Effective Techniques for Studying Algebra II/Trig - Tips and Suggestions

[lj19]

I'm in Algebra II/Trig. On my first 2 tests, I did not do good. I take notes, study, mostly understand the material, and get extra help sometimes. I want to know if anyone can help by giving me techniques or suggestions on ways to study for this class, in general or specific. Thank you.

 

[QuantumP7]

Definitely don't be afraid to ask your teacher questions.

You wrote that you take notes and study, but actually doing the problems, in my opinion, is the only way to get good at math. Practice makes perfect.

 

[lj19]

The notes are basically only solving problems.
Are there any other ways to study for algebra?

 

[PrimeQuest33]

Dear lj19,

Confidence (in my humble but confident opinion) is 85%-90% the key to learning any subject. We often hinder ourselves by our self-imposed fears... our lens to reality, so to speak, fraught with bias and negativity that we unwittingly create.

There are various mental techniques one can use to relax oneself and clear these fears. Just know, for starters, that you have a fine mind and obviously a desire to learn. That is a majority of the battle right there.

Also, math is a language. Like any subject or language, mastering it is a building-block process. Don't be ashamed if you haven't mastered certain early steps. Go back to Square 1 if necessary and be certain you've learned that building block... then move forward.

Math is a joy and great fun. It is a combination of deductive and inductive reasoning. We use logic to get from point A to B; we also see answers intuitively and then strive to prove them logically. Both ways are "right."

I think of mathematical equations like a teeter totter. We're looking for balance. Solving for that particular variable is simply a matter of adding, subtracting, multiplying, dividing, or taking to a particular power BOTH SIDES to ensure the equality is maintained. The ultimate goal is to get our friend (y or some other variable) isolated... all by himself ... so that we can see what he equals. If we have something very simple, such as 3y=x, and we're looking for y, we want to have y stand alone. So we multiply both sides by 1/3, and y is "cleared" (standing alone) and our right side becomes (1/3)x.

Higher branches of mathematics...calculus, differential equations, and more... are no different. As we manipulate the symbols of our mathematical language, we also want to see the beauty and applicability of what we've uncovered.

Sometimes we even expand our language and create new languages for the beauty and reality of what we see. Math is only a language to describe our ever-expanding view of the truth of reality, but what a wonderful language it is.

Best wishes to you. :)

 

[fss]

Not really. The best way to learn algebra is to do a lot of problems. It's a fairly straightforward subject at this level.

 

[lj19]

I think it's just a change to do algebra now, because in my school you have to take advanced algebra I, then advanced geometry, then advanced algebra II/trig.
I was just wondering, if anyone knew specific ways to study algebra material.
Are there any online resources to study algebra? The one I know is regentsprep.org but are there any more helpful sites?
Thanks.

 

[Ch3st3r]

Here's one to make you think... What is γ?

144 x 15.71 + γ x 15.71 = (144 + γ) 14.05

 

[Ch3st3r]

BTW... γ isn't -144... Just in case you thought you could take the easy way out and multiply everything by 0 (Zero) ;)) Have fun.

 

[willem2]

BTW... γ isn't -144...

why is y not equal to -144?

 

[Ch3st3r]

Because there is another Answer.

Like I said... if you say Y is -144 it means you end up multiplying both sides with Zero.

There is another answer, you just have to find it. Good Luck.

 

[madah12]

Wait you are saying
15.71(144+y)=(144+y)14.05?
wouldnt this mean that that 14.05 must equal 15.71? so how this be solved?

 

[Ch3st3r]

Ok here's another way of writing it...

2262.24 + y x 15.71 = (144 + y) 14.05

 

[Mentallic]

Here's one to make you think... What is γ?

144 x 15.71 + γ x 15.71 = (144 + γ) 14.05

BTW... γ isn't -144... Just in case you thought you could take the easy way out and multiply everything by 0 (Zero) ;)) Have fun.

I don't know what kind of math you're using, but in my world, the answer is -144 and only -144. Unless you want to try pull some mathemagic trick on me.

 

[madah12]

http://www.wolframalpha.com/input/?i=2262.24+++y+*+15.71+=+(144+++y)+14.05+
y=-144
or are you saying wolfram lies?

 

[Ch3st3r]

I apologise, madah, I made an error... the Equation is : -

144 * 15.71 + y * -6.28 = (144 * y) 14.05

But hey, thanks for showing me wolframalpha.com ... What a fantastic Webb site.

I'll let you work it out now...even with the help of wolframalpha.com ... if you must, lol.

My Apologies again. :( Chester.

 

[Mentallic]

I find it weird that you keep using numbers like 15.71 and why you would ask the question with two given numbers not already multiplied together? 144*15.71? Just type in 2262.24

 

[madah12]

144
2262.24-6.28y=2023.2y

2029.2y=2262
y=2262/2029.2=1.115
where is the trick or point lol?

