# Mathematics (MATH)

### Courses

**MATH 111 Fundamentals of Mathematics* (3 Hours)**

**Prerequisites:** AAC 112 with a grade of "C" or higher or appropriate score on the math placement test

Fundamentals of Mathematics is designed for the student who needs to improve or review basic math skills and concepts. This course includes computation using integers, fractions, decimals, proportions and percents along with an overview of measurement, geometry, statistics and linear equations. Fundamentals of Math provides the mathematical foundation upon which subsequent studies in mathematics and other areas depend. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details. This course does not fulfill degree requirements. This course is the first in a sequence of courses leading to MATH 116 or higher. 3 or 5 hrs. lecture / wk.

**MATH 115 Elementary Algebra* (3 Hours)**

**Prerequisites:** MATH 111 with a grade of "C" or higher or appropriate score on the math placement test

This is a beginning course in algebra, designed to help students acquire a solid foundation in the basic skills of algebra. Students will learn to simplify arithmetic and algebraic expressions, including exponential expressions, polynomials, rational expressions and radical expressions; solve equations and inequalities, including linear equations and quadratic equations; graph linear equations; and analyze linear equations. MATH 115 may fulfill some certificate requirements, but will not fulfill degree requirements. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details. This course is the first in a sequence of courses leading to MATH 116 or higher. 3 or 5 hrs. lecture/wk.

**MATH 116 Intermediate Algebra* (3 Hours)**

**Prerequisites:** MATH 115 with a grade of "C" or higher or appropriate score on the math placement test

This course focuses on arithmetic and algebraic manipulation, equations and inequalities, graphs, and analysis of equations and graphs. Students will simplify arithmetic and algebraic expressions, including those containing rational expressions, rational exponents, radicals and complex numbers; solve equations and inequalities including linear, quadratic, quadratic in form, as well as those containing rational expressions, radicals or absolute value; graph linear inequalities; and analyze functions and non-functions. 3 or 5 hrs.lecture/wk. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details.

**MATH 118 Geometry* (3 Hours)**

**Prerequisites:** MATH 115 with a grade of "C" or higher or appropriate score on the math placement test

This course is an informal approach to geometry. Topics will include lines, polygons, area, volume, circles, similarity, congruence and coordinate geometry. 3 hrs. lecture/wk.

**MATH 120 Business Mathematics* (3 Hours)**

**Prerequisites:** MATH 111 with a grade of "C" or higher or appropriate score on the math placement test

This is a course for the student who needs specific skills in mathematics to address business problems and business applications. Students will learn the mathematics involved in payroll, retailing, asset valuation, interest, finance, and the time value of money. Students will use a calculator and computer to solve a variety of applications. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details. 3 hrs. lecture/wk.

**MATH 130 Technical Mathematics I* (3 Hours)**

**Prerequisites:** MATH 111 with a grade of "C" or higher or an appropriate score on the math placement test

This course is the first of a two-semester sequence that will introduce the mathematical skills and concepts necessary in technical work. It will focus on the basics of algebra, geometry and their applications. Topics will include operations with polynomials, linear equations, systems of equations, formulas and basic geometry. 3 hrs. lecture/wk.

**MATH 131 Technical Mathematics II* (3 Hours)**

**Prerequisites:** MATH 130 with a grade of "C" or higher or an equivalent course with a grade of "C" or higher

This course is the second of a two-semester sequence on the mathematical skills and concepts necessary in technical work. It will focus on more advanced algebraic skills, solving equations, and trigonometry. The topics will include polynomials, rational expressions, radical expressions, complex numbers, solving quadratic, rational, radical, exponential and logarithmic equations, and working with basic trigonometry. 3 hrs. lecture/wk.

**MATH 165 Finite Mathematics* (3 Hours)**

**Prerequisites:** MATH 116 with a grade of "C" or higher or appropriate score on the math placement test

This course will emphasize the beauty, scope, practical applications and relevance of mathematics. It is designed to involve the students with the concepts as well as quantitative skills. Topics include set theory, symbolic logic, deductive reasoning, probability, mathematics of finance, systems of equations, matrix algebra, and linear programming. 3 hrs. lecture/wk. This course is only offered in the spring semester.

**MATH 171 College Algebra* (3 Hours)**

**Prerequisites:** MATH 116 with a grade of "C" or higher or MATH 131 with a grade of "C" or higher or appropriate score on the math placement test

This course focuses on the study of functions and their graphs, techniques of solving equations, and applications. Students will analyze and graph functions, including constant, linear, quadratic, piecewise-defined, absolute value, square root, polynomial, rational, exponential and logarithmic functions and non-functions; solve equations and inequalities, including polynomial equations, absolute value equations, radical equations, rational equations, exponential equations, logarithmic equations, systems of linear and non-linear equations and systems of linear inequalities; and apply functions in real-world situations. 3 or 5 hrs./wk.

**MATH 171H HON: College Algebra (1 Hour)**

One-credit hour honors contract is available to qualified students who have an interest in a more thorough investigation of a topic related to this subject. An honors contract may incorporate research, a paper, or project and includes individual meetings with a faculty mentor. Student must be currently enrolled in the regular section of the courses or have completed it the previous semester. Contact the Honors Program Office, COM 201, for more information.

**MATH 172 Trigonometry* (3 Hours)**

**Prerequisites:** MATH 171 with a grade of "C" or higher or appropriate score on the math placement test

This is a course in trigonometric functions and graphs. Emphasis will be on understanding function notation, definitions, algebraic relations, real-world applications, graphing in the real and complex plane, inverse functions, polar functions and vectors. 3 hrs. lecture/wk.

**MATH 172H HON: Trigonometry (1 Hour)**

One-credit hour honors contract is available to qualified students who have an interest in a more thorough investigation of a topic related to this subject. An honors contract may incorporate research, a paper, or project and includes individual meetings with a faculty mentor. Student must be currently enrolled in the regular section of the courses or have completed it the previous semester. Contact the Honors Program Office, COM 201, for more information.

**MATH 173 Precalculus* (5 Hours)**

**Prerequisites:** MATH 116 with a grade of "C" or higher or appropriate score on the math placement test

Note: MATH 173 is an accelerated course recommended for students with a strong high school math background (three to four years) who plan to take calculus. This course focuses on the study of functions and their graphs, solving equations and inequalities, recognition and creation of patterns, and the use of mathematical models. Included in the course are linear, power, polynomial, rational, radical, exponential, logarithmic, trigonometric, and absolute value functions. 5 hrs. lecture/wk.

**MATH 173H HON: Precalculus (1 Hour)**

One-credit hour honors contract is available to qualified students who have an interest in a more thorough investigation of a topic related to this subject. An honors contract may incorporate research, a paper, or project and includes individual meetings with a faculty mentor. Student must be currently enrolled in the regular section of the courses or have completed it the previous semester. Contact the Honors Program Office, COM 201, for more information.

**MATH 175 Discrete Mathematics and its Applications* (3 Hours)**

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

This course is designed to present the beauty, scope, practical applications and relevance of mathematics. It will focus on applications of general interest drawn primarily from the social and biological sciences and business. Topics will be placed in a historical context, and mathematical reasoning will be stressed. 3 hrs. lecture/wk.

**MATH 181 Statistics* (3 Hours)**

**Prerequisites:** MATH 171 or MATH 173 or an equivalent course with a grade of "C" or higher or appropriate score on the math placement test

This is a beginning course in statistical analysis, the skill of making sense of raw data, constructing graphical representations of data, developing models for making predictions, performing tests to determine significant change and finding intervals for population values. Students will learn the basics of descriptive statistics, probability, sampling, confidence intervals, distributions, hypothesis testing, regression and correlation. Use of technology will be incorporated into course topics. 3 hrs. lecture/wk.

**MATH 181H HON: Statistics (1 Hour)**

**MATH 191 Math & Physics for Games I* (4 Hours)**

**Prerequisites:** MATH 171 or MATH 173 with a grade of C" or higher or appropriate score on math placement test and GAME 121

This introductory course focuses on the mathematics and physics concepts needed to program a variety of video game scenarios. Student will learn to use vectors and matrix transformations to model the motion of physical objects in two and three dimensions. Students will also learn various computer programming methods in order to model these mathematical and physical concepts. 3 hrs. lecture and 2 hrs. lab/wk.

**MATH 210 Mathematics for Elementary Teachers I* (3 Hours)**

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on math placement test

This is the first of a two-course sequence for prospective teachers of elementary and middle school mathematics. The focus of this course is an in-depth investigation of the mathematical principles and concepts encountered in grades K-8. Topics include set theory, numeration systems, number sense, critical thinking, and problem-solving strategies. The use of appropriate techniques and tools, such as calculators, computers and manipulatives, will be integrated throughout the course in order to enhance the depth of understanding. 3 hrs. lecture/wk.

**MATH 212 Math for Elementary Teachers II* (3 Hours)**

**Prerequisites:** MATH 210 with a grade of "C" or higher or department approval

This is the second of a two-course sequence for prospective teachers of elementary/middle school mathematics. The focus of this course is an in-depth investigation of the mathematical principles and concepts encountered in grades K-8. Topics include probability, statistics, measurement, and shapes including congruency, similarity, and transformations. The use of appropriate techniques and tools, such as calculators, computers, and manipulatives, will be integrated throughout the course in order to enhance the depth of understanding. 3 hrs. lecture/wk. NOTE: the prerequisite of MATH 210 requires a grade of "C" or higher.

**MATH 214 Introduction to Teaching Math and Science I* (1 Hour)**

**Prerequisites:** MATH 171 with a grade of "C" or higher OR appropriate score on the math placement test OR department approval

This course allows math and science students to explore and develop an appreciation for teaching as a career. To support their learning, students will be introduced to the theory and practice that is necessary to design and deliver quality instruction. They will plan and implement lessons of an inquiry-based curriculum in an elementary classroom during the semester. MATH 214, ASTR 214, BIOL 214, CHEM 214, GEOS 214, PHYS 214 and PSCI 214 are the same course; enroll in only one. 1.25 hrs. lecture/wk.

**MATH 215 Introduction to Teaching Math and Science II* (1 Hour)**

**Prerequisites:** ASTR 214 or BIOL 214 or CHEM 214 or GEOS 214 or MATH 214 or PHYS 214 or PSCI 214 with a grade of C" or higher

Students learn about the middle school environment and work on math and science inquiry-based lesson analysis, design and assessment. Student partners will plan and teach three inquiry-based lessons in a middle school. The course emphasizes writing 5E lesson plans with a focus on the importance of using appropriate questioning and assessment strategies throughout the lesson, as well as how to analyze and modify a lesson based on personal reflections and observer feedback. By the completion of the course, students should be able to reflect on their personal suitability/interest in teaching secondary math or science, and develop a feasible pathway to a career in teaching. MATH 215, ASTR 215, BIOL 215, CHEM 215, GEOS 215, PHYS 215 and PSCI 215 are the same course; enroll in only one. 1.25 hrs. lecture/wk.

**MATH 225 Mathematics as a Decision Making Tool* (3 Hours)**

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

The focus of this course is to develop the quantitative skills and reasoning ability necessary to help students read critically and make decisions in our technical information society. A project tying this course to the student's own interest is a course requirement. Major topics include collecting and describing data, inferential statistics and probability, geometric similarity, geometric growth, symmetry and patterns. 3 hrs. lecture/wk.

**MATH 231 Business and Applied Calculus I* (3 Hours)**

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

This is the first course in calculus as it applies to business; the social, behavioral, and biomedical sciences; and other fields. Concepts include measuring the slope of a curve, writing equations of tangent lines, finding maximum and minimum points, determining the rate of change of a function, and measuring the area under a curve. Algebraic skills and application problems are stressed. Specific calculus topics include finding limits, differentiation of algebraic, exponential and logarithmic functions, and integration of algebraic and exponential functions. Trigonometry (MATH 172) can be taken concurrently with MATH 231 for those students planning to enroll in MATH 232 in subsequent semesters. 3 hrs. lecture/wk.

**MATH 231H HON: Bus. & Applied Calculus I (1 Hour)**

**MATH 232 Business and Applied Calculus II* (3 Hours)**

**Prerequisites:** MATH 231 and either MATH 172 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

This is the second course in a two-semester series on calculus that covers five techniques of integration, differentiation and integration of trigonometric functions, differential equations, and functions of several variables as applied to business, statistics, biology and the social sciences. 3 hrs. lecture/wk.

**MATH 232H HON:Bus. & Applied Calculus II (1 Hour)**

**MATH 241 Calculus I* (5 Hours)**

**Prerequisites:** Either (MATH 171 and MATH 172) or MATH 173 or an equivalent course with a grade of "C" or higher or an appropriate score on an placement test

This is the first of a three-semester sequence on calculus designed for engineering, physics and math majors. Rates of change, areas and volumes will be studied. To accomplish this, the students will study and apply limits and continuity. Differentiation and integration of algebraic, trigonometric and transcendental functions will also be a major focus of this course. 5 hrs. lecture/wk.

**MATH 241H HON: Calculus I (1 Hour)**

**MATH 242 Calculus II* (5 Hours)**

**Prerequisites:** MATH 237 or MATH 241 or an equivalent course with a grade of "C" or higher

This is the second course of a three-semester sequence on calculus. The emphasis will be an analytic, numerical and graphical approach to techniques of integration, and infinite series, including scientific applications. 5 hrs. lecture/wk.

