## Mathematics Corequisite (MCR)

### MCR 1 - Learning Support for Basic Technical Mathematics

### Course Description

Effective: 2017-08-01

### General Course Purpose

To enable qualified students to enter into credit bearing courses sooner, with the appropriate support, and with equal or better success than those students meeting course prerequisite requirements. The course provides support and enhancement of foundational and course content required of the credit course.

### Course Prerequisites/Corequisites

Prerequisites: Completion of any one of the MTE units 1-3. Corequisite: MTH 111.

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Technology
- Use appropriate technology in a given context.
- Students will engage in all course content described below in context to the technical fields being supported.
- Basic Skills
- Use a scientific calculator.
- Round-off numbers correctly.
- Identify significant digits.
- Use scientific notation
- Convert between units in both standard and metric
- Perform operations with signed numbers
- Basic Algebra
- Apply and interpret ratios and proportions
- Compute values in direct, indirect and inverse variation
- Solve single variable equations
- Locate and plot points on the xy plane
- Interpret the concept of slope using real world examples (including vertical and horizontal lines)
- Graph lines using a table of values with and without the domain provided
- Graph lines using the slope-intercept method when lines are in y=mx+b form and Ax+By=C form
- Write the equation of a line in slope-intercept form that models a real world situation when given the rate of change and initial value
- Make predictions using the equation of a line
- Geometry
- Classify triangles by their sides/angles.
- Calculate the perimeter and circumference
- Calculate the area of a polygon and circle
- Apply concepts of sector and arc length of a circle
- Recognize various geometric solids such as cylinder, cone, pyramid, prism and sphere.
- Calculate surface area and volume of various geometric solids
- Use the properties of inscribed and circumscribed polygons and circles to find unknown amounts
- Apply the concept of similar triangles
- Apply the Pythagorean theorem
- Convert between decimal degrees and DMS notation.
- Interpret and apply line and angle relationships.
- Trigonometry
- Properly use terms related to an angle(s).
- Define the trigonometric functions and their values
- Solve right triangles and their applications
- Identify the signs of the trigonometric function of angles greater than 90?
- Determine trigonometric functions of any angle
- To achieve the above objectives, the support course will cover appropriate topics such as those suggested below in both planned review and just-in-time remediation:
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions, decimals, and integers
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Evaluating expressions/functions for given values of variables
- Excel or similar applications
- Formulas
- Ratios and Proportions
- Percents

### Major Topics to be Included

- Basic Skills
- Basic Algebra
- Geometry
- Trigonometry

### MCR 2 - Learning Support for Fundamentals of Reasoning

### Course Description

Effective: 2017-08-01

### General Course Purpose

To enable qualified students to enter into credit bearing courses sooner, with the appropriate support, and with equal or better success than those students meeting course prerequisite requirements. The course provides support and enhancement of foundational and course content required of the credit course.

### Course Prerequisites/Corequisites

Prerequisites: Completion of any one of the MTE 1-3 modules. Corequisite: MTH 130

