GRE Math
What is the sum of angles in a polygon?
(n-2) x 180°
What equation can be used to rid of a negative number in a power and solve the problem?
(x/y)^-n = (y/x)^n If (3^-1 - 2^-1)^-1 then... (1/3 - 1/2)^-1 *find common denominator*----> (2/6-3/6)^-1 *solve* ----> (-1/6)^-1 Use equation: (-6/1)^1 = -6
What equation can be used to aide in the problem solving of a number to a power raised by another power? (y^a)^b?
(y^a)^b = y^ab
1/8 in Decimal Form
0.125
1/7 in Decimal Form
0.143 repeating (or 0.142857 repeating)
1/6 in Decimal Form
0.166667
1/5 in Decimal Form
0.2
1/4 in Decimal Form
0.25
1/3 in Decimal Form
0.33333 repeating
2/6 in Decimal Form
0.33333 repeating (due to the simplification to 1/3)
3/8 in Decimal Form
0.375
2/5 in Decimal Form
0.4 - All you need to do is take the values of 1/5 and multiply the numerator and result by that number (in this case, multiply 1 and 0.2 by 2 and you get 0.4)
1/2 in Decimal Form
0.5
If we have a fraction with equations in the numerator and denominator, what rule can we use to find a missing value?
A/B=C/D = AD=BC
When it comes to questions about splitting up something via ratios, how do you solve that?
Add up the ratios and that will give how many times we're splitting the object/thing. Then you take the added up ratio number and divide it by the object/thing we're splitting, then from there we see the amount that is being distributed.
Area of a trapezoid?
Area = (average of the bases)(height) Bases: 2 parallel sides Height: length of line perpendicular of the bases A = (b₁+b₂)/2(h)
Area of a Triangle Equation
Area = Base x Height / 2
How do you find the area of a circle?
Area = πr²
How do you find the area of a circular sector?
Area of sector/πr² = central angle/360°
If the fraction is BIGGER than the fraction subtracted, then this subtraction makes the resultant fraction...
BIGGER
If the fraction is SMALLER than the fraction added, then this addition makes the resultant fraction...
BIGGER
If the numerator gets BIGGER and the denominator gets SMALLER, the fraction gets...
BIGGER
If we add a number to the numerator and subtract a number from the denominator, whichever fraction has the larger numerator and smaller denominator is...
BIGGER
Making the denominator SMALLER makes the fraction gets...
BIGGER
By addition, if both the numerator and the denominator get BIGGER by adding the same number, the fraction gets...
Closer to 1 than the original fraction was
If we add two different values to the numerator and the denominator, the resultant fraction will be...
Closer to the amount added than the original fraction
Concentration Formula for Mixture Questions is
Concentration = amount of solute/total amount of solution x100
What happens when you change both values of the numerator and the denominator?
If the numerator gets BIGGER and the denominator gets SMALLER, then the fraction gets BIGGER. 3/8 < 4/7
What happens when the numerator and the denominator increase by addition?
If the same number is added to both the top and the bottom, the resultant fraction is closer to 1 than the original fraction (whether it be bigger than one or smaller than one; this is technically bringing the two fractions closer together)
What rule can be applied when comparing fractions?
In the fraction a/c + b/c, if a>b then we can assume that (a/c) > (b/c), assuming that c > 0 We can also assume that in the fraction s/p + s/q, if p>q then (s/p) < (s/q), assuming that p>0, q>0, s>0
If the interest rate isn't annual, but classified as quarterly, monthly or daily, how do you go about solving that problem?
Instead of raising everything to y for years of compound, we'd raise everything to the corresponding n for each time n = 4 for quarterly n = 12 for monthly n = 365 for daily
Can you compute a fraction with zero in the denominator?
No. Only when there's a zero in the numerator can we compute.
Can a fraction be separated into two separate fractions by addition/subtraction of the values in the denominator?
Nope. That can only be done in the numerator. A+B/C = A/C + B/C - RIGHT A/C+B = A/C + A/B - WRONG
What is the formula used for probability?
P(A or B) = P(A)+P(B)-P(A and B)
If the fraction is SMALLER than the fraction subtracted, then this subtraction makes the resultant fraction....
SMALLER
If the numerator gets SMALLER and the denominator gets BIGGER, the fraction gets...
SMALLER
For weighted averages, what concepts can you use to solve the problem?
Sums: Take the amount of object x it's average and then add all of those sums together to get answer. Proportions: Average of whole = A1 x P1 + A2 x P2 + A3 x P3
Surface area of a solid rectangle?
Surface Area = 2hw + 2wd + 2hd
What happens when the numerator and the denominator increase by multiplication?
The fraction will remain equal to the resultant fraction
What does inclusive mean in terms of numbers?
The set includes the first and last number stated and all other numbers in between
What happens if you change the numerator and keep the same denominator?
Then the fraction with the largest numerator is the biggest. 4/13 < 6/13 | 3/50 > 0/50 | 8/3 < 14/3
By multiplication, if both the numerator and the denominator get BIGGER, the fraction gets...
To be equivalent
What is the volume of a regular solid with the dimensions h w d?
V = hwd
How can 1/10 help us get the decimal values of other fractions that have denominators that are factors of 10?
We can multiply the denominator by whatever value it takes to get up to 100 and then multiply the numerator by the same value, get the fraction and then simplify. 1/20 = 1(5)/20(5) = 5/100 = 0.05 (1/100 is 0.01, so you can also multiply the original fraction and result by the integer you're trying to figure out and get the same answer)
What happens if we increase the numerator and decrease the denominator?
