Help me get this.

So comparing 3^17 + 3^18 to (4)3^17, apparently an easy way to solve this is as so:

Factor and you get: 3^17(1+3)=3^17(4). So the two items are equal.

???

Calming Down and Factoring

So I just finished reviewing all the math problems from my last practice test. Most of my issues are fairly correctable: not reading the problem carefully enough, reading carefully but forgetting an element of the question by the time I've completed some calculations, making problems more complicated than they have to be (this is a bit harder to correct as it requires the ability to translate problems into their simplest terms on first take, which is difficult for me as a "non-math" person who has been out of school for years), making simple errors in calculation, and so forth. There are a few concepts, however, that I need to review again. One of those is factoring polynomials. I've just been reviewing how to factor polynomials, and I want to share this great video I found on YouTube:

Know any middle schoolers or high schoolers who are learning to factor polynomials? I highly recommend you show them this video! I'm having so much fun taking polynomials from other YouTube videos on factoring polynomials, using this method, and getting the problems factored correctly before the other videos finish.

Here's another good one for cases in which you have four terms:

Students today are so lucky to have access to internet teachers! What cool stuff.

I'm having so much fun with factoring polynomials that I need to stop myself from doing more. Since factoring is just one of many concepts challenged by the GRE, I can't afford to spend more than a few minutes on it. Bummer. Time for me to go figure out something about factoring exponents in general, which apparently is the easiest way to realize that 3^17+3^18 is equal to (4)3^17. Also, I really need a tutorial in how to recognize problems that are best solved by unfactoring, that is using the FOIL method...and the simplest and fastest way to complete these problems. Any suggestions?

Bell Curve

Something I need to remember about the bell curve is that the major points are the curve are 2%, 16%, 50%, 84%, and 98%.

Percent Change: Remember This Formula?

Percent change = Difference/Original *100

Percentages--- From Words to Symbols

We all likely know that percent = something over 100, that is x/100.

Did you also know that in a word problem involving percentages, the following conversions can be made:

is...to...=
of, times product...to...* (multiplication symbol)
what...to...any varibable (example "x," "k," "s," "b, or "f")

So when a problem says 38 is what percent of 78, it is saying 38= ?/100 (78)

Square Roots to Know By Heart

I need to remember not only perfect square roots and that the square root of 1 is 1, but also:

The square root of 2=1.4 and the square root of 3=1.7.

Memorizing Common Fraction, Decimal, and Percentage Conversions

Have you noticed this (?) ...

I tend to use the blog (when studying) for things I need to memorize. I don't work through *how* to do the problems or complexities. I just focus on the basics of memorization here, while doing the rest of my studies on paper. Interesting.

Anyway, along those lines, my study guide recommends memorizing common fractions and decimals in the form of percentages in order to easily eliminate answers that are particularly off the mark.

Some are things I've naturally memorized in the course of my life, and I am sure you have too:

• 1.0 = 1/1 = 100%
• 2.0 = 2/1 = 200%
• 0.25 = 1/4 = 25%
• 0.5 = 1/2 = 50%
• 0.75 = 3/4 = 75%

Some are very familiar and perhaps already somewhat memorized, or easy to quickly figure out, even if I have to review them in order to recommit them to memory:

• 0.01 = 1/100 = 1%
• 0.1 = 1/10 = 10%
• 0.2 = 1/5 = 20%
• 0.4 = 2/5 = 40%
• 0.8 = 4/5 = 80%

Others I need to spend just a tad more time on to truly memorize:

• 0.333 = 1/3 (that part is familiar) = 33 1/3% (that I didn't realize)
• 0.6 = 3/5 (that part I would have had to calculate) = 60% (this I knew)
• 0.666... = 2/3 (that part is somewhat familiar) = 66 2/3% (that I didn't know)

Brush off Those Multiplication Tables

There are a couple mistakes on this video, but overall pretty good. I feel like if I worked out to it and said the answers as I went that it might help me brush up.

And then there is this this too...
multiplicationhiphopforkids.com

Cool!

I love these tricks...













And there's more, but it costs $42 to get them! Wah!

Once You Learn This System...

It might help for checking work:

Really Basic Math Review: Math Vocabulary

Factors vs. Multiples

As I recall, in b x c=a, b and c are factors of a

Someone please now explain what a multiple is in a way that does not have me confusing it with a factor. My brain just can't, for some reason, comprehend the difference.