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Use appropriate mathematical language in oral, written and graphical forms.
- Read and interpret real world advertisements, consumer information, government forms and news articles containing quantitative information.
- Use quantitative information from multiple sources to make or critique an argument.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Use multiple calculations to develop an answer to an open-ended question requiring analysis and synthesis of data.
- Develop personal problem solving processes and apply them to applications studied over an extended period of time.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Draw conclusions or make decisions in quantitatively based situations that are dependent upon multiple factors.
- Analyze how different situations would affect the decisions.
- Present written or verbal justifications of decisions that include appropriate discussion of the mathematics involved.
- Recognize when additional information is needed or the appropriate times to simplify a problem.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Evaluate the validity and possible biases in arguments presented in real world contexts based on multiple sources of quantitative information for example; advertising, internet postings, or consumer information.
- Technology
- Use appropriate technology in a given context.
- Use a computer or calculator to organize quantitative information and make repeated calculations using simple formulas. This would include using software like Excel or internet-based tools appropriate for a given context for example, an online tool to calculate credit card interest.
- Basic Algebra through Application
- Solve real world application problems requiring basic operations and simple linear equations.
- Perform operations with signed numbers (including whole numbers, decimals, and fractions)
- Simplify and evaluate algebraic expressions using the order of operations
- Solve simple linear equations - one step equations, two step equations and some multi-step equations requiring distributive property
- Determine the reasonableness of answers using estimation
- Linear Graphing Applied
- Through contextualized perspective,
- Locate and plot points on the xy plane
- Interpret the concept of slope using real world examples (including vertical and horizontal lines)
- Graph lines using a table of values with and without the domain provided
- Graph lines using the slope-intercept method when lines are in y=mx+b form and Ax+By=C form
- Write the equation of a line in slope-intercept form that models a real world situation when given the rate of change and initial value
- Make predictions using the equation of a line
- Graph and solve a system of two linear equations in an applied context
- Financial Literacy using Percents, Ratios and Proportions
- Create and simplify ratios
- Solve given proportions
- Solve real world problems using proportions
- Calculate percents, sales tax and discounts
- Create a budget to include percentages and a pie chart using appropriate software
- Calculate simple and compound interest
- Interpret credit scores and how they affect opportunities to buy on credit
- Solve problems which involve buying on credit, including add-on interest rate loans and home buying
- Calculate FICA and federal income taxes (simple cases)
- Descriptive Statistics
- Compute and interpret statistics (mean, median, mode, range, quartiles/percentiles) for data displayed in various formats, such as a boxplot, stem-and-leaf plots, frequency distributions, histogram, pie/line/bar graph
- Compare sets of data by comparing similarities and differences in their graphical displays and/or descriptive statistics
- Create graphical displays of data using spreadsheet software such as Excel
- Compute and interpret descriptive statistics for a set of real-world data, including mean, median, mode, range, standard deviation using spreadsheet software or a calculator
- Identify graphical displays or arguments that are misleading or involve the incorrect use of statistical concepts
- Measurement & Geometry
- Solve problems by applying measurement and geometry topics (such as measurement conversions, area, perimeter, volume, etc) in a variety of real world contexts
- Logic (Optional topic to support certain CTE programs.)
- Identify statements and form compound statements and negations using "and", "or", and "not"
- Use truth tables to determine the truth value of compound statements and to determine whether statements are equivalent
- Identify conditional statements. Write and determine truth values for the converse, inverse, and contrapositive of a conditional statement.
- Use truth tables to determine the validity of a syllogistic argument
- Draw and interpret Venn diagrams
- Distinguish between inductive and deductive reasoning
- Use inductive reasoning to find a pattern or to disprove a statement by finding a counterexample
- Trigonometry (Optional topic to support certain CTE programs.)
- Understand/use terms related to an angle(s).
- Define the trigonometric functions and their values
- Solve right triangles and their applications
- Understand the signs of the trigonometric function of angles greater than 90?
- Determine trigonometric functions of any angle
- To achieve the above objectives, the support course will cover appropriate topics such as those suggested below in both planned review and just-in-time remediation:
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Math Skills Topics
- Operations with fractions, decimals, and integers
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Evaluating expressions/functions for given values of variables
- Excel or similar applications
- Formulas
- Ratios and Proportions
- Percents

### Major Topics to be Included

- Basic Algebra
- Linear Graphing
- Financial Literacy using Percents, Ratios, and Proportions
- Descriptive Statistics
- Measurement and Geometry
- Logic (Optional)
- Trigonometry (Optional)

### MCR 3 - Learning Support for Technical Mathematics

### Course Description

Effective: 2017-08-01

### General Course Purpose

To enable qualified students to enter into credit bearing courses sooner, with the appropriate support, and with equal or better success than those students meeting course prerequisite requirements. The course provides support and enhancement of foundational and course content required of the credit course.

### Course Prerequisites/Corequisites

Prerequisites: Completion of any four of the MTE units 1-6. Corequisite: MTH 131.

