Prerequisite: Math Topics 3/4

Students will learn and apply algebraic concepts to solve real-world problems. Students will be helped to visualize, represent, model and solve problems that involve applications with business and science as well as make connections within the field of mathematics. The focus of the course will include topics such as absolute value, rate of change, linear functions and systems of equations and inequalities.

1. Foundations of Advanced Algebra

a. Words into Symbols - write expressions from a given situation

b. Simplify & evaluate expressions

i. Laws of exponents

ii. Rational and negative exponents

c. Solving Equations

d. Solving Inequalities

e. Absolute Value

i. Equations

ii. Inequalities

2. Functions

a. Definition

b. Vocabulary terms (input, output, independent, dependent)

c. Multiple Representations (symbolic, tabular, numeric and graphic)

d. Behavior (increasing, decreasing, constant - be able to name intervals on which each occurs)

e. Domain and Range (only in context of the representations listed in b - domain and range of functions that students are currently learning)

3. Rate of Change

a. What is a rate? - May need to go back to basics

b. Calculate rate of change from tables and graphs

c. Continue to reinforce behavior of graphs, have students use terminology when describing graphs

d. Make a connection between constant rate of change and linear graphs

e. Create graphs modeling a given situation and describe in words the information given in a graph

4. Linear Functions

a. Terminology: slope, intercepts

b. Domain and Range

c. Write equations of lines from given situations (graphs, tables, ordered pairs or words)

i. Slope-Intercept Form

ii. Point-Slope Form

iii. Standard Form

d. Motivate the need for different forms of lines through application problems

e. Piece-wise Defined Functions

i. Graph given equations

ii. Write equation given graph or word problem

iii. Identify Domain (points of discontinuity) and Range

iv. Absolute Value

f. Inequalities

i. Graphs

ii. Write inequality given word problem or graph

iii. Identify Domain and Range

iv. Absolute Value

5. Systems

a. Terminology

b. Types of Systems

c. Methods of Solving Systems

i. Graphically

ii. Substitution

iii. Elimination

iv. Matrices

d. Extend to 3 equations and 3 variables

e. Systems of Inequalities

### Requested competency code:

- Math

### Approved competency code:

- MTH3

What are the course prereqs?