# 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

1. Solve real world problems requiring an understanding of signed number concepts
2. Understand and apply the concepts of expression and equation
3. Understand and apply the principles for solving linear equations and inequalities
4. Understand and apply the concept of slope as rate of change
5. Apply algebraic methods to solve a variety of real world problems
6. Create and identify a linear relationship based on patterns in collected data
7. Generalize patterns and relationships using tables of values (ordered pairs), verbal rules, equations, and graphs
8. Understand and apply systems of equations in two variables including their graphs
9. Understand and apply the laws of exponents

### Instructional Objectives

SIGNED NUMBERS

1. Construct a number line and graph a given signed number.
2. Identify the signed number represented by a point on the number line.
3. Find the opposite of a signed number.
4. 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.
5. Given two signed numbers, use the symbols < and > to indicate their relationship
6. Find the sum or difference of two signed numbers
7. Find the product or quotient of two signed numbers.
8. Evaluate expressions involving sums, differences, products, quotients, and powers of signed numbers.
9. Solve application problems involving signed numbers, including finding averages and medians of data sets

PROPERTIES OF REAL NUMBERS

10. Explain in words what is known from the commutative, associative, inverse, and identity properties of addition and multiplication, and give examples of each
11. Apply the distributive property and give examples ALGEBRAIC EXPRESSIONS

ALGEBRAIC EXPRESSIONS

12. Identify variables, terms, numerical constants, and numerical coefficients.
13. Evaluate an algebraic expression or formula given numerical values for the variables
14. Combine like terms in an expression.
15. Multiply an expression by a constant using the distributive property.
16. Simplify a general linear expression.
17. Translate a verbal phrase into a mathematical expression.

SOLVING LINEAR EQUATIONS

18. Determine whether or not a given number is a solution to a given equation.
19. Solve equations of the form x + a = b and x -­‐ a = b.
20. Solve equations of the form ax = b and x/a =b.
21. Solve linear equations of the form ax + b = c and ax + b = cx + d.
22. Translate a verbal statement into a mathematical equation.
23. Solve linear equations using the distributive property
24. Solve linear equations having one solution, no solution, or an infinite number of solutions
25. Solve a formula for a given variable (solve literal equations)
26. Set up and solve algebraic application problems, including those involving area and perimeter of rectangles.
27. Solve linear inequalities in one variable and graph solutions on the number line

GRAPHING LINEAR EQUATIONS

28. Identify and interpret: coordinate system, number plane, origin, axis, quadrant, ordered pair, coordinate
29. Plot points with given coordinates in the number plane
30. Identify the coordinates of an ordered pair represented by a point in the number plane
31. Determine whether a given ordered pair is a solution to an equation
32. Given a linear equation, construct a table of ordered pairs and draw the graph of the line
33. Find the x-­‐ and y-­‐ intercepts of a line, given its equation
34. Graph linear equations of the form x = k and y = k
35. Use a linear equation to model data
36. Create and identify a linear relationship based on patterns in collected data
37. Understand and apply the concept of slope as rate of change
38. Find the slope of a line given two points
39. Find the slope from an equation of a line
40. Use slope to determine whether two lines are parallel, perpendicular, or neither
41. Write the equation of a line given its slope and y-­‐intercept
42. Graph a line given its slope and a point on the line
43. Write the equation of a line given its slope and any point on the line
44. Write the equation of a line given two points
45. Graph the solution set of a linear inequality in two variables

SYSTEMS OF LINEAR EQUATIONS

46. Identify a given ordered pair as a solution or non-­‐solution of a given system of linear equations
47. Solve systems of linear equations algebraically by the substitution method
48. Solve systems of linear equations algebraically by the addition method
49. Solve systems of linear equations having one solution, no solution, or multiple solutions
50. Solve applied problems using systems of two linear equations in two variables

EXPONENTS

51. State and apply rules of exponents
52. Evaluate numerical expressions having integer exponents
53. Simplify expressions with variables having integer exponents
54. Express a given number in scientific notation and in decimal notation
55. Write numbers in scientific notation
56. Perform operations on numbers in scientific notation and express the answers in scientific notation