### Course Objectives

- Communication
- Interpret and communicate quantitative information and mathematical and statistical concepts using language appropriate to the context and intended audience.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Critique and evaluate quantitative arguments that utilize mathematical, statistical, and quantitative information.
- Students will engage in all course content described below in context to the technical fields being supported.
- Basic Skills
- Use a scientific calculator.
- Round-off numbers correctly.
- Identify significant digits.
- Use scientific and engineering notation
- Convert between units in both standard and metric
- Apply basic algebraic principles
- Geometry
- Apply and interpret line and angle relationships.
- Classify triangles by their sides/angles.
- Calculate the perimeter of a polygon
- Calculate the circumference and chord length on a circle
- Calculate the area of a polygon
- Calculate the area of a circle
- Apply concepts of sector and arc length of a circle
- Recognize various geometric solids such as cylinder, cone, pyramid, prism, sphere and conic sections.
- Calculate surface area and volume of various geometric solids
- Apply the concept of similar triangles
- Trigonometry
- Properly use terms related to an angle(s).
- Classify triangles by their sides/angles.
- Know/apply the radian as a measure of an angle, convert between degrees and radians
- Define the trigonometric functions and their values
- Solve right triangles and their applications
- Identify the signs of the trigonometric function of angles greater than 90?
- Determine trigonometric functions of any angle
- Vectors
- Describe vectors and their components.
- Solve applications involving vectors.
- Perform addition and scalar multiplication with vectors
- Complex Numbers
- Interpret complex numbers and perform basic operations
- Convert between forms of rectangular, and polar complex numbers
- Perform basic operations with polar complex numbers
- To achieve the above objectives, the support course will cover appropriate topics such as those suggested below in both planned review and just-in-time remediation:
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions, decimals, and integers
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Evaluating expressions/functions for given values of variables
- Excel or similar applications
- Formulas
- Ratios and Proportions
- Percents
- Solving basic algebraic equations and inequalities
- Factoring
- Radicals of positive and negative numbers
- Identifying components of graphs, graphing, equations of lines.

### Major Topics to be Included

- Basic Skills
- Geometry
- Trigonometry
- Vectors
- Complex Numbers

### MCR 4 - Learning Support for Quant Reasoning

### Course Description

Effective: 2017-08-01

### General Course Purpose

### Course Prerequisites/Corequisites

Prerequisite(s): Completion of any three of the MTE modules 1-5 and Corequisite: MTH 154: Quantitative Reasoning

