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Mathematics Department
Mathematics student

Validation and Placement

4/C Mathematics Placement Exam

All 4/C midshipmen take the Mathematics Placement (pre-calculus) exam, which is a 70 question multiple-choice exam covering pre-calculus topics — exponents, fractions, factoring, solving equations, functions, graphing, word problems, logarithms, trigonometric functions, and geometry. This exam has now been made available to take online. Midshipmen are instructed to take this exam before they report to USNA. Calculators are not allowed on this exam. The exam is given in four parts on Blackboard. All four parts are timed but need not all be completed in the same setting. In fact, if you are careful to log out and exit (this causes the timer to pause), you can even pause for a break in the middle of an exam. Parts previously completed may not be returned to. It is important to follow the instructions on how the exam is to be taken, to prevent incorrect placement in a mathematics course.

SM005, Pre-calculus Mathematics

Midshipmen who correctly answer fewer than 45 of the 70 pre-calculus questions correctly are often placed in SM005, Pre-calculus Mathematics. Most of those who correctly answer at least 45 are put into a calculus course. For those close to the cutoff, other information may be used to determine placement, such as the math SAT score, high school courses and any education post high school. Towards the end of plebe summer, any midshipman who has been placed in pre-calculus who requests a retest is given the retest, if the chairman approves.

Calculus I

Midshipmen who do not validate Calculus I and who have not been placed in the pre-calculus course take Calculus I. The Mathematics Department has three different Calculus I courses. Plebes who answered a suitable number pre-calculus questions correctly and who are not placed in pre-calculus are placed in SM121, which is a four-hour course. Those who have good pre-calculus skills and answered a suitable number of calculus questions correctly correctly can be placed in SM122X (a 4 credit "accelerated calculus" course which, taken with the follow-on course SM221X, allows a plebe to get credit for 3 semesters of calculus in only 2 semesters). The exact percentages depends on staffing constraints and the Mathematics Department Chair's criteria decisions.

Validating Calculus I

Midshipmen who have finished the online pre-calculus exam have the opportunity to take an online multiple choice Calculus I exam. This exam is updated each year to reflect any changes in our first calculus course. Calculators are not allowed on the Calculus exams. A score of roughly 70% is needed to validate the course.

Calculus I can also be validated by means of AP exams. Those students who took AP Calculus in high school and scored a 4 or 5 on the AB exam (or on the AB portion of the BC exam) validate Calculus I. High scores on an IB exam also count as validation.

Validating Calculus II

Those who validate Calculus I and who have taken a course in Calculus II are invited back to take a Calculus II validation exam. The Calculus II exam is also multiple choice. Calculus I and II can also be validated by means of BC exams. Those who scored a 4 or 5 on the BC exam validate Calculus I and Calculus II.

Validating Calculus III

Those who validate Calculus II and have had a course in Calculus III are invited to take a Calculus III validation exam. The Calculus III exam is part multiple choice (to be taken online) and part long answer (to be taken with pencil and paper). If your online score is high enough, you will be invited to take the long answer test after arriving at the USNA.

In all placement decisions, special circumstances (previous college math courses, amount of time since last math course was taken, etc.) are considered. In general unless a plebe has a high enough AP score or IB score, to validate a course he or she must have taken that course already and must take a validation exam on it. Midshipmen are not generally permitted to retake validation exams. The same policies apply to validation of upper level courses.

Validating Statistics

A 4 or 5 on the AP Statistics exam allows you to validate SM219. However, SM219 is not a required course for every major, so this may or may not be helpful to you, depending on what major you select. Please see the Mathematics Department Chair if you wish to pursue this.

More details on the mathematics courses mentioned above can be found at the Dean's course catalog page.

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