series
 Radius of Convergence
 Interval of Convergence
 Properties
 Derivative
 Integral
 4. Expressing Functions as Power Series
 Taylor Series
 Maclaurin Series
 Definition
 Parametric Equations
 Conversion to Cartesian Equation
 Parametric Curves
 Graphing
 Tangents
 Areas
 Arc Length
 Polar Coordinates
 Conversions
 Polar to Cartesian
 Cartesian to Polar
 Polar Curves
 Graphing
 Tangents
 Areas
 Arc Length
 Conversions
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 MA 114, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Determining and computing convergence/divergence of sequences and series.
 Finding power series and Taylor and Maclaurin series representations of a given function
and determining
their intervals of convergence.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):
 Representing curves by parametric equations, and applying the methods of calculus to parametric curves.
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Computing integrals using various techniques including the methods of substitution,
integration by parts,
trigonometric substitution, partial fractions, and tables.  Evaluating improper integrals.
 Determining the slope of a tangent line to and the arc length of the graph of a parametric function.
 Calculating the slope of a tangent line to and the arc length of a polar graph, and
determining the volume
and surface area of solids formed by revolving regions bound by polar functions.
 Computing integrals using various techniques including the methods of substitution,
integration by parts,
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Using integration to solve application problems involving average value and work.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
 • Using integration to find the area between curves, volume of solids of revolution,
and the arc length of
graphs of a function.
 • Using integration to find the area between curves, volume of solids of revolution,
and the arc length of
Finite mathematics with applications to business, biology, and the social sciences.
Linear functions and inequalities, matrix algebra, linear programming, probability.
Emphasis on setting up mathematical models from stated problems.
Prerequisite: MA 109 or equivalent.
MA162FINITE MATHEMATICSAND ITS APPLICATIONS (UK Course) (3credit hours)
Official Course Description  Finite mathematics with applications to business, biology, and the social sciences. Linear functions and inequalities, matrix algebra, linear programming, probability. Emphasis on setting up mathematical models from stated problems.Prerequisites: MA 109 or equivalent. 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
 State the geometric interpretation of the solution to a linear programming problem
 Determine whether two events are independent or not
 Determine whether two events are mutually exclusive or not
 Use proper matrix notation to organize arrays of numbers and represent equations
 Write and understand permutations and combinations in their standard notation
 Write and understand probabilities in standard notation
 Write and understand set notation for unions, intersections, and complements
 Represent sets within Venn Diagrams and understanding such representations
 Perform matrix operations
 Find the inverse of a matrix
 Find the simple, compound, or conditional probability
 Determine unions, intersections, and complements of sets and events
 Determine the number of ways a task can be performed using counting principles
 Solve a system of linear equations by substitution, elimination, using matrix row operations, and using matrix equations
 Solve a linear programming problem graphically and by the simplex method
 Determine whether a problem involves permutations, combinations, or basic counting methods
 Determine whether a problem involves simple, compound, or conditional probability
 Set up and solve an application involving systems of equations
 Set up and solve an application involving linear programming
 Solve multistep problems that contain simple, compound and conditional probabilities
OFFICIALCOURSE OUTLINE (Approved Spring 2003)
 Linear Systems
 Solve linear systems of two or more variables by graphing, substitution, elimination or GaussJordan methods.
 Recognize consistent, inconsistent, and dependent systems
 Write solutions in parametric form
 Set up and solve applied problems
 Matrix Operations
 Recognize and be able to write coefficient matrices and augmented matrices
 Be able to define and identify square matrices, equal matrices, and matrices dimensions.
 Add and subtract matrices
 Perform scalar multiplication
 Perform matrix multiplication
 Find inverses
 Use inverses to solve systems
 Linear Inequalities
 Graph inequalities
 Graph systems of inequalities
 Identify corner points and feasible regions
 Solve optimization problems by substituting corner points into objectivefunctions.
 Identify standard maximization and minimization problems.
 Solve standard maximization simplex problems
 Solve duality problems using simplex
 Convert nonstandard optimization problems to standard maximum problems:
 Problems with ≥ constraints
 Problems with = constraints
 Problems with negative numbers on the righthand side of constraints
 Problems with a minimized objective function.
 Identify simplex problems without a single solution
 Multiple solutions
 Unbounded solutions
 No solutions
 Solve applied optimization problems using simplex and/or graphing methods.
 Sets
 Use, define and identify set builder notation, empty or null set, universal set, equal sets, subsets, proper subsets, elements, union, intersection, complements, disjoint sets
 Use and solve applied problems with Venn Diagrams
 Identify the number of elements in sets
 Combinatorics
 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
 Probability
 Identify and define experiment, outcome, trial, sample space, event, empirical probability, randomoutcomes
 Find probabilities of equally likely events in applied problems
 Find probabilities of compound events in applied problems
 union
 intersection
 complement
 Define and identify mutually exclusive events and independent events
 Solve applied conditional probability problems
 Solve applied probability problems using Baye’s Rule
 Markov Chains (OPTIONAL)
 Identify and define state matrices, transition matrices, markov chains, and steadystate matrices
 Solve applied problems involving Markov Chains
 Find steadystate matrices
 Identify regular matrices
 Solve applied problems using Bernouilli’s Formula (OPTIONAL)
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 specializedskills.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING (Approved Fall 2017)
In MA162, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Determining whether a problem involves permutations, combinations, or basic counting methods
 Determining whether a problem involves simple, compound, or conditional probability
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by(Gen Ed Comp A, B, C):
 Stating the geometric interpretation of the solution to a linear programming problem.
