Math 115

Course coordinator: Todd Eisworth

Textbook: Precalculus, 4th edition.  by J. Douglas Faires and James DeFranza

The suggested problems listed below are essentially sample homework assignments that adequately address the topics that will be covered on the final exam. The specific problems you are assigned in class may vary from instructor to instructor, so the following should be considered only as a guide. It does, however, give you a sense of what sorts of problems we expect you to be able to master.

 Desired Outcomes

Learning Outcomes for Pre-Calculus (Math 115) at Ohio University (Version of 3-14-07)

A student successfully completing MATH 115 should be able to accomplish the following:

• Represent functions* verbally, numerically, graphically, and algebraically.
• View a function as a set of ordered pairs or a correspondence between two sets.
• Find the domain and range of functions*.
• Perform translations and dilations of functions*.
• Perform operations (addition, subtraction, multiplication, division, composition) with functions*.
• Solve equations, including application problems.
• Find inverses of functions* and relate the graph of a function to the graph of its inverse.
• Analyze the graph of a function* to answer questions about the function (such as intercepts, domain, range, intervals where the function is increasing or decreasing, possible algebraic definitions, etc.)
• Use functions* to model a variety of situations.
• Express angles in both degrees and radians.
• Define the six trigonometric functions in terms of right triangles and the unit circle.
• Solve right triangles, including application problems.
• Solve oblique triangles, including application problems.
• Algebraically manipulate trigonometric expressions using fundamental trigonometric identities.
• Determine the amplitude, period, and displacement of trigonometric functions.
• Solve trigonometric equations, including applications.
• Define inverse trigonometric functions and find their domains, ranges, and graphs.
• Be able to graph conics (parabolas, ellipses, and hyperbolas) given their equations (which may involve "completing the square" and putting the equation in standard form), as well as foci and any asymptotes.

* This course should consider the following types of functions:

• polynomial
• rational
• root/radical/power
• exponential and logarithmic
• trigonometric and inverse trigonometric
• piece-wise defined

The above is based on  http://regents.ohio.gov/transfer/tags/CourseDescriptions.htm with modifications tailored to our course.

Final Exam

The final exam for Math 115 is a common final, so all students will be taking the final exam at the same time.

The exam will be built from problems in the textbook. The vast majority of these will be of the "routine" variety, which the authors of the textbook classify as "roughly the first 70% of each homework assignment".  Regardless of difficulty, all problems will be taken directly from the textbook, although specific numbers may be changed.  The best way to prepare for this exam is to attend class and do the homework assigned by your instructor. 

Calculator Policy

The use of calculators has become a standard part of the pre-calculus and calculus experience, and we recognize and value the contributions to understanding that a properly used calculator can bring. With this in mind, we encourage the use of calculators and related technology as a means to attain understanding of the material. However, the use of calculators will not be permitted on the final exam for the course.  There are two main reasons for this.  The first of these is our commitment to academic integrity, as it has become increasingly easy to utilize calculators in an unethical manner, particularly in conjunction with resources available on the internet. The second reason is a commitment to fairness, for not all calculators are created equal. Requiring the TI-82 or TI-83 does little to help the student who comes to college equipped with a TI-92, and yet it is even more unfair to allow the use of such powerful calculators for those students able to afford them.  Regardless, it is important for you, the student, to remember that the calculator is intended to help you master the material and it is not meant to act as a "royal road" to mathematics.

Exam Conflicts

The university has several regulations governing final exams, and the Registrar's Office website contains the relevant information.

Specific policies governing combined exams include the following (taken from the Registrar's website):

If a combined sections examination conflicts with a regularly scheduled exam, the instructor of the combined sections examination will schedule an alternate time with those students affected by the conflict. When a student finds he/she has a conflict between two combined sections examinations, he/she will report to the instructor in charge of the first of the two as listed in the combined sections final examination schedule above before the opening of the examination period. This instructor will plan a special examination for the student. If a student has an additional conflict, he/she will report to the instructor in charge of the second of the two courses as listed in the combined sections final examination schedule above. This instructor will arrange for an examination in this course at another time during the examination period.

Formulas

The final exam for Math 115 is intended to apply uniformly across all sections of the course. With this in mind, we have decided that the "What do I need to know for Calculus?" section of the Math 263 Student Handbook should act as the standard for which formulas need to be memorized for the final exam, and which will be given.

A list of these formulas (in pdf format) is available here.

Samples

The following are intended as a guide only --- your actually final exam will be of the same format, but the specific topics covered and problems asked may be different.

Interpreting Your Grade

(adapted from "A miniature guide for those who teach on How to Improve Student Learning" by Dr. Richard Paul and Dr. Linda Elder)

A-level work

Excellent overall, no major weaknesses

1. A-level work demonstrates real achievement in grasping what mathematical thinking is, along with the clear development of the range of skills and abilities contained in the course learning objectives.

