How to get my Math fully brushed up up to Highschool level?

[mark2142]

Hello, I was wondering how to check how much math I know and learn math up to High school level. Currently I am trying to learn the basic maths where I think i am weak. To give a light on how much i know, recently I learned that 1+1=2 is actually true. 1 cup + 1 cup = 2 cups. 2 cup - 1cup = 1 cup. 4 times 2 cup = 8 cups. and division. I have read some of the history of maths i.e. how math started with scratches on bones. But then I loose patience and get side-tracked into learning from other books (listed below). When I get overwhelmed by one book I try to learn from other My growth is slow. HELP !

I have some books from which I try to learn :
1. Crest of the Peacock
2. Works of Archimedes
3. Newtonprojects.com
4. Principia (Newton)
5. My School Textbooks

 

[jedishrfu]

I usually recommend the site MathIsPower4u.com its very comprehensive and covers middle school, high school and first-year college math summarized below:

• Number Sense: Fundamental concepts such as place value and basic arithmetic operations.

• Arithmetic/Prealgebra: Introduction to whole numbers, fractions, decimals, and basic algebraic concepts.

• Algebra 1 & 2: Topics range from introductory algebraic principles to more advanced concepts like functions, equations, and inequalities.

• Geometry: Exploration of shapes, sizes, relative positions, and properties of space.

• Trigonometry: Study of relationships between side lengths and angles of triangles.

• Calculus I, II, III: Comprehensive coverage of limits, derivatives, integrals, and multivariable calculus.

• Linear Algebra: Concepts including vector spaces, linear mappings, and matrices.

• Discrete Math: Topics such as logic, set theory, and combinatorics.

• Differential Equations: Methods and applications of solving differential equations.

• Statistics: Data analysis, probability, and statistical theories.

• Math for Liberal Arts: Mathematical concepts tailored for liberal arts studies.

• Standardized Test Preparation: Resources for exams like the SAT, ACT, and nursing-related tests.

• Graphing Calculator Tutorials: Guides on using TI-84 and TI-89 calculators, along with alternative tools like Desmos.

I got these resources using a chatGPT search:

1. Monroe University Math Placement Practice Test – This is a multiple-choice test that gives you instant feedback. It’ll help you see which topics you’re strong in and where you might need some extra practice.

Try it here

2. Math Mammoth Placement Tests – These tests cover math from grades 1-8 and are great for figuring out what concepts you might have missed along the way. They even come with answer keys so you can check your work.

Check it out here

3. Oregon State University Math Placement Exam – This test has 40 multiple-choice questions and is designed to see if you’re ready for college-level math. It’s a solid way to test your overall math skills.

Take it here

4. Math Placement Test Practice by Test Prep Review – If you want a mix of practice questions and study guides, this one’s for you. It covers everything from basic math to algebra and geometry.

Try it out

 

[symbolipoint]

@mark2142,
I recommend pre-algebra textbooks to start with. I long since lost familiarity with any such pre-algebra books, so I have no specific one to recommend. Study from it (your choice,...) as if you were a student in a class.

You have interest "high school level", so at the minimum, this means good basic Arithmetic and at least Elementary(Introductory) Algebra, and the typical rigorous sophomore full course of Geometry. You need to use a proper textbook for each. Study the Algebra first, thoroughly, as if you are some attending student. Could last 6 to 10 months;. then do the same with Geometry.

Somebody should give a bit of advice on progress assessments and customized tutorial guidance,...

 

[berkeman]

To give a light on how much i know, recently I learned that 1+1=2 is actually true.

Hmmm... How do you spell trolling?

 

[Mark44]

Hmmm... How do you spell trolling?

My thought as well, especially in a post in which the poster recently learned that 1 + 1 = 2 and lists Newton's Principia as a resource.

OTOH, perhaps the OP is being ironic or self-deprecating.

 

[symbolipoint]

Hmmm... How do you spell trolling?

My thought as well, especially in a post in which the poster recently learned that 1 + 1 = 2 and lists Newton's Principia as a resource.