 Using proper matrix notation to organize arrays of numbers and represent equations.
 Writing and understanding probabilities in standard notation.
 Representing sets within Venn Diagrams and understanding such representations
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Performing matrix operations.
 Finding the simple, compound, or conditional probability.
 Determining unions, intersections, and complements of sets and events.
 Determining the number of ways a task can be performed using counting principles.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Solving a system of linear equations by substitution, elimination, using matrix row operations, and using matrix equations.
 Solving a linear programming problem graphically and by the simplex method.
 Solving multistep problems that contain simple, compound and conditional probabilities.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
 Setting up and solving an application involving systems of equations.
 Setting up and solving an application involving linear programming.
Laboratory offered (only) as an adjunct to certain mathematics lecture courses. Offered only on a pass/fail basis.
Corequisite: Set by instructor.
Note: This is typically required as a corequisite for MA 113 Calculus I.
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
See competencies of the concurrent course.
COURSE OUTLINE
See course outline of the concurrent course.
GENERAL EDUCATION COMPETENCIES
See general education competencies of the concurrent course.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING
See student learning outcomes for quantitative reasoning of the concurrent course.
Laboratory offered (only) as an adjunct to certain mathematics lecture courses. Offered only on a pass/fail basis.
Corequisite: Set by instructor.
Note: This is typically required as a corequisite for MA 114 Calculus II.
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
See competencies of the concurrent course.
COURSE OUTLINE
See course outline of the concurrent course.
GENERAL EDUCATION COMPETENCIES
See general education competencies of the concurrent course.
STUDENT LEARNING OUTCOMES FOR QUANTITATIVE REASONING
See student learning outcomes for quantitative reasoning of the concurrent course.
Sets, numbers and operations, problem solving and number theory. Recommended only for majors in elementary and middle school education.
Prerequisite: MA 109 or MA 111 or consent of department.
MA 202 MATHEMATICS FOR ELEMENTARY TEACHERS (UK Course) (3 credit hours)
Official Course Description  Algebraic reasoning, introduction to statistics and probability, geometry, and measurement. Prerequisites: A grade of “C” or better in MA 201. Also recommended: a course in logic (e.g. PHI 120) or a course in calculus (e.g. MA 123). 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
 Develop an understanding of fundamental concepts of geometry including point, line, angle, and plane.
 Describe data and its characteristics including dispersion and central tendency, and solve problems involving these concepts.
 Understand concepts of symmetry such as congruence, similarity, proportionality, and isometries as they relate to various plane shapes.
 Select the appropriate representation for data display and interpret information presented in such graphical displays including bar graphs, line plots, circle graphs, and stem and leaf plots.
 Practice the process of measurement and identify units in the standard systems of measurement.
 Calculate the perimeter and area of various different shapes and the volume of various solids.
 Draw reasonable conclusions based on the characteristics of a data set, and solve problems that involve finding the probability of an event.
 Demonstrate an understanding of and solve application problems involving the concepts of permutations and combinations.
 Identify projections, cross sections, and decompositions of common two dimensional and three dimensional figures.
 Use deductive reasoning and counter examples to prove or disprove statements about two dimensional and three dimensional figures.
 Develop notions about probability of events empirically through simulations and calculate these probabilities.
OFFICIAL COURSE OUTLINE (Approved Fall 2007)
 Geometry and Measurement
 Develop visualization skills:
 Be familiar with projections, crosssections, and decomposition of common two and threedimensional figures.
 Represent threedimensional shapes in two dimensions and constructing threedimensional objects from twodimensional representations.
 Manipulate mentally physical representations of two and threedimensional shapes.
 Determine the rotational and line symmetries for twodimensional shapes.
 Develop familiarity with basic shapes and their properties:
 Know fundamental objects of geometry, including point, ray, line, and line segment.
 Develop an understanding of angles and how they are measured.
 Be familiar with plane isometries  reflections (flips), rotations (turns), and translations (slides).
 Understand congruence, similarity, and proportional reasoning via similarity.
 Learn technical vocabulary and understanding the importance of definition.
 Be familiar with currently available manipulatives and software that allow exploration of shapes.
 Understanding the process of measurement and measurement techniques:
 Recognize different aspects of size.
 Understand the idea of unit and the need to select a unit appropriate to the attribute being measured.
 Know the standard (English and metric) system of units.
 Use measurement tools such as rulers and meter sticks to make measurements.
 Estimate using common units of measurement.
