GRE Math Magoosh

"is"

"equals"

"of"

"multiply"

1730+1720= (factoring out multiply

(1720)(1710)+(1720)(1)= (1720)(1710+1)

If moving from m^2 to cm^2

(5m^2)*(100cm/1)^2= 50,000cm^2

(ab)n

(an)(bn)

Rebuilding the dividend formula

(dividend)=(divisor) x (quotient)+(remainder)

p^2+2pq+q^2

(p+q)^2 these are interchangable

1/20

.05

1/10

.1

2/3

.66666

3/4

.75

Four pythagorean triplets

1) 3,4,5 2) 5,12,13 3) 8,15,17 4)7,24,25 If you see these you know its a right triangle

3 question types

1) questions will give you some + and ask you to solve for another # 2) Questions that will ask you to solve algebraically for a variable 3) Proportional measuring questions

Multiplier for Increase

1+(P% as a decimal) 30%= 1+.3=1.3

Positive integers

1,2,3,4 etc

Multiplier for Percent Decrease

1- (P% as a decimal) 30%= 1-.3= .7

Counting factors of large numbers

1. Find the prime factorization (with exponents) 2. Make a list of exponents 3. add one to each exponent 4. Multiply all the numbers together

Square root of 2

1.4

Square root of 3

1.7

Are of a triangle

1/2bh

72 is____ of 360

1/5

56 is what % of 800

10% of 800 is 80 1% is 8, 8 X 7=56 7% of 800 is 56

10 squared

100

1 ft

12 inches

11 squared

121

Many interchangeable ways to talk about factors

13 is a factor of 78, 13 is a divisor of 78, 78 is divisible by 13, 78 is a multiple of 13

12 squared

144

1 square foot

144 square inches

(12/7) squared

144/49

90 is 15% of what number?

15% is 3 of 5% 90/3= 30, 30=5% need to multiply to equal 100 30 time 20 =600

4 squared

16

Prime Factorization of 1599

1600-1 (40squared)-(1 squared) (40+1)*(40-1) then (41)*(39) and (41)(3 *13)

Prime Numbers 2-59

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

Powers of 2 1-9

2,4,8,16,32,64,128,256,512

square root of 5

2.2

Equilateral Triangle

30-60-90 Triangle or 1-2 (largest side)- sr3 triangle

Normal distribution main percentages

34% (M-S) 13.5% (S-2S) 2.5%

If you have slots the first slot has 6 then next slot has

5,4,3,2,1 then multiply it all together

If bank pays 5% annual interest compounding quarterly

5/4=1.25%

What is 55% of 400

50% of 400 is 200 5% of 400 is 20= 55%= 220

9 squared

81

3 squared

9

If A and B have no factors in common greater than 1 their LCM is

A times B

Area of a trapezoid

A=(b1-b2/2)h

Angle is 135 then

Arc is 135

To find the length of an arc

Arclength/2(pi)r= angle/360

Average Speed

Average Velocity=total distance/total time

Circumference equation

C=2(pi)r or C=(pi)d

Adding and subtracting inequalities

Can add inequalities in the same direction but not different but can subtract in opposite not the same

Standard Deviation

Can only be positive or 0

Distributive Law Rules

Cannot split up addition or subtraction in the denominator, cannot distribute an exponent

Diameter equation

D=2r

Motion Questions

D=RT (distance, rate(speed) and time)

Integer Strategy 2

Don't forget about zeros and negatives

With equations with multiple fraction

Find LCM and do some fraction busting

x+8>13= 5<x<21

Greater than the difference and less than the sum

To get rid of the radical

Have to get it by itself

240 is 30% of what #?