OTOH, perhaps the OP is being ironic or self-deprecating.

Picky, picky, picky!

I took him seriously although the "1+1=2" part seems to not fit. I simply ignored that. I figured, I do not know the reasoning he said that.

 

[mark2142]

@mark2142,
I recommend pre-algebra textbooks to start with. I long since lost familiarity with any such pre-algebra books, so I have no specific one to recommend. Study from it (your choice,...) as if you were a student in a class.

You have interest "high school level", so at the minimum, this means good basic Arithmetic and at least Elementary(Introductory) Algebra, and the typical rigorous sophomore full course of Geometry. You need to use a proper textbook for each. Study the Algebra first, thoroughly, as if you are some attending student. Could last 6 to 10 months;. then do the same with Geometry.

Somebody should give a bit of advice on progress assessments and customized tutorial guidance,...

Can You recommend me one good book from each category namely pre algebra, algebra, geometry, arithmetic ?
I have Auffman, baker Introductory and intermediate Algebra book.

(no trolling)

 

[mark2142]

Somebody should give a bit of advice on progress assessments and customized tutorial guidance,...

Yes please.

 

[Mark44]

Currently I am trying to learn the basic maths where I think i am weak.

To give a light on how much i know, recently I learned that 1+1=2 is actually true. 1 cup + 1 cup = 2 cups. 2 cup - 1cup = 1 cup. 4 times 2 cup = 8 cups. and division.

The above really doesn't shed any light on your current knowledge of mathematics. On the contrary, what you wrote made two of us think you might be trolling. What would have been more helpful would be some examples of the types of topics you feel you need help with.

I have read some of the history of maths i.e. how math started with scratches on bones. But then I loose patience and get side-tracked into learning from other books (listed below).

Math history isn't helpful IMO if you're trying to address weak points you have.

I have some books from which I try to learn :
1. Crest of the Peacock
2. Works of Archimedes
3. Newtonprojects.com
4. Principia (Newton)
5. My School Textbooks

I never heard of the first one listed. Items 2, 3, and 4 might be interesting to you, but I don't see that they help in addressing weak points. Your school textbooks plus the topics listed by @jedishrfu would be helpful if you went through them in an organized and methodical way, not the scattershot approach suggested by your list.

 

[symbolipoint]

Can You recommend me one good book from each category namely pre algebra, algebra, geometry, arithmetic ?
I have Auffman, baker Introductory and intermediate Algebra book.

I have seen, bought, and used one or two books by Auffman & Baker (Barker?) for reviewing. They are good.

I would have to go digging, but at least for Geometry, there is or was Geometry by Baas, Charles, Johnson, & Kennedy; publisher Prentiss-Hall. That is not the only good book for Geometry.

 

[mark2142]

The above really doesn't shed any light on your current knowledge of mathematics. On the contrary, what you wrote made two of us think you might be trolling. What would have been more helpful would be some examples of the types of topics you feel you need help with.

I will be more specific in the future. Its negative numbers (integers) concept that I find unintuitive. I tried to learn by number line but I did not catch much. I searched other books but did not get it.

Your school textbooks plus the topics listed by @jedishrfu would be helpful if you went through them in an organized and methodical way, not the scattershot approach suggested by your list.

Its very informative site. Thank you @jedishrfu.

I actually don't know how to do it methodically. Sticking to the same topic till you get it always fails for me. Like negative numbers. I end up searching other books and then I don't get satisfactory answer anywhere.

 

[Mark44]

Its negative numbers (integers) concept that I find unintuitive. I tried to learn by number line but I did not catch much.

What is it about negative numbers that you find difficult?

Sticking to the same topic till you get it always fails for me.

Unfortunately, much of mathematics is sequential, in which success in a given topic depends on mastery of the preceding topics. For example, if you don't understand negative numbers, you won't be able to understand operations on them like addition, subtraction, multiplication, and so on. One of the threads you posted was about absolute values -- if you don't understand how numbers lie on the number line, working with absolute values will remain a mystery.

