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Jim Clipper
climber
from: forests to tree farms
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Feb 22, 2014 - 02:14am PT
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Not counting coup, but I liked Mr. Hartouni's snappy answers and sound advice ... Wasn't there something about inflection points too?
if it is any help whitemeat, i remember a math professor saying that he always felt some frustration before solving a problem, then relief when he found the answer.
Maybe check this site as a reward for every few problems you solve too.
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Clint Cummins
Trad climber
SF Bay area, CA
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Feb 22, 2014 - 02:18am PT
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(2x+4)(2x+5) for number 9 clint??? No, that doesn't work (you do get 4x^2 + 20, but you don't get 0*x).
But you are doing the "guessing" process of factoring right.
9. 4*x^2 + 20 = 0
This one you don't have to factor, because there is only one term with "x" in it. Factoring is for when there are both x^2 and b*x .
So for 9, just use simpler algebra to get the one x term on the left side and everything else on the right. Then it's fast to solve for x.
In general, there are just a couple of tools for quadratic equations, and you try to use the one that is fastest.
1. a*x^2 + c = 0
2. b*x + c = 0
Only one x term - just solve direct for x as above.
3. x^2 + b*x + c = 0
A. First try factoring as (x+r)(x+s), by guessing integers.
If c is negative, r and s are opposite sign, right?
If b is negative, at least one of r and s is negative.
B. If your guesses don't work, use the quadratic equation (it is slower
but always works, and it also tells you if the solution is imaginary).
4. a*x^2 + b*x + c = 0
If everything divides by a, do that and try factoring.
Otherwise use the quadratic equation.
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neebee
Social climber
calif/texas
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Feb 22, 2014 - 05:05am PT
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hey there say, ... clint and ed, are setting out some very good advice...
me, as mom, well, i'd say this:
go back and find out WHY you can't do this...
and build up from there...
once you solve that, the trail will be a lot easier...
build upon good foundation, however:
you may be failing the test here, first,
with my advice, :O
but the next time, hopeful, you'd be 'soaring above' :)
best wishes, hang in there...
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rgold
Trad climber
Poughkeepsie, NY
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Feb 22, 2014 - 11:16am PT
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It's nice that Clint has gone into full tutoring mode. I'm not going to do that myself, for reasons that should be evident from what I've already posted.
However, it is worth mentioning, perhaps as much for others who are curious as the OP, that the first two problems require a little more knowledge than the other factoring problems, specifically the rational roots theorem, the factor theorem, and the ability to do "long division" with polynomials. Descarte's rule of signs is not essential but can be helpful in cutting down on the possibilities to be checked.
As the name of the first theorem suggests, these techniques will only work if the polynomial happens to have a rational root, which is of course the case for the given problems. But there are cubics with integer coefficients, e.g. x^3 + x^2 - 1, which have no rational roots.
The problem of finding the roots of cubic polynomials and then of higher-degree polynomials has led to an enormous amount of mathematics, including the discovery and use of complex numbers and the ground-breaking work of Evariste Galois that settled all the original questions and opened the door to research questions that are still very much alive today.
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climbski2
Mountain climber
Anchorage AK, Reno NV
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Feb 22, 2014 - 11:37am PT
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Some thoughts on math in general. I hated school and wasn't about to put an ounce of extra effort into it. Generally I skated by but math was a weakness, not becuase I couldn't learn. I was pretty fair at picking it up when I put effort into it. Sounds a lot like what you said earlier.
The problem with math is this. It builds up and if your foundation isn't solid you will get lost and blow out at some point.
Sadly for those who hate school this makes math rough even if they have a decent head for it. In math you HAVE to do the work. It can't really be cheated.
Oh well it seems life has chosen a different path for you. Based on your writing and math skills and clear interest in not putting your effort in school I'd say college is out for a while and climbing will be in.
Not bagging on you one bit, and I might be wrong here. You gotta follow your heart in life especially if it's burning with specific dreams. In this I suspect you are a very lucky young man, I think you've got some burning dreams and that in my short 40 years of life experience seems one of the truly valuable things to have in life.
So my advice , Be kind to all you meet, help everyway you can wherever you find yourself, Become an expert in and study what you love. Grab the opportunities that come along from time to time. If I were you I'd consider YOSAR for a couple seasons or more.
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WBraun
climber
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Feb 22, 2014 - 01:20pm PT
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whitemeat -- "my math teacher gave me a review packet with 50 problems that I don't know how to do"
Throw them into the dumpster and go climbing.
Make the math guys do the math.
That's what they're there for.
Not everyone needs to know math beyond arithmetic.
Let all the math egomaniacs solve the math problems.
Just like brain surgeons solve those problems.
Not everyone needs to become a brain surgeon ....
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ydpl8s
Trad climber
Santa Monica, California
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Feb 22, 2014 - 01:55pm PT
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I was a math tutor for the Boys & Girls clubs last year. It had been at least 25 yrs since I had done any of the types of problems that were like what you show here. I tried using example problems and the textbook to get caught up before a tutoring session, but it was taking too long.
Some friends told me that the intardnet now has numerous great websites where you can go online and have a video tutor walk you through each type of problem. They give enough examples so that you can actually learn (or in my case relearn) the subject, it's a great resource, take advantage of it! I was able to prepare in 30 min. for a whole slew of different students at different levels of algebra and geometry.
