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- MATH 1314

### MATH 1314

# College Algebra

### Math 1314

**State Approval Code:**2701015419**Semester Credit Hours:**3**Lecture Hours per Week:**3**Contact Hours per Semester:**48

### Catalog Description

Real and complex numbers, relations and functions and their inverse; inequalities,
systems of equations, matrices, conic sections, exponential and logarithmic functions,
theory of equations, mathematical induction, sequences and series, binomial theorem,
probability, permutations, and combinations. (2701015419) (3-3-0) (fall, spring)

### Prerequisites

Two years of high school algebra and one year of geometry or MATH 0303.

### Course Curriculum

### Basic Intellectual Compentencies in the Core Curriculum

- Reading
- Writing
- Speaking
- Listening
- Critical thinking
- Computer literacy

### Perspectives in the Core Curriculum

- Establish broad and multiple perspectives on the individual in relationship to the larger society and world in which he/she lives, and to understand the responsibilities of living in a culturally and ethnically diversified world.
- Stimulate a capacity to discuss and reflect upon individual, political, economic, and social aspects of life in order to understand ways in which to be a responsible member of society.
- Recognize the importance of maintaining health and wellness.
- Develop a capacity to use knowledge of how technology and science affect their lives.
- Develop personal values for ethical behavior.
- Develop the ability to make aesthetic judgments.
- Use logical reasoning in problem solving.
- Integrate knowledge and understand the interrelationships of the scholarly disciplines.

### Core Components and Related Exemplary Educational Objectives

### Mathematics

- To apply arithmetic, algebraic, geometric, higher-order thinking, and statistical methods to modeling and solving real-world situations.
- To represent and evaluate basic mathematical information verbally, numerically, graphically, and symbolically.
- To expand mathematical reasoning skills and formal logic to develop convincing mathematical arguments.
- To use appropriate technology to enhance mathematical thinking and understanding and to solve mathematical problems and judge the reasonableness of the results.
- To interpret mathematical models such as formulas, graphs, tables and schematics, and draw inferences from them.
- To recognize the limitations of mathematical and statistical models.
- To develop the view that mathematics is an evolving discipline, interrelated with human culture, and understand its connections to other disciplines.

### Instructional Goals and Purposes

Panola College's instructional goals include 1) creating an academic atmosphere in which students may develop their intellects and skills and 2) providing courses so students may receive a certificate/an associate degree or transfer to a senior institution that offers baccalaureate degrees.

### General Course Objectives

Successful completion of this course will promote the general student learning outcomes
listed below. The student will be able

1. To apply problem-solving skills through solving application problems.

2. To demonstrate arithmetic and algebraic manipulation skills.

3. To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.

4. To construct appropriate mathematical models to solve applications.

5. To interpret and apply mathematical concepts.

6. To use multiple approaches - physical, symbolic, graphical, and verbal - to solve application problems

1. To apply problem-solving skills through solving application problems.

2. To demonstrate arithmetic and algebraic manipulation skills.

3. To read and understand scientific and mathematical literature by utilizing proper vocabulary and methodology.

4. To construct appropriate mathematical models to solve applications.

5. To interpret and apply mathematical concepts.

6. To use multiple approaches - physical, symbolic, graphical, and verbal - to solve application problems

### Specific Course Objectives

Major Learning Objectives Essential Competencies Upon completion of MATH 1314, the
student will be able to demonstrate:

1. Competence in application of the theorems and identities of exponents and radicals.

2. Competence in factoring using all patterns.

3. Competence in operations using complex numbers.

4. Competence in solving equations and systems of equations and systems of equations including quadratic forms and the use of matrices.

5. Competence in solution of stated problems.

6. Competence in the algebra of functions, composition of functions, and computation of inverses of one- to-one functions.

7. Competence in solving linear (affine), quadratic, and rational equations and inequalities, including those stated in terms of absolute value.

8. Competence in decomposing fractions into a sum of partial fractions.

9. Competence in applications of arithmetic and geometric series and sequences, permutations, and combinations.

1. Competence in application of the theorems and identities of exponents and radicals.

2. Competence in factoring using all patterns.

3. Competence in operations using complex numbers.

4. Competence in solving equations and systems of equations and systems of equations including quadratic forms and the use of matrices.