2. The work at the end of the course is, on the whole, clear precise, and well-reasoned, though there may be occasional lapses into weak reasoning.

3. Terms and notation are used effectively and accurately.

4. The work demonstrates a mind beginning to take charge of its own ideas, assumptions, inferences, and intellectual processes.

5. The A-level student usually analyzes issues clearly and precisely, usually formulates information clearly, usually distinguishes the relevant from the irrelevant, usually recognizes key questionable assumptions, usually clarifies key concepts effectively, typically uses language in keeping with educated usage, and shows a tendency to reason carefully from clearly stated premises.

6. A-level work displays excellent reasoning and problem-solving skills.

7. The A student's work is consistently at a high level of intellectual excellence.

B-level work

Demonstrates more strengths than weaknesses and is more consistent in high level performance than C-level work. It nevertheless has some distinctive weaknesses, though no major ones.

1. B-level work represents demonstrable achieving in grasping what mathematical thinking is, along with the clear demonstration of the range of skills and abilities contained in the course learning objectives.
2. The work at the end of the course is on the whole clear, precise, and well-reasoned, though with occasional lapses into weak reasoning.
3. Terms and notation are used effectively and accurately.
4. The work demonstrates a mind beginning to take charge of its own ideas, assumptions, inferences, and intellectual processes.
5. The B-level student often analyzes issues clearly and precisely, often formulates information clearly, usually distinguishes the relevant from the irrelevant, usually recognizes key questionable assumptions, usually clarifies key concepts effectively, typically uses language in keeping with educated usage, and shows a tendency to reason carefully from clearly stated premises.
6. B-level work displays good reasoning and problem-solving skills.

C-level work

Demonstrates more than a minimal level of skill, but it is also highly inconsistent with as many weaknesses as strengths.

1. C-level work illustrates some, but inconsistent, achievement in grasping what mathematical thinking is, along with an inconsistent demonstration of the range of skills and abilities contained in the course learning objectives.
2. The work at the end of the course shows some emerging mathematical thinking skills, but also pronounced weaknesses as well. Though some assignments are reasonably well done, others are poorly done; or at best are mediocre. There are more than occasional lapses into weak reasoning.
3. Terms and notation are sometimes used effectively, sometimes used inappropriately or ineffectively.
4. Only on occasion does C-level work display a mind taking charge of its own ideas, assumptions, inferences, and intellectual processes. Only occasionally does C-level work display display intellectual discipline and clarity.
5. The C-level student only occasionally analyzes issues clearly and precisely, formulates information clearly, distinguishes the relevant from the irrelevant, recognizes key questionable assumptions, clarifies key concepts, uses language in keeping with educated usage, reasons carefully from clearly stated premises, or recognizes important implications and consequences.
6. Sometimes the C-level student seems to be simply going through the motions of the assignment, carrying out the form without getting into the spirit of it.
7. On the whole, C-level work shows only modest and inconsistent reasoning and problem-solving skills, and sometimes displays weak reasoning and problem-solving skills.

D-level work

Demonstrates only a minimal level of understanding and skill.

1. D-level work shows only a minimal level of understanding of mathematical thinking, along with the development of some, but very little, of the range of skills and abilities listed in the course learning objectives.
2. The work at the end of the course on the whole shows only occasional mathematical thinking skills. Frequently, the work shows a pattern of illogical thinking and poor reasoning. Most assignments are poorly done, and there is little evidence that the student is reasoning through the assignment in a mathematical manner.
3. D-level work rarely shows any effort to take charge of ideas, assumptions, inferences, and intellectual processes.
4. In general, D-level work lacks discipline and clarity. The student rarely analyzes issues clearly and precisely, almost never formulates information clearly, rarely distinguishes the relevant from the irrelevant, almost never clarifies key concepts effectively, frequently fails to use language in keeping with educated usage, almost never reasons carefully from clearly stated premises, or recognizes important implications and consequences.
5. D-level work does not show good mathematical reasoning and problem-solving skills, and frequently displays poor reasoning and problem-solving skills.

F-level work

Demonstrates a consistent pattern of non-mathematical thinking

1. The student has not displayed any significant understanding of mathematical thinking, and has not demonstrated mastery of any of the skills and abilities listed in the course learning objectives.
2. The work at the end of the course is as vague, imprecise, and unreasoned as it was at the beginning of the course.
3. Little evidence that the student is genuinely engaged in the task of taking charge of his or her thinking; many assignments have been done without spending any significant effort on thinking his or her way through them, while others have not been done at all.
4. The student does not analyze issues clearly, does not formulate information clearly,  does not appear to distinguish between the relevant and the irrelevant, does not reason carefully from carefully stated premises, or trace implications and consequences.
5. The students work does not display discernable mathematical reasoning and problem-solving skills.