Mathematics
MAT 001- Math Ramp Up (MAT 001-004)
Module 1: Whole Numbers
- Read and write whole numbers
- Write whole numbers in expanded form
- Round whole numbers
- Perform addition, subtraction, multiplication and division with whole numbers
- Evaluate expressions involving exponents
- Evaluate expressions using the rules for order of operations
- Solve applied problems involving whole numbers
Module 2: Fractions
- Define and recognize prime numbers
- Factor composite numbers
- Find the prime factorization of a composite number
- Write improper fractions as mixed numbers and mixed numbers as improper fractions
- Perform addition, subtraction, multiplication and division with fractions and mixed numbers
- Solve applied problems involving fractions and mixed numbers
Module 3: Decimals
- Read and write decimal numbers
- Round decimal numbers
- Compare decimal numbers
- Write decimal numbers as fractions and fractions as decimal numbers
- Perform addition, subtraction, multiplication and division with decimal numbers
- Solve applied problems involving decimal numbers
Module 4: Signed Numbers
- Compare signed numbers
- Find the absolute value of a number
- Perform addition, subtraction, multiplication and division with signed numbers
- Solve applied problems involving signed numbers
Module 5: Algebraic Expressions and Translations
- Recognize and apply the properties of real numbers
- Translate algebraic expressions to word phrases
- Translate word phrases to algebraic expressions
- Write algebraic expressions using exponents
- Evaluate algebraic expressions and formulas
- Simplify algebraic expressions
- Solve applied problems involving algebraic expressions and formulas
Module 6: Solving Linear Equations and Inequalities
- Determine whether a given number is a solution of a given equation
- Solve linear equations
- Solve applied problems involving linear equations
- Solve literal equations for a particular variable
- Solve and evaluate formulas
- Solve and graph linear inequalities
- Solve applied problems involving linear inequalities
Module 7: Ratio, Proportion, and Percent
- Write ratios and rates in simplest form
- Solve applied problems involving ratios and rates
- Write and solve proportions
- Solve applied problems involving proportions
- Read and write percents
- Convert between fraction, decimal and percent
- Translate and solve percent equations
- Solve various applications involving percents
Module 8: Graphing Linear Equations in two variables
- Identify and plot points on the coordinate plane
- Identify the quadrants of the coordinate plane
- Find the slope of a line that passes through two given points
- Graph the line of a linear equation in two variables using a table of values, intercepts, and slope and y-intercept
- Determine if two given lines are parallel or perpendicular
- Write a given linear equation in general form and in slope-intercept form
- Identify the slope and y-intercept of an equation written in slope-intercept form
- Find the equation of a line given two points on the line or its slope and one point
Track A: Modules 70 – 73
Module 70: Graphing Calculator Skills
- Use a graphing calculator to:
- Perform basic arithmetic operations, emphasizing order of operation, powers and roots
- Graph equation
Module 71: Percentages, Absolute and Relative Differences and Application
- Convert percentages to fractions or decimals and fractions and decimals to percentages
- Solve percent equations for the amount, base or percent
- Calculate absolute and relative differences
- Use critical thinking skills to solve problems
- Use the Graphing Calculator to solve application problems
Module 72: Algebraic skills
- Solve equations involving square roots
- Solving quadratic equations
- Use critical thinking skills to solve problems
- Use the Graphing Calculator to solve application problems
Module 73: More Graphing and Line of Best Fit
- Review graphing linear equations in two variables
- Calculate the best fit line of a set of data, using the graphing calculator
- Determine the equation of the line of best fit
- Interpret the slope of the best fit line as a rate of change
- Use critical thinking skills to solve problems
Track B: Modules 80 – 85
Module 80: Systems of Linear Equations
- Solve systems of linear equations in two and three variables with the following methods: Graphing, Substitution, and Elimination
- Solve applied problems involving systems of equations
Module 81: Exponents and Polynomials
- Simplify expressions using the product, quotient, and power rules of exponents
- Simplify expressions with negative exponents
- Simplify expressions by raising products and quotients to a power
- Convert between scientific notation and decimal notation
- Multiply and divide using scientific notation
- Classify polynomials
- Identify the degree of terms and of polynomials
- Identify the coefficients of terms
- Write polynomials in descending order
- Evaluate polynomials
- Add, subtract, multiply, and divide polynomials
- Solve applied problems involving exponents and polynomials
Module 82: Factoring Polynomials
- Remove a common factor
- Factor trinomials whose leading coefficient is 1
- Factor trinomials whose leading coefficient is not 1
- Factor perfect square trinomials and the difference of squares
- Factor the sum and difference of cubes
- Solve quadratic equations by factoring
Module 83: Rational Expressions and Equation
- Simplify rational expressions
- Perform addition, subtraction, multiplication and division with rational expressions
- Solve equations containing rational expressions
- Solve applied problems using equations containing rational expressions.
