# Math Formulas for GRE

__GRE Math:__

ETS (Educational Testing Service) administers GRE or the General Record Examination at more than 700 test centers in 160 countries all around the world. The test takers get a chance to prove their skills and capability to handle college level courses. They also get an opportunity to fulfil their academic aims of studying in the best universities and colleges of the world. Students who are good at maths can take the Mathematics Subject Test to display their prowess in a specific field (which is math in here). While for them knowing math formulas is a necessity, even those students who take the GRE General Test that contains the Quantitative Section have to face questions based on various math formulas. Calculus, Algebra, Abstract and Discrete Mathematics and Geometry are few of the major topics covered in the math section. The Quantitative section alone contains questions based on data interpretation, understanding quantitative data, probability, and statistics. All of these topics connect to the application of certain formulas, which we shall discuss under the following headings.

__Formulas) for Geometry and Mensuration:__

There are some basic formulas that are covered in geometry, such as, finding the sum of sides of n-sided polygon, sum of quadrilateral being 360°, etc. However, there are more useful formulas for the math section. Those are:

- The measure of interior angles of any n-sided polygon: (n-2)x180/n.
- The sum of the measure of 'n' angles in a polygon having 'n' sides: (n-2) x 180.
- The measure of each interior angle in a polygon of 'n' sides: (n-2)x180/n.
- Area of a Rectangle: A=(side)² or A=½(diagonal)².
- Area of a Trapezoid: A=½(base₁+base₂)(height).
- Surface area of a cylinder with top and bottom: 2(pi)rh+2(pi)r².
- Volume of a Sphere: 4/3(pi)r³.
- Formula for a diagonal: l²+w²+h²=d².
- For any given area, the rectangle that exists with the smallest perimeter is a Square (versus a rectangle).
- For a given perimeter, the rectangle with the largest Area is a Square (versus a rectangle).

__Formulas for Algebra:__

For the algebra section, following points provide some important formulas:

- (x-y) (x+y)=x²-y²
- (x-y)²= x²-2xy+y²
- (x+y)
^{²}= x²+2xy+y² - a(b+c)=(axb) +(axc)
- Slope of a plain: y₂-y₁/x₂-x₁
- Distance between two points (x1, y1) and (x2,y2) in a graph: √( x2- x1)+(y2-y1)
- y = mx + b

You can check out the link: http://www.sparknotes.com/testprep/books/gre/chapter2section2.rhtml for more algebra formulas for the test.

__Formulas for Calculus:__

You will need the calculus formulas only when you take the Mathematics Subject Test as about 50% questions of it are based on it. Let us discuss some formulas for calculus in the following points:

__Integration:__

- xn dx = x(n+1) / (n+1) + C,(n -1)
- bx dx = bx / ln(b) + C
- sin x dx = -cos x + C
- tan x dx = -ln|COs x| + C
- sec2 x dx = tan x + C
- cos h x dx = sin h x + C
- cot h x dx = ln |sinh x| + C
- cosec h x dx = ln |tan h(x/2)| + C

__Differentiation:__

- sin x = cos x
- cot x = - csc2 x
- cot h x = 1 - cot h2 x
- sinh x = cosh x
- ln(x) = 1/x
- xn = n x(n-1)
- (f(x) + g(x)) = f(x) + g(x)
- f(x)/g(x) = ( f '(x)g(x) - f(x)g '(x) ) / g^2(x) (quotient rule)
- f(x)g(x) = f'(x)g(x) + f(x)g '(x) (product rule)

The above mentioned calculus formulas are few of the most important ones, which could be applied for solving the Math subject test questions. If you want formulas for series (summation) expansion, you should check the link: http://www.math.com/tables/expansion/series.htm.

__Other Formulas:__

Under this heading, you shall learn about some formulas that are common to both the General Revised test and Math Subject Test in GRE. Here they are:

- For solving simple proportion sums, you should cross multiply and get your answer, i.e., a/b=c/d, ad=cb.
- To diminish and increase a number by z%, you must multiply the number with 1-z% and 1+z% respectively.
- If you have a number that is a result of diminishing/increasing another number by g%, then you should divide the resultant number by (1-g %)/( 1+g %) respectively.
- If a given arc measures up to 'x', then the length of the arc is calculated by: x/360 x 2(pi)r.
- If you have the measurement of 2 radii and an arc, then the area of the sector formed by them is given by: x/360 x (pi) r².
- Positive integers having exactly two positive divisors are always prime numbers.

The importance of knowing these formulas is that these not only save up your time, it also make you more efficient and confident while solving math questions. Use the math formulas that are discussed above while practicing GRE math questions. Learn these and try to incorporate them in your practice routine. You can also use flashcards containing math formulas for a better learning experience.

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