GRE Math Section

Sum of Angles of a Triangle

180 degrees ALWAYS *The sum of the angles of ANY triangle, will ALWAYS equal 180 degrees*

The sum of angles for a straight line always equals ______________. ?

180 degrees!

Sum of angles in n-gon

180(n-2) where n: is the number of angles Ex: if a shape has 7 angles, the total sum of the angles would be: 180*(7-2) = 180*(5) = 900

2^1 = 2^2 = 2^3 =

2 4 8

A negative raised to any ODD power is ______________.

ODD

On the exam, the word "number" always means any real number, not just positive integers.

Remember this includes negative numbers, 0, and fractions & decimals!!!

Important Prime Facts:

*Notice, 1 is NOT a prime number. Prime numbers have two factor, 1 and the number itself, but 1, only has one factor, itself. *Notice: 2 is the ONLY EVEN prime number, ALL other even numbers are divisible by 2, and hence are not prime. The gre LOVES to test these 2 facts!!!!

Rule: (a+b)(a-b) = a^2 + b2

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

Other tips/notes for order of operations:

*always chose to cancel out as much as you can before you multiply!!!* -If multiplying layers of parenthesis/grouping symbols, we have to work our way from the inside out. (we take the innermost grouping symbol & then at that innermost level, we do exponents, then multiplication & division, then addition & subtraction) & then we move outside to the next layers!

If zero is the base, then zero to ANY positive number is always zero.

0^n = 0 is n > 0

One raised to ANY power, is always _________ .

1 If the base is 1, then the exponent doesn't matter! One to ANY power, is ALWAYS one. 1^n = 1 for all of n

If an exponent is not written, we can assume that the exponent is ______.

1 We can assume that the exponent is 1.

Operations with fractions

1) Adding & Subtracting Fractions; finding the common denominator -Finding the LCD: (see video "Integer Properties") 2) Multiplying Fractions; cancellation ALWAYS CANCEL BEFORE YOU MULTIPLY 3) Division with fractions: (which is actually multiplying whatever is in the numerator, by the reciprocal of whatever is in the denominator ) -Including when a number is divided by a fraction, and when a fraction is divided by a number!

Mixed Numerals vs. Improper Fractions: Summary

1) Be comfortable changing back and forth between improper fractions & mixed numerals 2) If you need to determine the position of a fraction on the number line, mixed numerals may be a little more helpful 3) For calculations involving multiplication, division or powers, ALWAYS USE IMPROPER FRACTIONS!!!!! -Mixed numerals will be USELESS!!!

Summary of Intro to Exponents:

1) Fundamentally, b^n means n factors of b multiplied. 2) One to ANY power, is one. 3) Zero to any POSITIVE power is always zero. 4) A negative to an even power power is positive; a negative to an add power is negative 5) An equation with an expression to an even power equal to a negative, has NO solution. But an odd power, can equal a negative. 6) Know the basic powers of the single digit numbers

PEMDAS --> GEMDAS "Order of Operations"

1) Grouping Symbols: (Parenthesis, brackets, square roots, long fraction bars, the exponent "slot") 2) Exponents 3) Multiply/Divide 4) Add/Subtract

Doubling & Halving Summary:

1) In any product, we always have the option of finding half of one factor & doubling the other; this does not change the resultant product. 2) When doubling one number, it will make it a round number, a multiple of 10 or 100, then doubling that number and halving the other can enormously simplify the calculation. 3) Sometimes, we apply the procedure twice in succession, for example, when one factor is 25 or a multiple of 25.

Fraction Properties (Part 2):

1) More on Cancelling and Order of Operations Big Idea #1) Multiplication & Division are at the SAME level of priority in GEMDAS and can be done in any order! Big Idea #2) Cancelling is a form of division: it is the division of the same factor in the numerator and the denominator Big Idea #3) ALWAYS cancel BEFORE you multiple. Always always make the numbers smaller before you make them bigger!!

In Solving Equations:

1) Our goal is to find the unknown value of the variable (obvs hah!) 2) Mathematically, it's always legal to do ANY arithmetic operation to both sides of an equation. -As long as we remember to do whatever we want to do, TO BOTH SIDES OF THE EQUATION 3) We "undo" the Order of Operations (GEMDAS) to isolate the variable This means, we do GEMDAS backwards, starting with/ = SADMEG 4) If the variable is on both sides, we begin by collecting all terms with the variable on one side!

