Nipissing University




On this page you will find information to help you successfully complete not just MATH 1036/1037 but all of your university courses. This section is quite long so a table of contents is provided for quick access to the concept you wish to read about.



It is recommended that before lecture you read through the sections that will be covered that day. The purpose of this is to familiarize yourself with the concepts that your professor will be lecturing on, thus allowing you to better understand the lecture. With a course such as Calculus it is a little hit-or-miss on exactly which sections will be covered in a lecture. At the end of class, ask your professor which topics he/she hopes to cover in the next lecture. This will give you a fairly good idea of how much you should read.

Remember that you are just reading to familiarize yourself with the topic, not fully comprehend every aspect of it. Keeping this in mind will make it seem less of a pre-lecture chore. More information on how to read the textbook can be found below in the Reading the Textbook section. The reading should be done either on the day of the lecture or the night before so that it is still fresh in your mind when you arrive for lecture.

Right before a lecture it is a good idea to review your notes from the last 10 or 20 minutes of the previous lecture. By doing this you will be ready to learn the next concept right away or if the last lecture ended in the middle of an example, you will know what the example is about. A great time to do this reading is in the few minutes before class while you are waiting for the professor to start the lecture.


There are many strategies for reading a textbook. Two of the most popular are listed here.


When reading to prepare for a lecture (see Lecture Preparation above) an easy-going approach is used. Since the focus of this reading is on familiarizing yourself with concepts, some areas of each section should be read and some can simply glanced over. In order to better explain this method and what should be read or glanced over, here is a walkthrough of how to read a section:

READ the introduction

Reading the introduction is beneficial because it introduces the concept of that section in the most basic terms. This allows you to easily understand the basics behind the concepts covered.

GLANCE over theorems/formulae/proofs:

These items often involve detailed and sometimes complex parts which may be confusing and in the case of proofs, might not be fully relevant to the most basic comprehension of the concept. This does not meen that proofs are unimportant and don't apply to a concept. In fact they are just the opposite! Understanding a proof is one of the best ways to understand a concept. However, this reading is not for understanding. It is meant so you can better follow a lecture. Therefore you should just skim over the theorems, formulae, and proofs so you will have an idea what is going on when your professor goes over them in detail.

TRY examples before glancing over them:

Before reading the walkthrough solution of examples provided throughout sections try to complete the example by yourself. If you get stuck, look at the next step in the textbook and try to finish the example from there. By doing this exercise, you reinforce your knowledge on the subject and if that example is done in class, you will be able to follow along easier.

READ the conclusion:

The conclusion restates the concepts in a simple form to enhance basic understanding of the concept. If your textbook does not have a conclusion at the end of the section, look after theorems or formulae are stated or proved. Complex theorems and formulae are often restated there in simpler terms.

TRY a few problems:

Look through the problems at the end of the section to see general question types and what questions based on the concepts covered in the section look like. Then choose a few problems to try. Don't attempt questions that look too difficult here. Remember, you just want to know what the section is about, not fully understand it. So choose questions that can be easily answered.

Above all, remember that this reading is only meant to give you some background knowledge on the subjects that will be covered in the lecture. If you don't understand something, make a note of it, pay extra attention at that part of the lecture, and ask your professor during or after lecture if you still need clarification. Don't worry about completely understanding the concepts while reading before the lecture.


The other reading strategy to be mentioned is how to read the textbook in preparation for tests or exams. This is more intense reading than the lecture preparation reading. The introduction and conclusion should be read in the same manner as before but the other parts of the chapter have significant changes in how they are read. Here is a list of the changes from the lecture preparation reading.

UNDERSTAND theorems/formulae:

Anything which is in a box such as a theorem, formula, fact, axiom, definition, etc. should be understood to the best of your ability. These are often the items needed to solve problems, so understanding them and how to apply them should be the focus of this reading.

READ proofs:

One of the best ways to understand a concept is understanding where it comes from and why it works. If you are able to understand the proof of a concept you will be better able to apply that concept in problem solving. Hence you should try and understand the proofs provided in the textbook.

COMPLETE examples before glancing over them:

When preparing for lecture you were encouraged to attempt examples once with the aid of the textbook. This time you should again try the examples but without the aid of the text. If you need the aid of the textbook to complete examples, then use it. After you have read the rest of the chapter, attempt these examples again without the textbook. This should be repeated until you can complete all the relevant examples without referring to the textbook or your lecture notes.

TRY a few problems:

When choosing problems to try do not choose the easier ones that you know you can solve. Instead, focus on moderate questions that give you some difficulty. When you can do those easily without referring to the textbook, try some harder questions. The harder questions often require you to have a deeper understanding of the concepts, so in attempting to complete them you are reinforcing your knowledge of the concepts of the section.

