Precalculus and Calculus Placement Exams
The Department of Mathematical Sciences offers Precalculus and Calculus placement exams to students who would like to place out of one or more of the following introductory precalculus and calculus courses.
- 21-090 Precalculus
- 21-120 Differential and Integral Calculus
- 21-122 Integration and Approximation
The exams are multiple choice and are given at the level of a final exam for the corresponding course. Students who pass a placement exam will receive a prerequisite waiver (not course credit) for the corresponding course. The content covered in each exam is summarized below:
21-090 Precalculus
Description: Extensive treatment of topics chosen to prepare students for the study of calculus. Preliminary topics include algebraic techniques and linear and nonlinear inequalities. Special emphasis is given to polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric functions and their graphs, as well as basic and analytic trigonometry.
An example reference text is OpenStax Precalculus. In this text, content for the exam will come from the following sections:
- Chapter 1: Sections 1.1-1.7
- Chapter 2: Sections 2.1-2.3
- Chapter 3: Sections 3.1-3.8
- Chapter 4: Sections 4.1-4.7
- Chapter 5: Sections 5.1-5.5
- Chapter 6: Sections 6.1-6.3
- Chapter 7: Sections 7.1-7.6
- Chapter 8: Sections 8.1-8.2
21-120 Differential and Integral Calculus
Description: Functions, limits, derivatives, logarithmic, exponential, and trigonometric functions, inverse functions; L'Hospital's Rule, curve sketching, Mean Value Theorem, related rates, linear and approximations, maximum-minimum problems, inverse functions, definite and indefinite integrals; integration by substitution and by parts. Applications of integration, as time permits.
An example reference text is OpenStax Calculus, Volume 1. In this text, content for the exam will come from the following sections:
- Chapter 1: Sections 1.1-1.5
- Chapter 2: Sections 2.1-2.5
- Chapter 3: Sections 3.1-3.9
- Chapter 4: Sections 4.1-4.8, 4.10
- Chapter 5: Sections 5.1-5.7
As the topic of Integration by Parts is covered in 21-120, Section 3.1 of OpenStax Calculus, Volume 2 will also be covered on this exam.
21-122 Integration and Approximation
Description: Integration by trigonometric substitution and partial fractions; arclength; improper integrals; Simpson's and Trapezoidal Rules for numerical integration; separable differential equations, Newton's method, Euler's method, Taylor's Theorem, including a discussion of the remainder, sequences, series, power series. Parametric curves, polar coordinates, vectors, dot product.
An example reference text is OpenStax Calculus, Volume 2. In this text, content for the exam will come from the following sections:
- Chapter 1: Sections 1.1-1.7
- Chapter 2: Sections 2.4, 2.7
- Chapter 3: Sections 3.1-3.7
- Chapter 4: Sections 4.1, 4.3
- Chapter 5: Sections 5.1-5.6
- Chapter 6: Sections 6.1-6.4
- Chapter 7: Sections 7.1-7.4
Content for the exam will also include Newton’s Method from Section 4.9 of OpenStax Calculus, Volume 1. While 21-122 also covers introductory topics on vectors and the dot product found in Sections 2.1-2.3 of OpenStax Calculus, Volume 3 , this content will not be on the exam.
Placement exam schedule and registration
These exams are offered only to incoming first-year or external transfer students. They are offered on the following days of orientation week:
- Monday, 8am: 21-090 exam
- Tuesday, 8am: 21-120 exam
- Wednesday, 8am: 21-122 exam
Students should consult their advisor for any questions about which exams to take, and must register for all exams they plan to take. The registration deadline is MONDAY, AUGUST 4.
A student with no credit or prerequisite waivers who wishes to place out of 21-090 must start with the 21-090 placement exam on Monday. A student who already has a prerequisite waiver for 21-090 may start with the 21-120 placement exam on Tuesday. A student who already has 21-120 credit may start with the 21-122 placement exam on Wednesday.
Students may register for multiple exams, but may only take subsequent exams if they pass the previous one, or already have credit or a prerequisite waiver for the previous one. Students and advisors will be notified whether they pass each exam on the same day they take the exam.
Exam administration
Registered students will be notified of the exam location before orientation week. Students should arrive for their exam by 7:45am so they may begin promptly at 8am. The exam will be administered on paper. Scratch paper will be provided. Students must bring their CMU photo ID and two pencils, and will be required to present their ID when the exam is complete.
Academic Integrity
You cannot use any aids (textbooks, phones, notes, integral tables, friends, calculators, etc.) If you are observed using any aids, your exam will be invalidated, your advisor will be informed, and you may be subject to disciplinary action as per the university policy on academic integrity.
If you have any questions or concerns, please contact calcplacement@cmu.edu.