Grouping Symbols:

1) Parenthesis ( ) 2) Straight Brackets [ ] 3) Square Root (square root is a grouping symbol: If we have a bunch of things underneath the square roots sign, these things are grouped together and have to happen first. Before we can take the square root, & before we can do operations outside of the of root. *No operations can pass through the square root 4) The Long Fraction Bar *anything that happens to the denominator, MUST also happen to the numerator 5) The Exponent "slot" -all the stuff that is UP in the exponent, must happen together. & it has to be done first, then we can compare the power & then we can do any operations that are outside of the exponent situation.

Summary of Fraction Properties (Part 2)

1) Patterns of Cancellation available in fraction multiplication 2) We can split fractions by adding/subtracting in the NUMERATOR, but NOT in the denominator The denominator must remain unchanged! 3) The shortcut of multiplying a fraction by its denominator: (remember: we must multiple both the NUMERATOR and DENOMINATOR) (fraction) x (denominator) = (numerator) 4) simplifying complex fractions!!

Summarizing Squaring Shortcuts

1) To square a multiple of 10, square the digit(s) without the zero, then tack on two zeros at the end. 2) To square a number ending in 5: a) remove the 5, leaving the remaining digits(s) b) add one to the remaining digits(s) c) multiply the numbers in (a) & (b) d) put this product in front of 25 3) If we know the value of n^2 (ex: if n is a multiple of 10 or 5), then we can get the next square up, (n+1)^2, by adding n and (n+1)

Summary of Working with Percents:

1) Use percents as multipliers (decimals) and the method for solving simple percent problems 2) Using the same method (using multiplies---decimals) to find an unknown percentage 3) Fraction shortcuts for percents

Mental Math: Addition & Subtraction

1) You can simplify mental for addition of two digit numbers by treating the digits separately ex: 47 - 36 = ? Well, 40 + 30 + 13 = 83 so... (70+13) = 83 2) You can also treat the digits separately in subtraction if the number subtracted has both digits smaller. ex: 48 - 26 = 22 ..... (4-2=2 & 8-6=2 ...... 22 ) 99-34 = 65 ..... (9-3=6 & 9-4=5 ...... 65 ) 79-23 = 56 ..... (7-2=5 & 9-3=6 ...... 56 ) 84-41 = 43 ..... (8-4=4 & 4-1=3 ...... 43 ) 3) If in subtraction, the second number (the one being subtracted from the bigger number) has a bigger digit in the ones place. ex: 56-19 Well, we can simplify this, by adding a new number to each of them, and the difference won't change! ex: a-b = (a+k) - (b+k) (essentially... (+k) - (+k) = 0 (it cancels out to zero) examples: 56 - 19 = 37 .......... (adding +1 to each: 57 - 20 = 37) 71 - 26 = 45 .......... (adding +4 to each: 75 - 30 = 37) 83 - 17 = 66 .......... (adding +3 to each: 86 - 20 = 66)

Fraction-to-Decimal Conversions to be very familiar with:

1/2 = 0.5 1/4 = 0.25 3/4 = 0.75 1/3 = 1.333333......... 2/3 = 0.6667 (6 rounded up to 7 at very end bcuz it repeats) 1/5 = 0.2 2/5 = 0.4 3/5 = 0.6 4/5 = 0.8 1/6 = 0.16667 (6 rounded up at very end bcuz it repeats) 5/6 = 0.83333... 1/7 = 0.14287 (constantly repeating entire "0.14287" ....... so 1/7 = ~ 0.143 1/8 = 0.125 3/8 = 0.375 5/8 = 0.625 7/8 = 0.875 1/9 = 0.11111111....... 7/9 = 0.7777......... 1/10 = 0.1 1/100 = 0.01 1/1000 = 0.001 soo.... helpful for: 1/20 = (1/20)*(5/5) which equals = 5/100 = 0.05 etc!