Skipping a topic you don't understand, and then going off to some other random topic is not a useful way to learn mathematics. That's why I said that your list of resources wasn't helpful - specifically, Archimedes and Newton's Principia, among others.

 

[mark2142]

Skipping a topic you don't understand, and then going off to some other random topic is not a useful way to learn mathematics. That's why I said that your list of resources wasn't helpful - specifically, Archimedes and Newton's Principia, among others.

much of mathematics is sequential, in which success in a given topic depends on mastery of the preceding topics.

Ok I’ll try to do my best to not go for random topics. The thing is I worry how much time it will take to learn a particular topic that I pick up. It gets overwhelming very quickly.

Can you tell me how to calculate how much time a particular topic takes so that I can relax in between my study sessions ?
Also how to be sure that I am making progress in understanding the topic ?

 

[Mark44]

The thing is I worry how much time it will take to learn a particular topic that I pick up. It gets overwhelming very quickly.
Can you tell me how to calculate how much time a particular topic takes so that I can relax in between my study sessions ?

There's no way I can advise you on how much time it will take for you to learn a given topic. However, it's a good idea to take a break from time to time to do something else. It's usually not productive to grind away hour after hour on something you're not making progress on. Sometimes, taking a break to eat, exercise, sleep, whatever, can allow your brain to come up with a fresh perspective on things.

Also how to be sure that I am making progress in understanding the topic ?

Work some problems related to that topic. Pretty much any textbook will have a set of problems for each main topic, and the same is true for some of the more helpful websites. If you're not able to do a specific problem, post a question here at PF.

Aside from the one that @jedishrfu suggested, there's also khanacademy.org, which has lots of videos on major mathematics areas as well as physics, chemistry and other areas.

 

[mark2142]

There's no way I can advise you on how much time it will take for you to learn a given topic. However, it's a good idea to take a break from time to time to do something else. It's usually not productive to grind away hour after hour on something you're not making progress on. Sometimes, taking a break to eat, exercise, sleep, whatever, can allow your brain to come up with a fresh perspective on things.

Work some problems related to that topic. Pretty much any textbook will have a set of problems for each main topic, and the same is true for some of the more helpful websites. If you're not able to do a specific problem, post a question here at PF.

Aside from the one that @jedishrfu suggested, there's also khanacademy.org, which has lots of videos on major mathematics areas as well as physics, chemistry and other areas.

Thanks man

 

[symbolipoint]

I will be more specific in the future. Its negative numbers (integers) concept that I find unintuitive. I tried to learn by number line but I did not catch much. I searched other books but did not get it.

That is a very serious problem. I do not mean that my being any kind of smart-alec. I am not trying to write like I'm a smart-alec. You need special instructive help.

 

[symbolipoint]

Based on posts #13 & 14,
To study "Pre-Algebra" - 2 to 4 months
To study "Algebra 1" - 3 to 10 months
To study "Geometry" - ~7 to 11 months

One should give comments on study scheduling. From me? ..... maybe later.

 

[mark2142]

One should give comments on study scheduling. From me? ..... maybe later

Yes and thank you.

Based on posts #13 & 14,
To study "Pre-Algebra" - 2 to 4 months
To study "Algebra 1" - 3 to 10 months
To study "Geometry" - ~7 to 11 months

Thanks man.

 

[robphy]

I learned that 1+1=2 is actually true. 1 cup + 1 cup = 2 cups. 2 cup - 1cup = 1 cup. 4 times 2 cup = 8 cups.

In intro physics classes, I try to stress the importance of units, which you displayed consistently in these examples.
But there are important non-examples, like:

• 1 foot + 1 inch =2 ____ (using a standard unit)
• 1 foot + 1 cup =

 

[symbolipoint]

• 1 foot + 1 inch =2 ____ (using a standard unit)
• 1 foot + 1 cup =

Those remind me about so-called "Dimensional Analysis".