Mathematics Exams With Solutions

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Calculus Diagnostic and Placement Exams, with Solutions

Tests to determine whether you are ready to take calculus, and at what level.

• The Citadel has Practice Problems and Solutions for the Placement Test for Calculus I/Precalculus
• Iowa State Placement Exams for Algebra, Trig and Calculus.
• Mt. San Antonio College Calculus Placement Examination.
• NYU Sample placement exams with solutions to test readiness for Calc I, Calc II and Calc III.
• South Dakota State has sample Gateway Exams for Calculus Math 123.
• SUNY Buffalo has online quizzes that test you on the algebra needed for calculus.
• University of Colorado Calculus diagnostic test for advanced, multiple variable calculus, with solutions.
• University of Manitoba Calculus diagnostic test. Self scored.
• UC San Diego Web-based Calculus Readiness Test.
• SMU has a sample precalculus placement exam to indicate whether you have the background to take precalculus.(pdf)
• UC Berkeley Online Calculus Placement Examination Project. Generates a multiple choice diagnostic exam, then immediately grades it and shows you the answers. From James A. Sethian, Theodore A. Slaman and W. Hugh Woodin. See also a previous calculus placement exam.
• University of Utah Calculus diagnostic test. Solutions are here.
• Vanderbilt U. sample Calculus Placement Examinations with answers
• University of Wisconsin, Madison sample Calculus Placement Examination

Precalculus Exams with Solutions

Precalculus generally covers Algebra, Trigonometry, Cartesian geometry, functions, etc. Possibly some matrix theory and more advanced topics.

• Kansas State University Math 150 Trigonometry old exam archive, some with solutions. Text: Fundamentals of Trigonometry, by Swokowski and Cole. See also the Math 100 College Algebra old exam archive, 1997-2010. Text College Algebra, by Beecher, Penna & Bittinger
• University of Manitoba has practice precalc exams with solutions, organized by subject. From Manitoba provincial examinations.
• University of Washington has an extensive archive of precalculus (Math 120) exams with solutions. Textbook: Precalculus by Collingwood and Prince. The text (PDF) is available free online.
• East Tennesse State University sample precalc exam.
• Georgia Tech final exam with solutions. Textbook: Larson and Hostetler.
• Indiana Southeast University practice precalc final exam problems with solutions.
• Middle Tennesse State University sample precalculus exam.
• Washington University in St. Louis has a large collection of Math exams with solutions, including precalculus.
• UT El Paso SOS Math has sample precalc 1 test problems with answers. Organized by topic. Also precalc 2
• Mathematical Radical collection of precalculus exams with solutions.

AP Calculus Exams with Solutions

The Advanced Placement Calculus Exams are generally taken in High School, and can often be used for college credit. There are two such exams in calculus, Calculus AB and Calculus BC, which covers more material.

• The AP Calculus AB Exam site: Has past exams and sample problems for AP calculus exam.
  
• AP exams from the University of Houston: Sample AP exams with solutions, calculus AB and BC
  
• University of Arkansas School for Mathematics, Sciences and the Arts has old AP exams, 1969-1998. Thirty years of AP exam problems with solutions.
• AP free response: More AP exam problems, 1991-2007, with solutions. From Marizza Bailey at the Arkansas School for Mathematics, Sciences and the Arts.

Calculus Exams

Calculus I Exams with Solutions (Limits, Derivatives etc)