First 8 prime numbers NEED TO KNOW THESE BY MEMORY

2, 3, 5, 7, 11, 13, 17, 19

The first 17 prime numbers:

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

Important Basic Powers of Single Digits to have Memorized:

2^1 = 2 2^2 = 4 2^3= 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256 2^9 = 512 3^1 = 3 3^2 = 9 3^3= 27 3^4 = 81 4^1 = 4 4^2 = 16 4^3= 64 4^4 = 256 5^1 = 5 5^2 = 25 5^3= 125 5^4 = 625 6^1 = 6 6^2 = 36 6^3= 216 7^1 = 7 7^2 = 49 7^3= 343 8^1 = 8 8^2 = 64 8^3= 512 9^1 = 9 9^2 = 81 9^3= 729 *KNOW ALL MULTIPLES OF 10: very simple! positive numbers = how many zeros negative = putting #'s behind the decimal point

Some examples of prime factorization:

9 = 3 x 3 10 = 2 x 5 12 = 2 x 2 x 3 15 = 3 x 5 24 = 2 x 2 x 2 x 3 (or 2^3 x 3) 100 = 2 x 2 x 5 x 5 (or 2^2 x 5^2) 105 = 3 x 5 x 7 462 = 2 x 3 x 7 x 11 4680 = 2^3 x 3^2 x 5 x 13

Right Isosceles Triangle

A triangle with one right angle and two equal sides. (angles/sides) Sides will equal: 45 degrees = x 45 degrees = x 90 degrees = x root 2 the hypotenuse side = x root 2

Number Sense & Percents: Some Tips/Tricks

A very efficient way of handling percents is using number sense. The basic approach often involves: Finding 10% of the number & sometimes, 1% of the numbers Example: What is 80% of 200? Well, 10% of 200 = 20 We need 8 of these (8 x 10 = 80%) So, 20 x 8 = 160 80% of 200 = 160 56 is what percent of 800? Well, 10% of 800 = 80 1% of 800 = 8 So, (5*80) + (6*8) = (400) +

prime number

A whole number greater than 1 that has exactly two factors (1 and itself), and NO other factors. In other words, a prime number is NOT divisible by any number lower than itself, other than 1. ex: Prime numbers less than 20: 2, 3, 5, 7, 11, 13, 17, 19 Prime numbers between 20 - 60: 23, 29, 31, 37, 41 43, 47, 53, 59 *Notice: 1 is NOT a prime number. Prime numbers have two factors, 1 and the number itself, but 1 only has one factor, itself. *Notice: 2 is the ONLY EVEN prime number, All other even numbers are divisible by 2, and hence are not prime. very good to know these for the test

Area of a trapezoid

A=1/2(b1+b2)h

Whenever squaring numbers that end in 5:

Any number ending in 5 is halfway between two multiples of 10. The product of the number in front of the zeros in those two multiples of ten is crucial for figuring out the square of the number ending in 5. 75^2 = ? *Well, remember it will always end in "25" So... 75 = is in between 70 and 80 *soooo....... (7 x 8 = 56) 56, is the number we will put in front of the -25. 75^2 = 5625

Area of a circle:

Area of a Circle = πr2

Area of a Triangle

Area of triangle = (1/2)bh (1/2) x base x height

Word Problems with Fractions:

As a general rule, when translation from words to math: is ---> "equals" of ---> "multiply"

Example of an equation that has NO solution: (x-1)^2 = -4 Why?

Because there is NOTHING that we can SQUARE that will give us a negative answer. It HAS to be positive! Because it is being raised to an EVEN number, therefore, there is NO SOLUTION.

KNOW the rule/area of: A 30, 60, 90 Triangle

COME BACK HERE WHEN YOU GET TO THIS LESSON 30, 60, 90 = 2x: hypotenuse x: side opposite of 30 degrees X√3: side opposite of the 60 degrees

Changing from Decimals to Percent's:

Changing from Decimals to Percent's: We are simply "un-dividing by 100" which is essentially, multiplying by 100! Thus, we move the decimal two places to the right 0.68 = 68 % 0.075 = 7.5 % 2.3 = 230 %

Changing from Fractions to Percent's:

Changing from Fractions to Percent's: This is trickier, unless you know the Fraction-to-Decimal conversions, discussed in: "Conversions: Fractions & Decimals" Video First: Convert the fractions to decimals (you may want to use rounding at times) Second: Move the decimal over 2 places to the right Examples: 3/8 = 0.375 ... = 37.5% 2/3 = ~ 0.6667 = 66.67% 59/100 = 59% 17/1000 = 0.017 ... = 1.7%

Changing from Percent's to Decimals:

