Prerequisites


Prerequisites for Calculus I at CMU

As stated in the CMU Bulletin, the prerequisite for Mth 132 is Mth 130 (Precalculus Mathematics) or equivalent.

Traditional high school mathematics programs always have a course equivalent to Precalculus Mathematics but the course is often given a different name. It might also be called Mathematical Analysis or it might be Trigonometry and College Algebra. The latter name is also common at community colleges. In a high school curriculum, this course is almost always a year long course. Math 130 is only one semester in length at CMU but trigonometry is treated separately here (in Mth 106) and is a prerequisite for Math 130 at CMU. Even though the word "calculus" is embedded in the name Precalculus, Mth 130 contains no actual calculus content.

You should know that the course you took is equivalent to Precalculus in the following cases.

  • If the school you attended offers a calculus course and the course you took was the immediate preceeding prerequisite course for calculus at that school.
  • If you have actually taken a calculus course and you were advised there that your prerequisite courses were sufficient.
  • If the school you attended did not offer a calculus course but you were specifically informed by your teacher that calculus would be the next course to take.

Who should take Calculus I

Adequately prepared students who enjoy the challenge of mathematics courses should consider Calculus I. It satisfies the requirement of Subgroup B of the University Program and is otherwise suitable as a general elective on most degree programs. If a grade of C or better is earned, it also satisfies the Mathematics Competency Requirement.

Calculus I is also a program requirement on a number of different academic majors, especially in those offered by departments within the College of Science and Technology. You should carefully examine the Bulletin's description of the major programs that are possibilities for you to see if Calculus I is a requirement. If so, completing Calculus I early leaves the door open to those program choices. If you think that graduate school is a possibility, you should examine some typical graduate programs in your field(s) of interest to see if calculus is a requirement. Sometimes this will be the case even when it is not required for an undergraduate degree in the same area.

Finally, Calculus I is a prerequisite for a many higher level mathematics courses and for a number of courses offered by other departments than mathematics. Thus, it is probably the elective of choice for a student with a good precalculus background who wants a mathematics course that would support many different future options. At the same time it is a course with much cultural and historical significance. Even so, there are other options for a mathematics elective that can as well or better serve the interests and needs of some students. If you think that you might be such a student consult the University Bulletin and a mathematics advisor.

Should you take Mth 130 before Calculus I?

The Mathematics Department web site now contains a brief (ten question) diagnostic test designed to provide some clues to any student perplexed about this question. It is a good idea to read the following discussion and also check out the description and use of that quiz at www.cst.cmich.edu/units/mth/advising/M132diag.htm

To make this decision you will need to carefully consider several features of your background.

What weight should the requirements of your planned major have in the decision about your entry course?

The short answer is, "very little". Depending upon the program you are beginning, you may receive a printed program suggesting Calculus I in a specific semester. You should follow that advice only if all the other placement advice supports that choice. The questions, "Should I take calculus?" and "When should I take calculus?" address very different issues. The description of the planned program addresses the first question. Keep in mind that attempting Calculus I before completing adequate preparation can result in a need to withdraw and may do more ultimate damage to your progress than taking an extra semester or two to become prepared.

Special circumstances

Here are some special circumstances that might make your decision about entry course more difficult. In any of these cases, there would be merit in discussing the matter with a mathematics advisor.

  • You have not taken any mathematics course for a number of years.
  • Your mathematics placement score is very high but your high school grades are low.
  • Your mathematics placement score is very low but your high school grades are high.
  • Your mathematics placement scores vary drastically from your verbal scores.
  • You studied mathematics outside of the United States.

An additional placement assessment

Additional calculus placement assessments can be obtained from a variety of sources. Here is one without a scoring scale but which helps identify the kinds of prerequisite competencies that are needed for good success in calculus.

This test is fairly difficult as a prerequisite test. However, it is also rather complete and would be useful in helping you identify weaknesses in your preparation. Calculus instructors regularly report that topics from this test are a cause for students performing poorly in Math 132.

The Adobe Acrobat Reader is required to view and print copies of these documents.

Prerequisite assessment test

Answers

Discussion of mathematics placement considerations

What was your most advanced previous mathematics course?

The answer to this question can be the main determining factor for whether to take Mth 130 before Calculus I. If you have completed a college course which transfers to CMU as Mth 130 and you earned a grade of C or better, you should be set for Mth 132. Otherwise, if your highest level course was a high school course, it is important to decide how it compares to Mth 130.

