## February Exams

On the week of February 21, 2011, you will take the following two exams.
• Performance Exam I (Monday, Feb 21)
• Written Exam I (Wednesday, Feb 23)

Both exams will take place during the regular class period. Room assignments for the Performance Exam can be found in the Resources folder on cTools.

The Written Exam will take place in 1084 (our usual classroom), 7:10pm-8:30pm.

### Office Hours next week

• Monday, February 21, 2011: 2-4pm SOE 2614. (Note the unusual room!)
• Tuesday, February 22, 2011: noon-2pm, 1856 East Hall.
No office hours on Wednesday.

### Performance Exam

The possibilities for the performance exam are described here (requires login).

Update, 02/16/2011: A rubric and sample problem for the performance exam is now available on cTools. On Saturday evening, the exact task that you perform will be released.

### Written Exam

Doing well on the Written Exam entails mathematical mastery of the following topics.

• Euclid's Lemma -- including understanding/stating its conditions and conclusions, and using it in proofs.
• Structure of a Proof by Contradiction -- you should, for example, understand and be able to prove the claim that the square root of a prime number is irrational.
• Leftover sequences for long-division of integers -- including using leftover sequences and the long division algorithm theorem for integers in proofs
• Explanation for the long division algorithm -- including the statement of why long division for integers and polynomials works, the rationale for each step; and for integer division, the distinction between the part of the dividend left after each subtraction step and the leftover.
• Long division algorithm for polynomials, factor theorem, Degree n Theorem, Fundamental Theorem of Algebra (statement only for FTA) -- using these ideas to find roots and prove facts about roots.
• Factors of polynomials, roots of polynomials, roots of complex numbers -- and their connections to each other.
• Synthetic division -- its precise relationship to the long division algorithm, as well as using it to test for roots.
• DeMoivre's Theorem -- using it to find roots of complex numbers, understanding its relation to factors of polynomials and roots of polynomials.

While studying for the Written Exam, it would be a good idea to do the Problem Sets again, the examples in the Class Summaries and Slides, the problems from the review session, as well as the problems described in the cTools file on Performance Exam Possibilities.

I can promise that one of the unperformed tasks on the Performance Exam Possibilities will show up on the Written Exam, and you will be assessed with the standards described in that file! Update: A problem very similar to the proof of irrationality on the Performance Exam Possibilities will show up on the Written Exam. This problem will be worth 15 points, and will be graded according to the rubric in this sample solution.

Here is an example exam solution to one of the sample problems. Please note the way that the abbreviations capture the meanings spelled out in detail in the sample solution above. You can think of a good exam write-up as a good blackboard version of a proof.