**MATH 242H HON: Calculus II (1 Hour)**

**MATH 243 Calculus III* (5 Hours)**

**Prerequisites:** MATH 242 with a grade of "C" or higher or an equivalent course with a grade of "C" or higher

This is the third course in a three-semester sequence on analytic geometry and calculus. Topics include vector-valued functions, functions of several variables, multiple integration, and vector analysis. 5 hrs. lecture/wk.

**MATH 243H HON: Calculus III (1 Hour)**

**MATH 246 Elementary Linear Algebra* (3 Hours)**

**Prerequisites:** MATH 242 or an equivalent course with a grade of "C" or higher

This sophomore-level introduction to linear algebra uses a matrix-oriented approach, with an emphasis on problem solving and applications. The course focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, orthogonality and vector spaces. Students are expected to use technology for matrix operations. 3 hrs. lecture/wk.

**MATH 246H HON: Elementary Linear Algebra (1 Hour)**

**MATH 254 Differential Equations* (4 Hours)**

**Prerequisites:** MATH 243 with a grade of "C" or higher or an equivalent course with a grade of "C" or higher

This course will cover standard types of equations that involve rates of change. In particular, this is an introductory course in equations that involve ordinary derivatives. Both qualitative and quantitative approaches will be used. Standard types and methods will be covered, including Laplace transforms, infinite series, and numerical methods. Basic linear algebra will be developed to solve systems of differential equations. 4 hrs. lecture/wk.

**MATH 254H HON: Differential Equations (1 Hour)**

**MATH 285 Statistics for Business* (4 Hours)**

**Prerequisites:** MATH 231 or MATH 241 or an equivalent course with a grade of "C" or higher Note: Students transferring MATH 285 to the University of Kansas must have CIS 201 as a corequisite

This is a beginning course in calculus-based statistical analysis with an emphasis on applications to business. The skill of making sense of raw data is important, and includes constructing graphical representations of data, developing models for making predictions, performing tests to determine significant change and finding intervals for population values. Students will learn the basics of descriptive statistics, probability, sampling, confidence intervals, hypothesis testing, linear regression, and an introduction to quality control. Students must have an understanding of calculus concepts in order to successfully complete this course. 4 hrs. lecture/wk. Students transferring MATH 285 to KU must have CIS 201 as a corequisite.

**MATH 292 Special Topics:* (1-3 Hour)**

**Prerequisites:** Department approval

MATH 292 allows students to investigate in-depth a single theme or topic in mathematics. This may be accomplished by expanding upon a subject introduced in current course offerings or exploring a subject not addressed in the curriculum of the mathematics department. Special Topics may be repeated for credit but only on different topics. Total contact hours vary with topic.

# MATH 111

**Title:**Fundamentals of Mathematics***Number:**MATH 111**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** AAC 112 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

Fundamentals of Mathematics is designed for the student who needs to improve or review basic math skills and concepts. This course includes computation using integers, fractions, decimals, proportions and percents along with an overview of measurement, geometry, statistics and linear equations. Fundamentals of Math provides the mathematical foundation upon which subsequent studies in mathematics and other areas depend. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details. This course does not fulfill degree requirements. This course is the first in a sequence of courses leading to MATH 116 or higher. 3 or 5 hrs. lecture / wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Compute with integers, fractions, and decimals.
- Apply the rules of order of operation to simplify numerical expressions.
- Perform calculations and conversions using the U.S. and metric systems of measurement.
- Demonstrate the use of ratios, proportions and percentages.
- Calculate perimeter, circumference, area, and volume of geometric figures.
- Use geometry to determine triangle and angle relationships.
- Calculate the mean, median, and mode of a set of numbers.
- Interpret statistical charts and graphs.
- Use rounding to estimate results and determine if answers are reasonable.
- Solve application problems.
- Solve basic linear equations.

### Content Outline and Competencies:

I. Whole Numbers A. Identify place value of the digits in a whole number; read whole numbers; write whole numbers; compare the size of whole numbers using inequality symbols. B. Round whole numbers; estimate results using rounding. C. Add, subtract, multiply, and divide whole numbers. D. Evaluate expressions written in exponential form. E. Apply the rules of order of operation to whole numbers. F. Use the tests for divisibility for 2, 3, 5, and 10. G. Determine if a number is prime or composite; determine the prime factorization of whole numbers; find least common multiple and greatest common factor. H. Solve applications using whole numbers. II. Fraction Notation A. Identify the numerator and denominator of a fraction; identify whether a fraction is proper or improper; identify mixed numbers; change mixed numbers to improper fractions; change an improper fraction to a mixed number; compare the size of fractions using inequality symbols. B. Simplify fractions; identify equivalent fractions; change a fraction to an equivalent fraction with a different denominator. C. Add, subtract, multiply, and divide fractions and mixed numbers. D. Apply the rules of order of operation to fractions and mixed numbers. E. Solve applications using fractions. III. Ratios and Proportions A. Define a ratio; create a ratio. B. Determine if a proportion is true. C. Solve proportions. D. Solve applications using proportions. IV. Decimal Notation A. Identify place value of the digits in a decimal number; read decimal numbers; write decimal numbers. B. Round decimal numbers; estimate results using rounding. C. Add, subtract, multiply, and divide decimals. D. Compare the size of decimals using inequality symbols. E. Apply the rules of order of operation to decimals. F. Change from fraction notation to decimal notation; change from decimal notation to fraction notation. G. Solve applications using decimals. V. Percent Notation A. Define percent; change from percent notation to fraction notation; change from percent notation to decimal notation; change from fraction notation to percent notation; change from decimal notation to percent notation. B. Solve percent problems by using proportions and/or by using basic equations. C. Solve applications using percents. VI. Measurement A. Convert from one unit of measurement to another in the U.S.. System. B. Convert from one unit of measurement to another in the Metric System. C. Convert between U.S.. and metric measurements. D. Solve applications using U.S. and metric measurements. VII. Geometry A. Classify angles; identify supplementary and complementary angles. B. Identify rectangles, squares, parallelograms, triangles and trapezoids. C. Calculate the perimeter of polygons; calculate the circumference of circles; calculate the perimeter and circumference of composite figures. D. Calculate the area of a rectangle, a square, a parallelogram, a triangle, and a trapezoid; calculate the area of composite figures. E. Calculate the volume of rectangular solids, circular cylinders, spheres, and circular cones. F. Define similar figures; determine if two triangles are similar; use a proportion to find a missing side of similar triangles. G. Use the Pythagorean theorem to determine the missing side of a right triangle. H. Solve applications using geometry. VIII. Signed Numbers A. Compare the size of signed numbers using inequality symbols. B. Evaluate absolute value expressions. C. Add, subtract, multiply, and divide signed numbers. D. Apply the rules of order of operation to signed numbers. E. Solve applications using signed numbers. IX. Introduction to Algebra Topics A. Identify constants, variables, terms, and coefficients in algebraic expressions. B. Identify like terms; add and subtract like terms. C. Apply the distributive property to algebraic expressions. D. Simplify algebraic expressions; evaluate algebraic expressions; translate words into algebraic expressions. E. Solve simple linear equations using the addition and multiplication properties of equality. X. Statistics A. Calculate the mean, median, and mode of a set of numbers. B. Read tables, circle graphs, line graphs and bar graphs. C. Interpret tables, circle graphs, line graphs and bar graphs.

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers and/or Unit Projects 40% - 80% Homework, Quizzes and/or Small Projects 0% - 50% Final Exam** 10% - 40% **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a ‘C’ for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

### Caveats:

- To successfully complete the pre-requisite(s) for this course, a student must earn at least a "C" in the pre-requisite course(s) or earn an appropriate score on a placement exam. If a student is found not to have successfully fulfilled the pre-requisite(s) for this course, the student will be dropped from the course.

### Student Responsibilities:

### Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.

# MATH 115

**Title:**Elementary Algebra***Number:**MATH 115**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 111 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This is a beginning course in algebra, designed to help students acquire a solid foundation in the basic skills of algebra. Students will learn to simplify arithmetic and algebraic expressions, including exponential expressions, polynomials, rational expressions and radical expressions; solve equations and inequalities, including linear equations and quadratic equations; graph linear equations; and analyze linear equations. MATH 115 may fulfill some certificate requirements, but will not fulfill degree requirements. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details. This course is the first in a sequence of courses leading to MATH 116 or higher. 3 or 5 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Simplify arithmetic and algebraic expressions including exponential expressions, polynomials, rational expressions, and radical expressions.
- Factor algebraic expressions.
- Solve linear equations and inequalities
- Solve quadratic equations.
- Graph linear equations.
- Analyze linear equations.

### Content Outline and Competencies:

I. Arithmetic and Algebraic Manipulation A. Evaluate arithmetic expressions using the order of operations B. Evaluate algebraic expressions C. Apply the laws of exponents to simplify expressions containing integer exponents D. Express numbers in scientific notation E. Perform addition, subtraction, multiplication, and division on polynomial expressions F. Factor expressions with common factors, expressions that require grouping, quadratic expressions, and difference of square expressions G. Perform addition, subtraction, multiplication, and division on rational expressions H. Calculate radicals, approximating those that are irrational I. Simplify radicals of any order using the product and quotient rules II. Equations and Inequalities A. Solve linear equations in one variable B. Solve proportion equations C. Solve linear inequalities in one variable showing solutions on a number line D. Solve literal equations that do not require factoring E. Solve quadratic equations by factoring F. Solve quadratic equations by using the square root property G. Solve equations developed from number, geometry, proportion, and percent applications III. Graphs on a coordinate plane A. Graph linear equations by plotting points B. Graph linear equations using intercepts C. Graph linear equations using the y-intercept and slope IV. Analysis of equations and graphs A. Identify the x-intercept, y-intercept, and slope of a line given its graph B. Construct an equation of a line given its graph C. Construct an equation of a line given its slope and y-intercept D. Construct an equation of a line given its slope and a point E. Construct an equation of a horizontal line F. Construct an equation of a vertical line G. Determine whether or not an equation is linear H. Calculate the slope of a line passing through two given points

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers and/or Unit Projects 40% - 80% Homework, Quizzes and/or Small Projects 0% - 50% Final Exam** 10% - 40% **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a ‘C’ for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

### Caveats:

- To successfully complete the pre-requisite(s) for this course, a student must earn at least a "C" in the pre-requisite course(s) or earn an appropriate score on a placement exam. If a student is found not to have successfully fulfilled the pre-requisite(s) for this course, the student will be dropped from the course.

### Student Responsibilities:

### Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.

# MATH 116

**Title:**Intermediate Algebra***Number:**MATH 116**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 115 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This course focuses on arithmetic and algebraic manipulation, equations and inequalities, graphs, and analysis of equations and graphs. Students will simplify arithmetic and algebraic expressions, including those containing rational expressions, rational exponents, radicals and complex numbers; solve equations and inequalities including linear, quadratic, quadratic in form, as well as those containing rational expressions, radicals or absolute value; graph linear inequalities; and analyze functions and non-functions. 3 or 5 hrs.lecture/wk. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Factor algebraic expressions.
- Simplify arithmetic and algebraic expressions including those containing rational expressions, rational exponents, radicals, or complex numbers.
- Evaluate functions.
- Solve equations in one variable including quadratic, quadratic in form, and those containing rational expressions, radicals, or absolute value.
- Solve equations in more than one variable including systems of linear equations and literal equations.
- Solve equations developed from applications.
- Solve inequalities in one variable including linear and quadratic inequalities.
- Graph linear inequalities on a coordinate plane.
- Construct equations of lines and circles.
- Identify characteristics of functions and non-functions.

### Content Outline and Competencies:

I. Arithmetic and Algebraic Manipulation A. Factor quadratic in form expressions, sum of cubes expressions, and difference of cubes expressions B. Perform addition, subtraction, multiplication, and division on rational expressions C. Simplify complex fractions D. Apply the laws of exponents to simplify expressions containing rational exponents E. Apply the laws of radicals to perform addition, subtraction, and multiplication F. Rationalize denominators containing radicals G. Simplify radicals containing negative radicands H. Perform addition, subtraction, multiplication, and division on complex numbers I. Evaluate functions II. Equations and Inequalities A. Solve linear inequalities in one variable showing solutions on a number line and in interval notation B. Solve literal equations that require factoring C. Solve systems of linear equations in two variables D. Solve quadratic equations by completing the square E. Solve quadratic equations by using the quadratic formula F. Solve equations that are quadratic in form G. Solve quadratic inequalities in one variable showing solutions on a number line and in interval notation H. Solve equations containing rational expressions I. Solve equations containing radicals J. Solve absolute value equations in one variable K. Solve equations developed from mixture, motion, work, and geometry applications III. Graphs on a coordinate plane A. Graph linear inequalities B. Graph quadratic equations C. Graph circles IV. Analysis of equations and graphs A. Construct an equation of a line given two points B. Construct an equation of a line perpendicular to a given line through a specific point C. Construct an equation of a line parallel to a given line through a specific point D. Construct an equation of a circle given its center and radius E. Calculate the distance between two points F. Determine the center and radius of a circle by completing the square G. Determine the midpoint between two points H. Distinguish between functions and non-functions using the vertical line test I. Identify the domain and range of a function given its graph

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers and/or Unit Projects 40% - 80% Homework, Quizzes and/or Small Projects 0% - 50% Final Exam** 10% - 40% **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a ‘C’ for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

### Caveats:

- To successfully complete the pre-requisite(s) for this course, a student must earn at least a "C" in the pre-requisite course(s) or earn an appropriate score on a placement exam. If a student is found not to have successfully fulfilled the pre-requisite(s) for this course, the student will be dropped from the course.