 Compare units and relate measurements within each of the two common systems of measure, English and metric.
 Understand that measurements are approximate and that different units affect precision.
 Understand role of in measurement.
 Understand and use Pythagorean Theorem.
 Understand length, area, and volume:
 Know what is meant by one, two, and threedimensions.
 See rectangles as arrays of squares and rectangular solids as arrays of cubes.
Updated 11172017  Recognize the behavior of measure (length, area, and volume) under uniform dilations.
 Devise area formulas for triangles, parallelograms, and trapezoids; knowing the formula for the area of a circle; be familiar with volume and surface area formulas for prisms, cylinders, and other threedimensional objects.
 Decompose and recompose nonregular shapes to find area or volume.
 Understand the independence of perimeter and area; surface area and volume.
 Develop visualization skills:
 Data Analysis, Statistics, and Probability
 Design data investigations (optional):
 Understanding the kinds of questions that can be addressed by data.
 Make decisions on what and how to measure.
 Be familiar with how surveys and statistical experiments are designed and what can be learned from them.
 Understand what constitutes a random sample and how bias is reduced.
 Describe data:
 Describe shape: symmetric versus skewed data distribution and what this indicates about the question being addressed by the data. (optional)
 Describe spread: range, outliers, clusters (optional), gaps (optional), and what these indicate about the question being addressed by the data.
 Describe center: mean, median, and mode and what these indicate about the question being addressed by the data.
 Be familiar with different forms of graphical data representation, e.g. line plots, histograms, line graphs, bar graphs, box plots, pie charts, stemandleaf plots, among others; recognize that different forms of representation communicate different features of the data and that some representations are more appropriate than others for a given data set.
 Comparing two sets of data (not always of the same size).
 Draw conclusions:
 Choose among representations and summary statistics to communicate conclusions.
 Understand variability and the role it plays in decision making. (optional)
 Understand some of the difficulties that arise in sampling and inference.
 Recognize some of the ways that statistics and graphical displays of data can be misleading.
 Develop notions of probability:
 Making judgements under uncertainty.
 Assign numbers as a measure of likelihood to singlestage and multistage events.
 Understand conditional probability and some of its applications.
 Be familiar with the idea of randomness.
 Develop empirical probabilities through simulations; relate to theoretical probability.
 Understand the notions of expected value and fairness and use probability to determine fairness. (optional)
 Design data investigations (optional):
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 MA 202, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Developing an understanding of fundamental concepts of geometry including point, line, angle, and plane.
 Describing data and its characteristics including dispersion and central tendency, and solve problems involving these concepts.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by (Gen Ed Comp A, B, C):
 Understanding concepts of symmetry such as congruence, similarity, proportionality, and isometries as they relate to various plane shapes.
 Selecting the appropriate representation for data display and interpret information presented in such graphical displays including bar graphs, line plots, circle graphs, and stem and leaf plots.
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Practicing the process of measurement and identify units in the standard systems of measurement.
 Calculating the perimeter and area of various different shapes and the volume of various solids.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Drawing reasonable conclusions based on the characteristics of a data set, and solve problems that involve finding the probability of an event.
 Demonstrating an understanding of and solve application problems involving the concepts of permutations and combinations.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by (Gen Ed Comp A, D):
 Identifying projections, cross sections, and decompositions of common two dimensional and three dimensional figures.
 Using deductive reasoning and counter examples to prove or disprove statements about two dimensional and three dimensional figures.
 Developing notions about probability of events empirically through simulations and calculate these probabilities.
Algebraic reasoning, introduction to statistics and probability, geometry, and measurement.
Prerequisite: A grade of "C" or better in MA 201.
Also recommended: a course in logic (e.g. PHI 120) or a course in calculus (e.g. MA 123).
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
 Develop an understanding of fundamental concepts of geometry including point, line, angle, and plane.
 Describe data and its characteristics including dispersion and central tendency, and solve problems involving these concepts.
 Understand concepts of symmetry such as congruence, similarity, proportionality, and isometries as they relate to various plane shapes.
 Select the appropriate representation for data display and interpret information presented in such graphical displays including bar graphs, line plots, circle graphs, and stem and leaf plots.
 Practice the process of measurement and identify units in the standard systems of measurement.
 Calculate the perimeter and area of various different shapes and the volume of various solids.
 Draw reasonable conclusions based on the characteristics of a data set, and solve problems that involve finding the probability of an event.
 Demonstrate an understanding of and solve application problems involving the concepts of permutations and combinations.
 Identify projections, cross sections, and decompositions of common two dimensional and three dimensional figures.
 Use deductive reasoning and counter examples to prove or disprove statements about two dimensional and three dimensional figures.
 Develop notions about probability of events empirically through simulations and calculate these probabilities.
OFFICIAL COURSE OUTLINE (Approved Fall 2007)
 Geometry and Measurement
 Develop visualization skills:
 Be familiar with projections, crosssections, and decomposition of common two and threedimensional figures.
 Represent threedimensional shapes in two dimensions and constructing threedimensional objects from twodimensional representations.
