GRE MATH, Magoosh Math GRE Formulas, GRE Math formulas

ratio of to

"of" top "to" bottom 30 oranges of 120 apples 20/12

Algebra-Multiplying Monomials

(5y^3)(6y^2)=30y^5 Add exponents when multiplying

Algebra-Simplifying Expressions

(6xy-5x)-(4xy-3y)= 2xy+5x+3y

Solving Equations-Eliminating Fractions

(a/b)(b/a)=1 2/5x=8 5/2 * 2/5 x = 5/2 * 8 x=20

Stats-Weighted Average

(proportion) x (group A average) + (proportion) x (group B average) + ...

graph linear equation

...

Exponent Laws - 1 and 0 as bases

1 raised to any power is 1. 0 raised to any nonzero power is 0. Any nonxero number to the power of 0 is 1 (i.e. 7^0 =1)

Word Problem-Sequences

1+2+3+...+n = [n(n+1)/(2)]

Combined work,how long would it take for everything to work together

1/r+1/s=1/time (inverted) R=2 s=twice as long so 1/2+1/4=3/4=4/3

Word Problems-Work Rate

1/total work = (1/work rate 1) + (1/work rate 2) output=rate*time

Fast Fractions

1/x + 1/y = (x+y)/xy

TRAPEZOID

A=(b1+b2/2)h

Area of a Triangle

A=1/2bh Multiply the base (b) by the height (h) and divide by 2. Note: angles in a triangle always add up to 180 degrees

Area of a rectangle

A=lw

Area of a square

A=s2

Area of a Circle

A=πr^2 Note: all circles equal 360 degrees

Compound interest

Amount× (1+ interest rate (time)(# of times compounded anually)/#of times coumpounded anually. Divide fraction first then add 1

Coordinate Geometry-Lines

Any line can be represented by y=mx+b, where m is the slope and b is the y-intercept. This is called slope-intercept form. The slope of a line can be found subtracting the y values of a pair of coordinates and dividing it by the difference in the x values: slope=m= (y2-y1)/(x2-x1) To find the y-intercept plug in zero for x and solve for y To find the x-intercept, plug in zero for y and solve for x An equation like x = 3 is a vertical line at x = 3; an equation like y = 4 is a horizontal line at y = 4. If given two points and asked to find the equation of a line that passes through them, first find the slope using the above formula, then plug one of the points into y = mx+b and solve for b. The slopes of two lines which are perpendicular to each other are in the ratio of x : -1/x, where x is the slope of one of the lines (think: negative reciprocal)

Geometry-Trapezoids

Area= (Base1+Base2)/2 *height

Geometry-Triangles

Area= 1/2 b*h An isosceles right triangle (45-45-90) has sides in a ratio of x :x :x square root (2) A 30-60-90 triangle has sides in a ratio of x:x square root(3): 2x, with the 1x side opposite the 30 degree angle An equilateral triangle has three equal sides. Each angle is equal to 60 degrees. Any given angle of a triangle corresponds to the length of the opposite side. The larger the degree measure of the angle, the larger the length of the opposite side. A right triangle has a right angle (a 90 degree angle); the side opposite the right angle is called the hypotenuse and is always the longest side. For a right triangle with legs A and B and hypotenuse C: A^2+B^2=C^2. This is called the Pythagorean Theorem. Memorize Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Multiples are also Pythagorean Triples The length of the longest side can never be greater than the sum of the two other sides The length of the shortest side can never be less than the positive difference of the two other sides

Geometry-Rectangles

Area= lx w, where l=length and w=width Perimeter=2l+2w

Geometry: Circles

Area=pi*r^2 Circumference=2*pi*r A circle has 360 degrees. An arc is the portion of the circumference of a circle in x degrees of the circle. Arc Length= (x/360)2*pi*r Area of sector= (x/360)pi*r^2 A fraction of the circumference of a circle is called an arc. To find the degree measure of an arc, look at the central angle. A chord is a line segment between two points on a circle. A chord that passes through the middle of the circle is a diameter. If two inscribed angles hold the same chord, the two inscribed angles are equal. An inscribed angle holding the diameter is a right angle (90 degrees).

