# Freshman Math Program - TRS 92 - Intermediate Algebra

## TRS 92 Learning Objectives

Note: All objectives allow for the use of a calculator unless otherwise noted.

**92-1 Equations**

Given a linear equation with one variable, students will be able to solve by…

- Clearing fractions
- Using the distributive property
- Using the addition and multiplication properties

Given a literal equation, students will be able to…

- Solve for the given variable

Given the conversion factors, students will be able to…

- Set up a unit analysis problem to make a conversion with multiple steps

**92-2 Inequalities**

Given an inequality (with one variable) students will be able to…

- Solve algebraically
- Graph the solution
- Describe the solution using inequality notation

Given an inequality (with two variables) students will be able to…

- Solve the solution graphically

**92-3 Functions**

Given a function in any of the four forms (algebraic, table, graph, in context), students will be able to…

- Identify a function as a relationship of the dependent variable being dependent upon the independent variable
- Demonstrate the proper use of function notation
- Identify dependent and independent variables in context
- Evaluate functions
- Identify domain and range based on a graph

**92-4 Linear Functions**

__General__

Given the equation for a linear function, students will be able to …

- Create a table
- Change equation from standard to slope-intercept form
- Write an equation using parallel relationships

__Intercepts__

Students will be able to …

- Solve for vertical and horizontal intercepts from an equation in standard form
- Identify vertical intercept from slope-intercept form
- Interpret intercepts in context

__Slope__

Students will be able identify the slope of a linear function given …

- Two points
- A graph

Given a graph, equation, or context, students will be able to …

- Identify type of slope (negative, positive, zero, undefined)

Given a context, students will be able to …

- Interpret the meaning of the slope

__Equations__

Students will be able to write equations for linear functions given …

- Slope and one point (other than vertical intercept)
- Table of values
- Context with ARC and initial value

Students will be able to …

- Identify and write equations for horizontal and vertical lines

Given an equation, students will be able to …

- Solve for independent and dependent values
- Interpret the solution to an equation in context

**92-5 Graphing**

Students will be able to graph a linear function by hand given …

- An equation
- A table
- A point and a slope
- Two points

Using the graphing calculator with a standard window or with a given a window, students will be able to…

- Graph linear functions
- Graph exponential functions
- Identify the solution to a system of equations using technology

**92-6 Systems of Equations**

Given a system of equations, students will be able to…

- Identify the number of solutions (e.g., one, infinitely many, none)
- In the case of one solution to a system of linear equations, solve for the solution to that system using the elimination or substitution method
- Identify the solution graphically
- Interpret the solution if the system is given in context

**92-7 Exponential Functions**

Given an exponential function, students will be able to…

- Identify the growth or decay factor
- Determine the growth or decay rate
- Write an equation from a vertical intercept and a rate, both with and without context

**92-8 Expressions**

Given algebraic expressions, students will be able to…

- Use the Laws of Exponents to simplify expressions containing exponents (positive, negative
*, zero,*and rational) - Change simple rational exponent expressions to radical form
- Simplify numeric radicals with a calculator
- Add, subtract, and multiply polynomial expressions
- Factor polynomialsd( GCF, trinomials with leading coefficient of 1)
- Perform multiplication and division with scientific notation using the Laws of Exponents

**92-9 General Mathematical Skills**

- Estimate and determine if an answer is reasonable and justify reasoning
- Explain mathematical concepts and procedures using appropriate mathematical terminology in writing
- Use the TI–83 calculator to perform calculations and to graph equations using a standard window or a given window
- Organize and update a math portfolio as directed in the portfolio guide