Whichever fraction has the BIGGEST numerator and SMALLEST denominator is the LARGEST
Distributive Law Equation
a(b+c) = ab + ac
What equation can be used to figure out the relationship between distance, time and speed?
d=ts This is interchangeable, so it can be used in multiple different ways depending on what information is given
What is the length of a diagonal between opposite vertices of a rectangular solid with dimensions h w d?
diagonal² = h² + w² + d² | | V diagonal = √h² + w² + d²
What equation is used for finding combination (no order matters) probability?
nCr = (n/r) = n!/r!(n-r)! ! = All of the numbers leading up to stated number i.e., 10x9x8x7x6x5x4x3x2x1 r = number of items being chosen at that time n = total number of items in the set
1/9 in Decimal Form
0.111111 repeating This means whatever value is added to this fraction will be that digit repeating. 2/9 = 0.22222 repeating 3/9 = 0.33333 repeating (due to simplification to 1/3) etc.
3/6 in Decimal Form
0.5 (due to the simplification to 1/2)
4/8 in Decimal Form
0.50 (due to simplification to 1/2)
3/5 in Decimal Form
0.6
5/8 in Decimal Form
0.625
2/3 in Decimal Form
0.66667
4/6 in Decimal Form
0.66667 (due to simplification to 2/3)
3/4 in Decimal Form
0.75
4/5 in Decimal Form
0.8
7/8 in Decimal Form
0.875
5/6 in Decimal Form
0.88883 repeating
Compound Interest formula/concept
A = Amount in account P = # being multiplied (principal) r = multiplier of percent y = How many compound years I = annual interest rate A= p (r^y) - Shows how much is in the account based on the principle number and the percent of that number in compound years A = P(1+ I/100)^y - Shows how much is in the account based on the principle number being multiplied to the percent of the annual interest rate and the percent of the annual interest rate being multiplied however many years are in the compound.
What rule can be used to find the sum of a question that states the mean of x amount of numbers?
If m is the mean of n numbers, then the sum of the numbers is n x m.
What do you use if you have the square root of a number times a number (i.e. Square root of 8x18)
√a x √b
What equation can be used if two different numbers are being multiplied and are squared by the same number?
a^n*b^n = (ab)^n
How do you find the length of a circular arc?
arc length/2πr = arc angle/360°
Square of Sum Equation
a²+2ab+b² = (a+b)² a²-2ab+b² = (a-b)²
Difference of Two Squares Equation
p²-q² = (p+q)(p-q)
What equation can be used to solve a number raised to a fraction?
x^1/n = n√x
What equation can be used if the same base number is being raised to the nth power?
x^a = x^b, then a = b (only if x≠0)
What equation can be used if two numbers are squared by different numbers and are being divided by each other?
x^a-b
What equation can be used to find the sides of a triangle?
x²+y² = d²
What is the equation of a straight line?
y = mx + b
What does the degrees of a quadrilateral add up to?
360°
What happens to the direction if the inequality when you cross-multiply?
It stays pointing in the same direction that it did before
What happens if you change the denominator and keep the numerator the same?
Making the denominator BIGGER makes the fraction SMALLER Making the denominator SMALLER makes the fraction BIGGER 2/5 > 2/7 | 3/11 < 3/10
What happens when you get a problem like this: (x + 1/6)/(x + 6/15)
Multiply the numerator and denominator of the big fraction by each denominator of inner fractions
How do you find the distance between two points on an x,y axis?
Pythagorean Theorm: distance² = run² + rise²
If the fraction is BIGGER than the fraction added, then this addition makes the resultant fraction...
SMALLER
Making the denominator BIGGER makes the fraction gets...
SMALLER
What happens when you have a mixture problem where the amounts of two different solutions are initially unknown?
Set up simultaneous equations: First one will be the "total" equation, that is total volume or total mass/weight Second one will be about the amount of solute
What happens if the numerator and denominator increase by different values?
The resultant fraction is closer to the value that was added compared to where the original fraction is. If the original fraction is SMALLER than the fraction being added, then this makes the result BIGGER than the original fraction. If the original fraction is BIGGER than the fraction being added, then this makes the result SMALLER than the original fraction.
What happens if the numerator and the denominator decrease by different values?
The resultant fraction is farther away from the value that was subtracted compared to where the original fraction is. If the original fraction is SMALLER than the fraction being subtracted, then this makes the result SMALLER than the original fraction. If the original fraction is BIGGER than the fraction being subtracted, then this makes the result BIGGER than the original fraction.
Can a fraction be separated into two separate fractions by addition/subtraction if there's addition and subtraction in both the numerator and the denominator?
Yup. You can only separate the numerator by this rule though, denominator needs to stay the same. A+B/C+D = A/C+D + B/C+D
When are Mixed Numeral Fractions useful?
They're useful if we need to locate a fraction on a number line which could then help with comparison of fractions. DO NOT USE FOR MULTIPLYING, DIVIDING OR RAISING A NUMBER TO A POWER
When it comes to addition and separating one fraction into two, what is the rule?
We can separate the fraction into two fractions by addition or subtraction only in the NUMERATOR, we cannot do this in the denominator a+b/c = a/c + b/c
When are Improper Fractions useful?
When you are multiplying, dividing or raising a number to a power
When solving an equation with decimals, can you multiply by 10 to rid of the decimals and make the math easier?
YUP. You should probably do this every time if they're not asking for your answer in decimal form because somehow the whole number is the answer.
What if there's a question with mixed numerals and all of the answers are in mixed numerals?
You should convert the mixed numeral from the question into an improper fraction, calculate and then convert back into a mixed numeral so you can answer the question correctly.