Statistics-Mean, Median, Mode

Average or mean: For a set of n numbers: total sum / n Median: Middlemost value when numbers are arranged in ascending order; for an even amount of numbers,take the average of the middle two Mode: The number that occurs most frequently Example: 2, 3, 3, 4, 5, 6, 6, 6, 7: Mean = 42/9, Median = 5, Mode = 6 If the numbers in a set are evenly spaced, then the mean and median of the set are equal: {30, 35, 40, 45, 50, 55}

Word Problems-Distance, Rate, and Time

D=R*T R=D/T T=D/R Average Speed= Total distance traveled/total time

Distance

D=rt

Divisibility by 6

Even number and sum of digits is divisible by 3

Inequality

Like regular equations with the following exception: Multiplying or dividing an inequality by a negative number reverses the sign of the inequality. If w<x and x<y, then w<y If a<b and c<d, then a+c<b+d (not true for subtracting, multiplying, or dividing |x| <3 then ,3<x<3; if |x| > 3, then x>3 or x > -3

What is the ratio of 2 ratios (a:b and b:c, what us a:c)

Multiply a:b by a and b:c by b a:b:c= a:c

Permutation (how many outcomes)

N!/(n-k)!

Area of sector in circle

N/360 x area of circle (n=angle)

sum of all angles of a polygon

N=# OF SIDES

Roots-Perfect squares

Numbers with integers as their square roots: 4, 9, 16, etc To estimate square roots of numbers that aren't perfect squares, examine the nearby perfect squares. For example, to find square root of 50, you know that the square root of 49 is 7 and the square root of 64 is 8 so the square root of 50 must be between 7 and 8

Perimeter of a rectangle

P=2l+2w

Perimeter of a square

P=4s

Geometry-Squares

Perimeter= 4 s, where s=side Area= s^2

Simplifying roots

Separate the number into its prime factors and take out matching pairs: square root of 20 = square root of 2 x 2 x 5= 2* square root 5

Word Problems-Interest

Simple Interest: V=P(1+(rt/100)), where P is principal, r is rate, and t is time Compound Interest: V=P(1+ (r/100n)^nt) , where n is the number of times compounded per year

Divisibility by 3

Sum of digits divisible by 3

Divisibility by 9

Sum of digits is divisible by 9

Geometry-Quadrilaterals

The area of a square is s^2 (s = side). The diagonals of a square bisect one another, forming four 90 degree angles The diagonals of a rhombus bisect one another, forming four 90 degree angles The perimeter of a rectangle is twice its height plus twice its length (or, the sum of all its sides). The area of a parallelogram can be found multiplying base x height (the base always forms a right angle with the height).

Divisibility by 5

The last digit is either a 5 or a zero

Divisibility by 4

The last two digits of number are divisible by 4

Probability

The probability of an event: 0 = the event definitely won't occur 1 = the event definitely will occur 0.5 = there is a 50/50 chance the event will occur Probability that event A will happen: The complement of an event: The chance the event doesn't occur--so the complement of drawing a green ball is drawing a ball that isn't green. P(event happens) + P(event does not happen) = 1 Mutually exclusive events: Two events are mutually exclusive if they can't happen together: P (A and B) = 0 Events A and B (if they are independent events): P(A and B) = P(A) x P(B) Events A or B: A happens, B happens, or both A and B happen. P (A or B) = P(A) + P(B) - P(A and B) Events A and B (if A and B are dependent events): P(A and B) = P(A) x P(B|A) P(B|A) is the probability that B occurs given that A occurs (example: the probability of drawing a heart, assuming you already drew a spade).

Quadratics

This is the format of a quadratic equation: y=ax^2 +bx +c The graph of a quadratic equation is a symmetrical shape called a parabola, which open upwards if a > 0 and down if a < 0.

Geometry-Polygons

Total degrees=180(n-2) where n=# sides Average degrees per side or degree measure of congruent polygon = 180* (n-2)/n

Geometry-Rectangular Solids (including cubes)

V=height x depth x width Surface Area=2*height*width +2*width*depth+2*depth*height

Geometry-Cylinders

Volume=r^2pi*h Surface Area=2*pi*r^2 + 2*pi*r*h = 2*pi*r (r+h)

Geometry-Cubes

Volume=s^3 Surface Area=6s^2 The volume of a cube and the surface area of a cube are equal when s = 6

negative powers

^-2= 1/n^-2

Pythagorean Theorem

a2+b2=c2 This theorem can only be used for right triangles (triangles with a 90-degree angle). Common ones you may come across on the GRE are: 3:4:5 5:12:13 8:15:17

simple interest formula

amountx(rate)(time)

percent increase/decrease

ampint of decreaseor increase/originalx100 (80 to 100 20/80x100)

average of consecutive numbers

average of smallest and largest

sum of consecutive umbers

average x # of numbers 10 thro 50 60/2=30 30 x 41=1230

multiple roots

do radicals sepperate

solve sequence problem*

find difference between fifth and forth term n^2(n-1) -> 5^2(5-1)=

probability of A and b happening

find prob of a multiply by prob of b

inscribed figure circumfrence.

