## Math Essentials (MTE)

### Course Description

Effective: 2012-01-01

Includes operations and problem solving with proper fractions, improper fractions, and mixed numbers without the use of a calculator. Emphasizes applications and includes U. S. customary units of measure. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### 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.

<- Back to MTE 1

### Course Description

Effective: 2012-01-01

Includes operations and problem solving with positive decimals and percents. Emphasizes applications and includes U. S. customary and metric units of measure. Credit is not applicable toward graduation. Prerequisite(s): MTE 1 or qualifying placement score.
Lecture 1 hour per week.
1 credits

### 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.
• 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.

<- Back to MTE 2

### Course Description

Effective: 2012-01-01

Includes basic operations with algebraic expressions and solving simple algebraic equations using signed numbers with emphasis on applications. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### 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.

<- Back to MTE 3

### Course Description

Effective: 2012-01-01

Includes solving first degree equations and inequalities containing one variable, and using them to solve application problems. Emphasizes applications and problem solving. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### 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.

<- Back to MTE 4

### Course Description

Effective: 2012-01-01

Includes finding the equation of a line, graphing linear equations and inequalities in two variables and solving systems of two linear equations. Emphasizes writing and graphing equations using the slope of the line and points on the line, and applications. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### 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.

<- Back to MTE 5

### Course Description

Effective: 2012-01-01

The student will learn to perform operations on exponential expressions and polynomials. Students will also learn techniques to factor polynomials and use these techniques to solve polynomial equations. Emphasis should be on learning all the different factoring methods, and solving application problems using polynomial equations. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### 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.

<- Back to MTE 6

### Course Description

Effective: 2012-01-01

Includes simplifying rational algebraic expressions, solving rational algebraic equations and solving applications that use rational algebraic equations. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### 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.

<- Back to MTE 7

### Course Description

Effective: 2012-01-01

Lecture 1 hour per week.
1 credits

### 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.
• Calculate square roots via calculator.
• Estimate square roots.
• Calculate nth roots via calculator.
• Simplify using the properties of rational exponents.
• Simplify square roots.
• Simplify nth roots of variable expressions.
• Combine and simplify like 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.
• 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.
• Rationalizing the denominator (one term and two terms).
• Defining the imaginary unit and imaginary numbers.
• Simplifying square roots of negative numbers using the imaginary unit.
• Solving application problems involving radicals.

<- Back to MTE 8

### Course Description

Effective: 2012-01-01

Includes an introduction to functions in ordered pair, graph, and equation form. Also introduces quadratic functions, their properties and their graphs. Credit is not applicable toward graduation.
Lecture 1 hour per week.
1 credits

### 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.

<- Back to MTE 9