 Manipulate mentally physical representations of two and threedimensional shapes.
 Determine the rotational and line symmetries for twodimensional shapes.
 Develop familiarity with basic shapes and their properties:
 Know fundamental objects of geometry, including point, ray, line, and line segment.
 Develop an understanding of angles and how they are measured.
 Be familiar with plane isometries  reflections (flips), rotations (turns), and translations (slides).
 Understand congruence, similarity, and proportional reasoning via similarity.
 Learn technical vocabulary and understanding the importance of definition.
 Be familiar with currently available manipulatives and software that allow exploration of shapes.
 Understanding the process of measurement and measurement techniques:
 Recognize different aspects of size.
 Understand the idea of unit and the need to select a unit appropriate to the attribute being measured.
 Know the standard (English and metric) system of units.
 Use measurement tools such as rulers and meter sticks to make measurements.
 Estimate using common units of measurement.
 Compare units and relate measurements within each of the two common systems of measure, English and metric.
 Understand that measurements are approximate and that different units affect precision.
 Understand role of in measurement.
 Understand and use Pythagorean Theorem.
 Understand length, area, and volume:
 Know what is meant by one, two, and threedimensions.
 See rectangles as arrays of squares and rectangular solids as arrays of cubes.
 Recognize the behavior of measure (length, area, and volume) under uniform dilations.
 Devise area formulas for triangles, parallelograms, and trapezoids; knowing the formula
for the
area of a circle; be familiar with volume and surface area formulas for prisms, cylinders, and other
threedimensional objects.  Decompose and recompose nonregular shapes to find area or volume.
 Understand the independence of perimeter and area; surface area and volume.
 Develop visualization skills:
 Data Analysis, Statistics, and Probability
 Design data investigations (optional):
 Understanding the kinds of questions that can be addressed by data.
 Make decisions on what and how to measure.
 Be familiar with how surveys and statistical experiments are designed and what can
be learned
from them.  Understand what constitutes a random sample and how bias is reduced.
 Describe data:
 Describe shape: symmetric versus skewed data distribution and what this indicates
about the
question being addressed by the data. (optional)  Describe spread: range, outliers, clusters (optional), gaps (optional), and what these
indicate
about the question being addressed by the data.  Describe center: mean, median, and mode and what these indicate about the question
being
addressed by the data.  Be familiar with different forms of graphical data representation, e.g. line plots,
histograms, line
graphs, bar graphs, box plots, pie charts, stemandleaf plots, among others; recognize that
different forms of representation communicate different features of the data and that some
representations are more appropriate than others for a given data set.  Comparing two sets of data (not always of the same size).
 Describe shape: symmetric versus skewed data distribution and what this indicates
about the
 Draw conclusions:
 Choose among representations and summary statistics to communicate conclusions.
 Understand variability and the role it plays in decision making. (optional)
 Understand some of the difficulties that arise in sampling and inference.
 Recognize some of the ways that statistics and graphical displays of data can be misleading.
 Develop notions of probability:
 Making judgements under uncertainty.
 Assign numbers as a measure of likelihood to singlestage and multistage events.
 Understand conditional probability and some of its applications.
 Be familiar with the idea of randomness.
 Develop empirical probabilities through simulations; relate to theoretical probability.
 Understand the notions of expected value and fairness and use probability to determine
fairness.
(optional)
 Design data investigations (optional):
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 MA 202, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Developing an understanding of fundamental concepts of geometry including point, line,
angle,
and plane.  Describing data and its characteristics including dispersion and central tendency,
and solve
problems involving these concepts.
 Developing an understanding of fundamental concepts of geometry including point, line,
angle,
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or
numerically by (Gen Ed Comp A, B, C):
 Understanding concepts of symmetry such as congruence, similarity, proportionality,
and
isometries as they relate to various plane shapes.  Selecting the appropriate representation for data display and interpret information
presented in
such graphical displays including bar graphs, line plots, circle graphs, and stem and leaf plots.
 Understanding concepts of symmetry such as congruence, similarity, proportionality,
and
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed
Comp A, B):
 Practicing the process of measurement and identify units in the standard
systems of measurement.  Calculating the perimeter and area of various different shapes and the
volume of various solids.
 Practicing the process of measurement and identify units in the standard
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Drawing reasonable conclusions based on the characteristics of a data
set, and solve problems that involve finding the probability of an event.  Demonstrating an understanding of and solve application problems
involving the concepts of permutations and combinations.
 Drawing reasonable conclusions based on the characteristics of a data
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or
statistical analysis by (Gen Ed Comp A, D):
 Identifying projections, cross sections, and decompositions of common
two dimensional and three dimensional figures.  Using deductive reasoning and counter examples to prove or disprove
statements about two dimensional and three dimensional figures.  Developing notions about probability of events empirically through
simulations and calculate these probabilities.
 Identifying projections, cross sections, and decompositions of common
A course in multivariable calculus. Topics include vectors and geometry of space, threedimensional vector calculus, partial derivatives, double and triple integrals, integration on surfaces, Green's theorem. Optional topics include Stokes' theorem and the Gauss' divergence theorem. Lecture, three hours; recitation, two hours per week.
