HOW MANY MATH QUESTIONS IS ENOUGH?

[nycmathdad]

As most of you know, I am currently learning Calculus 1 on my own. I am having fun going through the textbook but came to a conclusion: IT IS TAKING FOREVER TO COMPLETE EACH SECTION. Textbook chapters are divided into sections or units.

After learning a section or unit, I then go to the questions. I answer 25 questions per section or unit. It takes me one week to complete one section or unit due to my current work schedule. The time has come for me to speed things up a bit.

There is NO TIME to answer every textbook question. Agree? I work overnight hours and thus sleep during the day. For example, I have been in chapter 1 now for 2 weeks. This makes no sense. Do you agree? Chapter 1 has about 6 or 7 sections or units. The entire textbook has 16 or 17 chapters.

MAIN QUESTION:

HOW MANY MATH QUESTIONS IS ENOUGH TO FULLY UNDERSTAND A CERTAIN TOPIC OR IDEA?

Honestly, I just cannot continue to study math at this rate. So, I came up with an idea. Moving forward, I plan to watch an entire math course (Calculus 1 for now) with professor Leonard on You Tube or Jenn from Calculus Workshop and, after each video session, work out the same problems they do as practice questions on my own.

Most teachers on You Tube or Jenn (not on You Tube) work out a decent amount of sample questions. I know Leonard works out at least 7 or 8 questions per video session. This amount of math questions should be enough, right? At the rate I'm going, it will take years to complete Calculus 1.

1. HOW MANY QUESTIONS IS ENOUGH?

2. WHAT DO YOU THINK ABOUT WORKING OUT THE SAME QUESTIONS THAT LEONARD OR JENN DO IN THEIR VIDEO SESSIONS? In other words, I watch them work out sample questions after sample questions and then tackle the same questions on my own. Good idea or bad?

3. IF YOU DISAGREE WITH 1 AND 2 ABOVE, WHAT CAN I DO TO LEARN THE MATERIAL WELL AND FAST?

Keep this in mind:

1. I am 55 years old. About to be 56 in April.

2. I don't want to complete my self-study of Calculus 1 when I am 60, if you know what I mean.

3. It took years for me to complete my Precalculus textbook. Did I say years? Yes, years due to lack of time.

4. I work 40 overnight hours. This is not an excuse. This is reality for me.

5. I am never going to stop answering math questions. I really love the subject but completing one section or unit per week is ridiculous. It's taking forever to complete chapter 1.

WHAT DO YOU SAY?

 

[jonah2.0]

As most of you know, I am currently learning Calculus 1 on my own. I am having fun going through the textbook but came to a conclusion: IT IS TAKING FOREVER TO COMPLETE EACH SECTION.

Must you really shout it out so loud?

Textbook chapters are divided into sections or units.

What's your point?

After learning a section or unit, I then go to the questions. I answer 25 questions per section or unit.

That's nothing.

It takes me one week to complete one section or unit due to my current work schedule. The time has come for me to speed things up a bit.

Why rush now when you took 14 years to review Precalculus?

There is NO TIME to answer every textbook question. Agree?

Disagree. There is always time.
Was there ever a time that you asked yourself while you were reading your favorite hooly book if There is NO TIME to read every page of it?

I work overnight hours and thus sleep during the day.

I was wondering when that will come up.

For example, I have been in chapter 1 now for 2 weeks. This makes no sense. Do you agree? Chapter 1 has about 6 or 7 sections or units. The entire textbook has 16 or 17 chapters.

So?

MAIN QUESTION:

HOW MANY MATH QUESTIONS IS ENOUGH TO FULLY UNDERSTAND A CERTAIN TOPIC OR IDEA?

Again, must you really shout so loud?
I remember reading SK and Jomo saying something about this a few weeks ago.
I'm sure you're bound to get a link to that thread sooner or later.
Personally, I like to answer them all.

Honestly, I just cannot continue to study math at this rate.

Why not?

So, I came up with an idea. Moving forward, I plan to watch an entire math course (Calculus 1 for now) with professor Leonard on You Tube or Jenn from Calculus Workshop and, after each video session, work out the same problems they do as practice questions on my own.