### Student Responsibilities:

### Disabilities:

If you are a student with a disability, and if you will be requesting accommodations, it is your responsibility to contact Access Services. Access Services will recommend any appropriate accommodations to your professor and his/her director. The professor and director will identify for you which accommodations will be arranged.

JCCC provides a range of services to allow persons with disabilities to participate in educational programs and activities. If you desire support services, contact the office of Access Services for Students With Disabilities (913) 469-8500, ext. 3521 or TDD (913) 469-3885. The Access Services office is located in the Success Center on the second floor of the Student Center.

# MATH 118

**Title:**Geometry***Number:**MATH 118**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 115 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This course is an informal approach to geometry. Topics will include lines, polygons, area, volume, circles, similarity, congruence and coordinate geometry. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Classify geometric figures in two and three dimensions.
- Find the perimeter and area of two-dimensional geometric figures.
- Find the surface area and volume of three-dimensional figures.
- Write deductive proofs.
- Apply theoretical results to applications.
- Verify the congruence of geometric figures.
- Verify the similarity of geometric figures.
- Construct geometric figures with compass and straightedge.
- Use coordinate equations to describe lines and circles.

### Content Outline and Competencies:

I. Geometric Shapes A. Describe points, lines, and planes. B. Compute the distance between two points on a number line. C. Define line segments, rays, and angles. D. Identify types of angles. E. Determine measures of angles with a protractor. F. Distinguish between complementary and supplementary angles. G. Define triangles and list their types. H. Define polygons and list their types. I. Define quadrilaterals and list their types. J. Identify lines of symmetry in a polygon. K. Find the angle measures in a polygon. L.I dentify prisms, pyramids, cylinders, cones, and spheres. M. Identify regular polyhedra and list their types. N. Convert linear dimensions using dimensional analysis. II. Perimeter, Area, and Volume A. Find the perimeter of a polygon. B. Find the circumference of a circle. C. Find the area of rectangles, triangles, parallelograms, and trapezoids. D. Find the area of a regular polygon. E. Find the area of a circle. F. Find the length of a missing side in a right triangle. G. Describe the relationship of sides of a 45°-45°-90° and of a 30°-60°-90° triangle. H. Find the surface area of prisms, pyramids, cylinders, cones, and spheres. I. Find the volume of prisms, pyramids, cylinders, cones, and spheres. J. Convert area and volume measures using dimensional analysis. III. Reasoning A. Draw conclusions. B. Apply conditional statements. C. Apply equivalent (biconditional) statements. D. Recognize valid and invalid deductions. E. Write the converse of a statement. F. Write a deductive proof. IV. Triangles A. Identify vertical angles and exterior angles. B. List the triangle congruence theorems. C. Prove two triangles are congruent. D. Prove corresponding parts of congruent triangles are congruent. E. Define medians and perpendicular bisectors F. Use theorems related to isosceles and equilateral triangles. G. Use theorems related to triangle inequalities. H. Construct segments and angles using a compass and straightedge. I. Construct perpendicular lines using a compass and straightedge. V. Parallel Lines and Quadrilaterals A. Identify alternate interior, alternate exterior, and corresponding angles. B. Use theorems derived from the Parallel Postulate. C. Prove the Angle Sum in a Triangle Theorem. D. Use the Exterior Angle Theorem. E. Use theorems related to quadrilaterals to determine side lengths and angle measures. F. Prove theorems related to quadrilaterals. G. Construct parallel lines using a compass and straightedge. H. Subdivide line segments using a compass and straightedge. VI. Similarity A. Solve problems related to ratio and proportion. B. Use triangle similarity theorems to prove two triangles are similar. C. Find the missing part of similar polygons. D. Use theorems related to the mean proportional in a right triangle. E. Use the Side Splitting Theorem VII. Circles A. Define arc, central angle, and inscribed angle. B. Determine measures of angles and arcs of a circle. C. Find areas of sectors and measures of arc length. D. Define chords and tangents. E. Determine measures of segments and angles formed by chords. F. Prove theorems related to circles. G. Construct tangent lines using a compass and straightedge. H. Find the center of a circle using a compass and straightedge. VIII. Coordinate Geometry A. Plot points in a coordinate system. B. Find the distance between two points in the plane. C. Determine if three points in the plane are collinear. D. Find the midpoint of a line segment. E. Find the slope of a line. F. Find the slopes of parallel and perpendicular lines. G. Find the equation of a line. H. Find the center and radius of a circle from its equation. I. Find the equation of a circle. J. Graph lines and circles from their equations. K. Prove theorems using coordinates.

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# MATH 120

**Title:**Business Mathematics***Number:**MATH 120**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 111 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This is a course for the student who needs specific skills in mathematics to address business problems and business applications. Students will learn the mathematics involved in payroll, retailing, asset valuation, interest, finance, and the time value of money. Students will use a calculator and computer to solve a variety of applications. This course may be offered as a Learning Community (LCOM) section. Please see the current credit course schedule for LCOM details. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Solve percent problems.
- Apply mathematics to payroll situations.
- Apply mathematics to retail situations.
- Apply mathematics to finance situations.
- Apply mathematics to the valuation of assets.
- Use a financial calculator and a computer to apply mathematics to business problems.

### Content Outline and Competencies:

I. The Mathematics of Percents. A. Solve for base, rate, or part in a basic percent problem. B. Solve for the old or new value in a percent increase problem. C. Solve for the old or new value in a percent decrease problem. II. The Mathematics of Payroll. A. Given an hourly wage with an overtime policy, find the gross pay. B. Given a commission structure or a piecework rate, find the gross pay. C. Use the Percentage Method to calculate federal and state withholding tax. D. Calculate FICA taxes; explain the purpose of FICA taxes. E. Calculate federal and state unemployment taxes. F. Calculate an employee’s net pay. G. Calculate the cost of employment; identify the employment taxes an employer must pay. H. Use a computer to analyze the effect of taxes on gross pay. III. The Mathematics of Retailing. A. Read and analyze an invoice; explain key abbreviations. B. Calculate trade, series, and cash discounts. C. Calculate markup based on cost. D. Calculate markup based on selling price. E. Calculate markdowns. F. Calculate the adjusted cost when shrinkage is present. G. Calculate the net profit. H. Calculate operating loss and absolute loss; explain the meaning of each. I. Calculate the amount of operating expenses from the percent. J. Calculate the breakeven point. IV. The Mathematics of Finance and the Simple Interest Formula A. Find the interest earned using the simple interest formula. B. Solve for principal, rate, or time in a simple interest problem. C. Calculate the interest, the proceeds, and the maturity value on a simple interest note or a simple discount note. D. Find the bank discount on a note; explain what discounting a note means in terms of a problem. E. Determine the effective rate (APR) of a note. F. Compute the payoff amount on a loan or note using the U.S. Rule. V. The Mathematics of Finance and Time Value of Money Problems A. Use the financial calculator to find the future value, initial value, time, or rate of a lump sum deposit problem. B. Use the financial calculator to find the future value, initial value, periodic payment, time, or rate of a savings plan. C. Use the financial calculator to find the future balance, present balance, periodic payment, time, or rate of a loan. D. Calculate the total interest earned in a time value of money problem. E. Calculate the present value of an annuity; explain the meaning of present value. F. Use a computer to solve time value of money applications; analyze computer results of time value of money applications. VI. The Valuation of Assets. A. Determine the value of ending inventory using Average Cost (Weighted Average), FIFO, and LIFO. B. Use the straight line depreciation method to find the value of an asset. C. Use the double declining balance depreciation method to find the value of an asset. D. Use the units of production depreciation method to find the value of an asset.

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# MATH 130

**Title:**Technical Mathematics I***Number:**MATH 130**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 111 with a grade of "C" or higher or an appropriate score on the math placement test

### Description:

This course is the first of a two-semester sequence that will introduce the mathematical skills and concepts necessary in technical work. It will focus on the basics of algebra, geometry and their applications. Topics will include operations with polynomials, linear equations, systems of equations, formulas and basic geometry. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Simplify numerical and algebraic expressions.
- Solve linear equations and systems of linear equations.
- Graph linear equations.
- Solve problems using geometric properties and formulas.
- Manipulate formulas including those used in technical work.

### Content Outline and Competencies:

I. Numeric Expressions A. Describe the properties of the real number system. B. Use the order of operations for the real number system to simplify mathematical expressions. C. Simplify expressions involving exponents and radicals. D. Determine the number of significant digits in a number. E. Use scientific notation and rounding appropriately in computation. F. Convert between scientific notation and standard notation. II. Algebraic Expressions A. Add and subtract polynomials. B. Multiply polynomials. C. Divide polynomials. D. Evaluate algebraic expressions. III. Linear Equations A. Solve linear equations. B. Solve formulas for a particular variable, including those used in technical work. C. Define ratio and proportion. D. Solve a proportion for a missing term. E. Solve a system of two or three equations by algebraic methods. IV. Basic Geometry Skills A. Define parallel lines and angles formed by a transversal; use these concepts to determine unknown angles. B. Classify triangles. C. Calculate area and perimeter of polygons. D. Calculate area and circumference of circles. E. Calculate volume and surface area of geometric solids. V. Graphing A. Plot points on the rectangular coordinate system. B. Graph straight lines. C. Define the slope of a line; use the slope to graph a line. D. Solve a system of equations by graphing.

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers, and/or Unit Projects: 40%-80% Homework, Quizzes, and/or Small Projects: 0%-50% Final Exam** 10%-40% **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a 'C' for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any low test score.

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# MATH 131

**Title:**Technical Mathematics II***Number:**MATH 131**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 130 with a grade of "C" or higher or an equivalent course with a grade of "C" or higher

### Description:

This course is the second of a two-semester sequence on the mathematical skills and concepts necessary in technical work. It will focus on more advanced algebraic skills, solving equations, and trigonometry. The topics will include polynomials, rational expressions, radical expressions, complex numbers, solving quadratic, rational, radical, exponential and logarithmic equations, and working with basic trigonometry. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Factor polynomials.
- Simplify and perform operations with rational expressions, radical expressions, and complex numbers.
- Solve quadratic, rational, radical, exponential and logarithmic equations.
- Use basic trigonometry.

### Content Outline and Competencies:

I. Algebraic Skills A. Factor polynomials. 1. Factor using greatest common factor. 2. Factor using grouping. 3. Factor trinomials. 4. Factor using the difference of squares. B. Simplify rational and radical expressions. C. Perform operations with rational expressions, radical expressions and complex numbers. D. Convert between exponential and logarithmic notation. E. Expand and condense logarithmic expressions using properties of logarithms. II. Equations A. Solve quadratic equations by factoring and by the quadratic formula. B. Solve problems involving direct, inverse, and joint variation. C. Solve equations involving rational expressions. D. Solve equations involving radical expressions. E. Solve exponential equations. F. Solve logarithmic equations. III. Trigonometry A. Define trigonometric functions using both a unit circle and a right triangle. B. Define angle measurement in both radians and degrees. C. Evaluate trigonometric functions of any angle. D. Define inverse trigonometric functions. E. Solve right triangles for missing parts. F. Solve application problems using right triangle trigonometry. G. Define vectors. H. Perform operations with vectors. I. Solve oblique triangles for missing parts using the Law of Sines and the Law of Cosines. J. Solve application problems using the Law of Sines and the Law of Cosines. K. Graph transformations of the sine and cosine functions.

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers, and/or Unit Projects: 40%-80% Homework, Quizzes, and/or Small Projects: 0%-50% Final Exam** 10%-40% **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a 'C' for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score.

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# MATH 165

**Title:**Finite Mathematics***Number:**MATH 165**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 116 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This course will emphasize the beauty, scope, practical applications and relevance of mathematics. It is designed to involve the students with the concepts as well as quantitative skills. Topics include set theory, symbolic logic, deductive reasoning, probability, mathematics of finance, systems of equations, matrix algebra, and linear programming. 3 hrs. lecture/wk. This course is only offered in the spring semester.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Apply set theory to practical applications.
- Determine the truth value of statements.
- Determine the validity of logical arguments.
- Use probability as a tool for predicting outcomes.
- Solve financial applications.
- Solve systems of equations and inequalities.
- Solve linear programming problems.

### Content Outline and Competencies:

I. Set Theory A. Model set problems with Venn Diagrams. B. Use set operations to calculate union, intersection, complement, and cardinality of sets. C. Identify subsets. II. Logic and Deductive Reasoning A. Define conjunction, disjunction, and negation of statements. B. Determine the truth value of simple and compound statements using truth tables. C. Write the converse, inverse, and contrapositive of a conditional statement. D. Determine the validity of an argument using direct, indirect, and transitive reasoning. III. Probability A. Use probability notation including the "or" condition and the "and" condition. B. Determine whether or not two events are mutually exclusive. C. Calculate mathematical expectation. D. Calculate conditional probabilities. E. Use counting formulas to determine permutations and combinations. IV. Mathematics of Finance A. Calculate simple and compound interest. B. Calculate the value of an annunity. C. Calculate the annual percentage rate. D. Analyze an amortization schedule. E. Calculate loan and credit card payments. V. Systems of Equations and Matrix Algebra A. Use linear functions to model applications. B. Solve systems of linear equations in two or more variables. C. Identify the dimension of a matrix. D. Use matrix operations (addition, multiplication, and scalar multiplication) to calculate resultant matrices. E. Use Gaussian elimination to solve an augmented matrix. VI. Linear Programming A. Graph systems of inequalities with all points of intersection. B. Determine the constraints and the objective function of a linear programming problem. C. Solve a linear programming problem graphically. D. Use the Simplex Matrix to solve linear programming applications.