5. Competence in solution of stated problems.

6. Competence in the algebra of functions, composition of functions, and computation of inverses of one- to-one functions.

7. Competence in solving linear (affine), quadratic, and rational equations and inequalities, including those stated in terms of absolute value.

8. Competence in decomposing fractions into a sum of partial fractions.

9. Competence in applications of arithmetic and geometric series and sequences, permutations, and combinations.

### General Description of Each Lecture or Discussion

After studying the material presented in the text(s), lecture, laboratory, computer
tutorials, and other resources, the student should be able to complete all behavioral/learning
objectives listed below with a minimum competency of 70%. Review of Fundamental Concepts
Upon completion of this section, the student will be able to correctly

1. Perform the operations of addition, subtraction, multiplication, and division on polynomials. CRS: I-B-1

2. Factor the following types of polynomials: a. Difference of two squares b. Trinomials c. Sum of two cubes d. Difference of two cubes

3. Reduce algebraic fractions.

4. Add and subtract rational (fractional) expressions.

5. Multiply and divide rational expressions.

6. Use the properties of exponents to simplify a numeric or algebraic expression containing rational exponents. CRS: I-B-1

7. Simplify an arithmetic or algebraic expression containing rational exponents.

8. Translate an expression containing rational exponents into a radical expression.

9. Translate an expression containing radicals into an expression containing rational exponents.

10. Simplify radical expressions; i.e., write in standard form. CRS: II-A-1

11. Combine radical expressions.

12. Multiply two radical expressions.

13. Rationalize a binomial denominator.

14. Find the sum, difference, product, and quotient of two complex numbers. CRS: I-B-1 Algebraic Equations and Inequalities Upon completion of this chapter, the student will be able to correctly

1. Find the solution set for a first degree equation. CRS: II-C-1

2. Solve a first-degree inequality in one variable. CRS: II-C-1

3. Solve a first-degree equation involving absolute value. CRS: II-C-1

4. Solve a first-degree inequality involving absolute value. CRS: II-C-1

5. Solve quadratic equations using the following methods: CRS: II-C-1 a. Square-root method b. Factoring c. Completing the Square d. Quadratic Formula

6. Solve equations involving radicals. CRS: II-C-1

7. Write an equation in quadratic form and solve. CRS: II-C-1

8. Solve inequalities involving quadratic and rational expressions. CRS: II-C-1 Functions and Graphs Upon completion of this section, the student will be able to correctly

1. Graph an ordered pair.

2. Name the coordinates of a given point.

3. Graph a first-degree equation.

4. Find the distance between two points in the plane.

5. Find the midpoint of a line segment joining two points.

6. Determine the slope of a line passing through two given points. CRS: III-C-1

7. Determine if two given, nonvertical lines are parallel, perpendicular, or neither. CRS: III-C-1

8. Given the standard form, write the equation of a line in slope-intercept form. CRS: III-C-1

9. Write the equation of a line given a point on the line and the slope of the line. CRS: III-C-1

10. Write the equation of a line passing through two given points. CRS: III-C-1 1

1. Write the equation of a line passing through a given point and parallel to the graph of a given equation. CRS: III-C-!

12. Write the equation of a line passing through a given point and perpendicular to the graph of a given equation. CRS: III-C-1

13. Find an equation of a circle, given the center and the radius. CRS: III-C-1

14. Find the center and radius of a circle, given the equation of the circle. CRS: III-C-1

15. Find an equation of a circle, given the center and a point on the circle. CRS: III-C-1

16. Find an equation of a circle, given the end points of its diameter. CRS: III-C-1

17. Find an equation of the circle, given the center and that it is tangent to one of the coordinate axes or through a given point. CRS: III-C-1