 

[Mentallic]

I don't know

He seems to be pretty hung on this problem though,
https://www.physicsforums.com/showpost.php?p=2920918&postcount=15"

 

[Ch3st3r]

The Trick or Point (as you put it) was to see if you were able to solve it...

But I've since found out a lot of people on this site either use Excell or Wolframalpha.

Now... Where's the point in that?

Thanks for your Reply, Chester

 

[annoymage]

lol metallic, the face your making,

pure smugness.

 

[madah12]

wait you expect people to use long division to figure out 2262/2029.2? also I used a normal calculator.

 

[PrimeQuest33]

Hi there. Good morning to all. I just saw this thread in my mailbox ... to solve 144 x 15.71 + γ x 15.71 = (144 + γ) 14.05

I like the way the equation makes my eyes cross (especially on a Monday morning, when they're glazed over anyway). x is not a variable but a multiplication symbol. γ resembles y, and it's an argument (on the right side of da equation). That's what makes the equation fun.

But unless I'm missing something, it seems to be pretty simple to solve...

15.71(144 + γ) = 14.05(144 + γ) Thus, y must be -144, for no other solution could render an equality with two disparate coefficients like 15.71 and 14.05 prefacing the same term (144 + γ).

Well, that's a female's take on things, and you know we're all crazy. Best wishes.

 

[Mentallic]

The Trick or Point (as you put it) was to see if you were able to solve it...

Is that to compare yourself to madah12 since you weren't able to solve it for yourself at first?
But if I remember correctly - since the posts were deleted - you pulled the same move in that thread that I linked to saying that y isn't equal to whatever the one and only answer was. Then you made a typo and corrected it. Seems like dejavu to me.

But I've since found out a lot of people on this site either use Excell or Wolframalpha.

Now... Where's the point in that?

For confirmation. And in this case it's to have indisputable evidence to reject your false claim.

lol metallic, the face your making,

pure smugness.

If my face was green and round, it would be an exact replica of my real facial expression.

 

[lj19]

I did this problem and y=14.9.

 

[Allenspark]

I don't know.. i did not have a problem solving it, and I am just a regular old algebra student.

Is combining the terms supposed to be the tricky part? once the problem is combined its pretty strait forward, even for me.

The coolest thing about this thread though.. is the link to that website. WOW. i can now check all my answers (like this one) before posting, or better yet, turning in homework.

y=1.14.

 

[Allenspark]

and to the OP, i find algebra best learned at home. I go to the lectures, take notes, then go home and research videos on you tube. Its amazing how many ways you can solve problems, the videos show lots of methods, and i apply the one that best fits my style.

I also tutor other students in the same level math as me, this helps me tremendously by explaining things over and over again.

 

[lj19]

To solve it I:
Multiplied 144 and 15.71 to get 2262.24.
The problem was then 2262.24(15.7+y)=(144 +y)(14.05).
Then I distributed 2262.24 to 15.7 and 2262.24 to y which equals 35517.168+2262.24y.
Then I distributed 14.05 to 144 and y which equals 14.05y+2023.2.
Then I subtracted the 2023.2 from both sides.
The problem then was: 33493.968+2262.24y=14.05y.
Then I subtracted 2262.24y from both sides.
Then the problem was 33493.968=14.05y.
Then I divided 33493.968 by 14.05 and y=14.9.

 

[Allenspark]

2262.24+-6.28y=2023.20y
-2023.20y-6.28y=-2262.24
-2029.48y=2262.24
y=1.114

i think you got your distribution wrong.. i did not distribute anything.

lets restate the problem for others to see.

144 * 15.71 + y * -6.28 = (144 * y) 14.05

 

[lj19]

Then I distributed 2262.24 to 15.7 and 2262.24 to y which equals 35517.168+2262.24y.
Then I distributed 14.05 to 144 and y which equals 14.05y+2023.2.

I distributed, because part of the problem is: 2262.24 (1.57 + y), and another part of the problem is: 14.05 (144 + y). Due to the addition sign you cannot combine anything in the parenthesis. So you would have to distribute the outer number being multiplied by the numbers and variables in the parenthesis.

 

[Allenspark]

I distributed, because part of the problem is: 2262.24 (1.57 + y), and another part of the problem is: 14.05 (144 + y). Due to the addition sign you cannot combine anything in the parenthesis. So you would have to distribute the outer number being multiplied by the numbers and variables in the parenthesis.

there is not addition within the parenthesis, that's multiplication. The left side was solved with order of operations. i could be wrong but that's what i get.

 

[lj19]

Here's one to make you think... What is γ?

144 x 15.71 + γ x 15.71 = (144 + γ) 14.05

2262.24+-6.28y=2023.20y
-2023.20y-6.28y=-2262.24
-2029.48y=2262.24
y=1.114

i think you got your distribution wrong.. i did not distribute anything.

lets restate the problem for others to see.

