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

 

OR

 

(F+L)*N/2

 

 

 

Math Word Roots

 

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"

 

 

 

Useful Math Tips For The SAT

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

 

 

 

Averaqe Consecutive Evenly-Spaced Numbers

 

 

Ex:  2,5,8,11,14,17 = (2+17) / 2    *** (last + first) / 2