## Math Essentials (MTE)

### MTE 1 - Operations with Positive Fractions

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency in operations and problem solving with positive fractions necessary to succeed in 100-level math courses.

### Course Prerequisites/Corequisites

Prerequisite: Qualifying placement score

### Course Objectives

- Write, simply and compare fractions.
- Express parts of a whole using fraction notation.
- Convert between improper fractions and mixed numbers.
- Express repeated factors using exponents.
- Find the prime factorization of a given number.
- Write fractions in simplest form.
- Compare two quantities in the form of a ratio or rate in simplest form.
- Find the least common multiple (LCM) of two or more whole numbers.
- Find the least common denominator (LCD) of two or more fractions.
- Determine the relationship (<, >, =) between two fractions with unlike denominators.
- Perform operations with fractions.
- Add and subtract fractions and mixed numbers with like denominators.
- Add and subtract fractions and mixed numbers with unlike denominators.
- Multiply fractions and mixed numbers.
- Divide fractions and mixed numbers.
- Simplify expressions involving fractions using order of operation.
- Solve application using U.S. customary units of measurement.

### Major Topics to be Included

- Write, simplify, and compare fractions.
- Perform operations with fractions.
- Solve applications using U.S. customary units of measurement.

### MTE 2 - Operations with Positive Decimals and Percents

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency in operations and problem solving with positive decimals and percents necessary to succeed in 100-level math courses.

### Course Prerequisites/Corequisites

Prerequisites: MTE 1 or qualifying placement score

### Course Objectives

- Demonstrate the meaning of decimal numbers.
- Convert decimals between standard notation and word notation.
- Identify place values in decimals.
- Perform operations with decimals.
- Add and Subtract decimals.
- Multiply decimals.
- Divide decimals.
- Simplify expressions using order of operations.
- Estimate decimals.
- Round decimals to a specific place value.
- Estimate sums, differences, products, and quotients with decimals.
- Demonstrate the relationship among fractions, decimals, and percents.
- Write parts of a whole using percent notation.
- Convert among fractions, decimals and percents.
- Order a list of fractions and decimals from smallest to largest.
- Solve basic percent problems.
- Calculate all values in the basic percent problem (percent, amount /part, and base).
- Calculate percent increase and percent decrease.
- Calculate sales tax and commission.
- Calculate simple interest.
- Read and interpret basic graphs.
- Read and interpret information from a pie graph.
- Calculate the percentage denoted by a pie graph.
- Read and interpret information from a bar graph.
- Read and interpret information from a line graph.
- Convert units of measure.
- Convert within the U.S. system.
- Convert within the metric system.
- Convert between U.S. and metric units using conversion tables.
- Convert units of time.
- Convert between Fahrenheit and Celsius temperatures.
- Solve application problems using U.S. customary and metric units of measurement.

### Major Topics to be Included

- Demonstrate the meaning of decimal numbers.
- Perform operations with decimals.
- Estimate decimals.
- Demonstrate the relationship among fractions, decimals, and percents.
- Solve basic percent problems.
- Read and interpret basic graphs.
- Convert units of measure.
- Solve application problems using U.S. customary and metric units of measurement.

### MTE 3 - Algebra Basics

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses in operations and problem solving with algebraic expressions and simple algebraic equations using signed numbers.

### Course Prerequisites/Corequisites

Prerequisites: MTE 2 or qualifying placement score

### Course Objectives

- Determine the absolute value of a number.
- Demonstrate proper use of exponents.
- Express repeated factors using exponents.
- Evaluate powers of numbers.
- Find the principal square root of a perfect square.
- Simplify expressions involving signed numbers.
- Add and subtract signed numbers.
- Multiply and divide signed numbers.
- Use the proper order of operations to simplify expressions containing multiple operations on signed numbers, including powers and square roots.
- Write numbers in scientific notation.
- Convert between integer powers of 10 and equivalent decimal numbers.
- Convert numbers between scientific notation and standard notation.
- Simplify algebraic expressions.
- Identify the properties of real numbers (Commutative, Associative, Distributive, Identity and Inverse Properties).
- Simplify an algebraic expression by combining like terms.
- Simplify algebraic expressions using the order of operations.
- Evaluate a formula or algebraic expression for given values of the variables.
- Solve one-step equations using the addition and multiplication properties.
- Solve one-step equations using rational numbers.
- Solve one-step equations using percents.
- Solve problems using proportions.
- Solve application problems including finding perimeter, area and volume.

