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52 Cards in this Set

  • Front
  • Back
RC - Noteboard
Use noteboard to keep track of passage key ideas and structure.
RC- Working the Passage
Don't spend too much time reading thoroughly, but rather spend time working the questions.
RC - Big Idea
Think of RC as long arguments. Look for conclusions and premises. Then ask, "What's the big idea?"
RC - Trigger Words - COD
Change of direction

On the other hand; but; nonetheless; although; notwithstanding; however; except; yet; while; despite; unless; nevertheless
RC - Trigger Words - Same as it ever was
No change:

First of all; in addition; by the same token; likewise; similarly; for example; thus
RC - Key Ideas Sentences
Pay close attention to:

1st & Last sent. of 1st paragraph

1st sent of each body paragraph

Last sent of passage
RC - What to look for
Main Point/Thesis

Author's Tone or Attitude

Main Idea/Function of Each Paragraph

Change of Direction or Conflicting Opinions/Theories

More of the same
RC - Translate the Question
Translate wordy, confusing questions into everyday language.

Read slowly

Don't get bogged down by difficult language.

Turn it into a simple, straightforward question.
RC - Paraphrasing the Answer
Do your best to answer the question in your own words before you go to the answer choices.
Exponents - Multiplying
Add the exponents

x^4*x^3 = x^7
Exponents - Dividing
Subtract the exponents

x^8/x^5 = x^3
Exponents - Raised to another exponent
Multiply the exponents

(x^3)^2 = x^6
Exponents - Negative
x^6/x^8 = x^6-8 = x^-2 = 1/x^2
Reciprocal
Product of the reciprocal's of a number equal 1.
5^0 =
Any nonzero number to the zero power equals 1
5^1 =
Any number to the first power equals itself. (5)
1^37 =
One to any power equals 1.
0^37 =
Zero to any power equals 0
0^0
Undefined
Raising a number between 0 and 1 to a positive power = ?
The numbers get smaller

(1/2)^2 = 1/4
Exponents - Rules to remember
A negative number raised to an odd power is negative.

A negative number raised to an even power is positive.
Scientific Notation - Positive Exponent
Move the decimal to the right of the number

7.8 * 10^5 = 780,000
Scientific Notation - Negative Exponent
Move the decimal to the left of the number

2.3 * 10^-4 = .00023
Square Root
Defined as the positive root only.
Square Root - Addition
You can add expressions with roots if they have the same number under the radical sign:

2√7 + 4√7 = 6√7
Square Roots - Multiplication
1st multiply numbers outside the radical sign, and then the numbers under radical.

3√6 * 2√3 = (3 * 2)√(6 * 3) = 6√18

Finally, simplify is possible:

6√18 = 6√(9*2) = 6*√9*√2 = 6*3*√2 = 18√2
Square Roots - Division
Combine expressions and then divide:

√60/√3 = √(60/3) = √20 = √4*√5 = 2√5

Also:

√(4/25)= √4/√25 = 2/5
Square Roots - GMAT Convention
1/√3 = √3/3
Square Root - Fraction
When you take the square root of a number between 0 and 1, you get a bigger number.

√1/4 = √1/√4 = 1/2
x^1/2 =

x^1/3 =
√x ---> 9^1/2 = √9 = 3

∛x ---> 27^1/3 = ∛27 = 3
Finding Factors
Find the first parts: F

Find the last parts: Two numbers that its product is last term and sum is middle term.

Finally determine signs. Middle term determines this.
Finding Roots
Set quadratics equal to zero

Factor the quadratic

Then solve for x
Factorials
!

5! = 5*4*3*2*1

n! = (n)*(n-1)*(n-2)*...*1
0! =?
0! = 1! = 1
9^4 * 9^3 / 9^5 =
9^2
(2x^2)^3 =
8x^6
3x^4 * 5x^7 =
15x^11
2x^3 * x^4 + x^7 =
3x^7
(y^3 + y^3)^3=
8y^9
7^4 / 7^2 / x^0 =
7^2 = 49
7^3 * 7 / 7^5
7^-1 = 1/7
Successive powers of 2 (or-2) =
Find by doubling:

2, 4, 8, 16,32, 64, ...
√12/√3 =
2
√3 * √27
√81 = 9
√(25/49)
5/7
2√x* 3√x^3 =
6x^2
√2 * √3 * √12 * √50 =
60
∛(6^3 * 6^3) =
36
√288/√108 =
(2√6)/3
Root shortcuts
√25 = 5 and √36 = 6, √30 is between 5 & 6

√144 = 12 and √169 = 13, √150 is between 12 & 13

√48 + √35 ≅ 7 + 6 ≅ 13
Permutations
Order matters = No divide

Key words: Arrangements, Order/orderings
Combinations
Order does not matter = Divide

Key words: Groups/groupings, combination