A
Simple Formula For Computing the Sum of All Numbers from F to L
∑(F,L)=
( L² - F² + F + L)/2
Where: F is the first number in the number line and L is the Last.
Example:
To add all the numbers from 1 to 10 Plug in 1 for F, and 10 for L.
(10² - 1² + 10 + 1)/2 =
(100 - 1 + 11)/2 =
110/2 = 55
The result is the same as adding all the numbers from 1 to 10 like this:
1+2+3+4+5+6+7+8+9+10=55
This works for all nonnegative integers where 0<F<L. You don't have to
start with 1
(F+L)*N/2
Algebra
From the 825 A.D. book, "ilm al-jabr w'al Maqa balah" (translated
"The Science of Cancellation and Reduction") by the great Iranian
Mathematician, Mohammed Ibn Musa al-Khowarizmi. After years of bad
pronunciation by Europeans, it came down as "aljabra" and,
eventually, "algebra"
Calculus
From the Latin "calculus" meaning "stone used for
reckoning"
Cosine
From the complement of sine because it is 90 degrees out of
phase.
Exponent
Means "placed out" from two Latin words: "ex" (out) and
"pon" (place)
Fraction
From the Latin "fractus" meaning, literally, "broken"
Geometry
Greek word geometria from geo (earth) and metro (measure)
Logarithm
Means "proportional number" from two Greek words: "logos"
(proportion) and "arithmetik" (number)
Why we use the letter "m" to denote the slope of a line
m is for the french verb "monter" which means to mount, to climb, or
to rise
Percent
Means "by the hundred" from two Latin words: "per" (by) and
"centum" (hundred)
Sine
From the Latin word sinus which means " folded cloth"
Trigonometry
Greek word "trigonometria" from Tri (three) gonia (angle) metro
(measure)
Zero
From the Arabic "zefirum" meaning "empty"
Plug in
numbers for variables.
On problems with
complicated formulas with a number of variables, it can be faster to plug in
actual numbers for each variable than to use formulas to figure out what the
variables are.
Estimate if you
can.
If you see that the
answer choices vary widely, use rounded off numbers in your calculations. For
example, you can round off 4,867 X 6,732 to 5,000 X 7,000, which would give you
35,000,000. By estimating, you can easily eliminate choices that are not close
to 35 million such as 35,000 or 35 billion.
Beware of the
traps.
When they write the
test, test makers include a number of traps that catch most students. Your job
is to not be fooled. Typical tricks test makers try to get away with include:
giving more information than you need to solve a problem, offering incorrect
choices that you can arrive at by partially completing the problem or by using
the correct information with wrong calculations, and giving numbers in the
answer choices that remind you of numbers in the equation. Be cautious of
answers that are too easy to calculate, especially at the end of the SAT Math
section when the problems are supposed to be the most difficult.
Know how to
answer the SAT I Student-Produced Response questions.
There are no
negative answers or answers greater than 9,999. Percentages must be filled in
as .75 or 3/4, NOT 75.
Eliminate
choices and guess.
If you can
eliminate one or two wrong answers then guess the correct one. The more wrong
answers you can eliminate the better your odds of picking the correct answer.
Be sure to mark these questions so if you have time at the end you can go back
and double check your choices.
Percent
Decrease / Percent Increase
Decrease:
Ex: 3% (.03)
decrease from 25 = what number?
Solution: 25 * .97
Increase:
Ex: 3% (.03) increase from 25 = what number?
Solution: 25 * 1.03
Ex: 2,5,8,11,14,17 = (2+17) / 2 *** (last + first) / 2