144 * 15.71 + y * -6.28 = (144 * y) 14.05

Which problem is the correct original problem?
(144)(15.71)(15.71 + y) = (14.05)(144 + y) or (144)(-6.28)(15.71 + y) = (14.05)(144)(y)?

 

[Allenspark]

Which problem is the correct original problem?
(144)(15.71)(15.71 + y) = (14.05)(144 + y) or (144)(-6.28)(15.71 + y) = (14.05)(144)(y)?

he changed it to this towards the bottom of the first page.
144 * 15.71 + y * -6.28 = (144 * y) 14.05

the original problem had a solution of -144.

 

[lj19]

I read this thread, I must've forgotten. After multiplying 144(-6.28)=904.32, the left side of the problem would be (904.32)(15.71 + y), so wouldn't you distribute the 904.32 to 15.71 and to y.

 

[Allenspark]

I read this thread, I must've forgotten. After multiplying 144(-6.28)=904.32, the left side of the problem would be (904.32)(15.71 + y), so wouldn't you distribute the 904.32 to 15.71 and to y.

he changed it to this towards the bottom of the first page.
144 * 15.71 + y * -6.28 = (144 * y) 14.05

the original problem had a solution of -144.

the left side is (144*15.71)+(y*-6.28)
The right side is (144*y*14.05)

 

[lj19]

For the left side, wouldn't you multiply -6.28 by 144? Then those equal 904.32.

 

[Allenspark]

For the left side, wouldn't you multiply -6.28 by 144? Then those equal 904.32.

im not sure why you would. the two multiplication problems on the left side are separated by addition.

 

[lj19]

Sorry, I meant to ask: Wouldn't you multiply 144 by 15.71 to get 2262.24, and then since there is an addition sign, distribute 2262.24 to y and to -6.28. Or could you use the foil method before simplifying?

 

[Allenspark]

Just simple order of operations solves this one. At least the way i see it.

 

[Mark44]

Here's one to make you think... What is γ?

144 x 15.71 + γ x 15.71 = (144 + γ) 14.05

Yes, this makes me think ... what a silly problem. I realize that you are all having a lot of fun with it, so more power to you, but after all is said and done, this is just a linear equation in y.

BTW... γ isn't -144... Just in case you thought you could take the easy way out and multiply everything by 0 (Zero) ;)) Have fun.

? If you multiply everything by 0, you get 0 = 0, which is obviously true but not very interesting. Chester, did you mean something else when you said "multiply everything by 0"?

 

[Allenspark]

Yes, this makes me think ... what a silly problem. I realize that you are all having a lot of fun with it, so more power to you, but after all is said and done, this is just a linear equation in y.



? If you multiply everything by 0, you get 0 = 0, which is obviously true but not very interesting. Chester, did you mean something else when you said "multiply everything by 0"?

read towards the bottom of the first page, he changed it after he realized it really was -144.

 

[lj19]

Could someone give me suggestions on how to do better on tests in this class?

 

[Allenspark]

Could someone give me suggestions on how to do better on tests in this class?

you can email me, i would be happy to go over stuff through gmail chat. Otherwise like i said earlier, i am a big fan of you tube videos, lots of different perspectives and approaches to problem solving.

 

[lj19]

Thanks, but no thank you on the emailing. Are there any specific people on YouTube that have a good selection of videos? One problem that occurred on the first test is that I ran out of time. There were 22 long questions that had to be completed in 40 minutes, and I did not finish, and I did not get everything I did complete right. On the second test, I did not get everything I completed right, but I completed the test.

 

[Allenspark]

You know, i don't have a favorit person, i search the problem that i am working on. Like "complex polynomial factoring" or "difference of cubes" etc. then i watch several of the videos to see how they differ and to reinforce the idea. If there is someone that i particularly like, i will go to there page and search through there stuff.

With that said, my textbook is not so great, but my professor is. I use the vids to explore all the ways to solve a problem.

 

[lj19]

Thanks for the suggestion.
Has anyone used any of the following sites?:
http://www.cliffsnotes.com/study_guide/Algebra-II.topicArticleId-38949.html
http://www.khanacademy.org/#Algebra
http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/index.htm

 

[Mark44]

I've heard a lot of good things about Khan Acadamy. I can't vouch for it personally, though.

 

[Mentallic]

Yes, this makes me think ... what a silly problem.

I thought I was the only one!

Could someone give me suggestions on how to do better on tests in this class?

If you know the layout of the next test (by being shown example tests and such) then definitely 100% certainly without a doubt go and do practice exams. This will give you a very good indication of how fast you need to go through the test if you set up exam conditions for yourself, such as timing yourself and marking your result after the exam by using an answer sheet or your teacher's help.

Good luck