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers and/or Unit Projects 40% - 80% Homework, Quizzes and/or Small Projects 0% - 50% Final Exam** 10% - 40% **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a 'C' for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

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### Student Responsibilities:

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# MATH 171

**Title:**College Algebra***Number:**MATH 171**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 116 with a grade of "C" or higher or MATH 131 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This course focuses on the study of functions and their graphs, techniques of solving equations, and applications. Students will analyze and graph functions, including constant, linear, quadratic, piecewise-defined, absolute value, square root, polynomial, rational, exponential and logarithmic functions and non-functions; solve equations and inequalities, including polynomial equations, absolute value equations, radical equations, rational equations, exponential equations, logarithmic equations, systems of linear and non-linear equations and systems of linear inequalities; and apply functions in real-world situations. 3 or 5 hrs./wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Analyze functions and their graphs.
- Sketch the graphs of functions, including constant, linear, piecewise-defined, absolute value, square root, polynomial, rational, exponential and logarithmic.
- Solve equations including polynomial, exponential and logarithmic equations.
- Solve systems of equations and systems of linear inequalities.
- Create mathematical models to solve application problems and make predictions.

### Content Outline and Competencies:

I. Analysis and graphing of functions and non-functions A. Use function notation. B. Recognize equations of functions and non-functions. C. Use concepts of symmetry, intercepts, left to right behavior, asymptotes, and transformations to sketch graphs of functions (constant, linear, quadratic, piecewise-defined, absolute value, square root, cubic, polynomial, rational, exponential, and logarithmic) and non-functions (circles). D. Determine the domain and range of a function. E. Write the equation of a function (constant, linear, quadratic, absolute value, square root, cubic, polynomial, rational, exponential, and logarithmic) or non-function (circle) given its description. F. Use graphs of functions for analysis. G. Find combinations and composites of functions. H. Find inverses of functions. II. Solutions of equations and inequalities A. Solve quadratic equations. B. Solve equations involving rational expressions, radicals, and absolute value expressions. C. Solve polynomial equations. D. Solve exponential equations. E. Solve logarithmic equations. F. Solve polynomial, absolute value, and rational inequalities. G. Solve systems of linear equations in three variables by various methods including matrices. H. Solve systems of non-linear equations. I. Graph systems of linear inequalities. III. Applications to Real-World Situations A. Apply equations to real-world situations, including but not limited to depreciation, growth and decay, and max/min problems. B. Examine and analyze data, make predictions and interpretations, and do basic modeling. C. Use systems of linear equations in three variables in various applications.

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# MATH 171H

No information found.# MATH 172

**Title:**Trigonometry***Number:**MATH 172**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 171 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This is a course in trigonometric functions and graphs. Emphasis will be on understanding function notation, definitions, algebraic relations, real-world applications, graphing in the real and complex plane, inverse functions, polar functions and vectors. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Apply trigonometric functions to real-world situations.
- Verify trigonometric identities.
- Solve trigonometric equations.
- Solve and find area of triangles using trigonometric formulas.
- Analyze the graphs of trigonometric, inverse trigonometric, and polar functions.
- Calculate products, quotients, powers, and roots of complex numbers in trigonometric form.

### Content Outline and Competencies:

I. The Six Trigonometric Functions A. Determine the six trigonometric functions of an angle in standard position given a point on its terminal side. B. Determine the remaining trigonometric functions of an angle given the value of one trigonometric function and the quadrant in which the angle lies. C. Determine the six trigonometric functions of an angle in a triangle given two sides. D. Calculate the six trigonometric functions of an angle using a calculator. E. Determine exact values of the six trigonometric functions given a 30°, 45°, 60°, or quadrantal angle. F. Determine the six trigonometric functions of an angle in standard position using reference angles. II. Applications A. Solve real world-problems involving angles of elevation and depression. B. Calculate the length of an arc and the area of a sector in a circle. III. Graphs of Trigonometric Functions A. Graph the six basic trigonometric functions of the form y = k + Afunc(Bx + C). B. Determine the equation of a function given its graph. C. Graph combinations of functions. IV. Trigonometric Identities A. Simplify trigonometric expressions using trigonometric identities. B. Prove trigonometric identities. C. Evaluate function values using sum, difference, double, and half angles identities. V. Inverse Trigonometric Functions A. Evaluate inverse trigonometric functions with and without a calculator. B. Evaluate expressions involving inverse trigonometric functions. VI. Trigonometric Equations A. Solve trigonometric equations on a given interval in degrees or radians. B. Solve trigonometric equations for all angle solutions. VII. Triangles A. Solve triangles using trigonometric ratios, the Law of Sines, or the Law of Cosines, where appropriate. B. Find areas of triangles. C Apply the solutions of triangles to real-world problems. VIII. Vectors A. Determine the magnitude and direction of vectors. B. Resolve vectors into components. C. Find the sum, difference, dot product, magnitude, and angle between two vectors in algebraic form. D. Apply vectors to real-world problems. IX. Complex Numbers A. Graph in the complex plane. B. Convert complex numbers from standard form to trigonometric form and vice versa. C. Find products, quotients, powers, and roots of complex numbers. X. Polar Coordinates A. Convert from rectangular to polar coordinates and vice versa. B. Convert equations from rectangular to polar form and vice versa. C. Graph polar equations.

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# MATH 172H

No information found.# MATH 173

**Title:**Precalculus***Number:**MATH 173**Effective Term:**Spring 2015**Credit Hours:**5**Contact Hours:**5**Lecture Hours:**5

### Requirements:

**Prerequisites:** MATH 116 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

Note: MATH 173 is an accelerated course recommended for students with a strong high school math background (three to four years) who plan to take calculus. This course focuses on the study of functions and their graphs, solving equations and inequalities, recognition and creation of patterns, and the use of mathematical models. Included in the course are linear, power, polynomial, rational, radical, exponential, logarithmic, trigonometric, and absolute value functions. 5 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Communicate algebraic and graphical information contained in mathematical models.
- Identify and represent functions using words, data on a table, points on a graph, or a formula.
- Identify appropriate domains and ranges.
- Build and use piecewise functions, compose functions, combine functions, and create, use and interpret inverse functions.
- Apply mathematical functions to model real world phenomena.
- Solve problem situations that are represented using a description, a table of values, a graph, or a formula.
- Demonstrate skills necessary to transition into Calculus.

### Content Outline and Competencies:

I. Concepts of Functions in Context A. Interpret a problem solution in context of a situation. B. Discuss appropriate notation for different contexts. C. Label answers including units and possible description in context. D. Calculate and interpret the average rate of change for a given problem situation. E. Discuss the relationship between a function and its inverse. F. Interpret an inverse function and inverse function values in context. II. Elementary Functions A. Determine whether a relation represented using words, a table of values, a graph, or a formula is a function. B. Convert from one representation of a function to another. C. Use function notation to symbolically represent functions. D. Graph parent functions including linear, power, polynomial, rational, radical, exponential, logarithmic, trigonometric, and absolute value functions. E. Apply the concepts of symmetry, intercepts, long-run behavior, periodic behavior, asymptotes, transformations, and maximums and minimums to analyze and graph functions. F. Use a graphing calculator or computer-generated graphs of functions for analysis. III. Domain and Range A. State the domains and ranges of parent functions including linear, power, polynomial, rational, radical, exponential, logarithmic, trigonometric, inverse trigonometric, and absolute value functions. B. Use the domains and ranges of the parent functions and the ideas of transformations, symmetry, periodic behavior, asymptotes, and pattern recognition to determine the domains and ranges of general functions. C. Connect the domains and ranges of functions with combinations, compositions, and inverse functions. IV. Function Relationships and Operations A. Find combinations and compositions of functions represented using a description, a table of values, a graph, or a formula. B. Use and create piecewise defined functions for a given problem situation. C. Represent an absolute value function as a piecewise defined function. D. Relate the concept of an inverse function to function composition, one-to-one functions, and domain/range relationships. E. Find inverse functions and use inverse function notation. F. Use function composition to verify an inverse function relationship. G. Graph an inverse function. V. Real World Applications through Modeling A. Determine a valid domain and range for situations represented in words, a table of values, a graph, or a formula. B. Use a given mathematical model to analyze a problem. C. Write a mathematical model for a problem situation represented as a description, a table of values, or a graph. D. Use a mathematical model to make predictions. E. Compare and contrast linear, exponential and logarithmic growth models. F. Use right triangle trigonometry and the Laws of Sines and Cosines to solve problems. VI. Problem Solving A. Develop proficiency in solving equations both by hand and with appropriate technology using pattern recognition, inverse function relations, or other algebraic techniques. B. Recognize techniques that potentially introduce extraneous solutions. C. Solve polynomial equations emphasizing the root-factor relationship and the number of expected solutions based on the Fundamental Theorem of Algebra. D. Solve exponential and logarithmic equations. E. Solve trigonometric equations using methods including algebraic techniques, inverse trigonometric functions, memorization of basic trigonometric values, trigonometric identities, and the use of technology. F. Analyze graphs of non-linear systems of equations to determine the number of solutions. VII. Calculus Transition Topics A. Evaluate the difference quotient and interpret it in the context of a problem situation. B. Verify trigonometric identities, including reciprocal identities, Pythagorean identities, sum, difference, double and half-angle identities. C. Write the trigonometric form of a complex number given in standard form and convert between the two forms. D. Sketch simple polar graphs. E. Use technology to approximate trigonometric function values. F. Determine the magnitude and direction of vectors, add and subtract vectors geometrically and algebraically, resolve vectors into components and evaluate dot products. G. Perform binomial expansions through pattern recognition and use of The Binomial Theorem. H. Investigate concavity as a rate of change. I. Define a radian and use radian measures. J. Generate sequences and associated sums using simple patterns and determine their formulas. K. Find general terms of sequences with emphasis on appropriate notation. L. Use sigma notation to express series. M. Evaluate finite arithmetic and geometric series, recognizing linear and exponential connections. N. Graph the inverse sine, inverse cosine, and inverse tangent functions.

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# MATH 173H

No information found.# MATH 175

**Title:**Discrete Mathematics and its Applications***Number:**MATH 175**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This course is designed to present the beauty, scope, practical applications and relevance of mathematics. It will focus on applications of general interest drawn primarily from the social and biological sciences and business. Topics will be placed in a historical context, and mathematical reasoning will be stressed. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Construct mathematical models using graphs, trees, difference equations, and matrices.
- Determine Eulerian and Hamiltonian paths and circuits.
- Utilize graph theory to find efficient solutions to routing, scheduling, and networking problems.
- Analyze selection methods in light of fairness criteria.
- Find terms of sequences and sums of sequences.
- Utilize recursive techniques in applications.
- Perform matrix operations.
- Develop and solve linear programming problems.
- Utilize sequences and/or matrices to analyze the behavior of processes.
- Place discrete mathematical topics in their historical context.
- Utilize technology to solve discrete problems.

### Content Outline and Competencies:

I. Graphs and Trees A. Define Euler paths and circuits. B. Identify Euler paths and circuits C. Define Hamilton paths and circuits. D. Identify Hamilton paths and circuits. E. Determine optimal solutions to routing problems. F. Define network. G. Define spanning tree. H. Determine optimal solutions to network problems. I. Discuss Euler’s and Hamilton’s contributions to graph theory II. Social Choice A. Introduce mathematically-oriented voting methods B. Define ballot counting. C. Define voting methods. D. Determine election winners and rankings. E..Define voting power. F. Calculate power distributions. G. Define fair-division problems. H. Calculate a solution to fair-division problems. I. Define apportionment. J. Calculate a solution to apportionment problems. K. Discuss the effect of apportionment methods in the U.S. Congress III. Recursion and Difference Equations A. Introduce sequences and functions in the context of recursion. B. Define recursive growth problems. C. Calculate recursive growth sequences. D. Introduce Fractals IV. Matrices A. Define matrix operations. B. Utilize matrices to solve systems of equations. C. Define a linear programming problem. D. Calculate solutions to linear programming problems using augmented matrices and an appropriate calculator. E. Calculate solutions to linear programming problems using the simplex method and an appropriate calculator.

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 181

**Title:**Statistics***Number:**MATH 181**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 171 or MATH 173 or an equivalent course with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This is a beginning course in statistical analysis, the skill of making sense of raw data, constructing graphical representations of data, developing models for making predictions, performing tests to determine significant change and finding intervals for population values. Students will learn the basics of descriptive statistics, probability, sampling, confidence intervals, distributions, hypothesis testing, regression and correlation. Use of technology will be incorporated into course topics. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

Upon successful completion of this course, the student should be able to:

- Use basic descriptive statistics to describe the distribution of univariate data indicating shape, center and spread.
- Use appropriate rules and properties to determine the probability of events.
- Classify random variables and use their associated probability distribution to solve problems.
- Explain the importance of random sampling and the Central Limit Theorem for use in inferential statistics.
- Use inferential statistics to estimate population parameters and perform hypothesis testing.
- Display and analyze bivariate data using correlation and regression analysis.
- Use technology to display and analyze data sets.