If 240 is 30% then 10% is 80 to get the whole 100% multiply by 10 the answer is 800

Simplifying expressions

If different powers group like terms

Isosceles Triangle

If two equal sides two equal angles and reverse

Supplementary angles

If two or more angle lie in a straight line those two angles together =180 degrees

QC C

In all options and ways they are equal

The nth number is the

Lowest number + multiple(n-1)

if there is an absolute value

Make sure to plug in and check to both equations if one of them doesn't work the answer only has one solution or NONE

Integer Strategy 1

Make sure you are dealing with integers

Median

Middle number of ordered list

LCM

P*Q/GCF (don't multiply first, cancel first)

Quantitative Comaprison A

Quantity A is ALWAYS greater

QC B

Quantity B is ALWAYS greater

If all the numbers are the same distance from the mean that is the

SD

T/F Any power of an odd number is still odd

T

Divisibility Rule for 4

The last 2 digits are divisible by 4

Divisibility Rule for 5

The last digit is 0 or 5

y<7

Then it could be 6.999999999999

In motion problems

Time matters

T/F Every positive factor greater than 1 has 2 factors

True: 1 and itself

Inscribed angles

Two chords at the vertex, the measure of the IA angle is half the arc

57^123

Units digit of 3

Volume and Surface Area of a Cylinder

V=(pi)r^2h, SA=2(pi)r^2+2(pi)rh

square root of y^2

absolute value of y

For a triangle two of the angles have to be

acute and the other would be acute, right or obtuse

b5d-8/h-4k7

b5h4/d8k7

For percent change if the decimal is less than 1

decrease=1-product

Divisibility Rule for 12

if the number is divisible by 3 and 4

2 D

if they go on the same wrote twice

For Ratios if you don't know the amount

just set the ratios with n and set one fo them equal to the number you have been given

Divisibility Rule for 2

last digit is even they are divisible by 2

Remainder questions

listing dividends, using the rebuilding the dividend formula

If a number less than 100 is not divisible by 1-10...

means it is prime

a to the n time a to the m

n+m

Combination Equation (use if it doesn't matter the order)

nCr=n!/r!(n-r)!

x^3 only has one solution

one positive or one negative

If two lines or segments meet at a right angle they are called

perpendicular

Circumference of a circle

pi x diameter

Emily don't forget about exponents!!

positives and negatives

If can either have a product or not have a product in the problem

put 2 for the number of things and then multiply the 2

To find the ratio of areas

scale factor squared (if all lengths are multiplied by scale factor)

If given x2-3x-43=11 solve for...

solve for 0

bisects

splits in half

square root of P +square root of Q does not equal

square root of P+Q

The space diagonal of a cube is

sr of 3 times the edge length

If consecutive numbers appear in algebraic expressions factor out but you have to know

t is an integer

If one multiplies every number on the list by K the mean and SD get multiplied by

that number

If there are to fraction equations on top of a fraction equation multiply by

the LCM in the numerator and denominator just equals 1

Absolute values

the distance from zero on the number line Ix-5I is the distance of x from +5

Two lengths of a triangle cannot add up to

the largest side of the triangle

Vertical Line

x=n

Horizontal Line

y=n

(3square root of 5)(7 square root of 2) simplify

(3*7)(square root of 5 *square root of 2)

for a slanted line through a 3D shape use 3D version of Pythagorean Theorem

(AD)^2=(AB)^2+(BC)^2+(CD)^2

Multiplying a fraction by its denominator

(fraction)x(denominator)=(numerator)

45-45-90 triangle equations

(hypotenuse)=sr of 2*(leg) and hypotenuse=s*sr2

(p/q)-n

(q/p)n

Mean

(sum of n entries/n) or n*(mean)=sum of entries

1/7

.143

1/6

.166

1/5

.2

1/4

.25

1/3

.33333

2/5

.4

1/2

.5

1 squared

1

a to the 0

1

4 notes on Data interpretation

1) Check the units int he question they may or may not match the data 2) Check the form of the question before you perform your calculations (fractions or percents) 3) Can use visual estimations 4) Don't confuse numerical differences with percent differences

3 facts about 3 equations with 3 unknowns

1) Depending on what the questions asks you may not have to solve all the way 2) Inside every big problem is a little problem 3)If the # of equation is fewer than the # of variables you cannot solve it

3 knowns for trapeziods

1) Exactly one pair of parallel sides 2) A+B=180 and C+D=180 3) If BC?? AD and if BA=CD then <B=<C, <A=<D and the diagonals have equal length

Rectangles 3 requirements

1) Four 90 degree angles 2) Have "big four" parallelogram 3) Diagonals are congruent

Four steps of solving a quadratic equation

1) Get everything equal to 0 2) Divide by any GCF 3) Factor 4) Linear equations to get answers

3 requirements of a rhombus

1) Have four equal sides 2) Have "big four" properties of Parallelogram 3) Diagonals are perpendicular