Module 84: Rational Exponents and Radicals
- Find square roots, cube roots and nth roots
- Approximate roots
- Find n√a-n where a is a real number
- Convert between radicals and rational exponents
- Simplify expressions containing radicals or rational exponents
- Use rational exponents to simplify radical expressions
- Use the distance and midpoint formulas
- Perform operations with radical expressions
- Rationalize denominators of radical expressions
- Rationalize denominators having two terms
- Solve equations that contain radical expressions
- Use the Pythagorean Theorem
Module 85: Inequalities and Quadratic Equation
- Solve Compound Inequalities
- Solve Absolute Value Equations and Inequalities
- Graph Linear Inequalities in two variables
- Solve Systems of Linear Inequalities
- Solve Quadratic Equations by the Quadratic Formula
- Apply Methods of Quadratics to Solve Application problem
MAT 006- Skills for College Math
- Solve applied problems involving whole numbers, fractions and mixed numbers, decimal numbers, signed numbers, algebraic expressions and formulas, linear equations and inequalities; ratios, proportions, rates, and percentages, Absolute and Relative Differences, powers and roots.
- Evaluate expressions using the rules for order of operations
- Round decimal numbers
- Compare signed numbers
- Translate algebraic expressions to word phrases and word phrases to algebraic expressions
- Write algebraic expressions using exponents
- Simplify and evaluate algebraic expressions and formulas
- Solve literal equations for a particular variable
- Convert between fraction, decimal and percent
- Identify and plot points on the coordinate plane
- Identify the slope and y-intercept of an equation written in slope-intercept form
- Calculate the best fit line of a set of data, using the graphing calculator
- Determine the equation of the line of best fit
- Interpret the slope of the best fit line as a rate of change
- Use critical thinking skills to solve problems
- Use the Graphing Calculator to solve application problems
MAT 007- Skills Development
Module 70: Graphing Calculator Skills
- Use a graphing calculator to:
- Perform basic arithmetic operations, emphasizing order of operation, powers and roots
- Graph equation
Module 71: Percentages, Absolute and Relative Differences and Application
- Convert percentages to fractions or decimals and fractions and decimals to percentages
- Solve percent equations for the amount, base or percent
- Calculate absolute and relative differences
- Use critical thinking skills to solve problems
- Use the Graphing Calculator to solve application problems
Module 72: Algebraic skills
- Solve equations involving square roots
- Solving quadratic equations
- Use critical thinking skills to solve problems
- Use the Graphing Calculator to solve application problems
Module 73: More Graphing and Line of Best Fit
- Review graphing linear equations in two variables
- Calculate the best fit line of a set of data, using the graphing calculator
- Determine the equation of the line of best fit
- Interpret the slope of the best fit line as a rate of change
- Use critical thinking skills to solve problems
MAT 008- Skills Development for Precalculus
- Solve systems of linear equations in two and three variables
- Simplify expression
- Work with polynomials
- Solve quadratic equations
- Work with rational expressions
- Determine the domain of rational expressions
- Solve and graph Inequalities
MAT 120- Math for Liberal Arts
- Interpret the results of a variety of voting and apportionment methods
- Analyze relevant financial scenarios involving loans, credit cards, mortgages, savings, and taxes.
- Apply the five-step statistical method when conducting a statistical study
- Work together with peers in collaborative groups to solve a variety of mathematical problems.
- Use the appropriate technology for problem solving
MAT 130- Elements of Mathematics I
- Apply problem solving techniques to evaluate mathematical situations
- Explain the characteristics of a variety of numeration systems
- Express mathematical ideas verbally and symbolically
- Develop different methods of teaching arithmetic algorithms
MAT 131- Elements of Mathematics II
- Apply the basic concepts of plane and transformational geometry
- Solve problems using the fundamental principles of probability
- Calculate area, volume, and surface area of polygons
- Analyze conditions that produce congruence or similarity of figures
MAT 165- Trigonometry for Engineering and Science
- Demonstrate the use of the definitions of Trigonometric functions, their graphs, and the units of measurement of angles, as they relate to circles and triangles.
- Verify Trigonometric identities.
- Solve trigonometric equations.
- Apply vector algebra to solve a variety of physics problems.
MAT 177- Statistics
- Communicate, analyze and interpret statistical information effectively through written, oral, numerical or visual methods.
- Demonstrate appropriate use of technology for data analysis
- Apply the appropriate statistical principles to analyze and solve problems
MAT 182- Precalculus for Business and Social Science
- Analyze the graphical characteristics of polynomial, rational, exponential and logarithmic functions.
- Use polynomial, rational, exponential and logarithmic functions to create and/or analyze models for real life applications relating to business and social science.
- Solve polynomial, rational, and exponential and logarithmic equations numerically, algebraically and graphically.
MAT 195- Precalculus for Engineering and Science
- Analyze the graphical characteristics of polynomial, rational, exponential and logarithmic functions.
