Prepare for GRE

 GRE

LINKS:

FIRST GROUP of EXAMPLES

Answers to first group of questions.

 

 

 Group 2

Group 2

Geometry topics

 include:

 parallel and perpendicular lines

the online calculator that is available from ETS.

 

I made a video to show that
sometimes an INEQUALITY can have
NO SOLUTIONS OR
All Real Numbers as a SOLUTION
HERE IS A LINK TO THIS VIDEO 

NEGATIVE POWERS (EXPONENTS)

VIDEO LINK

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FUNCTION NOTATION

VIDEO TO WATCH

LINK

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VIDEO LINK FOR #63

 VIDEOS 

LINK 1

Link #2

45-45-90 LINK

 

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So the picture at the right implies

we can form 120 letter arrangements

of the letters: W,A,G,O,N
AGONW, AGNOW, ANGOW, etc.

Some types of word problems are easily solved using Combinations:
Suppose that you are going to choose a small group of 3 items
from a larger group of 7 items.
You could list all the possible groups, if need be.
But, you can count the number of the possible groups
by just using COMBINATIONS.
7 choose 3 has _35__ possible groups

7! / (3! times 4!) = 35

(7*6*5*4*3*2*1*)

(3*2*1)(4*3*2*1)

Reduce by dividing top

and bottom by (4!)

= (7*6*5)/(3*2*1)

OR

LOOKING at PASCAL's TRIANGLE

See the row with 1, 7, 21, 35, 35, 21, 7, 1?

7 choose NONE has _1_ possible group

7 choose 1 has _7_ possible groups

7 choose 2 has _21_ possible groups

7 choose 3 has _35_ possible groups

7 choose 4 has _35_ possible groups

7 choose 5 has _21_ possible groups

7 choose 6 has _7_ possible groups

7 choose 7 has _1_ possible groups

   

7 choose NONE has _1_ possible group
7 choose 1 has _7_ possible groups
7 choose 2 has _21_ possible groups
7 choose 3 has _35_ possible groups
7 choose 4 has _35_ possible groups
7 choose 5 has _21_ possible groups
7 choose 6 has _7_ possible groups
7 choose 7 has _1_ possible groups

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Suppose we wish to arrange n = 5 people {a, b, c, d, e}, standing side by side, for

a portrait. How many such distinct portraits (“permutations”) are possible?

5! = 120.

Permutations of {a, b, c, d, e}

These are the 5! = 120 ways of arranging 5 objects,

 in such a way that all the different orders count as being distinct.

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I made a video to show that

sometimes an INEQUALITY can have
NO SOLUTIONS OR
All Real Numbers as a SOLUTION
HERE IS A LINK TO THIS VIDEO 

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NEGATIVE POWERS (EXPONENTS)

VIDEO LINK

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Everyone did well on #47

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We probably need to talk about
 FUNCTION NOTATION

VIDEO TO WATCH

BEFORE TRYING THE PROBLEM BELOW

LINK

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VIDEO LINK FOR #63

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TWO VIDEOS for help with #71

LINK 1

Link #2

45-45-90 LINK

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