### Course Objectives

- Communication
- Use appropriate mathematical language in oral, written and graphical forms.
- Read and interpret real world advertisements, consumer information, government forms and news articles containing quantitative information.
- Use quantitative information from multiple sources to make or critique an argument.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Develop an answer to an open-ended question requiring analysis and synthesis of multiple calculations, data summaries, and/or models.
- Develop personal problem solving processes and apply them to applications studied over an extended period of time.
- Reasoning
- Reason, model, and draw conclusions or make decisions with quantitative information.
- Draw conclusions or make decisions in quantitatively based situations that are dependent upon multiple factors. Students will analyze how different situations would affect the decisions.
- Present written or verbal justifications of decisions that include appropriate discussion of the mathematics involved.
- Recognize when additional information is needed or the appropriate times to simplify a problem.
- Evaluation
- Evaluate the validity and possible biases in arguments presented in real world contexts based on multiple sources of quantitative information - for example; advertising, internet postings, consumer information, political arguments.
- Technology
- Use appropriate technology in a given context.
- Use a spreadsheet to organize quantitative information and make repeated calculations using simple formulas.
- Explore internet-based tools appropriate for a given context - for example, an online tool to calculate credit card interest or a scheduling software package.
- Financial Literacy
- Simple Interest
- Define interest and understand related terminology.
- Develop simple interest formula.
- Use simple interest formulas to analyze financial issues
- Compound Interest
- Describe how compound interest differs from simple interest.
- Explain the mechanics of the compound interest formula addressing items such as why the exponent and (1+r/n) is used.
- Use compound interest formulas to analyze financial issues
- Show the difference between compound interest and simple interest using a table or graph.
- Borrowing
- Compute payments and charges associated with loans.
- Identify the true cost of a loan by computing APR
- Evaluate the costs of buying items on credit
- Compare loans of varying lengths and interest rates.
- Investing
- Calculate the future value of an investment and analyze future value and present value of annuities (Take into consideration possible changes in rate, time, and money.)
- Calculate profit from a sale of an investment
- Compare various investment options and understand when it is appropriate utilize them
- Perspective Matters - Number, Ratio, and Proportional Reasoning
- Solve real-life problems requiring interpretation and comparison of complex numeric summaries which extend beyond simple measures of center.
- Solve real-life problems requiring interpretation and comparison of various representations of ratios (i.e., fractions, decimals, rates, and percentages).
- Distinguish between proportional and non-proportional situations and, when appropriate, apply proportional reasoning. Recognize when proportional techniques do not apply.
- Solve real-life problems requiring conversion of units using dimensional analysis.
- Apply scale factors to perform indirect measurements (e.g., maps, blueprints, concentrations, dosages, and densities).
- Order real-life data written in scientific notation. The data should include different significant digits and different magnitudes.
- Modeling
- Observation
- Through an examination of examples, develop an ability to study physical systems in the real world by using abstract mathematical equations or computer programs
- Make measurements of physical systems and relate them to the input values for functions or programs.
- Examples: measure distance and time for a toy car, length of candle and time as it burns, length of vertical spring under different weights attached (linear); temperature and time for a refrigerated liquid as it warms (nonlinear)
- Compare the predictions of a mathematical model with actual measurements obtained
- Quantitatively compare linear and exponential growth
- Explore the mathematical and logical structures that enable familiar models encountered in daily life: Weather models, Financial models, Simple physical models, Normal and Exponential Population models.
- Mathematical Modeling and Analysis
- Assemble measurements and data gathered (possibly through surveys, internet, etc.) into tables, displays, charts, and simple graphs.
- Explore interpolation and extrapolation of linear and non-linear data. Determine the appropriateness of interpolation and/or extrapolation.
- Identify and distinguish linear and non-linear data sets arrayed in graphs. Identifying when a linear or non-linear model or trend is reasonable for given data or context.
- Correctly associate a linear equation in two variables with its graph on a numerically accurate set of axes
- Numerically distinguish which one of a set of linear equations is modeled by a given set of (x,y) data points
- Identify a mathematical model's boundary values and limitations (and related values and regions where the model is undefined). Identify this as the domain of an algebraic model.
- Using measurements (or other data) gathered, and a computer program (spreadsheet or GDC) to create different regressions (linear and non-linear), determine the best model, and use the model to estimate future values.
- Application
- Starting with a verbally described requirement, generate an appropriate mathematical approach to creating a useful mathematical model for analysis
- Explore the graphical solutions to systems of simultaneous linear equations, and their real world applications
- Numerically analyze and mathematically critique the utility of specific mathematical models: instructor-provided, classmate generated, and self-generated
- Validity Studies
- Identify logical fallacies in popular culture: political speeches, advertisements, and other attempts to persuade
- Relate the concept of a "statement" to the notion of Truth Value. Identify statements and non-statements
- Describe the differences between verbal expression of truth and mathematical expression of truth. Discuss the usefulness of symbolic representation of statements. Discuss the 2-valued nature of mathematical truth value, relate this to real world examples.
- Determine the logical equivalence between two different verbal statements (simple and compound) in real-world context.
- Relate the language of conditionals to the language of quantified statements
- Explore the relationship between quantified statements and conditional statements (e.g., "all scientists are educated" is equivalent to "if she is a scientist then she is educated.")
- Apply concepts of symbolic logic and set theory to examine compound statements and apply that to decision making of real-world applications.
- To achieve the above objectives, the support course will cover appropriate topics such as those suggested below in both planned review and just-in-time remediation.
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Domain and Range
- Graphing linear equations and inequalities
- Writing equations of lines given specific information
- Solving first degree equations and inequalities
- Evaluating expressions/functions for given values of variables
- Manipulating equations to solve for a given variable.
- Excel or similar applications
- Formulas
- Ratios and Proportions