### Major Topics to be Included

- Determining the absolute value of a number.
- Using exponents.
- Finding the principal square root of a perfect square.
- Simplifying expressions involving signed numbers.
- Writing numbers in scientific notation.
- Simplifying algebraic expressions.
- Evaluating formulas and algebraic expressions for given values of the variables.
- Solving one-step equations using the addition and multiplication properties.
- Solving problems using proportions.
- Solving application problems including finding perimeter, area and volume.

### MTE 4 - First Degree Equations and Inequalities in One Variable

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses in solving first degree equations and inequalities containing one variable and using them in applications.

### Course Prerequisites/Corequisites

Prerequisites: MTE 3 or qualifying placement score.

### Course Objectives

- Solve first degree equations in one variable.
- Solve first degree equations in one variable using the Addition Property of Equality.
- Solve first degree equations in one variable using the Multiplication Property of Equality.
- Solve first degree equations in one variable using the Addition Property of Equality and the Multiplication Property of Equality.
- Solve first degree equations in one variable that contain parentheses.
- Solve first degree equations in one variable with the variable on both sides of the equal sign.
- Solve first degree equations in one variable and identify the solution to an equation as finite, the empty set or all real numbers.
- Solve a formula or equation for one of its variables.
- Solve a formula or equation for one of its variables using the Addition Property of Equality.
- Solve a formula or equation for one of its variables using the Multiplication Property of Equality.
- Solve a formula or equation for one of its variables using the Addition Property of Equality and the Multiplication Property of Equality.
- Solve first degree absolute value equations containing a single absolute value.
- Solve first degree inequalities in one variable.
- Solve first degree inequalities in one variable stating the solution using inequality notation.
- Solve first degree inequalities in one variable stating the solution using interval notation.
- Solve first degree inequalities in one variable and graph the solution on a real number line.
- Solve application problems using a single first degree equation or inequality.

### Major Topics to be Included

- Solving first degree equations in one variable.
- Solving formulas and equations for one variable.
- Solving first degree absolute value equations containing a single absolute value.
- Solving first degree inequalities in one variable.
- Solving application problems using a single first degree equation or inequality.

### MTE 5 - Linear Equations, Inequalities and Systems of Linear Equations in Two Variables

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses with solving applications by finding the equation of a line, graphing linear equations and inequalities in two variables and solving systems of linear equations.

### Course Prerequisites/Corequisites

Prerequisites: MTE 4 or qualifying placement score.

### Course Objectives

- Define the properties of the rectangular coordinate system.
- Determine the coordinates of a point plotted on the coordinate plane.
- Determine whether an ordered pair is a solution to an equation in two variables.
- Graph a linear equation by finding and plotting ordered pair solutions.
- Graph a linear equation in two variables.
- Identify the x and y intercepts of a graph.
- Graph a linear equation by plotting intercepts.
- Graph an equation given in slope-intercept form.
- Graph a horizontal line given its equation.
- Graph a vertical line given its equation.
- Graph a linear inequality in two variables.
- Find the slope of a line.
- Find the slope of a line given two points on the line.
- Find the slope of a line given its equation in slope-intercept form.
- Find the slope of a line given its equation by converting to slope-intercept form.
- Find the slope of a line given its graph.
- Find the slope of horizontal and vertical lines.
- Write an equation of a line.
- Write an equation of a line in slope-intercept form given the slope and the y-intercept.
- Use point-slope form to write an equation of a line in slope intercept form given the slope and a point on the line.
- Use point-slope form to write an equation of a line in slope intercept form given two points on the line.
- Write the equation of a vertical line.
- Write the equation of a horizontal line.
- Find the equation of a line that is parallel or perpendicular to a given line and passes through a given point.
- Solve systems of linear equations.
- Determine if an ordered pair is a solution of system of equations in two variables.
- Solve systems of linear equations by graphing.
- Solve by elimination using substitution.
- Solve by elimination using addition.
- Identify a system of linear equations as consistent and independent, consistent and dependent, or inconsistent.
- Use function notation.
- Evaluate y = f(x) for specific values of x.
- Given the graph of y = f(x), evaluate f(x) for specific values of x.
- Given the graph of y = f(x), find x for specific values of f(x).
- Solve applications problems that require linear equations, inequalities and systems of linear equations in two variables.