• Bates sample calculus exams. Math 205. Textbook: Ostebee and Zorn or Hughes-Hallett, Gleason. Large collection of exams sorted by topics. Some with solutions.
• Bradley sample Calc I exams.
• Broward College old Calc I 2233 exams from Gregory Maxwell. Textbook: Larson and Edwards
• Clemson sample calculus exams. MthSc 106. Textbook: University Calculus, Weir, Hass, Thomas.
• Kansas State University Math 220 Calc I old exam archive, 1997-2010, some with solutions. Text: Calculus: Early Transcendentals , by James Stewart.. See also the Math 205 General Calculus and Linear Algebra archive, 1997-2010. Text: Applied Calculus, by Hughes-Hallett et al
• MIT sample calculus exams for Calc I. Textbook: Simmons.
• Michigan State sample calculus exams for Calc I. Textbook: Thomas, Weir, Hass, Giordano.
• Northern Illinois University sample calculus exams.
• Rutgers sample Calc 1 exam problems with answers. Math 151
• SUNY Stony Brook Math 125 sample calculus exams. Textbook: Stewart. Also see SUNY Stony Brook Math 131 sample calculus exams. Textbook: Stewart.
• Texas A and M sample calculus exams for Math 151, 1995-2010. Textbook: Stewart Calculus: Early Vectors.
• UC Berkeley sample calculus exams for Math 16A from Ming Gu. Textbook: Goldstein, Lay, Schneider and Asmar.
• University of Colorado, Boulder sample Calculus I exams with answers, APPM 1340 exams 2004-2009. Textbook: Essential Calculus, Stewart
• University of Colorado, Boulder sample Calculus I for engineers exams with answers, APPM 1350 exams 1996-2009. Text: Stewart.
• University of Illinois at Chicago Calc I old exams. Math 181. Textbook: Rogawski. No solutions.
• University of Michigan, Ann Arbor Math 115 Calculus I old exams. Textbook: Calculus by Hughes-Hallett, Gleason, et al.
• UT Austin sample calculus exams for Math 403L from Lorenzo Sadun. Textbook: Barnett and Ziegler.
• University of Wisconsin, Madison sample calculus I exams. Math 211. 2002-2006, No solutions.
• University of Wisconsin, Madison sample calculus I exams. Math 171. From Joe Miller.
• Mathematical Radical has a collection of Calculus I exams with solutions. Textbook: Thomas, Hass, Weir.

Calculus II Exams with Solutions (Integration, sometimes series etc)

• Bates sample calculus exams. Math 106. Textbook: Ostebee and Zorn or Hughes-Hallett, Gleason. Large collection of exams sorted by topics. Some with solutions.
• Kansas State University Math 221 Calc II old exam archive, some with solutions.
• Middlebury College Math 122 Calc II sample exams with solutions. Textbook: Stewart. From John R. Schmitt.
• Princeton Calc II sample exams with answers from Edward Nelson. Math 104. Textbook: Thomas' Calculus, Weir, Hass.
• Rutgers sample Calc 2 exam problems with answers. Math 152. See also Rutgers 2 and Rutgers 3.
• UC Berkeley Math 1B calculus exams. Textbook: Stewart.
• Clemson sample calculus exams. MthSc 107. Textbook: University Calculus, Weir, Hass, Thomas.
• University of Colorado, Boulder Calculus IB exams with answers, APPM 1345. Textbook: Essential Calculus, Stewart
• University of Colorado, Boulder Calculus II exams with answers, 1995-2009, APPM 1360. Textbook: Thomas' Calculus
• University of Georgia, Athens sample calculus exams. Math 2260. Textbook: University Calculus, Weir, Hass, Thomas.
• University of Illinois at Chicago Calc II sample exams. Math 181. Textbook: Rogawski. Some with solutions.
• University of Massachusetts Calc I exams. No answers. Textbook: Stewart.
• Notre Dame Calc II exams, Math 10350. Textbook: Larson, Hostetler and Edwards. httl
• Purdue Math 181 sample exams. Textbook: Thomas' Calculus ET, Weir, Hass, Giordano.
• SUNY Stony Brook sample calculus exams. Math 132. Textbook: Stewart
• Texas A and M sample calculus exams for Math 151, 1995-2010. Textbook: Stewart Calculus: Early Vectors.
• UC Davis sample calculus exams. Math 21B. Textbook: Thomas' Calculus ET, Weir, Hass, Giordano.
• University of Michigan, Ann Arbor Math 116 Calculus II old exams. Textbook: Calculus by Hughes-Hallett, Gleason, et al.
• University of Nebraska Lincoln Math 107 Calc II calculus exams. Textbook: Thomas' Calculus, Weir, Hass.
• UT El Paso has a nice website called SOS Math with many sample calculus exams.
• University of Wisconsin, Madison sample calculus II exams. Calculus and Introduction to Differential Equations. Math 213. 2005-2006. No solutions.
• University of Wisconsin, Madison sample calculus III exams. Math 222. 2004-2006. No solutions.
• University of Wisconsin, Madison sample Calculus II exams. Math 217. Textbook: Thomas' Calculus, Weir, Hass, Giordano. From Joe Miller.