Most teachers on You Tube or Jenn (not on You Tube) work out a decent amount of sample questions. I know Leonard works out at least 7 or 8 questions per video session. This amount of math questions should be enough, right? At the rate I'm going, it will take years to complete Calculus 1.

1. HOW MANY QUESTIONS IS ENOUGH?

You won't know how much is enough until you know much is too much.

2. WHAT DO YOU THINK ABOUT WORKING OUT THE SAME QUESTIONS THAT LEONARD OR JENN DO IN THEIR VIDEO SESSIONS? In other words, I watch them work out sample questions after sample questions and then tackle the same questions on my own. Good idea or bad?

Redundancy comes to mind.

3. IF YOU DISAGREE WITH 1 AND 2 ABOVE, WHAT CAN I DO TO LEARN THE MATERIAL WELL AND FAST?

Have you heard of the phrase "There is no royal road to Geometry"?

Keep this in mind:

1. I am 55 years old. About to be 56 in April.

2. I don't want to complete my self-study of Calculus 1 when I am 60, if you know what I mean.

3. It took years for me to complete my Precalculus textbook. Did I say years? Yes, years due to lack of time.

4. I work 40 overnight hours. This is not an excuse. This is reality for me.

5. I am never going to stop answering math questions. I really love the subject but completing one section or unit per week is ridiculous. It's taking forever to complete chapter 1.

WHAT DO YOU SAY?

I say being 55 (allegedly) is nothing compared to a member here who's 80 and still trying to learn Calculus.

Any help would be much appreciated, as I'm eighty-years-old and am trying to learn calculus by myself, a task that would be nearly impossible, if it weren't for the internet and lots of good books...which isn't really 'by myself,' I guess.

Derivative of the arcsin (2x)

In learning about how to find the derivative of inverse trig functions, I see two different formulas given, depending upon which text you use: You can, supposedly, use the first formula, d/dx (arcsin u) = u'/(1-u^2)^1/2, or you can use the second formula, d/dx (arcsin u) = 1/(1- x^2)^1/2...

www.freemathhelp.com

 

[Harry_the_cat]

Jonah, I think you just need to scroll past these posts.

 

[Deleted member 4993]

Jonah, I think you just need to scroll past these posts.

I agreel

 

[Deleted member 4993]

As most of you know, I am currently learning Calculus 1 on my own. I am having fun going through the textbook but came to a conclusion: IT IS TAKING FOREVER TO COMPLETE EACH SECTION. Textbook chapters are divided into sections or units.

After learning a section or unit, I then go to the questions. I answer 25 questions per section or unit. It takes me one week to complete one section or unit due to my current work schedule. The time has come for me to speed things up a bit.

There is NO TIME to answer every textbook question. Agree? I work overnight hours and thus sleep during the day. For example, I have been in chapter 1 now for 2 weeks. This makes no sense. Do you agree? Chapter 1 has about 6 or 7 sections or units. The entire textbook has 16 or 17 chapters.

MAIN QUESTION:

HOW MANY MATH QUESTIONS IS ENOUGH TO FULLY UNDERSTAND A CERTAIN TOPIC OR IDEA?

Honestly, I just cannot continue to study math at this rate. So, I came up with an idea. Moving forward, I plan to watch an entire math course (Calculus 1 for now) with professor Leonard on You Tube or Jenn from Calculus Workshop and, after each video session, work out the same problems they do as practice questions on my own.

Most teachers on You Tube or Jenn (not on You Tube) work out a decent amount of sample questions. I know Leonard works out at least 7 or 8 questions per video session. This amount of math questions should be enough, right? At the rate I'm going, it will take years to complete Calculus 1.

1. HOW MANY QUESTIONS IS ENOUGH?

2. WHAT DO YOU THINK ABOUT WORKING OUT THE SAME QUESTIONS THAT LEONARD OR JENN DO IN THEIR VIDEO SESSIONS? In other words, I watch them work out sample questions after sample questions and then tackle the same questions on my own. Good idea or bad?