if area of square is 36,each side of square is 6,find diagnaol like missing part of triangle

original before percent increase

if decrease divide by amount left(if 5% of 57000 divide by .95 from 57000)

find minimum and maximum lengths for side of a triangle

if one side is 7 one other side is 3 than greater than difference and less than sum.( 7-4=4 & 7+3=10) so between 4.1 aand 9.9

x is what percent of y

multiply x by 100 and divide by y

Combination formula (how many combos can be made)

n!/k! (N-k)! K= whats being chosen, n= # of larger group

count consecutive numbers

range +1

inequality equation

reverse side when divide

distance between points

same points jsut subtract x from x .different points make right triangle and use pythagory theorum

The Distance Formula

square root ([x2-x1]^2 + (y2-y1]^2) For finding the distance between (x1, y1) and (x2, y2)

find x and y intercepts of line

when x =0 is x intercept. y=0 y intercept b=y intercept

Exponent Laws-Negative exponents

x^(-1) = 1/x x^(-2) = 1/(x^2)

Factoring-Quadratic Polynomials

x^2+ax+b= (x+m)(x+n) where a is the sum of m and n and b is their product (i.e. x^2+5x-14=(x+7)(x-2)

Exponent Laws-Odd/even exponents

x^3=8 therefore x =2 but x^4-16 therefore x=2 and x=-2

Exponent Laws

x^A * x^B =x^ (A+B) (x^A)/(x^B) = x^(A-B) (X^A)^B = x(A*B)

Exponent Laws-Negative bases

A negative number raised to an even power is positive; a negative number raised to an odd power is negative

Geometry-Angles

A right angle is made up of 90 degrees A straight line is made up of 180 degrees If two lines intersect, the sum of the resulting for angles is 360 degrees

Prime Numbers Below 60

2, 3 , 5 , 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59

Ratios

2:5 boys to girls and 2:7 boys to total students

number of possibilities

3 5 8 and 3 digit number first number has 3 possibilities,second has 2 and third has one 3x2x1=6

add multiple divide roots

3 radicat 3 + radical 2= 4 radical 2. cannot add 3 radical 2 ND 2 RADCICAL 2

Pythagorean Triples

3-4-5, 5-12-13, 8-15-17, 7-24-25 Each side of certain right triangles are integers. These sets of numbers are called Pythagorean triples, and you should memorize some of them: 3-4-5, 5-12-13, 8-15-17, 7-24-25. A multiple of a Pythagorean triple is a Pythagorean triple (e.g., 6-8-10).

ratio

3/4 boys to girls. 135 boys how many girls 3/4=135/g 3x g=135x4 3g= 540 3/540=180

special right triangle sides

3:4:5, 5:12:13 8:15:17 7:24:25

special right triangle angles

45 45 90-oppisite sides are equal,30 60 90(bet 90-60 is x, bet 30-90 x sq rt of 3,bet 30 60 is 2x)

Circumference

C=2πr or C=πd 2r=d. π = 3.14 (or 3.14159)

Percent Change

Change/Original value (i.e. (52-40)/40)

Counting

Fundamental Counting Principle: If a task is comprised of stages, where... One stage can be accomplished in A ways Another can be accomplished in B ways Another can be accomplished in C ways ...and so on, then the total number of ways to accomplish the task is A x B x C x ... When tackling a counting problem: Identify/list possible outcomes Determine whether the task can be broken into stages Determine the number of ways to accomplish each stage, beginning with the most restrictive stage(s) Apply the Fundamental Counting Principle Factorial notation: n!= n x (n-1) x (n-2) x...x3x2x1 n unique objects can be arranged in n! ways. Example: There are 9 unique letters in the word wonderful, so we can arrange its letters in 9*8*7*... = 362,880 ways. Restrictions: number of ways to follow a rule=number of ways to ignore the rule-number of ways to break the rule Arranging objects when some are alike: n!/(A!) (B!) (C!)... Given n objects where A are alike, another B are alike, another C are alike and so on. Combinations: nCr=n!/(r!(n-r)! When the order does not matter - for example, picking any 3 friends from a group of 5. Permutations: nPr= n!/(n-r)! When the order does matter - for example, how many ways you could order 3 letters from the word PARTY?

Stats-Range

Greatest value - least value

Divisibility by 8

If the last three digits are divisible by 8

Adding roots

If the radical is the same in each term, combine the term. sqrt(3) + 4 sqrt(3) = 1 sqrt(3) + 4 sqrt(3) = (1 + 4) sqrt(3) = 5 sqrt(3)

Stats-Standard Deviation

If you're given a set of n numbers a, b, c, ... with a mean m: SD= The standard deviation represents the average distance the data values are away from the mean. Variance is the value inside the square root of the standard deviation =SD^2 If the standard deviation of a set of numbers is k, then k = 1 unit of standard deviation. 1 SD=68 2SD=95 3SD= 99.7