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mouse from merced
Trad climber
The finger of fate, my friends, is fickle.
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Feb 22, 2014 - 02:23pm PT
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Einstein could not do the math on his own work.
He relied on others for that.
Right on, WBrain!
As usual.
One who cannot do math is not stupid.
Just bored as hell.
If you can read the sign that says Camp 4, that's about all you will need.
Pratt walked away (climbed away) from physics.
I don't mean to step on Clint and the rest who are earnest.
You guys got the best of both worlds.
One needs to settle for one's own goals, not those of the rest.
"Infinity and Point Beyond."--Buzzed Lightyears
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micronut
Trad climber
Fresno/Clovis, ca
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Feb 22, 2014 - 02:30pm PT
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Don't listen to Werner Whitemeat!
Math (and all the other high school classes for that matter) are the "hauling" of the real world. Dirty, ugly, painful work that you gotta do if you want to be a bigwaller. Study, educate yourself while youre young, and climb until you're an old man. If you skip out and don't try hard and just go play all the time you'll be 40 years old working night shifts at Taco Bell. You've got moxy kid, we all know that. I hate math too, but get it done, don't cheat, do your own work, suffer a bit, and the summit will be within striking distance in no time.
See you this summer!
Scott
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PAUL SOUZA
Trad climber
Central Valley, CA
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Feb 22, 2014 - 06:21pm PT
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Be good at math because there will always be someone trying to take your money.
I was horrible at math all the way through high school. Spent five years in the Navy and then went back to school. Now, my highest level of math is calculus 1. While I never use calculus now, I know bullshit when I hear it.
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Guangzhou
Trad climber
Asia, Indonesia, East Java
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Feb 22, 2014 - 06:48pm PT
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As a Middle School math teacher, my advice is skip Number one and two and focus your time on the rest of the test. When all else is done and double checked, if you have time, go to 1 and 2.
Instead of asking for help on these equations, they are no problems in math, just equations, visit https://www.khanacademy.org/ and learn how to do these. Videos are short and excellent.
What class is this? Grade level?
Eman
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Gary Carpenter
climber
SF Bay Area
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Feb 22, 2014 - 07:07pm PT
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+1 for Kahn Academy
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whitemeat
Big Wall climber
San Luis Obispo, CA
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Topic Author's Reply - Feb 22, 2014 - 07:15pm PT
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alegebra 2
I am in 11 grade...
thanks for all the responses dudes! thanks for the life lessons too micronut :)
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Guangzhou
Trad climber
Asia, Indonesia, East Java
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Feb 22, 2014 - 07:30pm PT
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Wow, so different.We cover that in third and fourth quarter of Algebra I at my school. 8th graders.
With that said, my students don't climb, so you're one up on them fr sure.
Eman
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Guangzhou
Trad climber
Asia, Indonesia, East Java
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Feb 22, 2014 - 07:54pm PT
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I didn't like school in general and hatted math even more. Avoided the subject most of my life. Like you, when I started my own business, I ended up using it a lot When I sold the business, I was pretty comfortable with numbers in general.
My first middle school teaching position, they needed a teacher to teach an Algebra classes, so I added it to my teaching schedule. That was 11 years ago, now, I teach math, occasionally something else.
Over the years, I've had the opportunity to observe a lot of math classes. I think one reason students don't do well or enjoy the subject is that Math is often assigned and not taught.
I was being observed by a math teacher once, a peer to peer evaluation. She was very traditional with lots of Skill and Drill. When we spoke afterward, she explained to me that my Math class was "To much like Science." My student did hands on activities, collected data instead of reading it from a text, and talked among themselves about the material. She meant it as a criticism, I took it as compliment.
Get students excited about the classroom, they will start to enjoy the subject matter, once they are excited about the classroom and enjoy the subject matter, you can really begin teaching.
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overwatch
climber
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Feb 22, 2014 - 09:11pm PT
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You have to be trolling with the spelling
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wbw
Trad climber
'cross the great divide
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Feb 22, 2014 - 09:15pm PT
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For number 36: any 3rd degree polynomial function with real zeros of a,b and c will have 3 distinct linear factors of (x-a), (x-b) and (x-c).
So for your problem with given zeros of -3,0 and 5 the equation you are looking for is
f(x) = (x - -3)(x - 0)(x - 5), which is equivalent to f(x) = x(x + 3)(x - 5). It will be a polynomial with rational coefficients and a leading coefficient of 1. I'd multiply the rest out for you, but I generally charge $55/hr. for tutoring this stuff when I'm not teaching it in one of my Algebra 2 Advanced or Advanced Precalculus classes. (Never ceases to amaze me that parents will lay that kind of $$ down without a second thought, when their kid could get on Khan Academy, do a simple search and get excellent instruction for free.)
Personally, I admire your resourcefulness getting on the Taco for this, and cannot imagine what it must be like to sit in high school math classes having experienced the Shield. Good luck with that. Had I climbed El Cap before graduating high school, I never would have finished.
If you do choose to throw out the test and go climbing, I recommend that you not become one of those Valley lifer egomaniacs that thinks all Americans are stupid.
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Clint Cummins
Trad climber
SF Bay area, CA
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Feb 22, 2014 - 10:00pm PT
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But, Americans are stupid. Often. It's part of what makes life entertaining.
Not always, though. That's why it's a joke.
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