Calculus Challenge Exam

Host institution: UBC
Participating institutions: SFU, TWU, UBC, UFV, UNBC, UVic

Wednesday • June 10 • 2019 • 12:00-15:00 PDT

Sample Tests

Here are three sample examinations, in Adobe PDF format. Please note the following.

Exam Format. Sample Test 1 has some short-answer questions; the other two do not. The examiners make no promises regarding the style and format of the actual paper. Students should prepare to read and follow instructions carefully.

Calculators. Calculators are not permitted. Answers that are "calculator ready," like 3+ln(7), are fully acceptable.

Question style. Each exam contains several questions that deal with standard topics in a fresh or indirect way. The examiners are always looking for new ways to probe student's conceptual understanding and versatility with the material. All candidates will be expected to recognize and solve standard problems by standard methods, but only those who are able to adapt their methods to new situations will receive outstanding scores.

Showing work. Candidates are expected to show all the work leading to the answers they present. (The short answer questions of Sample Exam #1 are an exception.) In some cases it is acceptable just to write down the answer — for example, when asked to compute something routine like the derivative of cos(3x2+x). However, there are no part marks for incorrect answers obtained this way. A student who just writes down the incorrect (6x+1)tan(3x2+x) will likely score 0 (out of 3), while one who goes explicitly through the chain rule and finishes with the same expression may (perhaps) earn 1 point.

Answer format. On this page we provide answers only, not model solutions. It was neither useful nor feasible to list all possible acceptable answers, but in many cases several versions of the answer have been supplied. It should be clear from these that the calculator is seldom needed in the sample exams, and that unless explicitly asked for, "simplifying" is not required.

Sample Test 1: Questions, Answers

Sample Test 2: Questions, Answers

Sample Test 3: Questions, Answers