3. IF YOU DISAGREE WITH 1 AND 2 ABOVE, WHAT CAN I DO TO LEARN THE MATERIAL WELL AND FAST?

Keep this in mind:

1. I am 55 years old. About to be 56 in April.

2. I don't want to complete my self-study of Calculus 1 when I am 60, if you know what I mean.

3. It took years for me to complete my Precalculus textbook. Did I say years? Yes, years due to lack of time.

4. I work 40 overnight hours. This is not an excuse. This is reality for me.

5. I am never going to stop answering math questions. I really love the subject but completing one section or unit per week is ridiculous. It's taking forever to complete chapter 1.

WHAT DO YOU SAY?

rule of thumb - redo all the example problem s and

~10 excersize problems (whos answer s are g iven)

 

[nasi112]

I think that solving 1 problem in each section is enough for now to just get an idea of that section. This will let you finish reading the whole book in no time.

You would need to solve more questions in the same section whenever you encounter a problem that you could not solve.

Therefore, the sections will be as a reference that you get back to them whenever you need more skills and more ideas.

 

[Dr.Peterson]

rule of thumb - redo all the example problems and

~10 excersize problems (whos answers are given)

Agreed.

But in addition, I'd want to do at least one exercise in each group of similar problems, to make sure I covered all the major types I'm expected to be able to handle; and I wouldn't do only the first in a group, which in some books might be trivial.

Depending on the organization of the exercises and my confidence in my skills, I might skim the problems and pick out the ones I'm least sure of being able to do, rather than the easiest-looking (the last rather than the first in a group). Of course, sometimes it's hard to tell which problems teach different skills or involve different tricks.

 

[Steven G]

I think that you should 1st learn arithmetic. It should just take a few years. Then come back to this site after you mastered arithmetic and then ask for further instructions.

 

[JeffM]

Seriously, what’s the rush? You are an adult self-learner. The way to get a mathematical concept in your head is to use it repeatedly.

Looking at your data, let’s assume that your texts have ten chapters averaging 5 sections each. At a week a section, it will take aabout a year to cover on your own what would be half a year’s work with a teacher. That sounds quite respectable to me. You would likely have three hours of class time plus probably two to three hours homework and study time per week in a regular course. So if you are spending 7 hours per week on calculus, one hour a day, you are learning at about half the rate as you would in a class where you have the benefit of a teacher working from the same text you are relying on. Nothing to be ashamed of.

I am a little surprised that you must spend 7 hours to do 25 problems. Let’s say 6 hours because you need to spend time reading the text and understanding the worked examples. That works out to be about 20 minutes per problem That does strike me as excessive and suggests that you have not grasped the material before attacking the exercises.

Here is a counter-intuitive way that you may find lets you get the benefit of all the exercises provided without spending so much time on each problem. Usually, the earlier problems are meant to be easy. If you cannot solve those correctly and quickly, study your text again thoroughly before going on to more problems. If you cannot do problem 1 in a section quickly and correctly, there are only two possible reasons. One is that you made a careless error; the other is that you really have not yet grasped what the section is about. If, however, you can do the mechanical problems quickly and correctly, but have difficulty with the beginning word problems, that shows that you understand the technique but do not understand where and how it applies. That means you need to study the text again to try to figure out where the idea being discussed is useful.

In short, do not read the text once and flounder in doing problems. Read the text, start doing problems, and each time doing a problem takes forever or generates an incorrect error, study the text again to understand where you went wrong. Problems and text are not a strict sequence, but a dialogue.

 

[Deleted member 4993]

Seriously, what’s the rush? You are an adult self-learner. The way to get a mathematical concept in your head is to use it repeatedly.

Looking at your data, let’s assume that your texts have ten chapters averaging 5 sections each. At a week a section, it will take aabout a year to cover on your own what would be half a year’s work with a teacher. That sounds quite respectable to me. You would likely have three hours of class time plus probably two to three hours homework and study time per week in a regular course. So if you are spending 7 hours per week on calculus, one hour a day, you are learning at about half the rate as you would in a class where you have the benefit of a teacher working from the same text you are relying on. Nothing to be ashamed of.