18. Determine whether a given equation represents a circle, a point, or no graph. CRS: III-C-1

19. Sketch the graph of inequalities in the xy-plane. CRS: II-C-1

20. Determine whether a given relation is a function.

21. Determine from a graph if a relation is a function.

22. Given an equation, determine whether the relation is a function. 23. State the domain and range of a given relation.

24. Evaluate a function for specific value of the independent variable.

25. Evaluate a piecewise function for a specific value.

26. Use a Newton (i.e., difference) Quotient to measure the slope of a secant line determined by two points on a curve.

27. State the domain of a function that is specified by an equation. 28. Perform the following operations on functions: a. Addition b. Subtraction c. Multiplication d. Division e. Composition f. Inversion

Polynomial Functions: Graphs and Zeroes Upon completion of this section, the student will be able to correctly

1. Graph a quadratic function by determining a. the vertex b. if the parabola open upward or downward c. the y-intercept d. the x-intercepts (or zeros), if any

2. Graph a function containing absolute value expressions.

3. Graph a piecewise defined function.

4. Use synthetic division and the remainder theorem to find the required functional value of a polynomial function.

5. Use the factor theorem to determine whether a given first degree binomial is a factor of a given polynomial; and, if so, write the polynomial in factored form.

6. Find all the roots of an equation given in factored form and state the multiplicity of each root and the degree of the equation.

7. Use the quadratic formula and the factor theorem to write a polynomial as a product of binomial and/or trinomial factors.

8. Find a polynomial equation of least degree having given roots. Multiply the factors and simplify the equation.

9. Determine if a given number is a root of a given polynomial equation.

10. Graph a polynomial function over a specified interval. Exponential and Logarithmic Functions Upon on completion of this section, the student will be able to correctly

1. Find the inverse of a relation specified by a set of ordered pairs. 2. Determine if a given function is one- to-one.

3. Determine if the inverse of a relation is a function.

4. Find the inverse of a relation or function specified by an equation. 5. Sketch the graphs of exponential functions.

6. Write an exponential equation in logarithmic form.

7. Write a logarithmic equation in exponential form.

8. Evaluate a logarithmic expression.

9. Solve a logarithmic equation with one term in logarithmic form. 10. Use the properties of logarithms to write expressions as sums or differences of simpler logarithmic terms.

11. Write an expression as a single logarithmic term with coefficient of 1.

12. Evaluate logarithmic terms based on given information.

13. Find the approximate values of given common logarithms, using tables and/or calculators.

14. Solve a logarithmic equation involving common logarithms.

15. Use linear interpolation to find common logarithms for numbers that have more than two significant digits.

16. Use the conversion formula to evaluate logarithm of a number to a base other than 10.

17. Solve an exponential equation by methods such as a. equating bases b. logarithmic techniques.

18. Solve a logarithmic equation with more than one term in logarithmic form. Systems of Equations and Inequalities Upon completion of this section, the student will be able to correctly

1. Solve systems of linear equation in two variables using a. graphical methods; or b. algebraic methods such as i. addition/elimination ii. substitution

2. Solve systems of linear equations in three variables by using a triangular reduction method.

3. Solve systems of second degree equations in two variables.

4. Draw the graph of the solution set for a system of linear inequalities. Matrices and Determinants Upon completion of this section, the student will be able to correctly

1. State the dimensions of a given matrix.

2. Add and subtract matrices.

3. Solve matrix equations.

4. Find the product, if it is defined, of two given matrices.

5. Find the product of a scalar and a matrix.

6. Evaluate a determinant.

7. Solve an equation involving determinants.

8. Solve a system of equations using determinants and Cramer's Rule.

9. Solve systems of linear equation using augmented matrix techniques (i.e., Gauss-Jordan Elimination). This will require that the student also will be able to correctly a. Write the augmented matrix for a given system. b. Write the system of equations corresponding to a given augmented matrix. c. Solve systems of equations by using the three elementary row operations.