Calculus III Exams with Solutions (Multivariable calculus, etc)

• Bates sample multivariable Calc exams. Math 206. Textbook: Vector Calculus by Barr. Large collection of exams sorted by topics. Most with solutions.
• Cal Poly multivariable calculus practice exams with solutions. Math 143. Textbook: Stewart.
• Colgate some old exams with solutions. Math 113. Textbook: McCallum, Hughes-Hallett, Gleason.
• Columbia sample multivariable calculus exams. Textbook: Stewart. Also see multivariable exams at Math 2263 Fall 2009.
• Harvard sample multivariable calculus exam with solutions. Also see Math21a sample exams with solutions from 2006 and from Summer 2010 .http://
• Kansas State University Math 222 Calc II old exam archive, some with solutions.
• Minnesota multivariable calculus exams. Course 2263. Textbook: Stewart.
• MIT multivariable calculus exams. Course 18-02. Textbook: Edwards and Penney.
• Rice multivariable calculus exam with answers. Course 212. Textbook: Marsden and Tromba.
• University of Connecticut sample multivariable calculus exam with answers. Course 2110. Textbook: Stewart.
• University of Illinois at Chicago Calc III sample exams. Math 210. Textbook: Rogawski.
• UC San Diego Multivariable Calculus 20C, practice exams and solutions. Math 20C. Textbook: Stewart.
• University of Colorado, Boulder Calculus III exams with answers, 1999-2009, APPM 2350. Calc III Textbook: Thomas' Calculus
• University of Michigan, Ann Arbor Math 215 Calculus III old exams, with answers. Textbook: Stewart.
• University of Minnesota Math 2374 multivariable calculus old exams. Text: Marsden and Tromba, Vector Calculus, Fifth Edition. From Francisco Javier.

Calculus Exams with Solutions - various topics

• Princeton large collection of past calculus exams, Math 101, 102, 103, 104, 201, 203. No solutions. Textbook: Thomas' Calculus, Weir, Hass, Giordano.
• UC Davis sample calculus exams for four quarter cal sequence, with solutions. Textbook: Thomas, Weir, Hass: Math 21A, 21B, 21C, 21D. From Sara Hawkes.
• UC Merced old calculus exams with solutions, Math 21: Calculus I, Math 22: Calculus II, Math 23: Vector Calculus, Math 24: Linear Algebra and Differential Equations, Math 30: Calculus II for Biological Sciences, Math 32: Probability and Statistics.
• Toronto old calculus exams. No exam solutions, but lots of sample problems with solutions.
• Wabash College old calculus exams, some with solutions. Textbook: Thomas' Calculus, Weir, Hass, Giordano.
• Washington University has a collection of old calculus exams, many with solutions. Math 100, 127, 131, 132, 233.

Differential Equations Exams with Solutions

Exams for introductory courses on differential equations, usually covering introductory topics in Ordinary Differential Equations.

• Harvard differential equations for the life sciences. Exams with solutions.
• Kansas State University Math 240 old exam archive, many with solutions. Text: Elementary Differential Equations, A Geometric Approach, by A. Bennett
• Louisiana State University Differential Equation exams. A large selection with solutions.
• MIT sample exams from an open courseware offering. The whole Differential Equations course is available online.
• Penn State University old Differential Equation exams. Math 250 from Zachary S. Tseng. Also see Math 251 old Partial Differential Equation exams.
• RPI old exams with answers, 1989-2010. MATH 2400. Textbook: Boyce and DiPrima.
• Rutgers sample exams. Differential Equations 244.
• SUNY StonyBrook sample exams.
• Tufts University old exams with solutions, 1998-2010. Math 38. Textbook: Guterman and Nitecki.
• UC Berkeley Linear Algebra and DE sample exams for Math 54 from Prof. Ming Gu. Also see exams from Math 123.
• UCSD Math 20D Differential Equations old exams from Ed Bender and also Math 21D from Bruce Driver. Text: Boyce and DiPrima.
• University of Pennsylvania Math 425 Partial Differential Equations exams and answers from Dennis Deturck.
• University of South Carolina sample exams.
• University of Washington Math 307 sample exams.
• Washington U has a collection of old differential equations exams, many with solutions. Math 217.
• UT El Paso SOS Math site has sample DE exams.

