Validation and Placement

Required Mathematics Courses at USNA

All midshipmen at USNA must complete 4 core mathematics courses: Calculus I, Calculus II, Calculus III, and a fourth mathematics course that depends on the midshipman’s major. Midshipmen who have previously taken one or more of these Calculus courses are given the opportunity to attempt to validate (receive credit through testing) during Plebe Summer. Additional mathematics course validations, such as Differential Equations or Linear Algebra, occur later during Plebe Year.

There are dedicated plebe-only sections of Calculus I (SM121), Calculus II (SM122), and Calculus III (SM221P) offered in the fall semester. Here is the approximate percentage of each plebe class that starts in a given math course during the 4/C fall semester:

• SM187 Differential Calculus I: 6–10%
  
  
• SM121 Calculus I: 50–60%
  
  
• SM122 Calculus II: 20–30%
  
  
• SM221P Calculus III: 10–15%
  
  

4/C Mathematics Initial Exam

All 4/C midshipmen take an initial math exam during the first few days of Plebe Summer.

• No prior Calculus experience → take a placement exam covering pre-calculus topics (exponents, fractions, solving equations, factoring, functions, graphing, trigonometry, geometry, and logarithms). Results help determine whether the midshipman is ready to start in a one-semester Calculus I course (SM121) or should begin in SM187, a slower-paced two-semester Calculus I sequence.
  
  
• Prior Calculus experience → take a Calculus I validation exam. This is the only opportunity to attempt validation of Calculus I outside of AP scores.
  
  

SM187

About 6–10% of midshipmen are placed into SM187 Differential Calculus I during the fall semester. This two-semester sequence allows a more thorough review of pre-calculus and provides additional time to learn Calculus I material. Placement is based on placement exam performance, math SAT scores, high school courses, and prior education.

A midshipman who starts in SM187 will be required to take Calculus II (SM122) in summer school after Plebe Year. This ensures they are on track to take Calculus III during their 3/C fall semester and remain on pace to graduate on time.

Validating Calculus I

• Exam: During the first few days of Plebe Summer, midshipmen with prior Calculus experience may take the Calculus I validation exam. A score in the range of 70% (subject to adjustment by the department) is required to validate.
  
  
• AP Credit: Students who scored a 4 or 5 on the AP Calculus AB exam (or the AB subscore of the BC exam) validate Calculus I.
  
  
• IB Credit: The Math Department does not grant validation based on IB exam scores.
  
  

Validating Calculus II

• Exam: Midshipmen who indicated prior completion of Calculus II (Integral Calculus or AP Calculus BC) on their academic background survey will be invited to take the Calculus II validation exam, usually during the second week of Plebe Summer. This exam is multiple choice, and a score in the range of 70% (subject to adjustment) is required for validation.
  
  
• AP Credit: A score of 4 or 5 on the AP Calculus BC exam validates both Calculus I and Calculus II.
  
  

Validating Calculus III

• Exam: Midshipmen who indicated prior completion of Calculus III (Multivariable Calculus) on their academic background survey will be invited to take the Calculus III validation exam, typically during the second or third week of Plebe Summer. This exam includes both multiple-choice and free-response questions. A score in the range of 70% (subject to adjustment) is required for validation.
  
  

General Validation Guidance

• The Math Department does not validate courses based on high school or college transcript grades alone, regardless of institution.
  
  
• In general, to validate a course, a midshipman must have completed that course previously and either (1) pass a validation exam, or (2) have an accepted AP score.
  
  
• AP scores must be submitted to USNA before I-Day to ensure correct placement. If scores are not received, midshipmen may be placed in a lower course until official scores arrive.
  
  
• Upper-level courses (such as Differential Equations or Linear Algebra) can be attempted for validation later during Plebe Year, but not during Plebe Summer.
  
  

Frequently Asked Questions

Q: If I validate a math course, do I need to take a replacement course?
A: No. Each validation reduces the number of math courses you are required to take. For example, if you validate Calculus I and II, you only need to complete two additional math courses at USNA. Each validated course counts as 4 credits toward graduation.

Q: What happens if I fail a validation exam?
A: Nothing punitive. You simply start in the standard course sequence. You do not lose anything by attempting to validate.

Q: Can I take validation exams later if I don’t pass during Plebe Summer?
A: No. Validation exams for Calculus I–III are only offered during Plebe Summer (except through AP scores).

Q: Can I use a calculator on validation exams?
A: No. Validation exams are designed to be completed without a calculator.

Q: What if my AP scores are delayed?
A: Without official scores on file, you will be placed in the appropriate course based on exams and background. When scores are received, your placement will be updated if necessary.

Q: Can I validate higher-level courses like Differential Equations or Linear Algebra?
A: Yes, but not during Plebe Summer. These exams are offered later during Plebe Year.

Q: If I’m placed in SM187, will that put me behind for graduation?
A: No. SM187 students take Calculus II in summer school after Plebe Year and then Calculus III in the fall of 3/C year, keeping them on pace with their class.