I am a little surprised that you must spend 7 hours to do 25 problems. Let’s say 6 hours because you need to spend time reading the text and understanding the worked examples. That works out to be about 20 minutes per problem That does strike me as excessive and suggests that you have not grasped the material before attacking the exercises.

Here is a counter-intuitive way that you may find lets you get the benefit of all the exercises provided without spending so much time on each problem. Usually, the earlier problems are meant to be easy. If you cannot solve those correctly and quickly, study your text again thoroughly before going on to more problems. If you cannot do problem 1 in a section quickly and correctly, there are only two possible reasons. One is that you made a careless error; the other is that you really have not yet grasped what the section is about. If, however, you can do the mechanical problems quickly and correctly, but have difficulty with the beginning word problems, that shows that you understand the technique but do not understand where and how it applies. That means you need to study the text again to try to figure out where the idea being discussed is useful.

In short, do not read the text once and flounder in doing problems. Read the text, start doing problems, and each time doing a problem takes forever or generates an incorrect error, study the text again to understand where you went wrong. Problems and text are not a strict sequence, but a dialogue.

Superb advice.......

 

[nycmathdad]

Seriously, what’s the rush? You are an adult self-learner. The way to get a mathematical concept in your head is to use it repeatedly.

Looking at your data, let’s assume that your texts have ten chapters averaging 5 sections each. At a week a section, it will take aabout a year to cover on your own what would be half a year’s work with a teacher. That sounds quite respectable to me. You would likely have three hours of class time plus probably two to three hours homework and study time per week in a regular course. So if you are spending 7 hours per week on calculus, one hour a day, you are learning at about half the rate as you would in a class where you have the benefit of a teacher working from the same text you are relying on. Nothing to be ashamed of.

I am a little surprised that you must spend 7 hours to do 25 problems. Let’s say 6 hours because you need to spend time reading the text and understanding the worked examples. That works out to be about 20 minutes per problem That does strike me as excessive and suggests that you have not grasped the material before attacking the exercises.

Here is a counter-intuitive way that you may find lets you get the benefit of all the exercises provided without spending so much time on each problem. Usually, the earlier problems are meant to be easy. If you cannot solve those correctly and quickly, study your text again thoroughly before going on to more problems. If you cannot do problem 1 in a section quickly and correctly, there are only two possible reasons. One is that you made a careless error; the other is that you really have not yet grasped what the section is about. If, however, you can do the mechanical problems quickly and correctly, but have difficulty with the beginning word problems, that shows that you understand the technique but do not understand where and how it applies. That means you need to study the text again to try to figure out where the idea being discussed is useful.

In short, do not read the text once and flounder in doing problems. Read the text, start doing problems, and each time doing a problem takes forever or generates an incorrect error, study the text again to understand where you went wrong. Problems and text are not a strict sequence, but a dialogue.

I never said that it takes me 7 hours to answer 25 questions. This is crazy. I am not an A student but certainly better than 7 hours to complete 25 questions. Please read what Jenn from Calculus Workshop said to me in a recent email. I will not reveal my real name in any website. Just call me nycmathdad. By the way, I love your reply here. It's very detailed and shows that you care.

FROM JENN.

Thank you so much for your email - wow! what great questions!

HOW MANY MATH QUESTIONS IS ENOUGH TO FULLY UNDERSTAND A CERTAIN TOPIC OR IDEA? HOW MANY QUESTIONS IS ENOUGH?
I have found that most students find mastery after completing 8-12 questions, per section, on their own. This does not include the questions/problems that are done by an instructor as part of a lecture, but as homework.

WHAT DO YOU THINK ABOUT WORKING OUT THE SAME QUESTIONS THAT LEONARD OR JENN DO IN THEIR VIDEO SESSIONS?
I agree completely. I would work the questions along with the video. You can even pause the video and see if you can arrive at the answer before Leonard or myself As always, the more practice you get, the better you will be at understanding the material, but please keep in mind that you don't need to work 20+ problems to gain mastery, about 10 is sufficient.

