# Algebra I

MTH 097

## Course Description

Prerequisite: MATH LEVEL 3. Includes natural numbers, integers, first-degree equations and inequalities, special products, factoring, rational expressions and equations, graphs, and linear systems, exponents, and quadratic equations. May receive credit in only one of the following: MTH 107 or MTH 097 or SKMA 097 or SKMA 102. (Equivalent to first year high school algebra). Does not earn credit toward graduation. (45-0)

## Outcomes and Objectives

### Students will develop their skills in number patterns, relationships, and computation.

#### Objectives:

• Compute (add, subtract, multiply and divide) with signed numbers without the use of a calculator.
• Simplify numerical expressions with multiple operations and grouping symbols using the order of operations.
• Simplify rates and ratios.
• Compute the opposite, reciprocal, and absolute value of a given real number.
• Estimate the value of a numerical expression.
• Identify an approximate answer to an application problem prior to working it out.
• Identify the appropriate unit of an answer to a word problem.

### Students will develop their skills in the computation and recognition of algebraic expressions.

#### Objectives:

• Add, subtract, and multiply polynomial expressions.
• Simplify algebraic expressions with multiple operations and grouping symbols using the order of operations.
• Simplify algebraic expressions using the rules of exponents.
• Simplify algebraic expressions using the distributive property.
• Compare and contrast terms and factors.
• Simplify rational expressions.
• Factor polynomials by taking out a common factor.
• Factor trinomials.
• Factor binomials of the form x2 - y2
• Identify an algebraic expression that cannot be factored.
• Compute the opposite and reciprocal of a given algebraic expression.
• Identify and give examples of like and unlike terms.
• Identify and give examples of linear, quadratic, rational, and radical expressions.
• Compare and contrast expressions and equations.

### Student can solve a variety of equations, inequalities, and systems of equations.

#### Objectives:

• Solve a variety of linear, quadratic (using the factoring method and the quadratic formula), radical, and rational equations.
• Verify the solution of an equation.
• Recognize situations in which an equation has no solution or has multiple solutions.
• Solve a variety of linear inequalities.
• Verify the solution of a linear inequality.
• Recognize situations in which a linear inequality has no solution or multiple solutions.
• Use interval notation, relational symbols <, >, <, >) dimensional graph, or a verbal description to describe a set of numbers.
• Solve a variety of systems of linear equations.
• Verify the solution of a system of linear equations.
• Recognize situations in which a system of linear equations has no solution or multiple solutions.

### Student can recognize and understand concepts related to linear functions.

#### Objectives:

• Solve linear equations algebraically, graphically, and numerically.
• Solve systems of linear equations algebraically, graphically, and numerically.
• Compute the slope of a line in a variety of contexts.
• Identify the slope of a line as positive, negative, zero, or undefined.
• Interpret the slope of a line in context as a rate of change.
• Compute the y-intercept of a line in a variety of contexts.
• Interpret the y-intercept of a line in context as an initial amount.
• Compute the equation of a line in form in a variety of contexts.

### Students will develop their skills in the construction and interpretation of Cartesian graphs.

#### Objectives:

• Construct the graph of a line if given the equation of the line.
• Identify an appropriate scale for both axes when constructing a graph.
• Approximate one coordinate of a point on a graph is given the other.
• Identify graphs as linear or non-linear.

### Students will develop their problem-solving skills.

#### Objectives:

• Set up an equation or expression if given a word phrase.
• Describe in words the meaning of an expression or equation.
• Solve a variety of real world problems using the tools of algebra and mathematical modeling.

### Students will communicate effectively about mathematics.

#### Objectives:

• Use mathematics terminology effectively in writing and speaking.