MATH 1061 - College Algebra I

Credits: 4
Hours/Week: Lecture None Lab None
Course Description: This is a college-level algebra course. Topics include linear, quadratic, polynomial, rational, radical, exponential, logarithmic, and absolute value functions, graphs and equations. Course content will also cover linear, quadratic, polynomial, rational, and absolute value inequalities; systems of linear equations and inequalities, including basic matrix methods; data analysis, regression, and modeling.  A graphing calculator is required.  Instruction will be provided in the use of the TI-83/TI-84 calculator.  Note: MATH 1061 College Algebra I is the prerequisite for MATH 1070 - Survey of Calculus .  MATH 1061 College Algebra I is also one of the prerequisites for MATH 1062 - College Algebra II with Trigonometry  with Trigonometry which is the prerequisite for MATH 1081 - Single Variable Calculus I .  MnTC Goal 4
MnTC Goals
4 Mathematics/Logical Reasoning

Prerequisite(s): Placement into MATH 1061, or completion of MATH 0070  with a grade of C or higher. 
Corequisite(s): None
Recommendation: Eligible for college-level Reading and English.

Major Content

1. Preliminary Concepts
   1. The Cartesian plane
   2. Graphs and graphing calculators
   3. Lines in the plane
   4. Solving equations (linear, quadratic, absolute value, radical, simple rational)
   5. Solving inequalities (linear, quadratic, absolute value)
   6. Graphs of linear, absolute value, radical, and simple rational equations
   7. Linear, quadratic, and radical models
2. Functions and Their Graphs
   1. Functions
   2. Graphs of functions
   3. Transformations of functions
   4. Combinations and Composition of functions
   5. Inverse functions
3. Polynomial Functions
   1. Quadratic functions
   2. Higher degree polynomial functions
   3. Graphs of polynomial functions
   4. Real zeros of polynomial functions
   5. Polynomial equations
   6. Polynomial inequalities
   7. Complex numbers
   8. Fundamental Theorem of Algebra
   9. Polynomial models
4. Rational Functions
   1. Rational functions
   2. Graphs of rational functions
   3. Rational equations
   4. Rational inequalities
   5. Rational models
5. Data Analysis, Regression, and Modeling
   1. Linear regression
   2. Quadratic regression
   3. Cubic regression
   4. Quartic regression
   5. Power regression
   6. Exponential regression
   7. Logarithmic regression 
6. Exponential and Logarithmic Functions
   1. Exponential functions
   2. Logarithmic functions
   3. Properties of logarithms
   4. Graphs of exponential and logarithmic functions
   5. Exponential and logarithmic equations
   6. Exponential and logarithmic models
7. Systems of Equations and Inequalities
   1. 2 X 2 systems of linear equations
   2. Multivariable systems of linear equations
   3. 2 X 2 systems of linear inequalities
   4. Non-linear systems of equations
   5. Non-linear systems of inequalities

1. demonstrate critical and logical reasoning when solving problems.
2. determine the inverse of a function, if it exists.
3. determine real and complex zeros of polynomial functions.
4. apply the Fundamental Theorem of Algebra to factor polynomials.
5. analyze data to determine the type of relationship that exists between two variables using technology.
6. determine the best fit linear, quadratic, cubic, quartic, power, exponential, and logarithmic function using technology.
7. model and solve applied problems using linear, quadratic, polynomial, absolute value, radical, rational, exponential, logarithmic, and logistic functions.
8. communicate clearly a problem’s solution and its explanation for the intended audience in terms of the problem posed.
9. solve linear, quadratic, polynomial, absolute value, radical, rational, exponential, and logarithmic equations symbolically, numerically, and graphically.
10. solve linear, quadratic, polynomial, rational, and absolute value inequalities symbolically, numerically, and graphically.
11. solve systems of linear equations in two variables and in many variables symbolically and by performing basic matrix methods by hand and with technology.
12. solve systems of linear equations and inequalities in two variables graphically.
13. perform basic matrix operations such as addition, subtraction, multiplication, and inversion by hand and with technology.
14. graph linear, quadratic, polynomial, absolute value, radical, rational, exponential, and logarithmic functions by hand and using technology.
15. graph transformations of functions by hand.
16. determine properties of a function from its graph, such as intercepts, extrema, increasing, and decreasing.
17. determine the domain and range of a function symbolically and graphically.
18. determine the sum, difference, product, quotient, and composition of functions.

04. 02. Clearly express mathematical/logical ideas in writing.

04. 04. Apply higher-order problem-solving and/or modeling strategies.

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