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52 Cards in this Set
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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^68 = 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)*(n1)*(n2)*...*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 (or2) =

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 