### Major Topics to be Included

- Financial Literacy (Interest, Borrowing, and Investing)
- Perspective (Complex Numeric Summaries, Ratios, Proportions, Conversions, Scaling, Scientific Notation)
- Modeling (Observation, Mathematical Modeling and Analysis, Application)
- Validity Studies (Statements, Conclusions, Validity, Bias, Logic, Set Theory)

### MCR 5 - Learning Support for Statistical Reasoning

### Course Description

Effective: 2017-08-01

### General Course Purpose

### Course Prerequisites/Corequisites

Prerequisites: Completion of any three of the MTE modules 1-5 and Corequisite: MTH 155: Statistical Reasoning

### Course Objectives

- Communication
- Use appropriate statistical language in oral, written, and graphical terms.
- Read and interpret graphs and descriptive statistics.
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Understand what statistical question is being addressed, use appropriate strategies to answer the question of interest, and state conclusions using appropriate statistical language.
- Reasoning
- Reason, model, and draw conclusions or make decisions with quantitative information.
- Use probability, graphical, and numerical summaries of data, confidence intervals, and hypothesis testing methods to make decisions.
- Support conclusions by providing appropriate statistical justifications.
- Evaluation
- Identify errors such as inappropriate sampling methods, sources of bias, and potentially confounding variables, in both observational and experimental studies.
- Identify mathematical or statistical errors, inconsistencies, or missing information in arguments.
- Technology
- Use appropriate technology in a given context.
- Use some form of spreadsheet application to organize information and make repeated calculations using simple formulas and statistical functions.
- Use technology to calculate descriptive statistics and test hypotheses.
- Graphical and Numerical Data Analysis
- Identify the difference between quantitative and qualitative data
- Identify the difference between discrete and continuous quantitative data
- Construct and interpret graphical displays of data, including (but not limited to) box plots, line charts, histograms, and bar charts
- Construct and interpret frequency tables
- Compute measures of center (mean, median, mode), measures of variation, (range, interquartile range, standard deviation), and measures of position (percentiles, quartiles, standard scores)
- Sampling and Experimental Design
- Recognize a representative sample and describe its importance
- Identify methods of sampling
- Explain the differences between observational studies and experiments
- Recognize and explain the key concepts in experiments, including the selection of treatment and control groups, the placebo effect, and blinding
- Probability Concepts
- Describe the difference between relative frequency and theoretical probabilities and use each method to calculate probabilities of events
- Calculate probabilities of composite events using the complement rule, the addition rule, and the multiplication rule
- Use the normal distribution to calculate probabilities
- Identify when the use of the normal distribution is appropriate
- Recognize or restate the Central Limit Theorem and use it as appropriate
- Statistical Inference
- Explain the difference between point and interval estimates
- Construct and interpret confidence intervals for population means and proportions
- Interpret the confidence level associated with an interval estimate
- Conduct hypothesis tests for population means and proportions
- Interpret the meaning of both rejecting and failing to reject the null hypothesis
- Use a p-value to reach a conclusion in a hypothesis test
- Identify the difference between practical significance and statistical significance
- Correlation and Regression
- Analyze scatterplots for patterns, linearity, and influential points
- Determine the equation of a least-squares regression line and interpret its slope and intercept
- Calculate and interpret the correlation coefficient and the coefficient of determination
- Categorical Data Analysis
- Conduct a chi-squared test for independence between rows and columns of a two-way contingency table
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Domain and Range
- Graphing linear equations and inequalities
- Writing equations of lines given specific information
- Solving first degree equations and inequalities
- Evaluating expressions/functions for given values of variables
- Manipulating equations to solve for a given variable.
- Excel or similar applications
- Formulas
- Ratios and Proportions