Two things to know about Squares

1) It is a rhombus, rectangle, parallelogram 2) Don't assume something is a square only if they tell you

4 requirements of a Parallelogram

1) Opposites sides are parallel 2) Opposite sides are equal 3) Opposite angles are equal 4) The diagonals bisect each other

Greatest common factor of two numbers

1) Prime Factorization 2) Highest power of each number they have in common 3) multiply those 4) GCF is the sum

3 rules of word problems

1) When a word problem involves multiple travelers, trips, legs; each traveler, each trio, and/or each leg deserves is own DRT equation 2)Sometimes solve one equation and input 3) Otherwise 2+ equations w/ 2+ unkowns (substitution and elimination)

Consecutive Integers

1) a set of n consecutive integers will always contain one number divisible by N 2) If n is odd, then the sum of a set of n consecutive integers will always be divisible by N 3) in a set of 3 consecutive integers you could have 2 evens and 1 odds or 2 odds and 1 even. In a set of integers 2 evens and 2 odds

Ways to simplify a problem

1) add the same number to both quantities 2) subtract the same number from both quantities 3) Multiply or divide by the same positive #

b to the -3

1/b3

13 squared

169

How many degrees are in a "straight" angle?

180

14 squared

196

1=1ft/12 in

1=12in/1ft

m^3->cm^3

1m^3(100cm/1m)^3=1,000,000cm^3

Substitution Method

2 Equations with two variables set one to a variable and then input it into the other equation to solve for both variables

Cubes 6-9

216,343,572,729

15 squared

225

5 squared

25

Twice A is 100 less than three times B

2A=3B-100

Surface area of a rectangle 3d

2hw+2hd+2wd

Powers of 3 1-4

3,9,27,81

Pi=

3.14, 3, 22/7

If K, (K+200), (K+350) and 15K are all multiples of P, then P could equal which of the following?

300-200=150, 200-150=50 has to be lower then 50 but also a factor of 300,200,150,50

.6 x 60=

36

6 squared

36

1 hour

360 seconds

If you are adding the exponents don't have to solve but estimate

3x+3y=36 or x+y=12 (know the answer from these equations)

3 *(xy)=

3xy

2 squared

4

40 squared (easier trick)

4 squared plus 0 squared

Powers of 4 1-4

4,16,64,256

41 squared or n squared

41 squared = 40 squared plus 40 plus 41= 1600 plus 81= 1681

Isosceles Right Triangle

45-45-90 Triangle or 1-1-square root 2 triangle

7 squared

49

What is the smallest possible integer that, when divided by 12, has a remainder of 5?

5 because 5/12= 0 with a remainder of 5

Powers of 5 1-4

5,25,125,625

1 hour

60 min

Percent Increase

60%=1.6

8 squared

64

How many degrees are in a right angle?

90

-1/8?-1/2

> because -1/8 is closer to 0

For A=RT problems if they say they manufacture 36 stapler that is...

A

Arc

A piece of a circle

Area of an equilateral triangle with side S

A=(s^2sr of 3)/4

A is 50% of B

A=.5B

A is 50% greater than B

A=1.5B

Area of a triangle

A=1/2bh

Work Questions Equation

A=RT A= amount of work done (houses painted), R= the work rate (# of products per day), T=time

Area for two triangles

A=bh

Finding area in rhomuses

A=bh and if given base can find height by PT and knowing all sides are equal

finding area in rectangles

A=bh, h must be perpendicular to b

Proportional similar trianlges

AB/BC=DE/EF

For complicated questions

ALWAYS SIMPLIFY FIRST

Weighted averages

Add sums then average

Shrinking and Expanding Gaps: 2 travelers in opposite directions

Add the speed since the gap is shrinking

2 travelers are moving away from each other

Add the speeds: the speed in which the gap is expanding

To find even factors

All factor minus odd factors

Equilateral Triangle

All the angles are 60 degree and all sides are equal

Only way SD can be 0 if

All the numbers are the same

If an angle is along the diameter of the circle

Always 90 degrees

Tip for circles

Always find the radius first

For word problems

Always make equations for the two people or multiple participants

On a square root no answer if....