### Major Topics to be Included

- Properties of the rectangular coordinate system.
- Graphing linear equations in two variables.
- Graphing a linear inequality in two variables.
- Finding the slope of a line.
- Writing the equation of a line.
- Solving systems of linear equations.
- Using function notation.
- Solving application problems that require linear equations, inequalities and systems of linear equations in two variables.

### MTE 6 - Exponents, Factoring and Polynomial Equations

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses in solving applications using polynomial equations solved by factoring.

### Course Prerequisites/Corequisites

Prerequisites: MTE 5 or qualifying placement score.

### Course Objectives

- Perform operations on exponential expressions using the rules of exponents.
- Evaluate the product of two exponential expressions.
- Evaluate the quotient of two exponential expressions.
- Evaluate the power of a power of an exponential expression.
- Evaluate exponential expressions that contain negative exponents.
- Evaluate exponential expressions that contain combinations of products, quotients, power of a power and negative exponents.
- Multiply and divide numbers in Scientific Notation.
- Define, add, subtract, multiply and divide polynomials.
- Identify an expression as a monomial, binomial, trinomial or polynomial.
- Add, subtract, multiply and divide monomials using the rules of exponents.
- Add, subtract, and multiply binomials.
- Add, subtract, and multiply trinomials.
- Add, subtract, and multiply combinations of binomials and trinomials.
- Factor polynomials.
- Find the greatest common factor from a list of terms.
- Find the greatest common factor from a polynomial.
- Factor a polynomial by grouping.
- Factor trinomials of the form+ bx + c.
- Factor trinomials of the form a + bx + c, a1.
- Factor a difference of squares.
- Factor a sum of two cubes.
- Factor a difference of two cubes.
- Solve polynomial equations using factoring techniques.
- Solve application problems involving polynomial equations and factoring.

### Major Topics to be Included

- Operations on exponential expressions using the rules of exponents.
- Defining, adding, subtracting, multiplying and dividing polynomials.
- Factoring polynomials.
- Solving polynomial equations using factoring techniques.
- Solving application problems involving polynomial equations and factoring.

### MTE 7 - Rational Expressions and Equations

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses in solving applications using rational algebraic equations.

### Course Prerequisites/Corequisites

Prerequisites: MTE 6 or qualifying placement score.

### Course Objectives

- Identify a rational algebraic expression.
- Identify the real value of the variable for which a rational algebraic expression having a denominator of the formax + b is undefined.
- Identify all real values of the variable for which a rational algebraic expression having a denominator of the form ax2 + bx + c is undefined.
- Express a rational algebraic expression having negative exponents as an equivalent rational expression without negative exponents.
- Simplify rational algebraic expressions.
- Simplify a rational algebraic expression.
- Evaluate a rational algebraic expression given specific integral values for each variable.
- Perform arithmetic operations with rational algebraic expressions.
- Perform addition and subtraction of rational algebraic expressions having like denominators.
- Find the Least Common Denominator (LCD) of two or more rational algebraic expressions.
- Perform addition and subtraction of rational algebraic expressions having denominators that have no common factors.
- Perform addition and subtraction of rational algebraic expressions having denominators that have a common monomial factor.
- Perform addition and subtraction of rational algebraic expressions having denominators that have a common binomial factor.
- Perform multiplication of rational algebraic expressions and express the product in simplest terms.
- Use factorization to divide rational algebraic expressions and express the quotient in simplest terms.
- Simplify complex fractions.
- Divide a polynomial by a monomial.
- Perform polynomial long division having binomial divisors of the form ax+b.
- Solve rational algebraic equations.
- Solve application problems using rational algebraic equations.
- Write a rational equation to match the information given in an application problem.
- Solve an application problem using rational equations.

### Major Topics to be Included

- Identifying a rational algebraic expression.
- Simplifying rational algebraic expressions.
- Performing arithmetic operations with rational algebraic expressions.
- Solving rational algebraic equations.
- Solving application problems using rational algebraic equations.

### MTE 8 - Rational Exponents and Radicals

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in 100-level math courses in solving applications using rational exponents and radical equations.