### Content Outline and Competencies:

I. Descriptive Statistics

A. Define and distinguish between categorical (qualitative) and numerical (quantitative) data.

B. Distinguish between data from an observational study and data from a designed experiment.

C. Organize data in frequency tables and contingency tables.

D. Construct appropriate graphical displays of qualitative and quantitative data such as dotplots, histograms, stem-and-leaf diagrams, boxplots, bar charts, pie charts or scatterplots.

E. Describe the general shape of data such as skewed left, skewed right, normal or other symmetric.

F. Calculate the measures of center including mean, median and mode.

G. Calculate the measures of spread including range, standard deviation and interquartile range.

H. Explain the meaning of spread as it relates to a problem.

I. Use a statistical package on a graphics calculator or a computer to enter data and analyze results.

J. Determine potential outliers in a distribution.

K. Measure the position of a data point by computing a percentile.

L. Recognize features of misleading graphs.

II. Introduction to Probability

A. Solve basic probability problems.

B. Use probability notation including the “or” condition and the “and” condition.

C. Determine whether or not two events are mutually exclusive.

D. Determine whether or not two events are independent.

E. Calculate the probability of compound events.

F. Calculate conditional probabilities using conditional notation.

G. Explain the meaning of conditional probabilities.

III. Random Variables

A. Distinguish between discrete and continuous random variables.

B. Find and interpret the mean and the standard deviation of a discrete probability distribution.

C. Determine probabilities for a discrete random variable.

D. Recognize Bernoulli populations.

E. Solve probability problems of independent events with two outcomes for random variables that are binomially distributed.

F. Use the normal distribution to solve percent problems for normally distributed populations.

G. Use the normal distribution to solve probability problems for normally distributed random variables.

IV. Random Sampling and Sampling Theory

A. Calculate the mean for a distribution of sample means and/or proportions.

B. Calculate the standard deviation for a distribution of sample means and/or proportions.

C. Use the shape of a plot of a sample to decide if the sampling distribution appears to be normal.

D. Demonstrate use of the Central Limit Theorem for means and/or proportions.

V. Estimating the Mean

A. Construct a confidence interval for a population mean and a difference of two population means and interpret them in context.

B. Construct a confidence interval for a population proportion and a difference of two population proportions and interpret them in context.

VI. Hypothesis Tests

A. Perform a hypothesis test for a population mean and a difference of two population means and interpret results.

B. Perform a hypothesis test for a population proportion and a difference of two population proportions and interpret results.

C. Perform a hypothesis test with more than two categories for procedures using the Chi-square distribution.

D. Explain Type I error, Type II error, p-value, significance level and power of a test in context.

VII. Linear Regression

A. Draw a scatterplot in order to observe any association between the two variables.

B. Calculate a linear regression equation.

1. Interpret the regression equation parameters in terms of the problem.

2. Test significance of the slope.

3. Use the linear regression equation to make predictions.

4. Calculate the linear correlation coefficient and interpret its meaning.

5. Calculate the coefficient of determination and interpret its meaning.

### Method of Evaluation and Competencies:

40% - 80% Unit Exams, Unit Papers and/or Unit Projects

0% - 50% Homework, Quizzes and/or Small Projects

10% - 40% Final Exam**

**The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a “C” for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

90 – 100% = A80 – 89% = B

70 – 79% = C

60 – 69% = D

0 – 59 % = F

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 181H

No information found.# MATH 191

**Title:**Math & Physics for Games I***Number:**MATH 191**Effective Term:**Spring 2015**Credit Hours:**4**Contact Hours:**5**Lecture Hours:**3**Lab Hours:**2

### Requirements:

**Prerequisites:** MATH 171 or MATH 173 with a grade of C" or higher or appropriate score on math placement test and GAME 121

### Description:

This introductory course focuses on the mathematics and physics concepts needed to program a variety of video game scenarios. Student will learn to use vectors and matrix transformations to model the motion of physical objects in two and three dimensions. Students will also learn various computer programming methods in order to model these mathematical and physical concepts. 3 hrs. lecture and 2 hrs. lab/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Use coordinates and vectors to describe objects and space in two and three dimensions.
- Use matrices to transform between coordinate systems.
- Model particle and rigid body kinetics.
- Use the principles of physics to model the motion and collision of objects.
- Create programs which simulate the motion and collision of objects.

### Content Outline and Competencies:

I. Basic Math A. Write the equations of circles, lines, planes and spheres. B. Determine if two circles or two spheres are intersecting. C. Use trigonometry to determine the components of a vector and the angle produced by a vector. D. Analyze a trigonometric function for amplitude and period. E. Convert between polar and rectangular coordinates. F. Convert units of measurement. G. Construct code that will detect collisions between circles, lines, planes and spheres. II. Vectors A. Compare the concepts of scalar and vector. B. Add and subtract vectors. C. Multiply vectors by scalars. D. Normalize vectors. E. Find dot products and cross products of vectors. F. Find the angle between two vectors. G. Find the normal vector to a surface. H. Construct code that will perform vector arithmetic and normalization. III. Matrices A. Add, subtract, and multiply matrices. B. Multiply matrices by scalars. C. Describe translations using matrices and homogeneous coordinates. D. Describe scalings using matrices and homogeneous coordinates. E. Describe rotations using matrices and homogeneous coordinates. F. Construct code that will perform scaling, rotation, and translations on vectors and geometric objects. IV. Linear Motion A. Compute distance, displacement, velocity, speed, and acceleration for one-dimensional motion. B. Use vectors to describe displacements, velocities, and accelerations in two and three dimensions. C. Write equations which model the motion of projectiles. D. Use Newton's Laws to determine the effect of forces on the motion of an object. E. Solve for the motion of an object F. Calculate the work done by a force on an object. G. Calculate the kinetic energy, potential energy, and momentum of an object. H. Use conservation of energy and conservation of momentum to model the collision of objects. I. Construct code that can simulate the motion of a projectile. J. Construct code that can simulate the motion of an object according to Newton’s Laws of Motion. K. Construct code that can simulate the collision between two objects. V. Rotational Motion A. Compute angular displacement, angular velocity, and angular acceleration. B. Determine the angular motion caused by a torque on an object. C. Find the kinetic energy and angular momentum of a rotating object. D. Construct code that can model the three-dimensional motion of a rigid body incorporating the concepts of the conservation of energy and momentum, and Newton’s Laws of Motion.

### Method of Evaluation and Competencies:

40-80% Unit Exams, Unit Papers, and/or Unit Projects 10-50% Homework, Quizzes, and/or Small Projects 10-40% Final Exam The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a ‘C’ for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score. No student may be exempt from the final exam. Any student not taking the final exam will receive a score of zero for the final exam.

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 210

**Title:**Mathematics for Elementary Teachers I***Number:**MATH 210**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on math placement test

### Description:

This is the first of a two-course sequence for prospective teachers of elementary and middle school mathematics. The focus of this course is an in-depth investigation of the mathematical principles and concepts encountered in grades K-8. Topics include set theory, numeration systems, number sense, critical thinking, and problem-solving strategies. The use of appropriate techniques and tools, such as calculators, computers and manipulatives, will be integrated throughout the course in order to enhance the depth of understanding. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Apply set theory concepts.
- Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems.
- Demonstrate an understanding for whole number, integer, fraction, and decimal operations.
- Explain whole number, integer, fraction, and decimal algorithms.
- Demonstrate the use of factors, multiples, and prime factorization to solve problems.
- Use strategies of estimation to judge the reasonableness of results.
- Demonstrate the use of the place-value structure of the base-ten number system.
- Describe mathematical relationships and functions with tables, graphs, and rules.
- Apply ratios, proportions, and percents in problem solving.
- Describe how various cultures have impacted the historical development of mathematics.
- Identify characteristics of functions.

### Content Outline and Competencies:

I. Set Theory A. Determine if two sets are equal or equivalent. B. Write the subsets and proper subsets of a given set. C. Find the intersection of two sets. D. Find the union of two sets. E. Find the complement of a set. F. Use Venn diagrams to determine the validity of a set statement. G. Solve applications using Venn Diagrams. II. Whole Numbers A. Use the definitions of whole number operations to explain the elementary processes of addition, subtraction, multiplication, and division. B. Identify the properties of whole number addition and multiplication, such as closure, commutativity, associativity, distributive property, and identity element. C. Model situations that involve whole numbers using objects, pictures, and symbols. D. Estimate the results of whole number calculations. E. Use a variety of problem solving strategies and critical thinking skills with applications involving whole numbers. F. Apply the definition and properties of exponents to whole numbers. G. Use the correct order of operations when evaluating expressions. III. Integers A. Use the definitions of integer operations to explain the processes of addition, subtraction, multiplication, and division. B. Identify the properties of integer addition such as closure, commutativity, associativity, identity element, and additive inverse. C. Identify the properties of integer multiplication such as closure, commutativity, associativity, distributive property, zero multiplication, and identity element. D. Demonstrate operations on integers using a variety of manipulatives. E. Use a variety of problem solving strategies and critical thinking skills with applications involving integers. IV. Number Theory A. Use divisibility tests to determine if a given number is divisible by another. B. Classify numbers as prime or composite or neither. C. Apply the Fundamental Theorem of Arithmetic. D. Use the Sieve of Eratosthenes to find the primes less than 100. E. Find the greatest common divisor and the least common multiple of numbers using a variety of methods. V. Rational Numbers A. Write fractions in simplest form. B. Determine if fractions are equivalent. C. Arrange a set of fractions in numerical order. D. Use the definitions and properties of addition, subtraction, multiplication, and division of fractions. E. Express ratios as fractions in simplest forom. F. Solve for the missing term of a proportion. G. Demonstrate operations on fractions using a variety of manipulatives. H. Use a variety of problem solving strategies and critical thinking skills with applications involving fractions. VI. Decimal Numbers A. Write decimal numbers in expanded form. B. Convert from standard decimal notation to scientific notation and vice versa. C. Arrange decimal numbers in numerical order. D. Use standard algorithms to add, subtract, multiply, and divide decimal numbers. E. Round decimal numbers to a specified place value. F. Convert a fraction to a decimal number. G. Convert repeating decimal numbers and terminating decimal numbers to fractions. H. Convert numbers in percent form to fractional or decimal form and vice versa. I. Use a variety of problem solving strategies and critical thinking skills with decimal and percent applications. VII. Numeration Systems A. Convert Roman numerals to Hindu-Arabic numerals and vice versa. B. Convert Egyptian numerals to Hindu-Arabic numerals and vice versa. C. Convert Babylonian numerals to Hindu-Arabic numerals and vice versa. D. Convert Mayan numerals to Hindu-Arabic numerals and vice versa. E. Write Hindu-Arabic numerals in expanded form. F. Convert numerals from one base system to another. G. Trace the historical development of the Hindu-Arabic number system. VIII. Functions and Relations A. Identify relations as functions. B. Identify the domain and range of functions.

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers, and/or Unit Projects 40%-80% of grade Homework, Quizzes, and/or Small Projects 0%-50% of grade Final Exam 10%-40% of grade Grade Criteria: A = 90 – 100% B = 80 – 89% C = 70 – 79% D = 60 – 69% F = 0 – 59% The final exam must count at least as much as any unit exam, unit paper or unit project. At the instructor’s discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 212

**Title:**Math for Elementary Teachers II***Number:**MATH 212**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 210 with a grade of "C" or higher or department approval

### Description:

This is the second of a two-course sequence for prospective teachers of elementary/middle school mathematics. The focus of this course is an in-depth investigation of the mathematical principles and concepts encountered in grades K-8. Topics include probability, statistics, measurement, and shapes including congruency, similarity, and transformations. The use of appropriate techniques and tools, such as calculators, computers, and manipulatives, will be integrated throughout the course in order to enhance the depth of understanding. 3 hrs. lecture/wk. NOTE: the prerequisite of MATH 210 requires a grade of "C" or higher.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Demonstrate an understanding of elementary probability.
- Demonstrate an understanding of elementary statistics.
- Demonstrate an understanding of measurement systems and conversion of units.
- Demonstrate an understanding of the attributes of geometric shapes.
- Demonstrate an understanding of the relationship between geometric shapes through similarity, congruence, and constructions.
- Demonstrate an understanding of motion geometry.

### Content Outline and Competencies:

I. Probability A. Determine the probability of outcomes of simple experiments. B. Determine the probability of outcomes of complex experiments. C. Determine the probability of events involving conditional probability. D. Determine the odds in favor of and against different events. E. Determine the expected value of an experiment. F. Solve problems involving the concepts of permutations and combinations. G. Distinguish between theoretical probability and experimental probability. II. Statistics A. Interpret statistical graphs such as line graphs, stem-and-leaf plots, pictographs, histograms, circle graphs, and box plots. B. Draw statistical graphs such as line graphs, stem-and-leaf plots, pictographs, histograms, circle graphs, and box plots. C. Determine measures of central tendency such as mean, median, mode, and their applications to box plots and percentiles. D. Determine measures of dispersion such as range, variance, and standard deviation. E. Describe the attributes of the normal distribution. F. Recognize misleading statistics. III. Measurement A. Calculate temperature conversions for Celsius and Fahrenheit. B. Measure items using both English and metric units. C. Convert measurements within the English system. D. Convert measurements within the metric system. E. Use dimensional analysis to convert measurements between the English system and the metric system. F. Calculate the perimeter and the area of polygons. G. Calculate the circumference and area of circles. H. Apply the Pythagorean Theorem to right triangles to find measurements. I. Calculate the surface area and volume of figures such as prisms, cylinders, pyramids, cones, and spheres. IV. Geometric Shapes A. Describe the attributes of different 2- and 3-dimensional shapes. B. Describe the attributes of different types of angles. C. Draw basic 2- and 3-dimensional shapes. D. Explain the relationships between angles formed by parallel lines intersected by transversals. E. Solve problems involving angle measurement. F. Describe the attributes of the Platonic solids. V. Relationships between Geometric Shapes A. Apply the concept of congruent triangles to constructions. B. Construct parallel lines, perpendicular bisectors and angle bisectors. C. Inscribe a regular polygon in a circle. D. Solve problems involving congruency properties. E. Solve problems involving similar figures. VI. Motion Geometry A. Find the image of geometrical shapes under various translations and rotations. B. Find the image of geometrical shapes under various reflections. C. Find the image of geometrical shapes under various size transformations with a given scale factor. D.Analyze the properties of tessellations.