Linear Algebra Exams with Solutions

• Bates sample linear algebra exams. Math 205. Textbook: Lay or Strang. Large collection of exams sorted by topics. Most with solutions.
• Clark University linear algebra exams, along with notes and explanations from Prof D. Joyce.
• Colby College linear algebra exams.
• College of the Redwoods linear algebra exams.
• Harvard University linear algebra and differential equations exams. Textbook: Bretscher. From Oliver Knill.
• Kansas State University Math 551 Applied Matrix Theory old exam archive, many with solutions. 1994-2006.Text Linear Algebra for Engineers and Scientists Using MATLAB, by K. Hardy,
• Loyola University linear algebra exams.
• Northeastern University linear algebra exams.
• MIT sample exams from a course taught by Prof. Gilbert Strang.
• Princeton large collection of past linear algebra exams, Math 200, 202, 204, 217. No solutions.
• University of Colorado, Boulder Differential Equations and Linear Algebra exams with answers, 1992-2009, APPM 2360. Textbook: Farlow, Hall, McDill and West, Differential Equations and Linear Algebra
• University of Waterloo Linear Algebra tests sorted by subject.
• University of Toronto large collection of linear algebra exams.
• University of Minnesota Math 4242: Applied Linear Algebra exams with solutions. Text: Applied Linear Algebra by Olver and Shakiban. From Francisco Javier.

Mixed Collections of Mathematics Exams with Solutions

• Northwestern University has a variety of old math exams with answers. Math 104, 110, 202, 211, 220, 224, 230, 234, 240, 250, 290 and 330 exams.
• UC Berkeley sample exams in Numerical Analysis. No solutions.
• UC Davis old exams from a variety of Math courses. No solutions.
• UCSD old exams for 10C, 15B, 20B, 20C, 20D, 20E, 20F, 103A, 103B, 166, 184A, 188. From Ed Bender, with answers.
• University of Pennsylvania has old Final Exams with solutions for Calc I Math 103, Calc II Math 104, Multivariable Calculus Math 114, Probability Math 115, Linear Algebra Math 240 and Complex Analysis Math 241
• Washington University old exams in a variety of Math courses, with solutions.
• University of Colorado, Boulder APPM 3570: Applied Probability exams with answers. Textbook: "A First Course in Probability" by Sheldon Ross.

Actuarial Exams with Solutions

• Society of Actuaries has an archive of past actuarial exams, with solutions.
• Casualty Actuarial Society past actuarial exams with solutions, statistics and discussion.
• actuarialoutpost.com past actuarial exams.
• Actuarial Review Problems Multiple choice problems with solutions, covering precalc to multivariable calculus, from Ronald Miech at UCLA.
• Be An Actuary has sample exams.
• SUNY Binghamton sample exams.

Math Tutorial websites

• Harvey Mudd College has online tutorials from precalc through linear algebra and differential equations.
• Paul's Online Math Notes has tutorials and summaries from algebra through differential equations. From Paul Dawkins at Lamar University.
• Armstrong Atlantic State University has a College Algebra tutorial.
• University of Akron has a review of Algebra in 10 lessons.
• Math Archives has a list of sites with online tutorials.
• Math Forum Ask Dr. Math has a list of questions and answers organized by topic.
• Calculus-help has calculus tutorials by topic.

Other Math Exam sites

• PostYourTest.com Users post their exams on this website. All subjects, including some calculus exams.