# MATH 1324

# Mathematics for Business & Social Science I (formerly, Finite Mathematics)

### Math 1324

**State Approval Code:**2703015219**Semester Credit Hours:**3**Lecture Hours per Week:**3**Contact Hours per Semester:**48

### Catalog Description

Mathematical functions and graphs, linear systems of equations, matrices, linear programming, mathematics of finance; applications. 2703015219 (3-3-0) (fall)

### Prerequisites

TISP math completed and two years of high school algebra and one year of geometry or MATH 1314: College Algebra

### 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

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

Upon completion of **MATH 1324**, the student will be able to demonstrate:

1. Competence in solving *m x n *linear systems and in solving problems leading to an *m x n *system.

2. Competence in solving a linear programming problem given an objective function and a system of constraints.

3. Competence in formulating the objective function and a system of constraints necessary to solve a stated problem.

4. Competence in graphing functions which are not linear, in the algebra and composition of functions, and their application to problem solving.

5. Competence in solving problems involving compound interest, compound discount, ordinary simple annuities, and debt extinction by amortization and sinking funds.

6. Competence in solving problems involving permutations, combinations, and probability.

### 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%.

Sets, Linear Equations, and Functions

1. Give an example of and/or use in an applied situation the following symbols and terms a. set builder (set specification) notation b. null or empty set c. element d. universal set e. subset f. proper subset g. equality of sets h. total number of possible subsets (and proper and nonempty) of a given set

2. Define the following terms: a. relation b. domain c. range d. function

3. Apply (identify) the above terms in applied problems.

4. Sketch the graph of a relation and determine by using the function vertical line test if it is the graph of a function.

5. Determine the domain and range of a relation that is specified via a graph.

6. Determine the slope of a line given two ordered pairs.

7. Determine the slope of any given horizontal line.

8. Identify the slope of any given vertical line as **undefined**.

9. Given two sets of ordered pairs, determine if the indicated line segments are parallel, perpendicular, or neither.

10. Graph an equation of the form y = c or x = c, where c is a constant.

11. Graph an equation of the form y = mx + b. **CRS: III-C-1**

12. Write the equation of a line when given a point and the slope. **CRS: III-C-1**

13. Write the equation of a line when given a point and the equation of a line parallel
or perpendicular to the desired line. **CRS: III-C-1**

14. Write the equation of a line when given two points on that line. **CRS: III-C-1**

15. Write the equation of a line when given the x- and y-intercepts of that line. **CRS: III-C-1**

16. Write a linear cost function when given the variable cost and the fixed costs.

17. Write a cost function when given that (i) the function is linear and (ii) ordered pairs (q,p)

18. Solve a system of equations using the addition/elimination method. **CRS: III-C-1**

19. Translate word problems into systems of equations and solve. **CRS: III-C-1**

20. Find the break even point when given a linear cost function and a linear revenue
function. **CRS: III-C-1**

21. Find the market equilibrium point given the supply equation and the demand equation. ** **

**Matrices **Upon completion of this section, the student will be able to correctly

1. Determine the dimensions of a given matrix.

2. Write a zero matrix, given the dimensions.

3. Determine the conformability of two matrices for addition.

4. Add or subtract two (or more) conformable matrices.

5. Determine the conformability of two matrices to regular matrix multiplication.

6. Multiply two conformable matrices.

7. Find the dot product of two vector matrices.

8. Show, by example, that matrix multiplication is not commutative.

9. Solve a system of linear equations using the Gauss-Jordan Elimination Method. **CRS: III-C-1 **10. Solve a system of linear equations that is dependent.

11. Identify a system of linear equations as having "no solution."

12. Give a geometric interpretation to the solution(s) of a system of linear equations.

13. Find the inverse of a given nonsingular matrix and use it to solve a system of
linear equations. **CRS: III-C-1**

** Inequalities and Linear Programming **Upon completion of this section, the student will be able to correctly

1. Graph systems of linear inequalities.

2. Determine the values of x and y that maximize or minimize some linear function f(x,y) subject to a set of constraints.

3. Solve applied linear programming problems.

**Mathematics of Finance **Upon completion of this section, the student will be able to correctly

1. Compute simple interest.

2. Write a specified number of terms of a sequence.

3. Find certain specified terms of an arithmetic sequence.

4. Find sums of a specified number of terms of a given arithmetic sequence.

5. Compute the compound (future) amount and compound interest of money invested where interest is compounded at regular intervals.

6. Compute the compound (future) amount and interest on money where interest is compounded continuously.

7. Compute the effective annual interest rate of money invested at compound interest.

8. Find certain specified terms of a geometric series.

9. Find the sum of a specified number of terms of a given geometric sequence.

10. Compute the amount (future value) of an ordinary annuity.

11. Compute the present value of an ordinary annuity.

12. Compute the regular payments required to amortize a debt.

13. Compute the amount that must be invested periodically in a sinking fund to discharge a debt or other financial obligation at some specified time in the future.

**Introduction to Probability (As Time Permits) **Upon completion of this chapter, the student will be able to correctly

1. Apply the multiplication rule to find the number of ways an event can happen.

2. Determine the number of permutations of **n **things taken **r **at a time (both with and without repetition), **nPr**. **CRS: V-A-1**

3. Determine the number of permutations of n given objects when p of the n objects
are alike and of one kind, q of the objects are alike of a second kind, ..., up to
t others alike of still another kind. **CRS: V-A-1**

4. Determine the number of circular permutations of n distinct objects. **CRS: V-A-1**

5. Determine the number of combinations of n distinct objects taken r at a time, **nCr**. **CRS: V-A-1 **6. *Optional: *Use combinations to expand a binomial by the binomial theorem.

**7. Optional: Find a specified term of a given binomial raised to a given power without expansion.**

9. Given an experiment, describe a suitable sample space.

10. Define & compute the probability of an event, **E**, occurring. **CRS: V-B-1**

11. Define mutually exclusive events. **CRS: V-B-1**

12. Define the probability of the complement of the event **E. CRS: V-B-1**

13. Define random selection and use it in finding the probability of an event, **E**, occurring.**CRS: V-B-1**

14. Determine the hypergeometric probability of an event occurring. **CRS: V-B-1**

15. Define conditional probability and find **P(B|A CRS: V-B-2**

16. Find **P(A and B) **when **P(A) **and **P(B|A) **are available. **CRS: V-B-2**

17. Find **P(A or B). CRS: V-B-2 **18. Define independent events and apply this concept to finding probabilities in applied
problems.

### 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

Four (4) **Major Exams **at 15% 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, use the following link to access bookstore listings.