Portland Community College | Portland, Oregon

A scientific calculator and access to a graphing utility may be required.

Students are no longer required to have physical graphing calculators in MTH 60, 65, 70, 95, 111, or 112. Where physically possible instructors will demonstrate using Desmos, GeoGebra, or other online programs in class. Assessments requiring the use of a graphing utility may be done outside of proctored exams.

There is a required notation addendum which may be found at pcc.edu/programs/math/course-downloads.html.

Upon completion of the course students should be able to:

1. Recognize and apply the operations necessary to simplify expressions and solve equations.
2. Use variables to represent unknown quantities, create models, and make predictions using linear equations, quadratic equations, and systems of equations.
3. Identify and interpret the rate of change in linear data.
4. Distinguish between quadratic and linear relationships in symbolic, graphical, and verbal forms.
5. Interpret properties such as ordered pairs, and maximum and minimum values in a quadratic relationship.
6. Interpret information provided in function notation given a function expressed in graphical, symbolic, numeric, or verbal form.

Assessment Requirements

1. The following must be assessed in a proctored, closed-book, no-note, and no-calculator setting:
   1. Simplifying expressions
   2. Solving linear equations
   3. Solving systems of linear equations
   4. Graphing linear and quadratic equations
2. At least two proctored, closed-book, no-note examinations (one of which is the comprehensive final) must be given. These exams must consist primarily of free response questions although a limited number of multiple choice and/or fill-in-the-blank questions may be used where appropriate.
3. Assessment must include evaluation of the students ability to arrive at correct conclusions using proper mathematical procedures and notation. Additionally, each student must be assessed on their ability to use appropriate organizational strategies and write appropriate conclusions. Application problems must be answered in complete sentences
4. At least two of the following additional measures must also be used
   1. Graded homework
   2. Quizzes
   3. Projects
   4. In-class activities
   5. Portfolios

Review of algebraic concepts from introductory algebra that are necessary for success in intermediate algebra

1. Relations and Functions
   1. Use the definition of a function to determine whether a given relation represents a function.
   2. Determine the domain and range of functions given as a graph, given as a set of ordered pairs, and given as a table.
   3. Apply function notation in graphical, algebraic, and tabular settings.
      1. Understand the difference between the input and output.
      2. Identify ordered pairs from function notation.
      3. Given an input, find an output.
      4. Given an output, find input(s).
   4. Interpret function notation in real world applications.
      1. Evaluate the function at a particular input value and interpret its meaning.
      2. Given a functional value (output), find and interpret the input.
2. Manipulate Algebraic Expressions
   1. Perform operations on polynomial expressions and apply exponent laws to help simplify expressions.
   2. Simplify Radical Expressions
      1. Convert radical expressions to expressions with rational exponents and vice versa.
      2. Simplify, add, subtract, multiply and divide radical expressions.
      3. Use rational exponents to simplify radical expressions.
      4. Rationalize denominators with square roots in them.
      5. Use a calculator to approximate radicals using rational exponents.
3. Solving Equations
   1. Solve linear equations and inequalities in one variable.
   2. Solve systems of linear equations in two variables.
      1. Solve systems by graphing.
      2. Solve systems by the substitution method.
      3. Solve systems by the addition (elimination) method.
      4. Solve applications involving systems of two linear equations.
   3. Solve quadratic equations in one variable.
      1. Solve quadratic equations using the square root property.
      2. Solve quadratic equations using the Quadratic Formula including complex solutions.
         1. Simplify and approximate non-variable square roots including complex solutions.
         2. Use the Pythagorean Theorem to find missing sides of a right triangle.
   4. Solve radical equations that have a single radical term.
   5. Solve an equation using a graphing utility by finding points of intersection.
   6. Solve applications involving linear, quadratic, and radical equations of one variable.
   7. Work with literal equations
      1. Solve an equation for a specified variable in terms of other variables.
      2. Input values into a formula and solve for the remaining variable.
4. Graphs of Equations in Two Variables
   1. Graph linear equations.
      1. Graph a linear equation by finding the intercepts.
      2. Graph a linear equation given its slope and the vertical intercept.
      3. Create graphs where the axes are required to have different scales.
      4. Graph a linear equation given its slope and a point on the line.
      5. Use and interpret linear models of real world situations algebraically and graphically.
   2. Determine the slopes of lines from equations and graphs and interpret their significance as rates of change.
   3. Determine linear equations.
      1. Find an equation for a linear relationship given a graph of a line.
      2. Find an equation for a linear relationship given two points.
      3. Find an equation for a linear model given a verbal description of a relationship, first identifying the independent and dependent variables.
   4. Graph quadratic equations in two variables.
      1. Graph a quadratic equation by creating a table and plotting points.
      2. Graph a quadratic equation by finding the axis of symmetry, the vertex, and the intercepts.
      3. Use and interpret quadratic models of real world situations algebraically and graphically.
         1. Evaluate the function at a particular input value and interpret its meaning.
         2. Given a functional value (output), find and interpret the input.
         3. Interpret the vertex, the vertical intercept, and any horizontal intercept(s) using proper units.

The purpose of the MTH 70 class is to prepare students to be successful in MTH 95. Several topics in MTH 95 require that students have much more than an introductory understanding of MTH 60/65 material.  Algebraic concepts covered in MTH 70 will be used in MTH 95 with the expectation that students know and understand them.

Vocabulary is an important part of algebra. Instructors should make a point of using proper vocabulary throughout the course. Some of this vocabulary should include, but not be limited to, inverses, identities, the commutative property, the associative property, the distributive property, equations, expressions and equivalent equations.

The difference between expressions and equations needs to be emphasized throughout the course. A focus must be placed on helping students understand that evaluating an expression, simplifying an expression, and solving an equation are distinct mathematical processes and that each has its own set of rules, procedures, and outcomes.

Equivalence of expressions is always communicated using equal signs. Students need to be taught that when they simplify or evaluate an expression they are not solving an equation despite the presence of equal signs. Instructors should also stress that it is not acceptable to write equal signs between nonequivalent expressions.

Instructors should demonstrate that both sides of an equation need to be written on each line when solving an equation. An emphasis should be placed on the fact that two equations are not equal to one another but they can be equivalent to one another.

The distinction between an equal sign and an approximately equal sign should be noted and students should be taught when it is appropriate to use one sign or the other.

The manner in which one presents the steps to a problem is very important. We want all of our students to recognize this fact; thus the instructor needs to emphasize the importance of writing mathematics properly and students need to be held accountable to the standard. When presenting their work, all students in a MTH 70 course should consistently show appropriate steps using correct mathematical notation and appropriate forms of organization. All axes on graphs should include scales and labels. A portion of the grade for any free response problem should be based on mathematical syntax.

Instructors should remind students that the topics discussed in MTH 70 will be revisited in "MTH 95 and beyond." but at a much faster pace while being integrated with new topics.

Unit Conversions Reference Sheet: The following reference sheet may be provided to students during all exams and all other assessments. Items may be removed at an instructor’s discretion; however, nothing may be added.

https://spot.pcc.edu/math/download/MTH-65-70-reference.pdf