Prerequisite: MA 114 or MA 138 or equivalent.
COURSE OBJECTIVES (Approved Fall 2017)
Upon completion of this course, the student can:
 Perform the operations of addition, subtraction,
dot product, and cross product on vectors.  Find directional derivatives and the gradient of
functions of several variables.  Find relative extrema of functions of several
variables.  Evaluate line integrals within vector fields.
 Identify various surfaces, including quadric
surfaces, by their equations and their graphs.  Determine the equations of lines and planes and
find distances in space.  Find derivatives and integrals of vector valued
functions and tangent lines to space curves.  Determine the arc length, unit tangent vector,
principal unit normal vector, and curvature of a
vectorvalued function.  Find partial derivatives of and apply chain rule derivative techniques to multivariable functions.
 Find iterated integrals, double integrals over
regions, and double integrals in polar coordinates.  Evaluate triple integrals in polar, spherical, and
cylindrical coordinates.  Use Green's Theorem and the principle of path
independence to evaluate line integrals within
conservative vector fields.  Interpret derivatives of vector valued functions as
velocity and acceleration functions.  Find the equations of planes tangent to surfaces
and total differentials of functions of several
variables.  Use multiple integration to solve problems
involving volume, surface area, and center of
mass.
OFFICIAL COURSE OUTLINE (Approved Fall 2017)
 Vectors and Geometry in R2 and R3
 ThreeDimensional Coordinate System
 Vectors
 The Dot and Cross Products
 Equations of Lines and Planes
 Surfaces in R3
 Parametric Equations in R3
 Curves Defined by Parametric Equations
 Tangents and Area
 Arc Length
 VectorValued Functions
 Vector Functions and Space Curves
 Derivatives and Integrals of Vector Functions
 Arc Length and Curvature
 Velocity and Acceleration
 Partial Derivatives
 Functions of Several Variables
 Limits and Continuity
 Partial Derivatives
 Tangent Planes and the Total Differential
 The Chain Rules
 Directional Derivatives and Gradient Vectors
 Extrema
 Lagrange Multipliers
 Multiple Integration
 Double Integrals over Rectangles
 Iterated Integrals
 Introduction to Polar Coordinates
 Double Integrals in Polar Coordinates
 Applications of Double Integrals
 Triple Integrals
 Introduction to Cylindrical and Spherical Coordinates
 Triple Integrals in Cylindrical and Spherical Coordinates
 Vector Calculus
 Vector Fields
 Line Integrals and the Fundamental Theorem
 Green's Theorem
 Curl and Divergence
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 MA 213, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Performing the operations of addition, subtraction, dot product, and cross product on vectors.
 Finding directional derivatives and the gradient of functions of several variables.
 Finding relative extrema of functions of several variables.
 Evaluating line integrals within vector fields.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically
by (Gen Ed Comp A, B, C):
 Identifying various surfaces, including quadric surfaces, by their equations and their graphs.
 Determining the equations of lines and planes and find distances in space.
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Finding derivatives and integrals of vector valued functions and tangent lines to space curves.
 Determining the arc length, unit tangent vector, principal unit normal vector, and
curvature of a vectorvalued
function.  Finding partial derivatives of and apply chain rule derivative techniques to multivariable functions.
 Finding iterated integrals, double integrals over regions, and double integrals in polar coordinates.
 Evaluating triple integrals in polar, spherical, and cylindrical coordinates.
 Using Green's Theorem and the principle of path independence to evaluate line integrals
within
conservative vector fields.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Interpreting derivatives of vector valued functions as velocity and acceleration functions.
 Finding the equations of planes tangent to surfaces and total differentials of functions of several variables.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical
analysis by (Gen Ed Comp A, D):
 Using multiple integration to solve problems involving volume, surface area, and center of mass.
A course in ordinary differential equations. Emphasis is on first and second order equations and applications. The course includes series solutions of second order equations and Laplace transform methods.
Prerequisite: MA 213 or equivalent.
MA 214 CALCULUS IV (UK Course) (3 credit hours)
Official Course Description  MA 214 is a course in ordinary differential equations. Emphasis is on first and second order equations and applications. The course includes series solutions of second order equations and Laplace transform methods. Prerequisites: MA 213 or equivalent. 
