MAT-097 Objectives
MAT-097 Foundations of Algebra
Course Description
This course is a continuation of MAT-093, Foundations of Mathematics. Topics include signed numbers, algebraic expressions, solving and graphing linear equations and inequalities, exponents and scientific notation, introduction to polynomials, and systems of linear equations and their graphs. Technology is incorporated to facilitate problem solving. This course does not satisfy degree requirements. PREREQUISITE: Grade of C or better in MAT-093, Foundations of Mathematics or placement. Course may require an additional lab hour. Credit hours: 3.0.
Learning Outcomes
- Solve real world problems requiring an understanding of signed number concepts
- Understand and apply the concepts of expression and equation
- Understand and apply the principles for solving linear equations and inequalities
- Understand and apply the concept of slope as rate of change
- Apply algebraic methods to solve a variety of real world problems
- Create and identify a linear relationship based on patterns in collected data
- Generalize patterns and relationships using tables of values (ordered pairs), verbal rules, equations, and graphs
- Understand and apply systems of equations in two variables including their graphs
- Understand and apply the laws of exponents
Instructional Objectives
SIGNED NUMBERS
- Construct a number line and graph a given signed number.
- Identify the signed number represented by a point on the number line.
- Find the opposite of a signed number.
- Find the absolute value of signed numbers, and use absolute value to find the distance of a point on the number line from the origin.
- Given two signed numbers, use the symbols < and > to indicate their relationship
- Find the sum or difference of two signed numbers
- Find the product or quotient of two signed numbers.
- Evaluate expressions involving sums, differences, products, quotients, and powers of signed numbers.
- Solve application problems involving signed numbers, including finding averages and medians of data sets
PROPERTIES OF REAL NUMBERS - Explain in words what is known from the commutative, associative, inverse, and identity properties of addition and multiplication, and give examples of each
- Apply the distributive property and give examples ALGEBRAIC EXPRESSIONS
ALGEBRAIC EXPRESSIONS - Identify variables, terms, numerical constants, and numerical coefficients.
- Evaluate an algebraic expression or formula given numerical values for the variables
- Combine like terms in an expression.
- Multiply an expression by a constant using the distributive property.
- Simplify a general linear expression.
- Translate a verbal phrase into a mathematical expression.
SOLVING LINEAR EQUATIONS - Determine whether or not a given number is a solution to a given equation.
- Solve equations of the form x + a = b and x -‐ a = b.
- Solve equations of the form ax = b and x/a =b.
- Solve linear equations of the form ax + b = c and ax + b = cx + d.
- Translate a verbal statement into a mathematical equation.
- Solve linear equations using the distributive property
- Solve linear equations having one solution, no solution, or an infinite number of solutions
- Solve a formula for a given variable (solve literal equations)
- Set up and solve algebraic application problems, including those involving area and perimeter of rectangles.
- Solve linear inequalities in one variable and graph solutions on the number line
GRAPHING LINEAR EQUATIONS - Identify and interpret: coordinate system, number plane, origin, axis, quadrant, ordered pair, coordinate
- Plot points with given coordinates in the number plane
- Identify the coordinates of an ordered pair represented by a point in the number plane
- Determine whether a given ordered pair is a solution to an equation
- Given a linear equation, construct a table of ordered pairs and draw the graph of the line
- Find the x-‐ and y-‐ intercepts of a line, given its equation
- Graph linear equations of the form x = k and y = k
- Use a linear equation to model data
- Create and identify a linear relationship based on patterns in collected data
- Understand and apply the concept of slope as rate of change
- Find the slope of a line given two points
- Find the slope from an equation of a line
- Use slope to determine whether two lines are parallel, perpendicular, or neither
- Write the equation of a line given its slope and y-‐intercept
- Graph a line given its slope and a point on the line
- Write the equation of a line given its slope and any point on the line
- Write the equation of a line given two points
- Graph the solution set of a linear inequality in two variables
SYSTEMS OF LINEAR EQUATIONS - Identify a given ordered pair as a solution or non-‐solution of a given system of linear equations
- Solve systems of linear equations algebraically by the substitution method
- Solve systems of linear equations algebraically by the addition method
- Solve systems of linear equations having one solution, no solution, or multiple solutions
- Solve applied problems using systems of two linear equations in two variables
EXPONENTS - State and apply rules of exponents
- Evaluate numerical expressions having integer exponents
- Simplify expressions with variables having integer exponents
- Express a given number in scientific notation and in decimal notation
- Write numbers in scientific notation
- Perform operations on numbers in scientific notation and express the answers in scientific notation