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers, and/or Unit Projects 40-80% Homework, Quizzes, and/or Small Projects 0-50% Final Exam 10-40% **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a ‘C’ for the course. At the instructor’s discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 214

**Title:**Introduction to Teaching Math and Science I***Number:**MATH 214**Effective Term:**Spring 2015**Credit Hours:**1**Contact Hours:**1.25**Lecture Hours:**1.25

### Requirements:

**Prerequisites:** MATH 171 with a grade of "C" or higher OR appropriate score on the math placement test OR department approval

### Description:

This course allows math and science students to explore and develop an appreciation for teaching as a career. To support their learning, students will be introduced to the theory and practice that is necessary to design and deliver quality instruction. They will plan and implement lessons of an inquiry-based curriculum in an elementary classroom during the semester. MATH 214, ASTR 214, BIOL 214, CHEM 214, GEOS 214, PHYS 214 and PSCI 214 are the same course; enroll in only one. 1.25 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

Upon completion of this course, the student should be able to:

- Determine if teaching is a viable career path.
- Identify strategies for effective lesson planning and utilize these strategies to design and deliver inquiry-based lessons using the 5E Instructional Model.
- Demonstrate an awareness of personality and learning differences and discuss the implications for both teaching and learning.
- Use probing questions to elicit feedback to determine students' acquisition of knowledge.
- Revise lesson plans to reflect the needs of learners based on field experience gained in cooperation with a practicing classroom teacher.
- Research and identify relevant state and national teaching standards.
- Demonstrate proficiency in the use of technology for teaching, communicating, and collaborating.

### Content Outline and Competencies:

I. Teaching as a Career

A. Determine suitability/interest in teaching as a career through thoughtful self-reflection.

B. Explore pathways to a career in teaching.

C. Identify personal learning styles and discuss their implications for classroom interactions.

II. Strategies for Practical Lesson Design

A. Design and deliver inquiry-based hands-on lessons.

B. Write performance objectives for each lesson, including mathematics and/or science connections, and appropriate assessments for those objectives.

C. Use technology and the Internet to enhance classroom lessons, collaborate, and communicate.

III. Concepts and Components of Teaching Theory

A. Identify instructional strategies that meet the needs of diverse learners.

B. Distinguish between learner-centered and teacher-centered instructional strategies.

C. Discuss state and national science and mathematics standards and their implications for curriculum decisions.

D. Identify current issues in the theory and practice of teaching.

IV. Components of a Field Experience

A. Observe a math-science lesson taught by a cooperating teacher.

B. Interact with a population of diverse student learners in a school setting while teaching a lesson in an elementary school classroom.

C. Receive and synthesize feedback from a cooperating teacher as a peer and mentoring colleague in order to improve techniques.

### Method of Evaluation and Competencies:

Grading Scale:

90-100% = A

80-90% = B

75-79% = C

70-74% = D

0-69% = F

10-20% Active classroom participation

20-30% Lesson planning and associated activities

30-40% Completion of field experience and associated activities

20-25% Related assignments/homework

### Grade Criteria:

90-100% = A80-89% = B

75-79% = C

70-74% = D

0-69% = F

### Caveats:

To successfully complete the prerequisite(s) for this course, a student must earn at least a "C" in the prerequisite course(s) or earn an appropriate score on a placement exam. If a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course.

### Student Responsibilities:

### Disabilities:

# MATH 215

**Title:**Introduction to Teaching Math and Science II***Number:**MATH 215**Effective Term:**Spring 2015**Credit Hours:**1**Contact Hours:**1.25**Lecture Hours:**1.25

### Requirements:

**Prerequisites:** ASTR 214 or BIOL 214 or CHEM 214 or GEOS 214 or MATH 214 or PHYS 214 or PSCI 214 with a grade of C" or higher

### Description:

Students learn about the middle school environment and work on math and science inquiry-based lesson analysis, design and assessment. Student partners will plan and teach three inquiry-based lessons in a middle school. The course emphasizes writing 5E lesson plans with a focus on the importance of using appropriate questioning and assessment strategies throughout the lesson, as well as how to analyze and modify a lesson based on personal reflections and observer feedback. By the completion of the course, students should be able to reflect on their personal suitability/interest in teaching secondary math or science, and develop a feasible pathway to a career in teaching. MATH 215, ASTR 215, BIOL 215, CHEM 215, GEOS 215, PHYS 215 and PSCI 215 are the same course; enroll in only one. 1.25 hrs. lecture/wk.

### Course Fees:

### Textbooks:

http://bookstore.jccc.edu/### Supplies:

### Objectives

Upon completion of this course, students should be able to:

- Design inquiry-based middle school lesson plans, utilizing resources from exemplary inquiry-based science and mathematics lessons.
- Implement effective middle school teaching strategies based on the unique attributes of adolescents.
- Construct effective classroom learning activities using appropriate technology.
- Analyze data gained from pre- and post-assessments to evaluate student learning as a basis for revising lesson plans and teaching strategies.
- Employ techniques that offer educational equity among a population of diverse learners.
- Identify personal suitability/interest in teaching secondary math or science.

### Content Outline and Competencies:

I. Practical Lesson Design

A. Design inquiry-based lessons using the 5E Instructional Model.

B. Write measurable performance objectives for each lesson.

C. Develop applicable pre- and post-assessments for the performance objectives.

D. Analyze student data acquired through pre- and post-assessments to improve future lesson planning.

E. Incorporate technology into at least one lesson in a manner that encourages enhanced student interaction and learning.

II. Teaching Theory

A. Identify instructional approaches that meet the needs of diverse middle school learners.

B. Develop questioning strategies to effectively interact with students with varying abilities and learning styles in a middle school classroom.

C. Develop achievable solutions to preserve instructional equity in the classroom environment.

III. Field Experience

A. Reflect upon observations of lessons taught by an experienced math/science teacher.

B. Teach three inquiry-based lessons to a middle school math or science class.

C. Use probing questions to elicit feedback to determine students’ acquisition of knowledge.

D. Synthesize feedback from both mentor teachers and master teachers in order to improve teaching techniques.

E. Reflect on teaching experiences in order to enhance future classroom interactions.

### Method of Evaluation and Competencies:

15-25% Active classroom participation and attendance

20-30% Lesson planning and preparation

30-40% Field experiences, reflections and associated activities

10-20% Other assignments

100% Total

### Grade Criteria:

90 – 100% = A80 – 89% = B

75 – 79% = C

70 – 74% = D

0 – 69% = F

### Caveats:

To successfully complete the prerequisite(s) for this course, a student must earn at least a “C” in the prerequisite course(s). If a student is found not to have successfully fulfilled the prerequisite(s) for this course, the student will be dropped from the course.

### Student Responsibilities:

### Disabilities:

# MATH 225

**Title:**Mathematics as a Decision Making Tool***Number:**MATH 225**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

The focus of this course is to develop the quantitative skills and reasoning ability necessary to help students read critically and make decisions in our technical information society. A project tying this course to the student's own interest is a course requirement. Major topics include collecting and describing data, inferential statistics and probability, geometric similarity, geometric growth, symmetry and patterns. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Determine appropriate methods of collecting data.
- Describe and analyze data with the use of technology.
- Utilize principles of probability to predict outcomes.
- Recognize and describe patterns and symmetry found in nature.
- Apply concepts of geometric similarity to analyze size.
- Analyze mathematical models of population growth.
- Demonstrate knowledge of mathematics applied to another discipline.

### Content Outline and Competencies:

I. Data collection A. Describe characteristics of populations and samples. B. Examine methods of sampling, explaining sources of bias in these methods. C. Examine methods of experimentation, identifying sources of confounding in experiments. II. Descriptive statistics A. Describe data with graphical methods including histograms, box plots, scatterplots and regression lines. B. Describe data with numerical methods including measures of central tendency and measures of spread. C. Analyze data using a statistical package on a graphics calculator or a computer. III. Probability and inferential statistics A. Describe sample spaces for random experiments. B. Apply counting techniques to determine the number of possible outcomes of an experiment. C. Calculate the probability of a given event. D. Interpret features of the normal distribution including mean, standard deviation, and confidence intervals. IV. Patterns and symmetry A. Use geometric similarity to assess and interpret the physical limitations of size. B. Identify scaling factors relating to geometrically similar objects. C. Convert between different units of measure in U.S. Customary and Metric system. D. Recognize the golden ratio in geometric applications. E. Identify types of rigid motion such as rotation, reflection, and translation. F. Identify terms of the Fibonacci sequence from patterns found in nature. G. Apply concepts of arithmetic and geometric growth to financial and biological population models.

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 231

**Title:**Business and Applied Calculus I***Number:**MATH 231**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 171 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This is the first course in calculus as it applies to business; the social, behavioral, and biomedical sciences; and other fields. Concepts include measuring the slope of a curve, writing equations of tangent lines, finding maximum and minimum points, determining the rate of change of a function, and measuring the area under a curve. Algebraic skills and application problems are stressed. Specific calculus topics include finding limits, differentiation of algebraic, exponential and logarithmic functions, and integration of algebraic and exponential functions. Trigonometry (MATH 172) can be taken concurrently with MATH 231 for those students planning to enroll in MATH 232 in subsequent semesters. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Evaluate limits of functions using graphs, tables and algebraic methods.
- Demonstrate the use of limits to determine continuity of a function at a point.
- Determine differentiability of a function at a point using limits and graphs.
- Demonstrate the use of the limit definition to find the derivative.
- Differentiate algebraic, exponential and logarithmic functions.
- Produce equations of tangent lines.
- Demonstrate the use of derivatives to describe the behavior of a function.
- Apply derivatives in applications including economics, physics and social sciences.
- Antidifferentiate algebraic and exponential functions.
- Apply the Fundamental Theorem of Calculus to find the area under a curve and between two curves.

### Content Outline and Competencies:

I. Demonstrate a knowledge of limits A. Evaluating limits. 1. Evaluate a limit at a point using algebraic techniques or a table. 2. Evaluate a limit of a function at infinity using algebraic techniques or a table. 3. Evaluate a limit using a graph. 4. Evaluate left and right hand limits using algebraic techniques or a graph. B. Use of limits 1. Use of the limit to determine continuity of a function at a point. 2. Use a limit to determine differentiability of a function. 3. Use the limit definition of the derivative to determine differentiability of a function and to find the derivative of a function. II. Demonstrate a knowledge of derivatives A. Finding and estimating derivatives. 1. Find the derivatives of algebraic functions using the power rule, product rule, quotient rule and chain rule. 2. Find the derivatives of natural exponential and logarithmic functions. 3. Find the derivatives using implicit differentiation. 4. Use a graph to estimate the intervals over which the first derivative is positive or negative. 5. Use a graph to estimate the intervals over which the second derivative is positive or negative. 6. Find the equation of a tangent line to a curve at a given point. III. Using derivatives A. Apply derivative techniques to curve sketching 1. Using the first derivative, find critical points. 2. Determine the behavior of a function using the first derivative. 3. Using the second derivative, find inflection points. 4. Determine the concavity of a function using the second derivative. 5. Sketch a function using information gathered from the first and second derivatives. B. Apply derivative techniques to physical, economics and social sciences problems 1. Use derivatives to predict rates of change. 2. Use derivatives to determine the maxima/minima (optimization). 3. Use derivatives to determine outcomes in related rates problems. 4. Use derivatives to find and explain rates of change for position functions, including the relationship between position, velocity and acceleration. 5. Find extrema of functions with restricted domains. IV. Finding integrals A. Identify the antiderivative for a given function using elementary techniques. B. Identify the antiderivative for a given function using u-substitution. C. Apply the Fundamental Theorem of Calculus. 1. Evaluate a definite integral using elementary techniques. 2. Evaluate a definite integral using u-substition. 3. Calculate the area between two curves.

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 231H

No information found.# MATH 232

**Title:**Business and Applied Calculus II***Number:**MATH 232**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 231 and either MATH 172 or MATH 173 with a grade of "C" or higher or appropriate score on the math placement test

### Description:

This is the second course in a two-semester series on calculus that covers five techniques of integration, differentiation and integration of trigonometric functions, differential equations, and functions of several variables as applied to business, statistics, biology and the social sciences. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Differentiate trigonometric and multivariable functions.
- Integrate trigonometric and multivariable functions.
- Solve differential equations.
- Use calculus to solve probability problems.
- Use calculus to solve business application problems, e.g., Cobb-Douglas production function.