### Major Topics to be Included

- Graphical and Numerical Data Analysis
- Sampling and Experimental Design
- Probability
- Statistical Inference
- Correlation and Regression

### MCR 6 - Learning Support for PreCalculus I

### Course Description

Effective: 2017-08-01

### General Course Purpose

### Course Prerequisites/Corequisites

Prerequisites: Completion of any seven of the MTE modules 1-9 and Corequisite: MTH 161: Precalculus I.

### Course Objectives

- Relations and Functions
- Distinguish between relations and functions.
- Evaluate functions both numerically and algebraically.
- Determine the domain and range of functions in general, including root and rational functions.
- Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
- Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
- Determine and verify inverses of one-to-one functions.
- Polynomial and Rational Functions
- Determine the general and standard forms of quadratic functions.
- Use formula and completing the square methods to determine the standard form of a quadratic function.
- Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
- Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
- Determine if a function demonstrates even or odd symmetry.
- Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
- Identify intercepts, end behavior, and asymptotes of rational functions, and graph.
- Solve polynomial and rational inequalities.
- Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))
- Exponential and Logarithmic Functions
- Identify and graph exponential and logarithmic functions and their transformations.
- Use properties of logarithms to simplify and expand logarithmic expressions.
- Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
- Solve exponential and logarithmic equations using one-to-one and inverse properties.
- Solve application problems involving exponential and logarithmic functions.
- Systems of Equations
- Solve three variable linear systems of equations using the Gaussian elimination method.
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Domain and Range
- Squaring binomials
- Factoring
- Simplifying radical expressions
- Graphing linear equations and inequalities
- Writing equations of lines given specific information
- Solving first and second degree equations and inequalities
- Quadratic Formula
- Interval Notation
- Evaluating expressions/functions for given values of variables
- Solving radical and rational equations
- Simplifying complex fractions

### Major Topics to be Included

- Relations and Functions
- Polynomial and Rational Functions
- Exponential and Logarithmic Functions
- Systems of Equations and Inequalities

### MCR 7 - Learning Support for PreCalculus with Trigonometry

### Course Description

Effective: 2017-08-01

### General Course Purpose

### Course Prerequisites/Corequisites

Prerequisites: Completion of any seven of the MTE modules 1-9 and Corequisite: MTH 167: Precalculus with Trigonometry