Here are some personal tips for you, regarding practice questions, that I hope will help speed things up and get you through calculus quickly and with confidence:
1. If there are 25 questions in a section, which questions should you choose so that you gain mastery?
Work the first 4-5 questions and the last 4-5 questions in each section. As textbooks organize problems from easy to hard, you want to get your feet wet with the first 4 problems and then challenge yourself by working through the last 4 in the section, as these questions will definitely test your knowledge more thoroughly.

2. If you have a solutions manual for both the odd and even questions, then I would always choose to work the even questions over the odd ones. Why? Because textbook authors tend to put "harder" questions as even problems, because the answers will not be found in the back of the book.

3. The best advice to self-learning calculus is to watch the videos and complete the provided practice problems on our website. If you are able to answer the problems seen in the video as well as the practice worksheet then you can comfortably move on to the next section, knowing that you're ready. But if you prefer to work more examples from the textbook, then follow the tip in #1 and work the first four and the last four problems in each section.
I hope this helps.

Best,
Jenn

 

[nycmathdad]

Agreed.

But in addition, I'd want to do at least one exercise in each group of similar problems, to make sure I covered all the major types I'm expected to be able to handle; and I wouldn't do only the first in a group, which in some books might be trivial.

Depending on the organization of the exercises and my confidence in my skills, I might skim the problems and pick out the ones I'm least sure of being able to do, rather than the easiest-looking (the last rather than the first in a group). Of course, sometimes it's hard to tell which problems teach different skills or involve different tricks.

Dr. Peterson,

Please read what math teacher Jenn from Calculus Workshop said to me in a recent email. I will not reveal my real name in any website. Just call me nycmathdad. What do you think about what Jenn said?

FROM JENN.

Thank you so much for your email - wow! what great questions!

HOW MANY MATH QUESTIONS IS ENOUGH TO FULLY UNDERSTAND A CERTAIN TOPIC OR IDEA? HOW MANY QUESTIONS IS ENOUGH?
I have found that most students find mastery after completing 8-12 questions, per section, on their own. This does not include the questions/problems that are done by an instructor as part of a lecture, but as homework.

WHAT DO YOU THINK ABOUT WORKING OUT THE SAME QUESTIONS THAT LEONARD OR JENN DO IN THEIR VIDEO SESSIONS?
I agree completely. I would work the questions along with the video. You can even pause the video and see if you can arrive at the answer before Leonard or myself As always, the more practice you get, the better you will be at understanding the material, but please keep in mind that you don't need to work 20+ problems to gain mastery, about 10 is sufficient.

Here are some personal tips for you, regarding practice questions, that I hope will help speed things up and get you through calculus quickly and with confidence:
1. If there are 25 questions in a section, which questions should you choose so that you gain mastery?
Work the first 4-5 questions and the last 4-5 questions in each section. As textbooks organize problems from easy to hard, you want to get your feet wet with the first 4 problems and then challenge yourself by working through the last 4 in the section, as these questions will definitely test your knowledge more thoroughly.

2. If you have a solutions manual for both the odd and even questions, then I would always choose to work the even questions over the odd ones. Why? Because textbook authors tend to put "harder" questions as even problems, because the answers will not be found in the back of the book.

3. The best advice to self-learning calculus is to watch the videos and complete the provided practice problems on our website. If you are able to answer the problems seen in the video as well as the practice worksheet then you can comfortably move on to the next section, knowing that you're ready. But if you prefer to work more examples from the textbook, then follow the tip in #1 and work the first four and the last four problems in each section.
I hope this helps.

Best,
Jenn

 

[jonah2.0]

Beer soaked ramblings follow.

... Please read ...

... Please read ...

What's with the redundancy?
It's like you're on a campaign.

 

[JeffM]

I never said that it takes me 7 hours to answer 25 questions. This is crazy. I am not an A student but certainly better than 7 hours to complete 25 questions. Please read what Jenn from Calculus Workshop said to me in a recent email. I will not reveal my real name in any website. Just call me nycmathdad. By the way, I love your reply here. It's very detailed and shows that you care.

Excuse me if I misinterpreted your original post.

You said that a section has about twenty-five exercises and that you spend a week going through a section. I was assuming that you spent about an hour a day. That adds up to 7 hours to grasp the concepts and do the exercises.

