MTH 122AW - College Algebra - Extended Hours

Credits: 4
Instructional Contact Hours: 6

Reviews the mechanics of basic Algebra and solidifies understanding by using algebraic techniques, constructing mathematical models, solving problems and interpreting results. Includes: algebraic expressions; equations and inequalities; functions, inverse functions, and graphs; polynomial and rational functions; radical functions; exponential and logarithmic functions; matrices and determinants; systems of equations and inequalities; complex numbers; sequences and series. Credit may be earned in MTH 122W or MTH 122 AW, but not both. GRAPHING TECHNOLOGY IS REQUIRED.

This course is designed for students who need practice in foundational skills while engaging in college-level study of mathematics and problem-solving skills. Class sessions and assignments will reinforce prerequisite skills and topics through embedded support and just-in-time remediation.

Prerequisite(s): MTH 095 with a C or better OR HS GPA ≥ 2.5 OR SAT-M ≥ 530 OR ACCUPLACER (QRAS) ≥ 255 OR ACCUPLACER (AAF) ≥ 243 OR HS Math Course = Precalculus with a B or better taken within 5 years OR AP Calculus (AB) Score: 1-5 OR AP Calculus (BC) Score: 1-5 or Completion of Math GSP Process

Corequisite(s): None
Lecture Hours: 90 Lab Hours: 0
Meets MTA Requirement: Math
Pass/NoCredit: Yes

Outcomes and Objectives

1: Demonstrate understanding of notation describing sets of real numbers.

A. Understand set and interval notation.
B. Apply the operations of intersection and union.
C. Understand the composition of the real number system
D. Use interval notation to describe sets of numbers
E. Use inequality notation to describe sets of numbers
F. Convert between inequality and interval notation

2: Perform operations on polynomial functions.

A. Apply properties of positive integral exponents.
B. Perform addition, subtraction, multiplication and division of polynomial functions.
C. Perform synthetic division.
D. Factor polynomials.
E. Reduce rational expression to simplest form.
F. Add, subtract, multiply and divide rational expressions (including complex fractions).
G. Simplify numerical expressions using properties of exponents and the order of operations agreement.
H. Define polynomials
I. Determine the degree of a polynomials
J. Combine like terms
K. Multiply monomials
L. Use the associative, commutative and distributive properties to simplify numerical expressions.
M. Divide real numbers using long division

3: Perform operations on radical functions.

A. Apply the properties of rational exponents.
B. Add, subtract, multiply and divide radicals, expressing solutions in simplest form.
C. Convert between radical notation and rational exponents.
D. Simplify numerical expressions involving radicals.
E. Simplify numerical expressions involving rational exponents.

4: Solve problems relating to linear functions.

A. Graph ordered pairs of any relation and identify whether or not it is a function.
B. Graph any linear function.
C. Find the distance between any two points in the plane.
D. Find the slope of a line.
E. Find the equation of a line, given information.
F. Solve and graph a linear inequality.
G. Define absolute value of a number.
H. Calculate absolute values.
I. Solve absolute value equations and inequalities.
J. Graph inequalities on the number line.

5: Graph polynomial functions

A. Identify zeroes of linear functions.
B. Determine intercepts of linear functions.
C. Determine intercepts, axis of symmetry and maximum or minimum of a quadratic.
D. Graph any quadratic function.
E. Use synthetic division to identify zeros and graph any polynomial function.

6: Solve nonlinear equations or inequalities involving a function of one variable.

A. Find prime factorization of positive integers
B. Simplify numerical expressions in the form of the quadratic formula
C. Solve quadratic equations by factoring, the quadratic formula, and graphing.
D. Solve equations involving radicals.
E. Solve polynomial equations symbolically (using synthetic division).
F. Solve polynomial equations of degree greater than 2 using tables and graphs.
G. Solve quadratic inequalities.
H. Set up and solve application problems.

7: Demonstrate understanding related to logarithmic or exponential functions.

A. Convert exponential equations to log form.
B. Convert log equations to exponential form.
C. Evaluate logarithms.
D. Approximate log and exponential expressions using a calculator.
E. Recognize an exponential or logarithmic function and its graph.
F. Solve exponential or logarithmic equations.

8: Solve systems of equations.

A. Graphs systems of inequalities.
B. Determine intersection point of two lines algebraically.
C. Determine intersection point of two lines graphically.
D. Solve systems of 2 and 3 linear equations.
E. Solve linear programming problems.
F. Solve systems of inequalities graphically.
G. Set up and solve application problems.

9: Demonstrate understanding of matrices.

A. Define matrices
B. Write the augmented matrix for a system of linear equations.
C. Write the matrix equation for a system of linear equations.
D. Apply basic operations to matrices. (Add, Subtract, Multiply, Inverse)
E. Evaluate determinants.
F. Solve systems of equations by matrix methods.

10: Demonstrate understanding of complex numbers.

A. Simplify square roots of negative numbers.
B. Combine like terms.
C. Define numbers in the form a + bi.
D. Add, subtract, multiply, and divide complex numbers.
E. Solve quadratic equations with complex solutions.

11: Demonstrate understanding of sequences or series.

A. Define sequences.
B. Define series.
C. Evaluate factorials.
D. Find the terms of an arithmetic and geometric sequence.
E. Find the sum of an arithmetic and geometric series.
F. Apply the Binomial Theorem.

12: Communicate effectively about mathematics in writing.

A. Provide complete written solutions to problems using appropriate terminology.
B. Articulate important ideas and conclusions in writing.

13: Demonstrate problem-solving skills.

A. Solve real world problems involving linear equations, quadratic equations, exponential equations, logarithmic equations, rational equations, and systems of equations.
B. Use mathematical modeling to solve real world problems.
C. Clarify and analyze the meanings of words, phrases and statements.
D. Learn the meanings of relevant symbols used in the discipline and ways to use them.
E. Transfer problem solving strategies for use in new contexts.
F. Organize and present information or data in tables, charts, and graphs.
G. Use symbol systems to raise questions about models and proposed answers to problems.
H. Identify, state and clarify arguments or reasoning, including those codified by systems of symbols.
I. Generate and assess solutions to problems.

14: Use graphing technology to analyze solutions to problems.

A. Enter expressions on a graphing device.
B. Create graphs using graphing technology.
C. Create tables using graphing technology.
D. Graph linear, quadratic, radical, polynomial, exponential, or logarithmic functions.
E. Create a table of input/out pairs for any given function.
F. Determine an appropriate window to obtain a complete graph of a linear, quadratic, square root, exponential, or logarithmic function.
G. Find the intersection of any two functions.
H. Evaluate any numerical expression involving linear, quadratic, rational, square root, exponential, or logarithmic functions.