1. Perform the operations of addition, subtraction, multiplication, and division on polynomials. CRS: I-B-1

2. Factor the following types of polynomials: a. Difference of two squares b. Trinomials c. Sum of two cubes d. Difference of two cubes

3. Reduce algebraic fractions.

4. Add and subtract rational (fractional) expressions.

5. Multiply and divide rational expressions.

6. Use the properties of exponents to simplify a numeric or algebraic expression containing rational exponents. CRS: I-B-1

7. Simplify an arithmetic or algebraic expression containing rational exponents.

8. Translate an expression containing rational exponents into a radical expression.

9. Translate an expression containing radicals into an expression containing rational exponents.

10. Simplify radical expressions; i.e., write in standard form. CRS: II-A-1

11. Combine radical expressions.

12. Multiply two radical expressions.

13. Rationalize a binomial denominator.

14. Find the sum, difference, product, and quotient of two complex numbers. CRS: I-B-1 Algebraic Equations and Inequalities Upon completion of this chapter, the student will be able to correctly

1. Find the solution set for a first degree equation. CRS: II-C-1

2. Solve a first-degree inequality in one variable. CRS: II-C-1

3. Solve a first-degree equation involving absolute value. CRS: II-C-1

4. Solve a first-degree inequality involving absolute value. CRS: II-C-1

5. Solve quadratic equations using the following methods: CRS: II-C-1 a. Square-root method b. Factoring c. Completing the Square d. Quadratic Formula

6. Solve equations involving radicals. CRS: II-C-1

7. Write an equation in quadratic form and solve. CRS: II-C-1

8. Solve inequalities involving quadratic and rational expressions. CRS: II-C-1 Functions and Graphs Upon completion of this section, the student will be able to correctly

1. Graph an ordered pair.

2. Name the coordinates of a given point.

3. Graph a first-degree equation.

4. Find the distance between two points in the plane.

5. Find the midpoint of a line segment joining two points.

6. Determine the slope of a line passing through two given points. CRS: III-C-1

7. Determine if two given, nonvertical lines are parallel, perpendicular, or neither. CRS: III-C-1

8. Given the standard form, write the equation of a line in slope-intercept form. CRS: III-C-1

9. Write the equation of a line given a point on the line and the slope of the line. CRS: III-C-1

10. Write the equation of a line passing through two given points. CRS: III-C-1 1

1. Write the equation of a line passing through a given point and parallel to the graph of a given equation. CRS: III-C-!

12. Write the equation of a line passing through a given point and perpendicular to the graph of a given equation. CRS: III-C-1

13. Find an equation of a circle, given the center and the radius. CRS: III-C-1

14. Find the center and radius of a circle, given the equation of the circle. CRS: III-C-1

15. Find an equation of a circle, given the center and a point on the circle. CRS: III-C-1

16. Find an equation of a circle, given the end points of its diameter. CRS: III-C-1

17. Find an equation of the circle, given the center and that it is tangent to one of the coordinate axes or through a given point. CRS: III-C-1

18. Determine whether a given equation represents a circle, a point, or no graph. CRS: III-C-1

19. Sketch the graph of inequalities in the xy-plane. CRS: II-C-1

20. Determine whether a given relation is a function.

21. Determine from a graph if a relation is a function.

22. Given an equation, determine whether the relation is a function. 23. State the domain and range of a given relation.

24. Evaluate a function for specific value of the independent variable.

25. Evaluate a piecewise function for a specific value.

26. Use a Newton (i.e., difference) Quotient to measure the slope of a secant line determined by two points on a curve.

27. State the domain of a function that is specified by an equation. 28. Perform the following operations on functions: a. Addition b. Subtraction c. Multiplication d. Division e. Composition f. Inversion

Polynomial Functions: Graphs and Zeroes Upon completion of this section, the student will be able to correctly

1. Graph a quadratic function by determining a. the vertex b. if the parabola open upward or downward c. the y-intercept d. the x-intercepts (or zeros), if any

2. Graph a function containing absolute value expressions.

3. Graph a piecewise defined function.

4. Use synthetic division and the remainder theorem to find the required functional value of a polynomial function.

5. Use the factor theorem to determine whether a given first degree binomial is a factor of a given polynomial; and, if so, write the polynomial in factored form.

6. Find all the roots of an equation given in factored form and state the multiplicity of each root and the degree of the equation.