Changing from Percent's to Decimals: This is simply dividing by 100, so we move the decimal point 2 places to the left! Example: 42.5 % = 0.425 4 % = 0.04 0.25 % = 0.0025

Changing from Percent's to Fractions:

Changing from Percent's to Fractions: We simply put the percent over 100 After that, we may have to simplify a bit 20 % = 20/100 ... = 1/5 92 % = 92/100 ... 23/25 0.02 % = 0.02/100 ... = 2/10000 = 1/5000

Circumference of a Circle:

Circumference of a Circle = 2πr (two x pie x radius) or Circumference of a Circle = πd (pie x diameter)

Examples of equations with two possible solutions: x^2 = 4

Could be either: x = 2 or x = -2 Usually, the GRE will specify. But make sure to know this!

T or F: Diagonal cancellation in a proportion is legal.

FALSE -Diagonal cancellation in a proportion is ILLEGAL.

Combined Sign Rules:

If we multiply or divide numbers with the same signs, the result is positive. If we multiply or divide numbers with different signs, the result is negative.

Solving inequalities

If you multiply or divide by a negative, flip the inequality sign you MUST flip/reverse the inequality sign!!!

Illegal Cancellation in Proportions:

In a proportion, diagonal cancellation is 100% incorrect & illegal!!!!! DIAGONAL CANCELLATION = ILLEGAL !!!!

Summary of Legal Cancellation in Properties:

In a proportion, we can cancel vertically (in the numerator and denominator of the same fraction) or we can cancel horizontally (both numerators or both denominators on opposite sides)

If any product, we always have the option of finding half of one factor and doubling the other;this does not change the resultant product

In any multiplication, we can always double one factor and find half of the other, and the product will be the same ex: 16 * 35 (8)*(2*35) (8)*(70) 8*70=560

Integers

Include all positive and negative WHOLE numbers, as well as 0 (zero). Ex: -4, -3, -2, -1, 0, 1, 2, 3, 4,..... If a question asks about "integers", it could be any whole number (including 0). positive integers = the ordinary counting numbers (1,2,3,4,5,6,7,8,9,10,11,..........)

Divisibility Trick/Shortcut: (used this for testing to see if numbers under 100 are prime numbers)

Is 87 divisible by 3? Well, 87...... 8+7= 15 15 is divisible by 3..... 87 = divisible by 3! 87/3= 29 Is 83 divisible by 3? Well, 83..... 8+3=11 11 is not divisible by 3..... 83 = is NOT divisible by 3

raising a power to a power

Keep the base, multiply the exponents

Working with Percents: Method 1: Percents as Multipliers

Method 1: Percents as Multipliers: The decimal form of a percent is called the multiplier for that percent. This is because we simply can multiply by this form to take a percent of a number. 1) Remember than "is" means "equals" 2) Remember that "of" means "multiply" 3) Change any percent to the multiplier form (a decimal) 4) Replace unknowns with a variable Examples: What is 80% of 200? x = (0.80) * (200) = 160 240 is 30% of what number? 240 = (0.30) * x x = 800

Working with Percents: Method 2: Finding the Percent

Method 2: Finding the Percent: Example" 56 is what percent of 800? 56 = x*800 x = 56/800 = 7/100 = 0.07 = 7%

Working with Percents: Method Three: Percent & Fractions:

Method Three: Percent & Fractions: Use this approach ONLY if the percent is a very, very easy fraction, for example: 1/2 1/4 Such as: What is 75% of 280? Well, 75% = 3/4 3/4 * 280 = (factor out/cancel the 4's) ... 3 * 70 = 210 75% of 280 = 210

Percent Decreases:

Might be phrased as: Y decreased by 30% or X is 30% less than Y. Either way, this is a percent decrease for Y. Let's think about this. If Y decreases by 30%, most of the whole original part of Y is still there, except for 30% that's now missing Therefore, the multiplier for a 30% decrease is: 1 - 0.30 = 0.7 In general, if the problem talks about a P % decrease: (multiplier for a P% decrease) = 1 - (P% as a decimal)

Properties of Zero (0):

Multiplying by zero: anything times zero, always equals zero. We can NOT divide by zero. The Zero Product Property: -If the product of two numbers is zero, one of the factors MUST BE zero. ex: a x b = 0 so,..... then a = 0 , b = 0

Mixed Numerals vs. Improper Fractions:

ONLY used mixed numerals ( 5 & 1/3, 12 & 1/2, etc) if you need to locate the fraction on a number line or when it may be helpful to help compare sizes of fractions. Otherwise..... ALWAYS use Improper Fractions (16/3, 25/2, etc.) for solving multiplication, division, squaring, raising numbers, etc!!!!!! & if need be, convert back to mixed numerals at the end (if required) !!!!