### Content Outline and Competencies:

I. Additional Integration Techniques A. Calculate definite and indefinite integrals using integration by parts. B. Calculate definite and indefinite integrals using the Integration Tables. C. Determine value of definite integrals using numerical integration. D. Determine whether improper integrals converge. E. Apply l’Hôpital’s Rule to find limits. II. Multivariable Calculus A. Discover the need for and the use of functions of several variables. B. Discover how to compute the first and second partial derivatives of functions of several variables. C. Compute the value of double integrals. D. Locate the coordinates of any relative extrema of a function of two variables. E. Utilize Lagrange Multipliers to compute the maximum or minimum of a function subject to constraints. F. Find the best fitting line through three points using the method of least squares. (Optional) G. Use total differentials to obtain an approximation of an expression. (Optional) III. Differential Equations A. Identify differential equations. B. Solve differential equations using the method of separation of variables. C. Calculate approximate solutions to differential equations using Euler’s method. (Optional) D. Determine the qualitative behavior of solutions to differential equations. (Optional) E. Apply differential equations to problems, e.g. logistic growth. IV. Calculus and Trigonometric Functions A. Review the sine and cosine functions. B. Discover the derivatives of the sine and cosine functions. C. Discover the integrals of the sine and cosine functions. D. Extend the derivatives and integrals of the sine and cosine functions to the other trigonometric functions. V. Calculus and Probability Theory A. Define discrete probability B. Identify continuous probability density functions. C. Compute expected value and variance of a continuous random variable and compare to discrete probability. D. Convert a normal distribution function to a standard normal distribution function. E. Use the standard normal distribution function to calculate the probabilities of a random variable.

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 232H

No information found.# MATH 241

**Title:**Calculus I***Number:**MATH 241**Effective Term:**Spring 2015**Credit Hours:**5**Contact Hours:**5**Lecture Hours:**5

### Requirements:

**Prerequisites:** Either (MATH 171 and MATH 172) or MATH 173 or an equivalent course with a grade of "C" or higher or an appropriate score on an placement test

### Description:

This is the first of a three-semester sequence on calculus designed for engineering, physics and math majors. Rates of change, areas and volumes will be studied. To accomplish this, the students will study and apply limits and continuity. Differentiation and integration of algebraic, trigonometric and transcendental functions will also be a major focus of this course. 5 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Evaluate the limits of functions.
- State whether a function is continuous or discontinuous based on both the graph and the definition of continuity.
- Use limits to describe instantaneous rate of change, the slope of the tangent line and the velocity and acceleration of a moving particle.
- Differentiate algebraic, trigonometric, and transcendental functions explicitly and, where appropriate, implicitly.
- Use derivatives for curve sketching.
- Use and interpret the derivatives of functions to solve problems from a variety of fields, including physics and geometry.
- Integrate algebraic, trigonometric, and transcendental functions.
- Compute definite integrals using the Fundamental Theorem of Calculus.
- Integrate using numerical techniques, substitution, and parts.
- Use integration results to calculate areas, volumes, and mean values.

### Content Outline and Competencies:

I. Using Limits A. Evaluation of limits 1. Evaluate the limit of a function at a point both algebraically and graphically. 2. Evaluate the limit of a function at infinity both algebraically and graphically. 3. Use the definition of a limit to verify a value of the limit of a function. B. Use of limits 1. Use the limit to determine the continuity of a function. (KCOG) 2. Use the limit to determine differentiability of a function. (KCOG) 3. Apply the Intermediate Value Theorem. (KCOG) C. Limiting process 1. Use the limiting process to find the derivative of a function. (KCOG) II. Finding Derivatives A. Find derivatives involving powers, exponents, and sums. (KCOG) B. Find derivatives involving products and quotients. (KCOG) C. Find derivatives involving the chain rule. (KCOG) D. Find derivatives involving exponential and logarithmic functions. (KCOG) E. Find derivatives involving trigonometric (KCOG) and inverse trigonometric functions. F. Find derivatives involving implicit differentiation. (KCOG) III. Using Derivatives A. Curve sketching 1. Use the first derivative to find critical points. (KCOG) 2. Apply the Mean-Value Theorem for derivatives. (KCOG) 3. Determine the behavior of a function using the first derivative. (KCOG) 4. Use the second derivative to find inflection points. (KCOG) 5. Determine the concavity of a function using the second derivative. (KCOG) 6. Sketch the graph of the function using information gathered from the first and second derivatives. (KCOG) 7. Interpret graphs of functions. (KCOG) B. Applications of the derivative 1. Use the derivative to find velocity, acceleration, and other rates of change. (KCOG) 2. Use the derivative to find a tangent line to a curve at a given point. (KCOG) 3. Solve related rates problems. (KCOG) 4. Use optimization techniques in economics, the physical sciences, and geometry. (KCOG) 5. Use differentials to estimate change. (KCOG) 6. Use Newton’s Method. (KCOG) IV. Finding Integrals A. Find area using Riemann sums. (KCOG) B. Express the limit of a Riemann sum as a definite integral. (KCOG) C. Evaluate the definite integral using geometry. (KCOG) D. Approximate definite integral using the Trapezoid Rule and Simpson’s Rule. (KCOG) E. Evaluate definite integrals using the Fundamental Theorem of Calculus. (KCOG) F. Integrate algebraic, natural exponential, natural logarithm, trigonometric, (KCOG) and inverse trigonometric functions. G. Integrate indefinite integrals. (KCOG) H. Integrate by substitution. (KCOG) I. Integrate by parts. V. Using the Integral A. Apply the Mean-Value Theorem for Integrals. (KCOG) B. Calculate the area between curves using integration. C. Calculate the volume of a solid of revolution by the disk method. D. Calculate the volume of a solid of revolution by the washer method. E. Calculate the volume of a solid of revolution by the cylindrical shells method. F. Calculate the arc length and surface area of revolution using integration.

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

- To successfully complete the pre-requisite(s) for this course, a student must earn at least a "C" in the pre-requisite(s) or earn an appropriate score on a placement exam. If a student is found not to have successfully fulfilled the pre-requisite(s) for this course, the student will be dropped from the course.

### Student Responsibilities:

### Disabilities:

# MATH 241H

No information found.# MATH 242

**Title:**Calculus II***Number:**MATH 242**Effective Term:**Spring 2015**Credit Hours:**5**Contact Hours:**5**Lecture Hours:**5

### Requirements:

**Prerequisites:** MATH 237 or MATH 241 or an equivalent course with a grade of "C" or higher

### Description:

This is the second course of a three-semester sequence on calculus. The emphasis will be an analytic, numerical and graphical approach to techniques of integration, and infinite series, including scientific applications. 5 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Identify and use techniques necessary for integration.
- Use infinite series to approximate functions.
- Apply techniques of differential and integral calculus to parametric and polar equations.
- Use calculus to model and solve scientific applications.

### Content Outline and Competencies:

I. Inverse Trigonometric Functions A. Find derivatives involving inverse trigonometric functions. B. Find antiderivatives involving inverse trigonometric functions. II. Techniques of Integration A. Evaluate an integral using integration by parts. B. Evaluate an integral using the method of partial fractions. C. Evaluate an integral which involves powers of trigonometric functions. D. Evaluate an integral by using trigonometric substitutions. E. Evaluate an integral by using integral tables. F. Apply L'Hopital's Rule to evaluate limits involving indeterminate forms. G. Determine whether an improper integral converges or diverges. H. Test for the convergence or divergence of an improper integral using an appropriate test. I. Evaluate a convergent improper integral. III. Infinite Sequences and Series A. Determine whether an infinite sequence converges or diverges. B. Find the limit of a convergent sequence. C. Identify geometric series, telescoping series, harmonic series, p-series, alternating series, and power series. D. Determine whether an infinite series converges or diverges. E. Test for convergence or divergence of an infinite series using an appropriate test. F. Determine whether an infinite series converges absolutely or conditionally. G. Find the radius and interval of convergence for a power series. H. Write a power series which represents a function. I. Write a Taylor polynomial which represents a function. J. Calculate the error in approximating a function with an infinite series. IV. Parametric and Polar Equations A. Differentiate parametric equations. B. Calculate the length of a smooth parametrized curve. C. Calculate the surface area from a parametrized curve. D. Graph polar equations. E. Convert from rectangular to polar coordinates and vice-versa. F. Differentiate polar equations. G. Integrate polar equations. H. Calculate the area in the plane using polar coordinates. I. Calculate the area between two curves using polar coordinates. J. Calculate the length of a polar curve. K. Calculate the surface area of a surface of revolution using polar coordinates. V. Applications of Definite Integrals A. Calculate area between curves using integration. B. Calculate the volume of a solid of revolution using appropriate methods, including the disk, washer, or shell method. C. Calculate the arc length and surface area of revolution using integration. D. Calculate work, moments and centers of mass. E. Calculate fluid pressures and forces.

### Method of Evaluation and Competencies:

Unit Exams, Unit Papers and/or Unit Projects 40% - 80% Homework, Quizzes and/or Small Projects 0% - 50% Final Exam** 10% - 40% Grading scale: 90 - 100% A 80 - 89% B 70 - 79% C 60 - 69% D 0 - 59% F **The final exam must count at least as much as any unit exam, unit paper or unit project. In any course where unit exams are not proctored, the instructor may require that the student score at least a 70% on the final exam to earn a "C" for the course. At the instructor's discretion, the grade on all or any part of the final exam may replace any lower test score.

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 242H

No information found.# MATH 243

**Title:**Calculus III***Number:**MATH 243**Effective Term:**Spring 2015**Credit Hours:**5**Contact Hours:**5**Lecture Hours:**5

### Requirements:

**Prerequisites:** MATH 242 with a grade of "C" or higher or an equivalent course with a grade of "C" or higher

### Description:

This is the third course in a three-semester sequence on analytic geometry and calculus. Topics include vector-valued functions, functions of several variables, multiple integration, and vector analysis. 5 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Use vectors in the plane and in space.
- Analyze surfaces in space.
- Differentiate multivariable functions and vector-valued functions.
- Integrate multivariable functions and vector-valued functions.
- Analyze vector fields.
- Utilize the calculus of multivariable functions and vector calculus to solve applied problems.

### Content Outline and Competencies:

I. Vectors in the Plane and in Space A. Determine the components of a vector in the plane and in space and illustrate geometrically. B. Apply vector operations and properties and interpret them geometrically. C. Calculate the dot product to determine the angle between two vectors. D. Find the magnitude and direction of a resultant vector and illustrate geometrically. E. Determine a vector passing through two points. F. Determine whether two vectors are orthogonal G. Determine whether two vectors are parallel. H. Determine the projection of one vector onto another vector. I. Calculate the cross product for two vectors and interpret geometrically. J. Write the parametric equations for a line in space. K. Determine the equation for a plane. II. Surfaces in Space A. Identify equations of right cylinders and sketch graphs of these cylinders. B. Identify equations of quadric surfaces and sketch graphs of quadric surfaces. III. Vector-valued Functions A. Define vector-valued functions. B. Identify the space curve determined by a vector-valued function. C. Define differentiation and integration of vector-valued functions. D. Calculate derivatives of vector-valued functions. E. Calculate integrals of vector-valued functions. F. Identify intervals on which a parametrically defined curve is smooth. G. For a given position vector, calculate the velocity and acceleration vectors. H. Determine the principal unit tangent, unit normal and unit binormal vectors to a given curve at a given point. I. Determine the tangential and normal components of an acceleration vector. J. Calculate the arc length of a curve. K. Calculate the curvature of a curve. L. Calculate the torsion of a curve. M. Use position, velocity, acceleration, speed, and/or tangential and normal components of acceleration to analyze motion along a curve. IV. Functions of Several Variables A. Determine the domain of functions of several variables. B. Graph functions of two variables. C. Sketch level curves and level surfaces of multivariable functions. D. Define limits and continuity for multivariable functions. E. Determine limits or show that the limit does not exist for multivariable functions. F. Determine regions on which a multivariable function is continuous. G. Define partial derivatives. H. Calculate and interpret partial derivatives. I. Compute differentials. J. Define differentiability of multivariable functions. K. State the chain rule. L. Apply chain rule for multivariable functions. M. Compute and interpret directional derivatives. N. Calculate and interpret gradients. O. Find equations of tangent planes and normal lines to surfaces. P. Find critical points and classify as relative extrema or saddle points for functions of two variables. Q. Find extrema of functions of two variables. R. Solve applied optimization problems using multivariable functions. S. Utilize Lagrange multipliers to solve constrained optimization problems. V. Multiple Integration A. Define double and triple integrals. B. Set up and evaluate iterated multiple integrals in rectangular coordinates. C. Use polar coordinates to evaluate double integrals. D. Use cylindrical and spherical coordinates to evaluate triple integrals. (Note: Students’ prior familiarity with cylindrical and spherical coordinates should not be assumed.) E. Use double integrals to compute area in the plane. F. Use double and triple integrals to calculate volume. G. Use double integrals to compute surface area. H. Use double and triple integrals in applications including calculation of mass, center of mass, and moments of inertia. I. Implement a change of variables to evaluate a double integral. VI. Vector Analysis A. Define vector fields. B. Calculate divergence and curl for a vector field. C. Define conservative vector field. D. Determine whether a vector field is conservative or not. E. Calculate the potential function for a conservative vector field. F. Define line integrals. G. Evaluate a line integral over a given curve. H. Use line integrals to calculate work, circulation, and flow. I. Calculate flux of a vector field across a curve. J. Define path independence. K. Determine if a line integral is path independent. L. Apply the Fundamental Theorem of Line Integrals. M. Apply Green’s Theorem where appropriate. N. Define surface integrals. O. Evaluate surface integrals. P. Calculate flux of a vector field through a surface. Q. Parameterize a surface. R. Evaluate surface integrals over parameterized surfaces. S. Apply the Divergence Theorem where appropriate. T. Apply Stokes’s Theorem where appropriate.