OFFICIAL COURSE COMPETENCIES/OBJECTIVES (Approved Fall 2017)
 1. Identify and classify differential equations.
 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 (Approved Fall 2017)
 Classification of Differential Equations
 First Order Differential Equations
 A. Linear Equations with Variable Coefficients
 Separable Equations
 Exact Equations and Integrating Factors
 Existence and Uniqueness of Solutions
 Applications of First Order Equations
 Second Order Linear Differential Equations
 Homogeneous Equations with Constant Coefficients
 Fundamental Solutions of Linear Homogeneous Equations
 Linear Independence and the Wronskian
 Complex Roots of the Characteristic Equation
 Repeated Roots of the Characteristic Equation
 Solution of Nonhomogeneous Equations using Method of Undetermined Coefficients
 Variation of Parameters Method
H. Applications of Second Order Equations  Series Solutions near an Ordinary Point
 Higher Order Linear Differential Equations
 General Theory of nth Order Linear Equations
 Homogeneous Equations with Constant Coefficients
 Method of Undetermined Coefficients
 Laplace Transforms
 Definition of Laplace Transform
 Solution of Initial Value Problems using Laplace Transforms
 Step Functions
 Differential Equations with Discontinuous Forcing Functions
 Impulse Functions
 Eigenvalues and Eigenvectors
 Linear Dependence / Independence of Vectors
 Definition of Eigenvalues and Eigenvectors
 Solve Linear Systems with Constant Coefficients
 Complex Eigenvalues
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 MA 214, students will learn to:
 Interpret information presented in mathematical and/or statistical forms by (Gen Ed
Comp B):
 Identifying and classifying differential equations.
 Illustrate and communicate mathematical and/or statistical information symbolically,
visually, and/or numerically by
(Gen Ed Comp A, B, C): Solving application problems using differential equations involving simple and damped harmonic motion.
 Determine when computations are needed and execute the appropriate computations by
(Gen Ed Comp A, B):
 Solving differential equations by separation of variables.
 Solving homogeneous, exact, and linear differential equations.
 Solving differential equations with constant coefficients.
 Solving differential equations using reduction of order and variation of parameters.
 Apply an appropriate model to the problem to be solved by (Gen Ed Comp A, B, C):
 Solving application problems using differential equations of first order.
 Make inferences, evaluate assumptions, and assess limitations in estimation modeling
and/or statistical analysis by
(Gen Ed Comp A, D): Finding the Laplace transforms of common functions, and use Laplace transforms to
solve differential
equations.
 Finding the Laplace transforms of common functions, and use Laplace transforms to
solve differential
Provides individualized, accelerated, masterylevel progression through entrylevel 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 entrylevel college mathematics courses have been met.
Prerequisite: KCTCS placement examination.
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: Competencybased, masterylearning, emporium course that provides individualized instruction at a flexiblepace. Course allows for acceleration through developmental math requirements. May require multiple enrollments to complete all developmental math requirements based on student’s progress and program needs.
Advising Note: For any student who was previously enrolled in MAT011, please look for KYOTE Math
Placement scores and/or Special Credit by Exam received to verify collegelevel 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 twovariables 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 twovariables.
 Solve systems of linear equations in twovariables 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
 Block I: Prealgebra (Competencies 1 – 12)
 Whole Numbers
 Integers
 Fractions
 Decimals
 Order of Operations on Real Numbers
 Algebraic Expressions
 Basic Linear Equations
 Ratios & Proportions
 Basic Percents
 Geometry
 Block IIA: Preparation for Liberal Arts Mathematics (Competencies 13 – 24)
 General Linear Equations in onevariable
 Linear Inequalities in onevariable
 Linear Equations in twovariables
 Linear Inequalities in twovariables
 Systems of Linear Equations
 Rules of Exponents
 Square Roots and Basic Rational Exponents (1/n)
 Polynomials
 Basic Factoring
 Quadratic Equations
 Block IIT: Preparation for Technical Math
 General Linear Equations in onevariable
 Linear Inequalities in onevariable
 Linear Equations in twovariables
 Linear Inequalities in twovariables
 Systems of Linear Equations
 Rules of Exponents
 Square Roots and Basic Rational Exponents (1/n)
 Polynomials
 Measurement
 Scientific Notation
 Variation
 Block III: Preparation for College Algebra (Competencies 25 – 36)
 Absolute Value Equations and Inequalities
 Linear Equations in twovariables (including parallel & perpendicular)
 Functions
 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
Includes operations on integers, decimals and fractions. Introduces exponents, square roots, percents, ratios, proportions, prime factorization, basic geometry, algebraic expressions, basic linear equations, and applications.
Prerequisite: KCTCS placement examination.
Delivery Mode: OnlineOnly
Components: Lecture: 3.0 credits (45contact hours)
Implementation: n/a
Attributes: Remedial Mathematics
Advising Note: None
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
 State and use the properties of real numbers.
 Perform basic operations on integers, fractions, and decimals.
 Determine the absolute value of an integer, a fraction, or a decimal.
 Determine prime factorization of whole numbers.
 State and use the order of 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.
 Evaluate algebraic expressions.
 Simplify algebraic expressions.
 Use both the addition and multiplication properties to solve a linear equation.
 Solve problems involving ratio and proportion.
 Solve problems involving percents.
 Convert among fractions, decimals, and percents.
 Determine the length of the unknown side of a right triangle using the Pythagorean Theorem.
 Determine the perimeter, circumference, area, surface area, and volume of basic plane figures and solids.
 Solve applied problems using these competencies with real world applications.