A more in depth look at which problems should be chosen, as well as more test preparation hints, are provided in the Test/Exam Preparation section.


Assignments are usually longer and have harder questions than tests. Because of the increased length and difficulty many students have problems with assignments. Here are a few suggestions to help in completing them.

Work in Groups

Working in groups is a great way to help each other. The questions that you can easily solve may be different from the questions that one of the others can solve. By working together, you reinforce your knowledge of the questions you know and you get an explanation to help you understand the questions you don't. It should be noted that working in groups does not mean copying each other's work. If someone has the answer to a problem that you don't, do not just copy their answer. Ask the person to explain how they got their answer and why or how they did the steps that you don't understand. Then try the question on your own, asking for their help only where you need it. Doing this not only protects you from plagiarism (which is taken seriously at this university) but also increases your knowledge and understanding, which will help you on tests and exams.

Take a Break

When working on assignments it is not recommended that you work for too long in one sitting. Take breaks whenever you are completely stuck, feel youself getting tired of math, or are starting to get unproductive. These breaks should last between 15 and 30 minutes and should be spent thinking about something other than math. Go have something to eat, watch a television show, play a video game, or whatever relaxes you and takes your mind off math.

You should not work on an assignment for more than a few hours at a time (meaning the entire session including breaks and all time spent working on the assignment). You should find that by taking breaks and not working for extended periods of time, you will be able to solve more questions. By leaving and coming back to a question, you have a clearer perspective on it. Questions will also be quicker to solve because you will not be as mentally tired.

When You're Hopelessly Stumped, Move On

If you have tried your best on a question and are simply stumped, move onto another question. You can attmept the blank questions again at a later time. You may find that in completing other questions, you find techniques to help solve the one you are having problems with.

Visit the Math Drop-In

If you still cannot answer some questions, visit the Math Drop-In Center. The Drop-In is ran by math professors and upper year math students. They are all there to help you with your problems. If your professor is not at the drop-in, ask another professor or a math student for help. The upper year students have taken your courses and have shown considerable understanding of the concepts. The Drop-In is a place that almost every math student visits at some point throughout their studies. Everyone needs help at times, so don't be afraid to 'drop-in'.

Visit the Calculus Website

This website can also be an invaluable tool to help with assignments. The tutorials, tests, sample problems and other sections of this website were created to help students that are having problems with calculus. The examples, sample problems and test questions were designed around probable questions that you may see on tests or assignments. Most of the examples have full, detailed solutions that may help you solve some of your problems.

Ask Your Prof

If your professor wasn't available or was busy helping other students in the Math Drop-In Center, go see him/her during office hours and ask for help. Each professor has certain office hours, during which they are more than happy to help students with problems that they are having.

Never Leave a Question Blank

If you are still stuck after attempting all of the suggestions above, you should remember one last thing: never leave a question blank when handing in an assignment. By this point you have probably put hours of work into the solution, so show your professor this by writing down what you know. Otherwise, the professor has no way of knowing that you even attempted the problem. Even if all you know is a formula that might possibly apply to something at some point in the solution, write it down. You never know what you'll get part marks for. These part marks could be the difference between a passing or failing grade, so never leave a question blank.


When preparing for tests and exams, it is suggested that you follow the Test Preparation Reading Strategy explained above. The key components mentioned in that reading strategy are understanding of the concepts and being able to complete the proper questions without external aid, such as asking for help or referencing the text.


A common complaint of students is so called "math amnesia", where the pressures of testing, such as time constraints and the need to score high to keep grades up, cause students to forget formulae or make mistakes in solutions that they normally would not make. One step in overcoming this is a mental exercise to try and relieve the stresses of test writing. Convince yourself that your score on this test will not harm your overall grade in a large way. Another step is understanding the concepts that will be tested. By understanding where a formula or process comes from (I.E. the proof of the formula or explanation of it in your textbook) you can always use that information to complete a question even if you forget the formula that should be used. Another bonus of understanding where the formula comes from is that you are less likely to forget it in the first place since you have a deeper understanding of it.

Here is an example of how understanding where a formula or process came from allows you to complete a question, even though you may forget the actual formula or process.

Question: 3x4=? (Now say you forget how to multiply but you know the concept behind multiplication)
Answer: 3x4 'means' 3 groups of 4. So I can add 4 three times to get the answer. So 3x4=4+4+4=12. Therefore 3x4=12.

Although this is a simple example, it still shows that understanding a concept can allow you to answer questions even if you forget how to answer them.