A negative raised to any EVEN power is _________.

POSITIVE

Summary of Inequalities (Part 1):

Summary: 1) We can add & subtract with inequalities, exactly as we do with equations. 2) We can multiply and divide inequalities by positive numbers. 3) IF we multiple or divide an inequality by a NEGATIVE number, we MUST reverse/flip the direction of the inequality!!!!

Fraction Properties

Summary: 1) n/1 = n 2) fractions with zero, 0/n = 0 BUT, zero can NEVER be in the denominator od a fraction 3) n/n =1 4) reciprocals a) The "reciprocal" of a fraction, is the "flipped over" fraction, b/a. (as long as neither a or b = 0) b) The reciprocal of any fraction with its reciprocal = 1 ex: 4/7 * 7/4 = 1 c) One divided by any fraction, equals the reciprocal of that fraction ex: 1/(3/7) = 7/3 1/(2/5) = 5/2 1/(-5/9) = -9/5 d) If a number is bigger than 1, then its reciprocal is smaller, between 0 and 1. e) If a number is between 0 and 1, then its reciprocal is larger than 1.

Comparing Fractions:

Summary: 1) with same denominator, bigger numerator means a bigger fraction 2) with same numerator, bigger denominator means a smaller fraction 3) combine # 1 & #2 4) equivalent fractions 5) cross-multiplication 6) number sense comparisons

Intro to Percent's:

Summary: 1) what a percent is 2) percents --> decimals 3) percents --> fractions 4) approximating fractions as percents

T or F: Between any two numbers on the number line, no matter how close the two numbers are, there lies an infinity of points between them.

TRUE

T or F: Mixed Numerals (12 & 1/2, 5 & 3/4) are useful for any multiplication, division, raising, squaring, etc.

TRUE! always use improper fractions (25/2 or 23/4) instead!!!!!

EXPONENTS:

The number that is small and raised to show how many times to multiply the number by itself.

Percent Increases:

This might be phrased as: Y increased by 30% or x is 30% greater than Y Either way, this is percent increase for Y. Let's think about this. If Y increases by 30%, the whole original part of Y is still there, plus 30% more. Therefore, the multiplier for a 30% increase is: 1 + 0.3 = 1.3 In general, if the problem talks about a P% increase: (multiplier for a P% increase) = 1 + (P% as a decimal) Examples: An item originally cost $800. The price increased by 20%. What is the new price? New price = 800 * (1.2) = $960 After a 30% increase, the price of something is $78. What was the original price? x*1.3 = 78 x = 78 / 1.3 x = 60

When we need to divide N by 5, instead we can:

To divide any number by 5, we can simply double it and divide by 10. This order can be switched. Example: 1) double N 2) divide this by 10 OR: 1) divide n by 10 2) double this number We can do these steps in EITHER order!

Testing whether a larger number is a prime number:

To test whether any number less than 100 is prime, all we have to do is check whether it is divisible by one of the prime numbers less than 10. Which are: (only 4) 2, 3, 5, 7, *We ONLY have to check these! If a number less than 100 is NOT divisible by any prime divisor less than 10, then the number has to be prime.

If a question ask what numbers are or aren't factors of a certain number, what do we do? Example: Suppose we are told that: 4680 = 2^2 x 3^2 x 5 x 13 Which of the following numbers below, are or aren't factors of 4680? 25 = y or n 45 = y or n 65 = y or n 85 = y or n 120 = y or n 180 = y or n How do we find this answer?!?!

Using PRIME FACTORIZATION: Ex: 4680 = 2^3 x 3^2 x 5 x 13 25 = 5 x 5 .... no! (there is only one 5!) 45 = 3 x 3 x 5 ..... yes! 65 = 5 x 13 ... yes! 85 = 5 x 17 ... no! (there is no 17) 120 = 2^3 x 3 x 5 .... yes! 180 = 2^2 x 3^2 x 5 ... yes!

Volume of a Cylinder Formula

V=πr²h

What happens whenever we raise a power, to a power?