- Use polynomial, rational, exponential and logarithmic functions to create and/or analyze models for real life applications, such as optimization, growth and decay.
- Solve polynomial rational and exponential and logarithmic equations numerically, algebraically and graphically.
MAT 196- Accelerated Precalculus and Trigonometry for Engineering and Science
- Demonstrate the use of the definitions of Trigonometric functions, their graphs, and the units of measurement of angles, as they relate to circles and triangles.
- Verify Trigonometric identities.
- Solve trigonometric equations.
- Apply vector algebra to solve a variety of physics problems.
- Analyze the graphical characteristics of polynomial, rational, exponential and logarithmic functions.
- Use polynomial, rational, exponential and logarithmic functions to create and/or analyze models for real life applications, such as optimization, growth and decay.
- Solve polynomial rational and exponential and logarithmic equations numerically, algebraically and graphically.
MAT 201- Math Research I
- Conduct a literature search related to a math topic
- Collaborate with a mentor
- Communicate research results using appropriate format
- Articulate clear research question or problem
- Work autonomously in an effective manner, setting and meeting deadlines
MAT 202- Math Research II
- Conduct a literature search related to a math topic
- Collaborate with a mentor
- Communicate research results using appropriate format
- Articulate clear research question or problem
- Work autonomously in an effective manner, setting and meeting deadlines
MAT 203- Math Research III
- Conduct a literature search related to a math topic
- Collaborate with a mentor
- Communicate research results using appropriate format
- Articulate clear research question or problem
- Work autonomously in an effective manner, setting and meeting deadlines
MAT 204- Math Research IV
- Conduct a literature search related to a math topic
- Collaborate with a mentor
- Communicate research results using appropriate format
- Articulate clear research question or problem
- Work autonomously in an effective manner, setting and meeting deadlines
MAT 250- Discrete Math
- Use statements, logic operations, laws of operations, and rules of inference to construct valid mathematical arguments.
- Construct proofs, using a variety of methods and articulate the method used to the field of mathematics.
- Apply rules, laws, and properties to perform operations involving discrete structures such as sets, functions, sequences, sums, permutations, matrices, relations, graphs, and trees.
- Use discrete structures to create and/or analyze models for applications relating to Computer Science, Data Networking, Linguistic and many other diverse areas.
MAT 280- Calculus for Business and Social Science
- Solve applications related to exponential growth and decay Evaluate limits graphically, numerically, & analytically for a wide variety of functions.
- Evaluate derivatives analytically for the elementary functions, including inverse trigonometric functions and implicit functions.
- Apply derivatives and integrals to a variety of applications including, but not limited to optimization, elasticity of demand, marginals, etc.
- Sketch and analyze functions and their graphs using the first and second derivative
MAT 290- Calculus I for Engineering and Science
- Evaluate limits graphically, numerically, & analytically for a wide variety of functions.
- Evaluate derivatives analytically for the elementary functions, including inverse trigonometric functions and implicit functions.
- Apply derivatives to applications such as slope of a tangent line, velocity and acceleration, related rates, and optimization.
- Sketch and analyze functions and their graphs using the first and second derivative.
MAT 291- Calculus II for Engineering and Science
- Evaluate integrals analytically for a wide variety of functions, utilizing techniques such as integration by parts, trigonometric powers, trigonometric substitution, and partial fractions.
- Apply integration to applications such as area, volume, and work.
- Express and evaluate sequences and series explicitly and recursively.
- Find the Taylor and Maclaurin polynomial expansions for common functions.
MAT 292- Calculus III for Engineering and Science
- Use vectors to analyze lines and curves in 3 dimensional space, motion, lengths of curves, and curvature.
- Graph surfaces using contours and level curves.
- Calculate partial derivatives, directional derivatives, and gradient vectors.
- Apply the second derivative test to locate maxima, minima, and saddle points.
- Evaluate double and triple integrals in various coordinate systems.
MAT 295- Linear Algebra I
- Solve systems of linear equations in a variety of ways including row-reduction, matrix inverses, and Cramer’s Rule.
- Determine the determinant of a matrix.
- Examine the relationship between matrices and vector spaces including null space, basis, dimension, and rank.
- Perform operations of matrix algebra and appreciate the relationship between matrices and transformations.
- Model real-world applications using matrices.
MAT 296- Linear Algebra II
- Construct an orthonormal set using the Gram - Schmidt process.
- Determine eigenvalues and eigenvectors.
- Use matrices to solve problems such as least-squares and systems of linear differential equations.
- Connect Linear Algebra to other fields of study such as: economics, engineering and computer science.
MAT 298- Differential Equations
- Solve commonly-occurring types of differential equations explicitly by analytical techniques.
- Apply numerical methods to find approximate solutions to differential equations that cannot be solved analytically.
- Apply qualitative techniques to obtain information about solutions to differential equations without explicitly solving the differential equation.
- Model real-world applications using differential equations.