Now, you may average less time per week. Perhaps you spend two hours a week on average. Notice that that is less than half the time you would spend if you were taking a class and doing homework. If that is all the time you can afford, then that is all the time you can afford, but it certainly is not excessive for self-learning.

My fundamental point is that the more problems you do related to a particular topic, the more likely you are to grasp and retain the mechanics and applicability of that topic. If you can solve correctly 25 problems in 25 minutes, you definitely have that topic. On the other hand, if it takes you twenty minutes of careful work for you to get the wrong answer on a single problem, it makes no sense to start on another problem immediately; it makes more sense to go back to studying the text or asking a question here than continuing with the problems because that much work to get a wrong answer means you are missing some vital piece of what the section is about.

As a self-learner, the problems are the way you confirm that you understand; they are the only test a self-learner gets.

 

[Dr.Peterson]

2. If you have a solutions manual for both the odd and even questions, then I would always choose to work the even questions over the odd ones. Why? Because textbook authors tend to put "harder" questions as even problems, because the answers will not be found in the back of the book.

I totally disagree with #2. First, it is not my experience that even problems are harder; they are there so teachers can assign them and find out whether students learned from the odd problems. Second, if you have a solutions manual with the answers to all problems, you either illegally got a teacher's manual, or anyone can get it and the whole premise disappears. And, of course, she already said in #1 that you need to do both easy and hard problems to learn, which I agree with. This whole paragraph is inconsistent.

Also, of course, the particulars depend on the book. Books I use commonly have more than one kind of problem in a section, and they are not easy-to-hard across the whole set, only within one part.

Ultimately, all you need to do is to do enough problems to convince you that you could do all of them if you had time. If you have trouble on a hard one, go back to the text and then do an easier one. Take all the time you need. If you do less, and end up not learning it, what's the benefit in that? If you do more than you need, you'll just have more confidence (assuming you get them right -- and it you don't, then you've done less than you need!). I agree fully with JeffM that if you have half the time you'd put into an official course, then you can expect to go half as fast (or less, due to inefficiencies). Your speed seems reasonable to me! And there's no rush.

You also might want to spend less time posting sometimes, and more just learning, if time is the issue.

 

[JeffM]

I want to support something that Dr. Peterson said. Frequently a set of problems does not go easier to harder in some strict progression because there are different kinds of problems. For example, it is very usual to have a bunch of purely mechanical problems followed by a bunch of word problems. The first word problem may be materially easier than the last mechanical problem. Moreover, the last word problems may be much more challenging than the initial mechanical problems. So I don’t think much of Jenn’s advice.

On a different topic, I greatly dislike the failure to provide a complete answer key because it reduces the value of the book for self-study and review. But it is apparently illegal to provide such a key (another stupid piece of law). If your text provides a key to only half the problems, then the problems with answers are the ones of primary importance to self-learners. If you get all of those right, then you probably can get away with skipping the ones without answers. That reduces your problems by half. Of course if you cannot correctly do the ones with answers, then, after studying the topic again, you need to do the problems without answers.

 

[jonah2.0]

Beer soaked realization follows.

... Please read what Jenn from Calculus Workshop said to me in a recent email. ...

Just realized that you just shared a private email with the world.
Big etiquette mistake.
This from someone who just ranted about society going "bunkers".
I am so happy to know that I was raised in a different generation. Society today has totally flipped its lid. Society has gone bunkers. Common sense is out the window. Lord, have mercy on us all ...

 

[nycmathdad]

I totally disagree with #2. First, it is not my experience that even problems are harder; they are there so teachers can assign them and find out whether students learned from the odd problems. Second, if you have a solutions manual with the answers to all problems, you either illegally got a teacher's manual, or anyone can get it and the whole premise disappears. And, of course, she already said in #1 that you need to do both easy and hard problems to learn, which I agree with. This whole paragraph is inconsistent.

Also, of course, the particulars depend on the book. Books I use commonly have more than one kind of problem in a section, and they are not easy-to-hard across the whole set, only within one part.