### Course Objectives

- Relations and Functions
- Distinguish between relations and functions.
- Evaluate functions both numerically and algebraically.
- Determine the domain and range of functions in general, including root and rational functions.
- Perform arithmetic operations on functions, including the composition of functions and the difference quotient.
- Identify and graph linear, absolute value, quadratic, cubic, and square root functions and their transformations.
- Determine and verify inverses of one-to-one functions.
- Polynomial and Rational Functions
- Determine the general and standard forms of quadratic functions.
- Use formula and completing the square methods to determine the standard form of a quadratic function.
- Identify intercepts, vertex, and orientation of the parabola and use these to graph quadratic functions.
- Identify zeros (real-valued roots) and complex roots, and determine end behavior of higher order polynomials and graph the polynomial, and graph.
- Determine if a function demonstrates even or odd symmetry.
- Use the Fundamental Theorem of Algebra, Rational Root test, and Linear Factorization Theorem to factor polynomials and determine the zeros over the complex numbers.
- Identify intercepts, end behavior, and asymptotes of rational functions, and graph.
- Solve polynomial and rational inequalities.
- Interpret the algebraic and graphical meaning of equality of functions (f(x) = g(x)) and inequality of functions (f(x) > g(x))
- Exponential and Logarithmic Functions
- Identify and graph exponential and logarithmic functions and their transformations.
- Use properties of logarithms to simplify and expand logarithmic expressions.
- Convert between exponential and logarithmic forms and demonstrate an understanding of the relationship between the two forms.
- Solve exponential and logarithmic equations using one-to-one and inverse properties.
- Solve application problems involving exponential and logarithmic functions.
- Systems of Equations
- Solve three variable linear systems of equations using the Gaussian elimination method.
- Trigonometric Functions
- Identify angles in standard form in both degree and radian format and convert from one to the other.
- Find the arc length.
- Find the value of trigonometric functions of common angles without a calculator using the unit circle and right triangle trigonometry.
- Use reference angles to evaluate trig functions.
- Find the value of trigonometric functions of angles using a calculator.
- Use fundamental trigonometric identities to simplify trigonometric expressions.
- Graph the six trigonometric functions using the amplitude, period, phase and vertical shifts.
- Use trig functions to model applications in the life and natural sciences.
- Analytic Trigonometry
- Use the fundamental, quotient, Pythagorean, co-function, and even/odd identities to verify trigonometric identities.
- Use the sum and difference, double angle, half-angle formulas to evaluate the exact values of trigonometric expressions.
- Determine exact values of expressions, including composite expressions, involving inverse trigonometric functions.
- Solve trigonometric equations over restricted and non-restricted domains.
- Applications of Trigonometry
- Solve right triangles and applications involving right triangles.
- Use the Law of Sines and Cosines to solve oblique triangles and applications.
- Conics
- Identify the conic sections of the form: Ax^2 + By^2 + Dx + Ey + F = 0
- Write the equations of circles, parabolas, ellipses, and hyperbolas in standard form centered both at the origin and not at the origin.
- Identify essential characteristics unique to each conic.
- Graph equations in conic sections, centered both at the origin and not at the origin.
- Solve applications involving conic sections.
- Sequences and Series (Optional unit at the discretion of the department.)
- Identify the terms of geometric sequences.
- Find a particular term of geometric sequence.
- Determine the formula for the an term of geometric sequences.
- Find the sum of first n terms of finite geometric series.
- Find the sum of infinite geometric series.
- Introduce arithmetic concepts as time allows.
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Domain and Range
- Squaring binomials
- Factoring
- Simplifying radical expressions
- Graphing linear equations and inequalities
- Writing equations of lines given specific information
- Solving first and second degree equations and inequalities
- Quadratic Formula
- Interval Notation
- Evaluating expressions/functions for given values of variables
- Solving radical and rational equations
- Simplifying complex fractions

### Major Topics to be Included

- Relations and Functions
- Polynomial and Rational Functions
- Exponential and Logarithmic Functions
- Systems of Equations and Inequalities
- Trigonometric Functions
- Analytic Trigonometry
- Applications of Trigonometry
- Conics

### MCR 8 - Learning Support for Business Mathematics

### Course Description

Effective: 2017-08-01

### General Course Purpose

### Course Prerequisites/Corequisites

Prerequisites: Completion of any one of the MTE units 1-3. Corequisite: MTH 132.

### Course Objectives

- Communication
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Technology
- Use appropriate technology in a given context.
- Communication and Basic Skills
- Solve application problems by interpreting the materials presented, including determining the nature and extent of the information needed, and present the answer in standard English.
- Estimate and consider answers to mathematical problems in order to determine reasonableness.
- Correctly calculate sums, differences, products and quotients of whole numbers, fractions and mixed numbers, and decimal numbers without the use of a calculator.
- Perform basic calculator operations.
- Solve a formula for any specified variable.
- Convert decimal numbers and fractions to and from percents.
- Banking Applications
- Solve word problems using the basic percentage formula.
- Identify the component parts of a check, check stub and deposit slip.
- Perform simple banking transactions, rectify bank statements.
- Calculate simple interest, compound interest and simple discount.
- Use the formulas for maturity value and present value for simple interest loans.
- Use tables to calculate present value and future value.
- Find the monthly mortgage payment, interest and PITI and prepare a partial amortization schedule.
- Calculate sales, property, loans with closed-end credit and open-end credit.
- Taxes
- Calculate Payroll, income taxes.
- Calculate gross earnings based on salaries, commissions and wages.
- Calculate overtime earnings for wages, salaries, and commissions.
- Calculate State withholding taxes.
- Calculate FICA and Medicare taxes for employees and self-employed individuals.
- Calculate Federal withholding taxes using the wage bracket and percentage methods.
- Calculate an employer's Federal Tax Liability.
- Business Applications
- Complete an invoice.
- Calculate the selling price for an item using markup and markdown.
- Use the basic percentage formula to calculate trade, chain, quantity and cash discounts, and net cost.
- Use complements to calculate net cost.
- Calculate the equivalent single discount for a series discount.
- Determine the last date of a discount period.
- Calculate the selling price for an item using markup and markdown.
- Determine the break-even point and the amount of a profit/loss.
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions, decimals, and integers
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Evaluating expressions/functions for given values of variables
- Excel or similar applications
- Formulas
- Ratios and Proportions
- Percents