OFFICIAL COURSE OUTLINE
 Integers
 Properties of Real Numbers
 Basic Operations
 Absolute Value
 Prime Factorization
 Divisibility Tests
 Order of Operations
 Rounding
 Whole Number Powers of Integers
 Square Roots of Perfect Squares
 Fractions
 Common Denominators
 Basic Operations
 Absolute Value
 Order of Operations
 Ordering Fractions
 Whole Number Powers of Fractions
 Square Roots of Perfect Squares
 Decimals
 Basic Operations
 Absolute Value
 Order of Operations
 Ordering Decimals
 Rounding
 Whole Number Powers of Decimals
 Square Roots of Perfect Squares
 Algebraic Expressions and Equations
 Evaluating Algebraic Expressions
 Simplifying Algebraic Expressions
 Solving Linear Equations Using the Addition and Multiplication Properties
 Solving Linear Equations containing fractions (without clearing fractions).
 Ratios and Proportions
 Simplifying Ratios
 Solving Proportions
 Percents
 Converting among fractions, decimals, and percents
 Problems Involving Percents
 Geometry
 Perimeter and Circumference
 Area
 Surface Area
 Volume
 Pythagorean Theorem
 Applications
 Real Number Applications
 Ration and Proportion Applications
 Percent Applications
 Geometry Applications
Prepares students for Business Mathematics, Applied Mathematics, and Technical Mathematics. Includes properties of algebra, using formulas, solving linear equations, percentages, ratios, proportions, plotting points, graphing lines, exponents, and measurement. Encourages applications of algebra and effective use of technology.
Prerequisite: MAT 055 or equivalent as determined by KCTCS placement examination.
Delivery Mode: Online only.
Components: Lecture: 3.0 credits (45 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
Designed to develop the mathematical thinking skills and understanding needed for nonmath and nonscience majors, this onesemester course integrates numeracy, proportional reasoning, algebraic reasoning, and functions. This course provides an alternate path to collegelevel math courses other than college algebra.
Prerequisite: MAT 055 or equivalent as determined by KCTCS placement examination.
DeliveryMode: Online Only
Components: Lecture: 3.0 credits (45contact 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
 A. 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.
Delivery Mode: InPerson and Online
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
MartinGay, 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
 StraightLine Method
 DecliningBalance Method
 Sumof –theYear’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: AddisonWesley, Inc.
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: DelmarThompson Learning.
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 cofunctions 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 cofunctions 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: WadsworthThomson Learning.
 Smith, Karl J. (2003). Mathematics Its Power and Utility (7th ed.). Pacific Grove,
CA: Brooks/ColeThomson
Learning.  Smith (2002). Technical Mathematics (4th ed.). Albany, NY: Delmar/Thomson Learning.
 Kramer, A. D. (2002). Mathematics for Electricity & Electronics (2nd ed.). Albany,
NY: DelmarThompson
Learning.
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
A. Variation
B. Quadratic Equations
1. Factoring
2. Completing the square
3. Quadratic formula
C. Rational Equations
D. Ratio and Proportion
E. Rectangular Coordinate Plane
F. Phasor Form
G. Systems of Linear Equation Solution by Determinants
H. Exponential Equations
I. Logarithmic Equations
J. 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
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 1921 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 Precalculus course. Credit not available on the basis of special exam.) Prerequisites: One of the following:

OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
1. Recognize functions and specify the domain and the range of a given function. 2. Graph linear, quadratic, polynomial, rational, exponential, logarithmic and piecewise functions. 3. Write expressions from data, verbal descriptions or graph. 4. Solve polynomial, rational, exponential and logarithmic equations. 
5. Solve application problems using linear, quadratic, exponential, and logarithmic functions. 6. Perform operations with functions and find inverse functions. 7. Solve linear and nonlinear systems of equations. 8. 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
 Piecewisedefined 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.
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 1921 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 doubleangle 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
 DoubleAngle Formulas
 HalfAngle 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 doubleangle formulas.
 Solving general triangles using the Law of Sines and the Law of Cosines
Prepares students to enroll in a calculus sequence. Includes trigonometric functions, exponentials and logarithms, graphs, polar coordinates, conic sections, and systems of nonlinear equations. Students may not receive credit for both MAT 160 and either College Algebra or Trigonometry. Credit is not available by special examination. Lecture: 5 credits (75 contact hours).
Prerequisite: 1. Math ACT score of 23 or above, 2. Placement examination recommendation, or 3. Consent of instructor.
Official Course Description
Prepares students to enroll in a calculus sequence. Includes trigonometric functions,
exponentials and logarithms, graphs, polar coordinates, conic sections, and systems
of nonlinear equations. Students may not receive credit for both MAT 160 and either
College Algebra or Trigonometry. Credit is not available by special examination.
Prerequisites: One of the following:
 Math ACT score of 23 or above;
 Placement exam recommendation; or
 Consent of instructor.
OFFICIAL COURSE COMPETENCIES/OBJECTIVES
Upon completion of this course, the student can:
 Define a complex number and be able to add, subtract, multiply and divide complex numbers and simplify results.