One very helpful factor to consider is that course's position and role of in your high school curriculum. If the course was a calculus course (especially if it was an AP calculus course), it would be unusual for you to need to take Mth 130. If your high school offered calculus and the course you took was that high school's highest prerequisite for entering calculus, you should also probably not need Mth 130 unless you did not perform at a sufficiently high level in that course (The other questions become more important if the latter is the case.)

If your high school did not offer calculus but the course you took was the most advanced course offered and if it was advertised as appropriate preparation for calculus you should expect it to be a version of Mth 130 provided that it either contained a significant trigonometry component or had a full trigonometry course as a prerequisite. At one time it was fairly standard for this course to be preceded by two years of algebra and a year of geometry. Today there appears to be more variety, including slower pacing or courses which integrate geometry with algebra. In order to understand how you fit into the precalculus/calculus scheme, try to equate your experience to the two years of algebra and one year of geometry as a template.

If your final course was a probability and statistics course, you should seek the advice of a mathematics counselor. It would assist this advisor if you would bring along a written list of the mathematics courses that you took in high school.

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How well did you perform in this course?

If your most advanced high school mathematics class was a full year calculus course and if your grades were generally A's or if you have AP credit, you should strongly consider taking Calculus II unless some other factor casts doubt on your depth of understanding. If your high school calculus grades were often lower than B, you should not attempt a course higher than Calculus I. If any evidence suggests that your high school calculus performance was inhibited by a weak mathematics background, you should consider taking Mth 130 or possibly Mth 106 if mastery of trigonometry is an issue.

If your most advanced high school mathematics class was a close equivalent to Mth 130 and if your grades were mostly A's with possibly a few B's you should strongly consider taking Calculus I unless some other factor casts doubt on your depth of understanding. If your grades in the Mth 130 equivalent course were often lower than B you should expect to begin no higher than Mth 130 and may want to consider the prior courses, Mth 106 or Mth 107. Keep in mind that it would be unusual for a student who has taken a Mth 130 equivalent high school course to need to consider a lower class such as Mth 106 or Mth 107.

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How competitive was the program in which you took this course?

This factor is difficult to judge but should be considered for any danger signs. If your school was quite small, if not many students took mathematics during their senior year, if graduates who have taken all the mathematics offered at your school have tended not to do well in college mathematics classes, or if you did not take the classes taken by most of the college-bound students from your high school, then you should be cautious and consider placement test information very carefully. Do keep in mind that none of these concerns will necessarily predict a problem for you but caution is quite appropriate in this case.

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How would you describe your study skills and industry as a student?

It is often said that hard work will produce success. There is much merit in this advice but keep in mind that it is unlikely that simply a will to succeed through hard work will overcome a significantly deficient background. If you are highly motivated, able to work well independently, and are able complete academic tasks in spite of potential distractions, then you should take this as a good reason to attempt the highest level course for which you appear to have the prerequisite.

If, on the other hand, you have often deferred homework assignments to the absolute last moment, are easily distracted from your study, and have a strong feeling that college years should allow lots of time for recreation and extracurricular pursuits, you should probably be more conservative in selecting your starting level. An additional warning is that college professors can cite countless instances of students who performed dismally in courses for which they were apparently well qualified. It often seems that lack of attendance and poor study habits are fostered by a student's perception of having "had this material before." This suggests that you cannot be protected from a poor grade simply by beginning in a course well below your preparation level. Boredom can be an enemy here.

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What were your scores on the mathematics portion of your college entrance exams?

Most incoming freshmen at CMU will have received printed mathematics placement advice based upon ACT scores. These scores are valuable information but a healthy skepticism is a good idea. It is my opinion that grades received in high school courses and the content of those courses are your single best indicator for mathematics placement. In particular, if you completed your ACT tests during your junior year and then took a precalculus or calculus course during your senior year, your test scores may be less useful as a predictor. Look for your placement score results to reaffirm the placement advice you get from the other factors considered. If they do this, you can feel confident in proceeding as advised. If your scores are lukewarm in support of the other advice, count the other advice as the most important. If your scores produce wildly different advice from the other factors considered, proceed with considerable caution and consult with a mathematics advisor.

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