| MATA22 | Winter 2021 |
| University of Toronto |
Midterm- Format and Scope
(1) Equipment you will need:
• Reliable internet connection with capacity for video streaming.
• Computer equipped with webcam and two-way audio.
• UofT ID card.
• Pen and paper.
• Scanner or phone camera to digitize your answers.
• Printer (helpful, not required).
(2) Material of Responsibility: You are responsible for all the materials covered in the first 8 weeks of
the course.
Midterm II will be focused on the following
• Sections: 2.3, 2.4, 3.1, 3.2, 3.3, 3.4 (up to Example 3),4.1, 4.2 (Theorem 4.2.3 excluded) from the textbook
• lectures from week 4 to week 8 (including the end points),
• tutorial worksheets for TUT5, TUT6, TUT7 and TUT 8,
• all your quizzes after midterm I
• problem set 3
• all the Webwork after midterm I and including WW9
In particular, you are expected to know the exact definitions and meaning of every term that is used
in lectures, tutorials and homework,and be familiar with examples seen in lectures and tutorials.
(3) Test Format and Scope
1. The exam is valued at 100 points in total and is worth 20% of your entire course grade.
2. The test questions/problems are like those seen or implied in the lectures, in the assignments/solutions,
webwork, in the text or in your tutorials.
3. The test is well-balanced in both its coverage of the course material above and in its level of
difficulty. Some test questions are very easy, but most are medium and straightforward to solve. You
should expect at least one quite difficult question or parts of questions.
Here is a more detailed break down of the questions:
• Definitions: you will be given potential definitions to certain terms and asked to confirm, correct
or complete them. You should know all the definitions we gave in lectures or you read in reading
or asked to recite in tutorials word by word. This is the first and most important step in learning
math.
The best way to prepare for this is to make a definition document for yourself, go over the
definition document and try to reproduce every definition and meticulously compare your work
with the correct definition.
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• True/false: This question may be tricky. To practice, go over all the T/F questions in suggested problems in the textbook. There is al least one such question at the end of each chapter.
Acceptable justification is either a reasoning why the statement is true or an explicit counter
example. No formal proof required. Saying true or false without justification gets zero point.
These questions are extracted from our course material. You may need to remember facts you
proved in tutorials or problem sets or example you seen in WW as well.
• Examples: You will be given a description of a mathematical object and asked to give an explicit
example that matches the description. You may also be given a false statement with a counter
example and get asked to confirm or correct the counterexample.
• Calculation/standard proofs on an explicit example: These questions resembles or inspired from
your tutorials or WebWork. It is mostly straight forward. Some parts might be less straightforward and more conceptual.
• You may be given a statement with a proof and will be asked to carefully and completely justify
certain steps. You should have a good understanding of the problem sets for this question.
• You may be given a choice between writing a statement for a given proof or find flaws in a given
argument.
• You may be asked to carefully prove a statement you have seen in class, tutorials or problem sets.
• You are asked to carefully prove a statement you haven’t seen in class but are well equipped to
prove.
(4) How to Prepare
(a) Start by learning all the definitions word by word (this is extremely important, you should be
able to recite definitions word by word in order to be able to do anything in mathematics, feel
free to memorize them).
(b) Make sure you understand everything we did in the lectures (proofs and examples)
(c) Redo all TUT questions (don’t read them, use pen and paper and actually work them out) and
compare your works against the solution. If you can find a study partner to explain your work
to do. There is a great difference between writing math for yourself and writing it for another
person to understand. In exam, you should be formatting your work in such a way that another
classmate fully understands your work.
(d) While doing this, if you have difficulty with a question, go back and read the lecture notes
corresponding to that question.
(e) Redo webwork (on paper)
(f) Do as many textbook problems from the book as you need. Especially do the suggested ones.
(g) The next step is to make sure you understand and can do all the problem set questions, Some
questions in the exam resemble your problem sets and tutorial questions but are not identical to
them. You will succeed in those only if you UNDERSTAND the tutorial and problem set questions
well. Understanding math means you can explain it to others and can answer to question “why”
in every step. Ask why repeatedly, you should be able to reduce the answer to a definition of a
result (theorem, proposition, lemma) we proved in class or proved in the textbook. Don’t shoot
yourself in the foot by just reading the questions and solutions. That gives you a false sense of
understanding.
(h) Finally, do the practice exam. Note that they differ in difficulty level, format and are based on
the variation of the material offered during the semester the exam was written and other factors
specific to that semester. Some questions are on material we haven’t covered (for instance inverses
of matrices). Your exam will be based on the material we saw in our course.
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