7. Use the quadratic formula and the factor theorem to write a polynomial as a product of binomial and/or trinomial factors.

8. Find a polynomial equation of least degree having given roots. Multiply the factors and simplify the equation.

9. Determine if a given number is a root of a given polynomial equation.

10. Graph a polynomial function over a specified interval. Exponential and Logarithmic Functions Upon on completion of this section, the student will be able to correctly

1. Find the inverse of a relation specified by a set of ordered pairs. 2. Determine if a given function is one- to-one.

3. Determine if the inverse of a relation is a function.

4. Find the inverse of a relation or function specified by an equation. 5. Sketch the graphs of exponential functions.

6. Write an exponential equation in logarithmic form.

7. Write a logarithmic equation in exponential form.

8. Evaluate a logarithmic expression.

9. Solve a logarithmic equation with one term in logarithmic form. 10. Use the properties of logarithms to write expressions as sums or differences of simpler logarithmic terms.

11. Write an expression as a single logarithmic term with coefficient of 1.

12. Evaluate logarithmic terms based on given information.

13. Find the approximate values of given common logarithms, using tables and/or calculators.

14. Solve a logarithmic equation involving common logarithms.

15. Use linear interpolation to find common logarithms for numbers that have more than two significant digits.

16. Use the conversion formula to evaluate logarithm of a number to a base other than 10.

17. Solve an exponential equation by methods such as a. equating bases b. logarithmic techniques.

18. Solve a logarithmic equation with more than one term in logarithmic form. Systems of Equations and Inequalities Upon completion of this section, the student will be able to correctly

1. Solve systems of linear equation in two variables using a. graphical methods; or b. algebraic methods such as i. addition/elimination ii. substitution

2. Solve systems of linear equations in three variables by using a triangular reduction method.

3. Solve systems of second degree equations in two variables.

4. Draw the graph of the solution set for a system of linear inequalities. Matrices and Determinants Upon completion of this section, the student will be able to correctly

1. State the dimensions of a given matrix.

2. Add and subtract matrices.

3. Solve matrix equations.

4. Find the product, if it is defined, of two given matrices.

5. Find the product of a scalar and a matrix.

6. Evaluate a determinant.

7. Solve an equation involving determinants.

8. Solve a system of equations using determinants and Cramer's Rule.

9. Solve systems of linear equation using augmented matrix techniques (i.e., Gauss-Jordan Elimination). This will require that the student also will be able to correctly a. Write the augmented matrix for a given system. b. Write the system of equations corresponding to a given augmented matrix. c. Solve systems of equations by using the three elementary row operations.

### Methods of Instruction/Course Format/Delivery

Methods of Instruction/Course Format/Delivery: Methods employed will include Lecture/demonstration,
discussion, problem solving, analysis, and reading assignments. Homework will be assigned.
Faculty may choose from, but are not limited to, the following methods of instruction:
(1) Lecture (2) Discussion (3) Internet (4) Video (5) Television (6) Demonstrations
(7) Field trips (8) Collaboration (9) Readings

### Assessment

Faculty may assign both in- and out-of-class activities to evaluate students' knowledge
and abilities. Faculty may choose from – but are not limited to -- the following methods
Attendance Book reviews Class preparedness and participation Collaborative learning
projects Compositions Exams/tests/quizzes Homework Internet Journals Library assignments
Readings Research papers Scientific observations Student-teacher conferences Written
assignments

(3) Major Exams at 20% each 60% Homework Notebook/Folder 10% Note: There will be no
make-up exams. If you miss an exam your Final Exam percentage will be used as a substitute
for the missing grade. If you do not miss any exams, your one lowest Exam grade will
be replaced by the Final Exam percentage provided it (the Final Exam percentage) is
higher. Comprehensive Final Examination 30% Letter Grades for the Course will be assigned
as follows: A: 90 < Average < 100 B: 80 < Average < 90 C: 70 < Average < 80 D: 60
< Average < 70 F: 00 < Average < 60

### Text, Required Readings, Materials, and Supplies

For current texts and materials ,Larson College Algebra 8th ed ISBN 9781439048696