Answer is negative

If comparing fractions

CROSS MULTIPLY

Multiple Machines

Combining people/machines working together is the sum of the individual work rates, Cannot add or subtract times and amounts made in different times

Word Problems Tips

Determine answers working from the answer choices first

Mistake for average velocity

Do not average them!!!

Scatter Plots

Don't be afraid of the easy answer and if you don't know graph don't worry most people don't so just keep calm and you will be do better then others

With Work Questions

Don't cross multiply too big, simplify but cannot cross cancel only take out numbers from both demoniators

If there are strange operations

Don't panic they will explain it to you!

If Numbers are big for the PT

Don't square find the GCF

Divide by 5

Double then divide by 10

Absolute Values

Either equal the expression or equal the expression multiplied by a -1

if two lines intercept the same chord the two inscribed angles must be

Equal

Square root of 42*63

Find prime factorization

FOIL

First, Outer, Inner, Last

6 sided shape

Hexagon, has 9 diagonals, 720 degrees

Assuming in the GRE on geometry

If a line looks straight it is straight everything else don't assume

QC D

If it is possible to chose different choices to make different relationships

Answer D

If some choices make it one answer and some choices make another it is D

Percent increase

If the number does not double it is less than 100%

Divisibility rule for 6

If the number is even and if you add the number up and they're divisible by 3

Any number ending in 5

Is between 900 and 1600 3 time 4= 12 plus 25 approximately 1225- Any number ending in 5 is halfway btw two multiple of 10 the product in front of the zeros in those multiples of 10 is crucial for figuring out the square of the number ending in 5

1/.91 ? 1

Is greater than 1 because the numerator is greater than the denominator

For ratios if the ratio added together is not divisible by whole...

It does not work

T/F

Its illegal to distribute and exponent over additin and subtraction (2+4)2 cannot (22+42) have to do a quadratic equation

Scale Factor

K= DE/AB=EF/BC=DF/AC

For sequences

Make the sequence into an equation

If testmaker does a square roots

Means the answer is positive

Mode

Most often seen #

5/3P=Q what do you do?

Multiply by the reciprocal and turn numbers into the same or easier numbers

If the x is in a fraction such as x/2 then...

Multiply the entire equation even after the equals by the LCM

If you want to isolate x or the variable and its being multiplied by a fraction to remove it you need to...

Multiply the fraction by the reciprocal ab/c=a*b/c=b*a/c

If only use something once in the equation

Multiply them

If A is a factor of R, then the LCM of A and R

Must be R

If 7 K is a positive interger and if the square root of K >K then is K an integer?

No only happens if K is less than 1

If the two variable are the same but the = are different

No solutions

N-sided shape

Number of diagonals (n-3), number of triangles (n-2), sum of angles (n-2)*180 degree

For cross multiplication

Numerator to denominator from left to right and from denominator to numerator left to right

8 sided shape

Octagon

If multiplying a number by a multiple of 5

One factor was halved and the other was multiplied by 2 (16 x35)=(8x70)

Pythagorean theorem

Only works for right triangles, a^2+b^2=c^2 or leg^2+leg^2=hypotenuse^2

5 sided shape

Pentagon, has 5 diagonals, 540 degrees

The radius and a tangent line are

Perpendicular

Age word problems

Pick variable to equal age right now and if time changes everyones age needs to change

For exponents and square roots always

Plug back in

Integer

Positive and negative whole numbers

Unified Variables

R=mph, D=miles, T=hours and R=m/s, D=meters, T=seconds

Number

Real number (decimals, neagtive, zero)

Similar Triangles

Same shape but different triangles Sides in similar figures are proportional

Combining ratios strategy #2 (if given a number)

Set the ratio equal to the number and the unknown then do that again to find your number

Elimination Method

Set the two equation above each other make one of the variables the same by multiplying and then add and you solve for both equations

Gaps

Set up D=RT for the gap itself

2 travelers are traveling in the same direction and the faster is in front

Subtract and thats the way its expanding

T/F Every integer is a factor of itself

T

T/F square root of 0= 0

T

T/F with work problems you cannot add or subtract times but you can add or subtract rates

T

T/F you cannot square root a negative #

T

Instead of doing the mistake

Take DRT fro to velocities and set them equal ex. t1=D/20 and t2=D/30 -> D/20+D/30

Proportions

Take each average times the proportion and add up

For 3 problems and 3 variables add two of

The 3 equations and 2 of the other ones

a^2-b^2= (a+b)(a-b)

The a and b do not have to be in single digits

An angle with its vertex at the center of the circle equals

The central angle and the arc is that angle

Divisibility rule for 3

The sum of the digits is divisible by 3

Fundamental Counting Principle

The total # of ways to do the task simply will ebt he product of these #'s

If a question asks for the units digit

The units digit of any product will be influenced only by the units digits of the two factors (only need to consider single digit products

If 2 quantities are purely numerical (fractions, decimals, percents etc.)

