Because I'm never sure if the 400 or so subscribers to the MathNotations feed ever see revisions I've made to a post (which I do frequently!), I'm letting everyone know that the latest post displaying the calculus videos regarding the 'boring a hole through a solid sphere' problem has been updated a few times. I've restated the problem originally posted in the beginning of 2008 and I have annotated the video clips so that you can decide which ones you want to view. It is very long and may be at times as 'boring' as the title of the problem!! Hey, folks, it's a learning process for me and eventually I'll just post links on my blog to these videos which I will upload to YouTube.
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SAT Math Tips
READ/LEARN ALL OF THE FOLLOWING!
ZERO IS A 'WEIRDO'!
(W)hole
(E)ven
(I)nteger
(R)Rational/Real
(DO) Cannot Divide by O!
BUT Zero is NOT Positive and NOT Negative!
POSITIVE INTEGERS start from 1
PRIMES start from 2 (not 1)
INTEGERS can be NEGative (and zero!) as well as positive
MEMORIZE the formula for the nth term of an arithmetic sequence: a(n) = a(1) + (n-1)d.
Example: Consider the sequence of positive integers which leave a remainder of 3 when divided by 4. What is the 100th term?
Step 1: List the first few terms 3,7,11,15,... to see the pattern and recognize it is an arithmetic sequence.
Step 2: Identify the values which are given
First term or a(1) = 3
Common difference or d = 4
Number of terms or position of desired term or n = 100
Step 3: Substitute into formula and solve
a(100) = a(1) + (100-1)(4) = 3 + (99)(4) = 399
Of course there are other ways to find the 100th term such as 100 x 4 - 1 but the formula is so useful for so many types of questions it is worth learning!
Know the above by heart and you are way ahead of the game! These facts will absolutely be needed on your next SAT or standardized test!
ZERO IS A 'WEIRDO'!
(W)hole
(E)ven
(I)nteger
(R)Rational/Real
(DO) Cannot Divide by O!
BUT Zero is NOT Positive and NOT Negative!
POSITIVE INTEGERS start from 1
PRIMES start from 2 (not 1)
INTEGERS can be NEGative (and zero!) as well as positive
MEMORIZE the formula for the nth term of an arithmetic sequence: a(n) = a(1) + (n-1)d.
Example: Consider the sequence of positive integers which leave a remainder of 3 when divided by 4. What is the 100th term?
Step 1: List the first few terms 3,7,11,15,... to see the pattern and recognize it is an arithmetic sequence.
Step 2: Identify the values which are given
First term or a(1) = 3
Common difference or d = 4
Number of terms or position of desired term or n = 100
Step 3: Substitute into formula and solve
a(100) = a(1) + (100-1)(4) = 3 + (99)(4) = 399
Of course there are other ways to find the 100th term such as 100 x 4 - 1 but the formula is so useful for so many types of questions it is worth learning!
Know the above by heart and you are way ahead of the game! These facts will absolutely be needed on your next SAT or standardized test!
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About Me
- Dave Marain
- NJ, United States
- Recently retired math educator and Supervisor of Mathematics; 30 years experience as an Advanced Placement Calculus (BC) teacher; Former Author of Math Teachers of New Jersey Annual HS Math Contest; Former K-5 Chair of New Jersey Math Content Standards and Curriculum Frameworks; Former member of Math Item Review Committee for New Jersey High School Proficiency Assessment; Experienced SAT Math Instructor and author of SAT materials; speaker at many regional and national math conferences
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