However, these all are straight forward math vocab terms to me that I just needed to quickly review and recommit to memory:

product=result of multiplication
quotient=result of division
divisor=number you divide by
numerator=top number in a fraction
denominator=bottom number in a fraction

Eliminating Answer Choices in the Math Section

Here is one of those tricks to quickly eliminate answer choices from math questions without finishing all calculations for the problem. It involves returning to 5th or 6th grade math and just going through the options and crossing out those that simply don't fit due to basic arithmetic, once the problem is in its simplest form. Of course, it only works for a couple types of problems, that can be simplified into this form, but every bit helps.

pos x pos= positive
neg x neg= positive
post x neg= negative

even + even= even
odd + odd= even
even + off= odd

even x even= even
odd x odd= odd
even x odd= even

If these last two sets are forgotten, just knowing that the rules exist is helpful. Then you can plug in a couple numbers to figure out the rule.

Do You Remember "Please Excuse My Dear Aunt Sally?"

PEMDAS

You might remember learning this in your pre-algebra or early algebra days. It's a way to remember the order of operations for problems that require more than one type of operation.

Please=P=Parentheses
Excuse=E=Exponents
My=M=Multiplication...Dear=D=Division -->mutliplication and division are done together in the same step from left to right
Aunt=A=Addition...Sally=S=Subtraction -->addition and subtraction are done together in the same step from left to right

P...E...M/D -->....A/S -->

Handy to have tricks like that, I think. Good to be reminded. And fun to try a few problems to practice the order. Feel free to challenge me with a few problems to test my ability to follow order of operations.

October 12th True Confessions

I have a dark secret.

I do not have a memory for numbers. At all. In the 3rd grade we were required to memorize the multiplication table starting from the lower numbers and working our way up. It took me so long to complete the task of committing each to memory that the assignment ended before I was past 5x! I was so discouraged and ashamed that I never did finish. Instead, I developed a math phobia, though fortunately certain multiplication facts somehow did stick with me over the years of math that followed (for example: 6x6=36 and 9x9=81).

Still, in high school and college math classes, I depended on my calculator to make up for my basic math deficits. And it did. Until now. Now I don't get a calculator, and honestly, it freaks me out.

It is ironic that in my journey to grad school, the thing I am studying the most is third grade material. It is diminishing to my self-esteem, and I find myself regretful that I am "wasting" time now patching up things I let slip in the past. But this is a timed test, and seconds count. I need to be able to do the basic math almost without thinking so I can do the more complex math without hesitation.

If anyone has any tips for memorizing 5+ in the multiplication table, I am interested. My neice reminded me yesterday that I can use my hands to do 9x every interger through 10. I plan to memorize the 9x, but this is a good tool for double-checking my work so I can practice, say, while sitting in traffic. It also will make it easier for me to double-check my calculations during the test.

Any other ideas?

October 9th Math Review

Do you remember the handy rules for division? Here they are, for review. Since calculators aren't allowed during the GRE, I have to practice and increase my time with basic math.

• An interger can be divided by 2 if the units digit (the last digit of the number) can be divided by 2.
• An interger can be divided by 3 if the sum of its digits can be divided by 3.
• An interger can be divided by 4 if the last two digits form a number that can be divided by 4.
• An interger can be divided by 5 it the units digit is 0 or 5.
• An interger can be divided by 6 if it is divisble by both 2 and 3.
• I don't know a rule for 7 or 8. Do you? Oh wait, I just looked it up and for longer/bigger numbers, they are divisible by 8 if the last three digits form a number that is divisible by 8. Hmmm...not sure how useful that is. 7's rule also doesn't look particularly useful. If you double the last digit and subtract it from the larger number, if that number is divisble by 7 than so is the complete number. I think the lack of usefulness of these rules is why they weren't included in my GRE study guide.
• An interger can be divided by 9 if the sum of its digits can be divided by 9.
• An interger can be divided by 10 if the units digit (the last digit of the number) is 0.
• An interger can be divided by 11 (this one is complicated) if you add the odd digits and add the even digits to get two values, then subtract them, and the difference is an interger that is divisible by 11.
• An interger can be divided by 12 if it can also be divided by both 3 and 4.

Example by yours truly (please use the rules yourself and check my work):

549,810,653 (a totally random number)

• Not divisible by 2 because the last digit is a 3 which is not divisible by 2
• Not divisible by 3 because the sum of the digits, 41 if I added correctly, is not divisible by 3.
• Not divisible by 4 because the last two digits form a number, 53, which is not divisible by 4
• Not divisible by 5 because the last digit is not 0 or 5.
• Not divisible by 6 because it is not divisible by either 2 or 3.
• Unsure about 7 and 8.
• Not divisible by 9 because the sum of the digits, 41 if I added correctly, is not divisible by 9.
• Not divisible by 10 because the last digit is not a 0.
• Not divisible by 11 because 24-17 (if I did those sums correctly) is 7, which is not divisible by 11.
• Not divisible by 12 because it is also not divisible by 3 and 4.

It looks like 549,810,653 might just be a prime number. What do you think?

Edited 10/12/09: I found a handy prime number calculator online, and learned 549, 810, 653 is not prime...it is divisible by 7. Ah, one of my blind spots.