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 243H

No information found.# MATH 246

**Title:**Elementary Linear Algebra***Number:**MATH 246**Effective Term:**Spring 2015**Credit Hours:**3**Contact Hours:**3**Lecture Hours:**3

### Requirements:

**Prerequisites:** MATH 242 or an equivalent course with a grade of "C" or higher

### Description:

This sophomore-level introduction to linear algebra uses a matrix-oriented approach, with an emphasis on problem solving and applications. The course focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, orthogonality and vector spaces. Students are expected to use technology for matrix operations. 3 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Solve systems of linear equations using Gaussian methods, matrices, and vectors.
- Determine how the functional properties of linear transformations correspond to the properties of matrix multiplication.
- Perform basic operations involving determinants.
- Determine the solution set of a homogeneous system of linear equations, the span of a finite set of vectors, the null space and range of a linear transformation; apply their properties.
- Calculate eigenvalues and eigenvectors; use their properties to describe diagonalizable matrices.
- Construct a basis of perpendicular eigenvectors for a given matrix or linear transformation.
- Extend previous concrete concepts to the more general context of an abstract vector space.

### Content Outline and Competencies:

I. Matrices, Vectors, and Systems of Linear Equations A. Define matrices and vectors. B. Manipulate linear combinations, matrix-vector products, and special matrices. C. Solve systems of linear equations. D. Perform Gaussian elimination. E. Find the span of a set of vectors. F. Determine linear dependence and independence. II. Matrices and Linear Transformations A. Perform matrix multiplication. B. Construct inverse matrices with elementary matrices. C. Find the inverse of a matrix. D. Describe the relationship between linear transformations and matrices. E. Determine the composition and invertibility of linear transformations. III. Determinants A. Perform cofactor expansions. B. Use the properties of determinants. IV. Subspaces and Their Properties A. Define subspaces associated with matrices. B. Construct a basis for a subspace. C. Determine the dimension of a subspace. D. Determine the dimension of subspace associated with a matrix. E. Perform rotation of coordinate systems. F. Construct matrix representations of linear operators. V. Eigenvalues, Eigenvectors, and Diagonalization A. Determine eigenvalues and eigenvectors. B. Construct the characteristic polynomial of a matrix. C. Perform the diagonalization of matrices. D. Perform the diagonalization of linear operators. VI. Orthogonality A. Describe vectors with geometry. B.Construct orthonormal vectors. C. Perform least-squares approximation. D. Produce orthogonal projection matrices. E. Create orthogonal matrices and operators. F. Formulate symmetric matrices. VII. Vector Spaces A. Define vector spaces and their subspaces. B. Determine dimension and isomorphism. C. Develop linear transformations; find matrix representations. D. Define inner product spaces. ADDITIONAL TOPICS OF INTEREST (time permitting) Systems of linear equations in applications Matrix multiplication in applications LU decomposition of a matrix Eigenvalues in applications Singular value decomposition of a matrix Rotations of R3 in computer graphics applications

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 246H

No information found.# MATH 254

**Title:**Differential Equations***Number:**MATH 254**Effective Term:**Spring 2015**Credit Hours:**4**Contact Hours:**4**Lecture Hours:**4

### Requirements:

**Prerequisites:** MATH 243 with a grade of "C" or higher or an equivalent course with a grade of "C" or higher

### Description:

This course will cover standard types of equations that involve rates of change. In particular, this is an introductory course in equations that involve ordinary derivatives. Both qualitative and quantitative approaches will be used. Standard types and methods will be covered, including Laplace transforms, infinite series, and numerical methods. Basic linear algebra will be developed to solve systems of differential equations. 4 hrs. lecture/wk.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Calculate solutions to first-order ordinary differential equations.
- Calculate solutions to higher-order ordinary differential equations.
- Calculate solutions to differential equations using infinite series.
- Utilize the concepts of vector space, basis, and dimension in solving systems of equations.
- Calculate eigenvalues and eigenvectors.
- Calculate solutions to systems of first-order ordinary differential equations.
- Utilize the concepts of differential-equation theory in applied modeling activities.

### Content Outline and Competencies:

I. Basic concepts A. Define ordinary versus partial derivatives. B. Discriminate between ordinary and partial differential equations. C. Determine the order of a differential equation. D. Discriminate between linear and nonlinear differential equations. E. Define a solution to a differential equation. F. Utilize direction fields in interpreting solutions of differential equations. II. First-Order Differential Equations A. Utilize the existence and uniqueness theorem for first-order differential equations. B. Calculate solutions to linear first-order ordinary differential equations. C. Utilize the existence and uniqueness theorem for first-order linear differential equations. D. Calculate solutions to separable first-order ordinary differential equations. E. Utilize first-order ordinary differential equations in modeling activities. III. Numerical Methods A. Utilize Euler’s Method to approximate initial-value problem solutions. B. Utilize improvements on Euler’s Method to approximate initial-value problem solutions. C. Utilize the Runge-Kutta methods to approximate initial-value problem solutions. IV. Linear Algebra A. Perform elimination using pivots for a given system of equations. B. Define vector spaces and subspaces. C. Define linear independence and dependence. D. Define a basis for a vector space or subspace. E. Define the dimension for a vector space. F. Calculate the eigenvalues and associated eigenvectors for a given matrix. V. Systems of Differential Equations A. Define higher-order linear differential equations. B. Transform higher-order linear differential equations to systems of first-order differential equations. C. Utilize the eigenvalue-eigenvector method in solving systems of homogeneous linear differential equations with constant coefficients. D. Determine the linear dependence or independence of a set of solutions. E. Calculate solutions given real distinct, real repeated, and complex roots of the characteristic equation. F. Define fundamental solutions of linear homogeneous equations. G. Classify solutions of second-order linear homogeneous equations as to underdamped, critically damped, or overdamped. H. Construct the general solution of nonhomogeneous linear systems utilizing the method of variation of parameters. I. Analyze the stability of equilibrium solutions. J. Utilize the phase plane in solving systems. K. Analyze the solutions of almost linear systems. L. Utilize systems of differential equations in modeling activities. VI. Series Solution Techniques A. Review power series. B. Construct series solutions near an ordinary point. C. Construct solutions for Euler equations VII. The Laplace Transform A. Define the Laplace transform. B. Utilize Laplace transforms in solving initial-value problems. C. Solve initial-value problems involving step functions. D. Solve initial-value problems involving discontinuous forcing functions. E. Solve initial-value problems involving impulse functions. F. Utilize the Convolution theorem

### Method of Evaluation and Competencies:

### Grade Criteria:

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 254H

No information found.# MATH 285

**Title:**Statistics for Business***Number:**MATH 285**Effective Term:**Spring 2015**Credit Hours:**4**Contact Hours:**4**Lecture Hours:**4

### Requirements:

**Prerequisites:** MATH 231 or MATH 241 or an equivalent course with a grade of "C" or higher Note: Students transferring MATH 285 to the University of Kansas must have CIS 201 as a corequisite

### Description:

This is a beginning course in calculus-based statistical analysis with an emphasis on applications to business. The skill of making sense of raw data is important, and includes constructing graphical representations of data, developing models for making predictions, performing tests to determine significant change and finding intervals for population values. Students will learn the basics of descriptive statistics, probability, sampling, confidence intervals, hypothesis testing, linear regression, and an introduction to quality control. Students must have an understanding of calculus concepts in order to successfully complete this course. 4 hrs. lecture/wk. Students transferring MATH 285 to KU must have CIS 201 as a corequisite.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

Upon successful completion of this course, the student should be able to:

- Organize data using statistically valid methods.
- Use a computer to perform statistical calculations; analyze the statistics in computer printouts.
- Describe data using measures of central tendency and measures of dispersion.
- Use sample spaces, formulas, and the laws of probability to solve problems.
- Identify and construct probability distributions; calculate expected value and variance for a probability distribution.
- Construct confidence intervals; explain the meaning in terms of the problem.
- Perform hypothesis tests; explain the conclusion using the language of statistics.
- Perform and use linear regression.
- Apply statistical reasoning to business applications.

### Content Outline and Competencies:

I. Basic Descriptive Statistics: Organizing and describing data

A. For a given set of data, draw a dotplot, histogram, stem-and-leaf

diagram, and a boxplot.

B. Describe the general shape of data, skewed left, skewed right, or

symmetric.

C. Calculate the measures of central tendency including mean, median,

and mode.

D. Calculate the measures of dispersion including range, variance, and

standard deviation; explain the meaning of standard deviation as it

relates to a problem.

E. Use a computer package to enter data and analyze results.

II. Introduction to Probability: Finding the theoretical probability of

an event

A. Construct the sample space for an experiment.

B. Use the Fundamental Counting Rule to predict the number of things in

a sample space.

C. Determine whether or not two events are mutually exclusive.

D. Determine whether or not two events are independent.

E. Calculate conditional probabilities.

III. Random Variables and Probability Density Functions (p.d.f.)

A. List all possible values of a discrete random variable along with its

probabilities.

B. Use calculus to generate a continuous cumulative density function (c.d.f.)

C. Determine the expected value and the variance of a discrete p.d.f.

D. Determine the expected value and the variance of a continuous

p.d.f.

E. Determine the covariance and correlation of a discrete joint p.d.f.

IV. Special Probability Distributions: Using statistics in the “real world”

A. Use the Binomial distribution to solve problems with two outcomes and independent events.

B. Use the Hypergeometric distribution to solve problems involving sampling without replacement.

C. Use the Poisson distribution to solve problems involving occurrences of events that happen randomly over time, such as the number of customers entering a store.

D. Use the Exponential distribution to solve problems describing the time between events such as the predicted time between customers.

E. Use the Normal distribution to solve problems that are normally distributed.

V. Random Sampling and Sampling Theory: Generating distributions for

sample means

A. Calculate the mean for a distribution of sample means.

B. Calculate the standard deviation for a distribution of sample

means.

C. Perform a normal probability plot; describe the shape of the

population based on the plot.

D. Analyze the Central Limit Theorem.

VI. Estimating the Mean: Using statistics to determine averages and

deviations of a population

A. Construct a confidence interval for a population mean; explain the meaning in terms of a problem.

B. Construct a confidence interval for a population proportion;

explain the meaning in terms of a problem.

C. Construct a confidence interval for a population median.

D. Construct a confidence interval for a population standard deviation.

VII. Hypothesis Tests: Finding significance

A. Perform a hypothesis test for a population mean using a sample mean.

B. Perform a hypothesis test for a population proportion using a sample

proportion.

C. Perform a hypothesis test for two population means.

D. Perform a hypothesis test with more than two categories.

E. Explain Type I and Type II errors with respect to a problem.

VIII. Linear Regression: Making predictions with linear data

A. Calculate a linear regression equation; explain the equation in

terms of the problem.

B. Use a linear regression equation to make predictions about data.

C. Calculate the coefficient of determination for a linear regression

equation; use the coefficient of determination to explain the strength of

the regression equation.

IX. Quality Control: Using statistics in the work setting

A. Provide a brief history of quality control including a discussion of

W. Edwards Deming.

B. Construct basic control charts using the distributions learned in

the course.

### Method of Evaluation and Competencies:

Evaluation of student mastery of course competencies will be accomplished using the following methods:

Unit Exams, Unit Papers and/or Unit Projects 40% - 80%

Homework, Quizzes and/or Small Projects 0% - 50%

Final Exam** 10% - 40%

**The final exam must count at least as much as any unit exam, unit paper

or unit project. In any course where unit exams are not proctored, the

instructor may require that the student score at least a 70% on the final

exam to earn a ‘C’ for the course. At the instructor's discretion,

the grade on all or any part of the final exam may replace any lower test

score.

### Grade Criteria:

90 – 100% = A80 – 89% = B

70 – 79% = C

60 – 69% = D

0 – 59 % = F

### Caveats:

### Student Responsibilities:

### Disabilities:

# MATH 292

**Title:**Special Topics:***Number:**MATH 292**Effective Term:**Spring 2015**Credit Hours:**1**Contact Hours:**1**Lecture Hours:**1

### Requirements:

**Prerequisites:** Department approval

### Description:

MATH 292 allows students to investigate in-depth a single theme or topic in mathematics. This may be accomplished by expanding upon a subject introduced in current course offerings or exploring a subject not addressed in the curriculum of the mathematics department. Special Topics may be repeated for credit but only on different topics. Total contact hours vary with topic.

### Course Fees:

None### Textbooks:

http://bookstore.jccc.edu/### Supplies:

Refer to the instructor's course syllabus for details about any supplies that may be required.### Objectives

- Perform computations or algorithms relevant to the Special Topic.
- Apply the Special Topic to real-world situations.
- Describe the theoretical structure behind the Special Topic.
- Demonstrate conceptual understanding of the Special Topic.
- Describe how the Special Topic relates to the broader study of mathematics.

### Content Outline and Competencies:

The content outline and competencies will vary, depending on the special topic being offered. The Special Topics course competencies must follow standard format for JCCC course outlines. The Special Topics proposer will submit competencies to the Mathematics Division Curriculum Committee for review and approval.

### Method of Evaluation and Competencies:

Methods will vary depending on the Special Topic. Homework 0 - 90% Projects 0 - 90% Tests 0 - 90% Final 10% - 50%