MAT224 Winter 2022
University of Toronto
Midterm- Format and Scope
(1) Time and duration: Midterm one is on Friday Feb 18th, 6-8pm. If you filled out the alternative
sitting request due to an academic conflict, you have received instructions about your starting time
via email.1 The midterm is timed and will be administered online. You will have 120 minutes to
finish the test. There will two parts. Part A: This part is administered through a Quercus quiz and
consists of short answer and multiple choice questions. Incorrect choices in this part may affect your
grade negatively. Part B: This part is administered through Gradescope and consists of writing and
proof-based questions.
Detailed instructions, logistics, rules, and availability interval of each part will be published one day
before the test.
(2) Equipment you will need:
Reliable internet connection for the duration of the exam.
Pen or pencil and paper.
Scanner or phone camera to digitize your answers.
(3) Material of Responsibility: You are responsible for knowing the material presented in following
sections of our course textbook:
Sections: 5.1, 5.2, 1.1, 1.2, 1.3, 1.4, 1.6, 2.1, 2.3, 2.4, 2.5, 2.6 .
Exclusions: Sec 5.2 Example 5.2.9 and 5.2.10
Sec 2.3-2.6: Any discussion related to matrix representation of a linear transformation denoted by
[T ]βα is excluded for this midterm. In particular, the following results and examples are excluded:
Proposition 2.3.7, Proposition 2.3.8, Example 2.3.9, Corollary 2.3.13, Proposition 2.3.14, Example
2.3.16, and Example 2.3.18, Proposition 2.5.9, Proposition 2.5.13, Example 2.6.6, 2.6.9, Proposition
2.6.11
You are expected to be familiar with row reduction technique and matrix manipulations introduced in
Linear Algebra I. In particular, you are expected to be able to solve a system of linear equation via
row reduction, identify leading entries and find a basis for null space and column space of a matrix.
Although you will not be directly tested on these concepts, you will need them to approach some
questions.
Moreover, you are responsible for knowing your tutorial worksheets up to and including TUT 4, all
suggested problems from the textbook, all your WeBWork questions up to and including WeBWork
5, and the written homework 1 and 2. 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 able to recite the
statements of any result (theorem, proposition, corollary) you refer to in your work.
1if you did fill out the form and were not contacted via email, please send an email to admin224
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(4) Test Format and Scope
1. The test is worth 15% 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.
You should expect to get questions of the following types:
Conceptual: These questions involve very little computation, and measure your conceptual
understanding of the material and your ability to connect concepts and draw conclusion. Most of
the questions will be of this type.
Proof/justification: You will be asked to prove certain statements. You will be asked to prove
at least one statement that you may have not seen before, put are equipped with proving based on
what you have seen proofs to. You may also be asked to decide the truth value of some statements
and justify your choice by a short proof or a counter example. .
Procedural: These are questions that ask you to apply a procedure to solve a problem. These
questions resembles those in your WebWork and some tutorial questions. They are mostly straight
forward.
(5) How to Prepare
(a) Know the definition of every term we saw word-by-word.
(b) You are expected to be able to cite all the results you use in your proofs. There are many results
in our textbook. A way to decide which ones to focus on is by finding those we talked about in
lectures and those you were asked questions about in reading quizzes. Make sure you understand
everything we did in lectures, in particular you can cite and apply the results we talked about in
lectures.
(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, if you are asked to justify your work you should be formatting
your work in such a way that the grader fully understands your work.
(d) Do all suggested problems listed in our reading assignment page.
(e) While doing this, if you have difficulty with a question, go back and read the textbook section
corresponding to that question. Do not reread what you already read and understood.
(f) Redo WeBWork (on paper)
(g) The next step is to make sure you understand and can do all the written homework 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 homework
questions well. Understanding math means you can explain it to others and can answer to
question ”why” in every step. Ask why repeatedly. Your answer to ”why” should be of the form
”by definition…”, ”by theorem…” etc.
(6) Acceptable and non-acceptable aids during exam:
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(a) You may consult your course notes or our textbook during the exam. However, your time is
calculated for writing the test completely focused, without any distraction. Consulting course
notes may be in fact distracting and causes you loosing some time.
(b) For this exam any use of outside help: internet, any communication electronically or in person
with your peers or any other person during our exam time is considered academic dishonesty.
Any instance of academic dishonesty that comes to our attention will have severe consequence.
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