Then it must be true either that one is bigger than the other or that the two are equal

If all 3 valuables are the same....

There are infinite solutions

Quadratic Equations: ax2+bx+c=0 or (x-q)(x-p)=0

There are two solutions

If you input a square root

Think of the positive and negative

If P is a multiple of R anytime you add or subtract it...

Those are multiples

T/F 0 is an even number

True

T/F 1 is not a prime number

True

T/F Can not cancel to + and - equations on top of each other

True

T/F If a negative base if exponent is even result is positive if exponent is odd result is negative

True

T/F cannot square anything and get a negative number

True

T/F even if the product is an integer maybe the numbers aren't integers

True

For percent increase

Turn it into a percent

Regular pentagon

all angles are 108 degrees

Regular hexagon

all angles are 120 degrees

Regular octagon

all angles are 135 degrees

Rule of multiplying fractions

always cancel before you multiply

(a/b)n

an/bn

If P and Q are multiples of r add or subtracting (or times but not divide) P and Q

are multiple of r

xy and yx

are the same thing

Find area of a sector

area of sector/(pi)r^2= angle/360

1/2 as exponents get higher

base gets smaller

Area of a rectangle

bh

Find length of triangles

by subtracting coordinates

addition and subtraction

can remove the parenthesis

Sequential Percent changes

can't cancel out the increase and decrease because the number changes

If = what can't you cancel

diagonal or cross canceling

Average speed equation

distance/time

If something has equal length chord then

equal length arcs

if two lines are parallel and there is a line through it the angles directly across from each other are

equal to each other

"is" or "are"

equals sign

Dividing fractions

flip the second one

Volume of a 3d shape

for a cube its s^3 for others its is h*w*d

For obtuse triangles

have to extend the the line in order to fine the height

30-60-90 triangle equations

hypotenuse=2*(short leg) and (long leg)=sr of 3 (short leg)

x2+5=0

impossible cannot square to get a negative +

For percent change if the decimal is more than 1

increase= product -1

(am)n

m*n

am/an=

m-n

Find the percent of increase or decrease

multiplier= new/old increase m= 1+ (answer) decrease m= 1- (answer)

Combining ratios strategy #1

multiply both ratios to get the same of the double number

To get rid of a square root in the denominator

multiply by the reciprocal and the root over itself

To get rid of messy fractions

multiply the numerator and denominator of the big fraction by each denominator of the inner fractions

If all prime factors have an even exponent

must be a perfect square

Compound interest monthly

n=12

Compound interest daily

n=365

Compound interest quarterly

n=4

To find odd factors

repeat counting factors procedure but ignore factors of 2

Profit=

revenue-cost

Multiplication and division of negatives across inequalities

reverses the order of inequalities

2 travlers are move in the same direction but slower in front

subtract that is the way it is shrinking

If you have to arrange things in a certain order the total number of order is

the product of n and ever positive integer less than n

All radii in one circle have

the same length

Divisibility rule for 9

the sum of digits is divisible by 9.

In any triangle of any two sides must be greater than...

the third side

For Multiple questions that rely on each other to understand make 6 boxes chart

the variables plus the totals and fill in the holes

Weighted average formula

the weight 1(w1)+weight 2(w2)/R+W

If bs=bt

then s=t

13x<x2

then x has to be greater then 13

Average time for a trip

total distance/total time

If you need to find a length of a slanted line

use pythagorean theorem

If = what can you cancel

vertical and horizontal

Doesn't have to be a factor for exponents

x to the 5(x to the 7 and x to the 5)

If y=5+x and y=12-x and if y squared equals x squared plus K then K equals

y-x=5 and y+x=12 K=y squared - x squared then K=5*2