 Define function, relation, domain, range.
 Determine the distance between two points and the midpoint of a line segment using appropriate formulas.
 Complete the square to obtain the standard form of the equation of a circle.
 Graph functions by recognizing horizontal and vertical shifts, reflections across the yaxis, stretches and compressions, and even and odd functions.
 Identify and form the sum, difference, product and quotient of two functions.
 Determine the domains of sum, difference, product and quotient of functions.
 Evaluate a difference quotient.
 Identify the vertex formula for a quadratic function.
 Use completing the square to obtain the vertex formula from the standard equation of a quadratic function.
 Graph polynomial functions.
 Find zeros of a polynomial function.
 Determine horizontal, vertical and oblique asymptotes of rational functions.
 Graph rational functions, displaying their domain, intercepts and asymptotes.
 Define onetoone functions and inverses of functions.
 Find and verify the inverse of a function.
 Simplify exponential expressions.
 Evaluate and graph exponential functions.
 Solve exponential equations and applications thereof.
 Demonstrate the inverse relationship between exponential and logarithmic functions.
 Convert between logarithmic and exponential form.
 Graph logarithmic functions.
 Simplify logarithmic expressions.
 Solve logarithmic equations and applications thereof.
 Define positive angle, negative angle, standard position of an angle, degree, minute, second, coterminal angles, radian measure.
 Convert between radian measure and degree measure.
 Compute an arc length and the area of a circular sector.
 Define the circular functions, including their domains.
 Define the trigonometric functions in right triangle trigonometry.
 Find trigonometric values for specific angles.
 Use the basic trigonometric identities to simplify trigonometric expressions and solve equations involving trigonometric functions.
 Find the measure of an angle from its trigonometric values.
 Solve applied problems using trigonometry.
 Sketch graphs of the trigonometric functions and modifications thereof.
 Graph the inverse trigonometric functions36. Prove trigonometric identities.
 Solve equations involving inverse trigonometric functions.
 Use the Law of Sines and Law of Cosines to solve triangles.
 Sketch simple polar equations.
 Solve nonlinear systems of equations.
 Graph and write equations for the conic sections.
MAT 160 COURSE OUTLINE
 Complex Number Operations
 Addition and subtraction
 Multiplication
 Division
 Simplification of i to any power
 Relations and Rectangular Coordinates
 Definitions of function, relation, domain, range
 Distance and midpoint formulas
 Circles
 Graphing Techniques
 Horizontal and Vertical Shifts
 Horizontal and Vertical reflection
 Stretching and Compressing
 Even and odd functions
 Operations and Composition
 Sum, difference product and quotient of two functions
 Domains of sum, difference, product and quotient of two functions
 Composites and their domains
 Difference quotient
 Functions
 Quadratic functions
 Polynomial functions
 Roots, endbehavior, and turning points
 Intermediate Value Theorem
 Boundedness Theorem
 Zeros (Theory of Equations)
 Rational functions
 Horizontal, vertical and oblique asymptotes
 Graphing rational functions
 Inverse functions
 Definitions of one to one and inverse functions
 Horizontal line test
 Finding and verifying inverses
 Exponential Functions
 Rules of exponents
 Definition of exponential function
 Graph exponential functions
 Solve exponential functions with the same base
 Compound interest
 Logarithmic Functions
 Logarithmic and exponential expressions
 Definition of logarithm
 Graphing logarithmic functions
 Evaluating Logarithms
 Solve applied logarithmic problems
 Change of base theorem
 Exponential and Logarithmic Equations and Applications
 Exponential growth and decay problems
 Compound interest
 Angles
 Definition of positive angle, negative angle, standard position, coterminal angles,
degree and radian
measure of angles.  Conversion between radian and degree measure
 Arc length
 Area of a sector
 Conversion between decimal degree measure and degrees, minutes, seconds
 Definition of positive angle, negative angle, standard position, coterminal angles,
degree and radian
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 nondifferentiable 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
 Onesided limits
 Continuity
 Infinite limits (f(x)→±∞)
 Limits as x→±∞
 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 nondifferentiable 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.
 Using the derivative of a function to find the equation of the line tangent to the
graph of the function at a given
 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.
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.
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 commonsense 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 nonsampling variability.
 Identify strategies for understanding nonsampling 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 online poll, a CBS Evening News callin poll, a Gallup randomdialing poll, and a doortodoor 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 handson repeated sampling.
 Produce a non95% 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
commonsense inferences.
Explain the difference between sampling variability and nonsampling 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
commonsense 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 handson 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 non95% 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: StudentCentered Activities for Learning Statistical Reasoning, current edition, by William Rayens,
VanGriner Publishers
StatCrunch Student 6Month Access Code
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 realworld
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 pvalue, 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 realworld 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
 tDistributions
 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
 Pvalues
 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
 ChiSquare Interpretation
 ChiSquare Test of Homogeneity
 ChiSquare 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
 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)
 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. VanGriner Publishing. ISBN13: 9781617401060  My Stat Lab