Another common complaint is that while doing practice problems, students either pick the wrong problems to do or picked the right problems but forgot how they solved them. The solution is simple but also quite laborious. When choosing questions to do, use the "Suggested Exercises" sheets handed out in class. Professors will often take questions directly from the suggested problems, or will use slightly modified questions on tests. Of course, you need not do all of the suggested questions. If you have no problem completing a certain problem type, choose only the hardest suggested problem of that type. If you had difficulty with any of the questions, redo them after you're done the rest of the questions until you can do all the problems with minimal difficulty and no help from any source such as a friend, classmate, or textbook.

One suggestion is to start a seperate notebook reserved just for solving practice problems. This way you have fast access to previous solutions and can see at a glance what problem types you had the most trouble with. This is especially important for final exam preparation as it allows you to minimize your time searching for appropriate examples or solutions, giving you have more time to spend practicing examples.

As a final note on practice problems, do not be timid about having to do an excessive amount of examples. The more examples you do, the better you will be at solving them. There is nothing wrong with having to do 60 questions 3 times each if that's what it takes to understand that topic.

As can be seen, test preparation can be a lot of work. Don't save it for the last minute. You should start preparing for the next test as soon as you know when it is. At the latest start preparing a week in advance of the test.


Taking tests can often be a stressful situation causing you to forget what you know and make 'silly mistakes' such as -1-1=2, instead of -2. The most important thing to remember is to RELAX.

At least a week before the test you should start following the strategy laid out in the Test/Exam Preparation section.

The last 30 minutes before you come to class should be spent doing something fun and interactive. Studying right up to the test/exam can often leave students confused about concepts and stressed by what they don't understand, leading to "math amnesia". So play a video game, play a card game, do a crossword. Do anything that makes you have to think and perform a task, as well as takes your mind off the test. Interactive activities such as these will help stop concepts from getting confused as well as alleviate some stress.

Arrive at class at least 15 minutes before the test starts so you can spend that time reviewing the concepts you need to review the most and have time to ask your classmates for last minute help.

If you are stuck on a question, skip it and come back if there is time when you're done the other questions. Try to never leave a question blank. Sometime time constraints can force you to leave questions unanswered, but if you have the time, fill in what you know about questions you cannot answer. You may get part marks for your partial solution and part marks add up. Writing down partial solutions for a few questions you cannot answer could mean the difference between a 40% and a 60%.

If you finish as much as you can do before time is up, check over your solutions. Make sure you solved the right questions and that you didn't make any 'silly mistakes'. Check if you remember anything else that could help you solve those questions that you didn't completely answer.

Above all else RELAX, STAY CALM, and DON'T STRESS before or during the test/exam.


This section is devoted to tips which either don't fit into any other category or were provided by past students who took this course.

Don't Skip Sections

If you ever come across a concept or topic you do not understand don't skip it and never return to it. Many concepts in this course build on previous concepts so by skipping one concept you may not have the basic understanding needed to understand future concepts. Since this new concept you do not fully understand can also be the basics behind another concept then you may not understand the next one either. It is quite easy for this to continue perpetually throughout the course and can make even the simplest topics covered at the end of the term be beyond your understanding.

This is one of the hardest errors to correct as well because the longer you leave trying to understand the first concept you skipped, the more you have to learn and the less likely you are to bother trying. Therefore skipping topics should be avoided at all costs. Use the resources on this website, ask your professor for help during office hours, visit the Math Drop-In Center, ask a classmate, try sample problems, or hire a tutor. Do everything in your power to understant all the topics you can.

Do Lots of Examples

One of the best ways to learn is by doing. Take advantage of this and tons of problems especially problems on topics you are having difficulty with. For more information on which problems to do see the Practice Problems section.

Keep a Notebook of Problems

As suggested in the Practice Problems section keep a seperate notebook for problems. Every problem you solve or attempt to solve should be in this notebook. This lets you quickly see where you went wrong, what you need to work on, and quickly reference solutions to maximize studying time.

Don't Make Math a Chore

Try to make math as fun and exciting as possible. If you make completing a math assignment or studying for a test into a chore then you may not learn as much and the purpose of the assignment or test (which is to help you learn and understand) may be defeated. A great way to make math more exciting is having math parties. Get together with a group of classmates and study together or help eachother through the assignment. For more information on working in groups, see the Completing Assignments section.

Ask for Help

When all else fails, ask somebody for help. Go see your professor during office hours, ask a classmate, go to the Math Drop-In Center, hire a tutor, or ask anyone else who may be able to help you. Sometimes all you need is to hear a concept explained in different words to allow you to understand the concept. Asking for help can be a valuable source of different explanations and can often help with your understanding of a topic.

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