### Major Topics to be Included

- Communication and Basic Skills
- Banking Applications
- Taxes
- Business Applications

### MCR 9 - Learning Support in Mathematics for Health Professions

### Course Description

Effective: 2017-08-01

### General Course Purpose

### Course Prerequisites/Corequisites

Prerequisites: Completion of any one of the MTE units 1-3. Corequisite: MTH 133.

### Course Objectives

- Communication
- Problem Solving
- Make sense of problems, develop strategies to find solutions, and persevere in solving them.
- Reasoning
- Reason and draw conclusions or make decisions with quantitative information.
- Evaluation
- Technology
- Use appropriate technology in a given context.
- Students will engage in all course content described below in context to the allied health fields being supported.
- Topics in Arithmetic
- Interpret relative value of decimals and perform basic arithmetic of decimals.
- Interpret relative value of fractions and perform basic arithmetic of fractions.
- Simplify arithmetic expressions using the order of operations
- Calculate powers and roots of numbers
- Topics in Measurement and Conversions
- Convert units in the metric system.
- Use dimensional analysis to convert units between metric, nonmetric, household measures, apothecary measures, and temperatures.
- Topics in Algebra and Graphing
- Solve linear equations.
- Solve problems involving percents and ratio proportions.
- Simplify and solve basic exponential and logarithmic expressions and equations. Include applications pertaining to allied health.
- Graph linear equations.
- Recognize the characteristics of linear, quadratic, and exponential functions as presented in their graphs.
- Topics in Statistics
- Interpret data presented in frequency distribution tables, bar graphs or histograms, pie charts, or line graphs.
- Compute mean, median, mode, and standard deviation for a data set.
- Topics in Geometry
- Use geometric formulas to calculate perimeter, area, surface area, volume.
- Be able to measure angles with a protractor.
- Solve problems involving angle measure.
- Topics in Allied Health
- Solve problems involving dilutions and dosages.
- Solve problems involving reconstituting solutions.
- Solve problems involving IV flow rates.
- Student Skills Topics
- Class activities may include:
- Reviewing notes from class lectures
- Activities on taking good notes
- Analyzing personal time management
- Correcting textbook homework
- Predicting test questions
- Correcting tests
- Preparing for tests
- Asking good questions
- Exploring skills for using technology effectively
- Discussions may include the following topics:
- Using a planner/electronic device to keep up with assignments
- What work needs to happen outside of classes
- How does one use class notes?
- Why and when is it important to read the text?
- What does the instructor mean when he/she asks me to show my work?
- Math Skills Topics
- Operations with fractions, decimals, and integers
- Order of Operations
- Exponents involving positive and negative bases
- Laws of Exponents (including fractional and negative)
- Evaluating expressions/functions for given values of variables
- Excel or similar applications
- Formulas
- Ratios and Proportions
- Percents

### Major Topics to be Included

- Basic Arithmetic
- Measurement and Conversions
- Algebra and Graphing
- Statistics
- Geometry
- Allied Health Applications