We multiple the exponents!!!

Doubling & Halving

When simplifying a problem: One factor loses a factor of 2, and the other factor gains a factor of 2. In other words, one factor is halved, and the other is doubled - & the product remains the same!

When do you flip the inequality sign?

When solving for the equation, where the coefficient is negative

When do we switch the order of GEMDAS (Order of Operations) and solve it backwards?

When solving for x in certain algebraic problems!

Equation Solving for X / Algebra

When trying to solve for x, always tackle the problem by employing the Order of Operations (GEMDAS), BACKWARDS!!! So starting with Subtraction/Adding, and then multiplication/division,... & so on!!!!) Why do we do this? Think of the order of how we PUT ON our shoes, & versus how we take them off. The order is switched!

Whenever squaring numbers that end in 5:

When we square any number ending in 5 - the squared number ends in 25. That's always what will form the rightmost two digits.

prime factorization:

a number written as the product of all its prime factors Breaking down a composite number until all of the factors are prime

Abstract Combinations Formula

nCr = n!/r!(n-r)! *MAY need to know this, possible!

Operations with Proportions:

a/b = c/d 1) Legal Cancellation in Proportions: Obviously, we can cancel factors in the numerator & denominator of the same fraction (Vertical Cancellation) -vertical cancellation!!! 2) We can cancel factors in the two NUMERATORS on opposite sides (horizontal cancellation ) -horizontal cancellation!!! 3) We can cancel factors in the two DENOMINATORS on opposite sides (horizontal cancellation) -horizontal cancellation!!! Legal Cancellation in proportions: -In a proportion, we can cancel VERTICALLY (in the numerator and denominator of the same fraction) or we can cancel HORIZONTALLY (both numerators and denominators on opposite sides)

Fundamental Definition of an Exponent:

b^n b = the base n = the exponent b^n = is the power Basic Terms: 7^8 = a) 7 to the power of 8 b) 7 to the eight x^2 = x "squared" x^3 = x "cubed"

Do NOT forget about ALL numbers (not just the positive integers/ordinary counting numbers) Examples: decimals ,fractions, etc

don't forget about these! ex: could be 1/4, 1/5, 1/6, 1/8, or 3.3, 5.7, 4.1 ...... etc.

prime factorization:

every integer greater than 1 that's not prime, can be expressed as a product of primes. This product is called, the prime factorization.

Real Number

is any number on the number line. This includes round numbers, as well as fractions & decimals. It could be a positive, negative, or zero.

General Volume Formula

length x width x height

Combinations Formula

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

Figuring out possibility of combinations, (where order doesn't matter):

nCr = nC(n-r) where n = number we are selecting form r = amount being selected from larger number Example: A manager has 6 employees, and has to pick 3 to form a committee. How many combinations are possible? Well, using our formula: 6C3= 6C3 6*5*4/3*2*1= 20 20 possible combinations! formula I MIGHT need to know: nCr = n! / (r!)((n-r)!)

Squaring Shortcuts

n^2 + n + (n+1) = (n+1)^2 If we know the square of any value, n^2 , then we can add that value, n , and the next integer up, (n+1), and this will result in the next square. (n+1)^2 Ex: 40^2=1600 41^2= ? 41^2 = 40^2 + 40 +41 41^2 = 1681 If we know the square of any value, n^2 , then we can add that value, n , and the next integer up, (n-1), and this will result in the next square. (n-1)^2 Ex: 70^2 = 4900 69^2 = ? 69^2 = 70^2 - 70 - 69 69^2 = 4900 - 70 - 69 69 ^ 2 = 4761

Remember when analyzing numbers on number lines; If the number circled is an open number, then it is ________________. If the number circled is shaded/ solid circle, then it is __________________.

not included: (less than or greater than) included (less than or equal to, greater than or equal to)

Slope:

slope = rise/run slope formula = (y2 - y1) / (x2 - x1)

Absolute Value:

the absolute value of a number gives the distance of the number from the origin (0). ex: Absolute value of [-14] = 14 Absolute value of [6] = 6 Absolute value of [0] = 0 Absolute value of [-77] = 77

super basic review: the result of addition = __________ the result of subtraction = ____________ the result of multiplication = _______________ the result of division = ______________________

the result of addition = sum the result of subtraction = difference the result of multiplication = product the result of division = quotient

Area of a circle

πr²