Ultimately, all you need to do is to do enough problems to convince you that you could do all of them if you had time. If you have trouble on a hard one, go back to the text and then do an easier one. Take all the time you need. If you do less, and end up not learning it, what's the benefit in that? If you do more than you need, you'll just have more confidence (assuming you get them right -- and it you don't, then you've done less than you need!). I agree fully with JeffM that if you have half the time you'd put into an official course, then you can expect to go half as fast (or less, due to inefficiencies). Your speed seems reasonable to me! And there's no rush.

You also might want to spend less time posting sometimes, and more just learning, if time is the issue.

I agree. In fact, not rushing is key to success in any subject. For example, I made it as far as Section 1.3 (Continuity) and then decided to go back to Section 1.1. I scored an 85 percent on the Section 1.3 test but a lot of guessing correctly is the reason for that score.

I just felt that the section on continuity did not sink in well enough to proceed in the textbook. I am now learning how to estimate limits using a table of values. It's ok but boring. I am also learning how to find limits graphically. Not too bad for now.

 

[nycmathdad]

I want to support something that Dr. Peterson said. Frequently a set of problems does not go easier to harder in some strict progression because there are different kinds of problems. For example, it is very usual to have a bunch of purely mechanical problems followed by a bunch of word problems. The first word problem may be materially easier than the last mechanical problem. Moreover, the last word problems may be much more challenging than the initial mechanical problems. So I don’t think much of Jenn’s advice.

On a different topic, I greatly dislike the failure to provide a complete answer key because it reduces the value of the book for self-study and review. But it is apparently illegal to provide such a key (another stupid piece of law). If your text provides a key to only half the problems, then the problems with answers are the ones of primary importance to self-learners. If you get all of those right, then you probably can get away with skipping the ones without answers. That reduces your problems by half. Of course if you cannot correctly do the ones with answers, then, after studying the topic again, you need to do the problems without answers.

1. The problems without answers does not serve a purpose. How would I know if my answers are correct or not?

2. I don't have a computer or laptop. Using the phone to provide my math work in LaTex form is really hard and takes too much time.

3. Jeff, I work 40 overnight hours during the week. Answering all the problems with answers will take forever to complete one chapter. Understand?

4. After the continuity Section 1.3, I decided to go back to Section 1.1. I scored 85 percent on the Section 1.3 test but guessing has a lot to do with that score.

5. Anything else I should know?

 

[JeffM]

1. The problems without answers does not serve a purpose. How would I know if my answers are correct or not?

You must learn to check your answers. Everyone makes mistakes. Everyone must learn how to find and correct those mistakes. Learning from mistakes is very powerful.

2. I don't have a computer or laptop. Using the phone to provide my math work in LaTex form is really hard and takes too much time.

I do not get the relevance. You can use paper and pencil without any need for LaTeX.

3. Jeff, I work 40 overnight hours during the week. Answering all the problems with answers will take forever to complete one chapter. Understand?

No. I do not understand. You have a certain limited amount of time when you are free and mentally capable of doing math. That I understand. Let’s say that is four hours. You need an hour to read a section carefully and thoroughly. That leaves only three hours to do problems. 180 minutes. With 24 problems, that is 7.5 minutes per problem. If you thoroughly understand the topic and work carefully, that seems ample: some easy problems will take far less, and the hardest problems may take ten or twelve minutes, but 7.5 minutes seems a generous average if you have thoroughly mastered the material.

Notice that four hours is the minimum you would expect to spend if you were taking a course. The idea that you can learn as fast when self-teaching as you can if taught by someone fully conversant with the material is simply ridiculous. You should expect that mastering calculus on your own will take at least two years. If you think that it can be mastered in three or four months by working only a few hours per week, you are wrong.

4. After the continuity Section 1.3, I decided to go back to Section 1.1. I scored 85 percent on the Section 1.3 test but guessing has a lot to do with that score.

Continuity, Riemann sums, limits, etc. are the hardest parts of calculus. It took professional mathematicians two hundred years to develop these concepts. If it takes you six weeks to master them, that is hardly surprising. Most of calculus is considerably easier if your algebra is solid.