### Course Prerequisites/Corequisites

Prerequisites: MTE 7 or qualifying placement score.

### Course Objectives

- Demonstrate the equivalence of radical and rational exponent forms.
- Convert between square root and a1/2 forms.
- Convert between nth root and a1/n forms.
- Convert between combinations of nth root and mth power and am/n forms.
- Compute and estimate radicals.
- Calculate square roots via calculator.
- Estimate square roots.
- Calculate nth roots via calculator.
- Simplify radicals and radical expressions.
- Simplify using the properties of rational exponents.
- Simplify square roots.
- Simplify nth roots of variable expressions.
- Simplify radicals by using the multiplication property of radicals.
- Simplify radicals by using the division property of radicals.
- Perform operations (add, subtract, multiply) on radicals and radical expressions.
- Define like radicals.
- Combine and simplify like radicals.
- Multiply and simplify radicals.
- Rationalize the denominator (one term and two terms).
- Simplify radicals by rationalizing a denominator with one term.
- Simplify radicals by rationalizing a denominator with two terms.
- Solve radical equations.
- Define the imaginary unit and imaginary numbers.
- Define i = the square root of -1
- Define imaginary numbers
- Simplify square roots of negative numbers using the imaginary unit.
- Solve application problems involving radicals.
- Solve problems involving right triangles.
- Solve problems involving the Pythagorean Theorem.
- Solve problems involving the distance formula.

### Major Topics to be Included

- Demonstrating the equivalence of radical and rational exponent forms.
- Computing and estimating radicals.
- Simplifying radicals and radical expressions.
- Performing operations (add, subtract, multiply) on radicals and radical expressions.
- Rationalizing the denominator (one term and two terms).
- Solving radical equations.
- Defining the imaginary unit and imaginary numbers.
- Simplifying square roots of negative numbers using the imaginary unit.
- Solving application problems involving radicals.

### MTE 9 - Functions, Quadratic Equations and Parabolas

### Course Description

Effective: 2012-01-01

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in selected 100-level math courses in solving applications using functions, quadratic functions and their properties.

### Course Prerequisites/Corequisites

Prerequisites: MTE 8 or qualifying placement score.

### Course Objectives

- Determine if a relation is a function and identify the domain and range of the function.
- Determine if a list of ordered pairs, graph, or equation is a function.
- Determine the domain and range of a function given as a list of ordered pairs.
- Determine the domain and range of a function given as a graph.
- Determine the domain of a function given as an equation.
- Evaluate y=f(x) for constant values of x and for specific monomials and binomials.
- Find all roots of quadratic equations using both the square root method and the quadratic formula.
- Find the roots of quadratic equations of the form ax 2 + c = 0 .
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is a positive perfect square, (i.e. the quadratic is factorable).
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is positive, but not a perfect square.
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is zero.
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is negative.
- Describe the roots of a quadratic based upon the discriminant in all cases.
- Analyze a quadratic function to determine its vertex by completing the square and using the formula.
- Write a quadratic function in vertex form y=a(x-h)2 + k by completing the square for quadratics with a=1 and identify the vertex (h,k).
- Write a quadratic function in vertex form y=a(x-h)2 + k by completing the square for quadratics with a not equal to 1 and identify the vertex (h,k).
- Find the vertex of a quadratic equation y=ax2 + bx + c using the formula method supplied.
- Graph a quadratic function, using the vertex form, indicating the intercepts and vertex.
- Determine whether the parabola opens upward or downward.
- Plot the vertex of the parabola.
- Determine the axis of symmetry for the parabola.
- Plot the x-intercepts of the parabola, if they exist.
- Plot the y-intercept of the parabola and complete the graph with additional points as needed.
- Apply knowledge of quadratic functions to solve application problems from geometry, economics, applied physics, and other disciplines.
- Solve problems involving area optimization.
- Solve problems involving revenue optimization.
- Solve problems involving the motion of falling objects.

### Major Topics to be Included

- Determine if a relation is a function and identify the domain and range of the function.
- Find all roots of quadratic equations using both the square root method and the quadratic formula.
- Analyze a quadratic function to determine its vertex by completing the square and using the formula.
- Graph a quadratic function, using the vertex form, indicating the intercepts and vertex.
- Apply knowledge of quadratic functions to solve application problems from geometry, economics, applied physics, and other disciplines.