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f(n)=p∧n, n is an integer and p is a p…

line l passes through (⁻2,3) and (0,5)…

A={even prime numbers}... B={integers bet…

G={1,2,25,6,8}... a=mean of G, b=median o…

Since ƒ(n)=p^n, then ƒ(4)=p⁴, ƒ(3)=p³ Then ... ƒ(4)=2f(3)... p⁴=2p³…

When two lines are perpendicular, their slopes are opposite r…

Since there is only one even prime number, namely 2, A = {2}.…

The mean of G(average )=24/6 =4... The median of G (middle valu…

f(n)=p∧n, n is an integer and p is a p…

Since ƒ(n)=p^n, then ƒ(4)=p⁴, ƒ(3)=p³ Then ... ƒ(4)=2f(3)... p⁴=2p³…

line l passes through (⁻2,3) and (0,5)…

When two lines are perpendicular, their slopes are opposite r…

HIGH: Area of a triangle?

HIGH: Volume of a cube?

HIGH: Volume of a cylinder?

How do you multiply fractions?

A=1/2bh. The height of the triangle must be measured by a lin…

V=s³

V=πr²h (This is just the area multiplied by the height)

Multiply numerator times numerator and denominator times deno…

HIGH: Area of a triangle?

A=1/2bh. The height of the triangle must be measured by a lin…

HIGH: Volume of a cube?

V=s³

HIGH: Area of a triangle?

HIGH: Volume of a cube?

HIGH: Volume of a cylinder?

How do you multiply fractions?

A=1/2bh. The height of the triangle must be measured by a lin…

V=s³

V=πr²h (This is just the area multiplied by the height)

Multiply numerator times numerator and denominator times deno…

HIGH: Area of a triangle?

A=1/2bh. The height of the triangle must be measured by a lin…

HIGH: Volume of a cube?

V=s³

how many integers can be square that r…

Formula for sum of sequence?

List the 5 points on box plots

IQR =?

6 { +- 1, +-2, +-3}

n (a1 +an) /2 or n(1st number + last number)/2.

min, Q1 -25%, median - 50%, Q3 - 25%, Max

IQR = Q3- Q1 = middle 50%

how many integers can be square that r…

6 { +- 1, +-2, +-3}

Formula for sum of sequence?

n (a1 +an) /2 or n(1st number + last number)/2.

Perfect Squares 1-15

Number is multiple of 12

Number is a multiple of 9

Slope given 2 points

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits is a multiple of 3; the last two digits…

sum of the digits is a multiple of 9.

m= (Y2-Y1)/(X2-X1)... ex: (1,3); (5,6)... m = (6-3) / 5-1) = 3/4

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Number is multiple of 12

The sum of the digits is a multiple of 3; the last two digits…

Time per question: Sentence Equivalence

Time per question: Text Completion

Time per question: Reading Comprehension

Time per question: Quantitative Compar…

45 seconds

30-90 seconds, depending on the number of blanks

1 min 30 seconds; plan to complete a short passage (2 questio…

1 min 15 seconds

Time per question: Sentence Equivalence

45 seconds

Time per question: Text Completion

30-90 seconds, depending on the number of blanks

Intergers

Real Number

PEMDAS

Commutative Property

Any counting number including negative numbers

Numbers that appear on the number line including pi, the squa…

1. Parentheses... 2. Exponents... 3. Multiplication/Division... 4. Add…

a + b = b + a... A x B = B x A

Intergers

Any counting number including negative numbers

Real Number

Numbers that appear on the number line including pi, the squa…

Perfect Squares 1-15

Number is multiple of 12

Number is a multiple of 9

Slope given 2 points

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits is a multiple of 3; the last two digits…

sum of the digits is a multiple of 9.

m= (Y2-Y1)/(X2-X1)... ex: (1,3); (5,6)... m = (6-3) / 5-1) = 3/4

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Number is multiple of 12

The sum of the digits is a multiple of 3; the last two digits…

Divisible by 3

Divisible by 4

Divisible by 6

Divisible by 9

Sum of digits is multiple of 3

Last 2 digits are multiple of 4

Sum of digits is multiple of 3... Last digit is even

Sum of digits is multiple of 9

Divisible by 3

Sum of digits is multiple of 3

Divisible by 4

Last 2 digits are multiple of 4

Primes

Pythagorean triples

Greatest Common Factor/divisor

Area of a parallelogram

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

(3, 4, 5)... (5, 12, 13)... (8, 15, 17)... (7, 24, 25)

biggest factor shared by 2 numbers -- easiest way to find is…

A=bh

Primes

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

Pythagorean triples

(3, 4, 5)... (5, 12, 13)... (8, 15, 17)... (7, 24, 25)

Perfect Squares 1-15

How to recognize if a # is a multiple…

Area of a rectangle

How to recognize a # as a multiple of 9

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits it a multiple of 3 and the last two dig…

A = length x width

The sum of the digits is a multiple of 9.

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

How to recognize if a # is a multiple…

The sum of the digits it a multiple of 3 and the last two dig…

Average

Median

Mode

Range

Sum of Terms, over, the Number of Terms

The middle term of a set in sequential order

The term that occurs most frequently

The difference between the greatest term and the least term

Average

Sum of Terms, over, the Number of Terms

Median

The middle term of a set in sequential order

Absolute Value

Prime Numbers

Order of evaluation

Is X divisible by of 2 or 4?

If x< 0 then -x; If x≥0 then x

Numbers only divisible by 1 and themselves

PEMDAS = Parens, Exponents, Mult, Div, Add, Subtract

Is the last digit divisible by 2 or 4?

Absolute Value

If x< 0 then -x; If x≥0 then x

Prime Numbers

Numbers only divisible by 1 and themselves

Ratio

For every 40 games a baseball team pla…

x%

A vintage bowling league shirt that co…

The amount of one object compared to the amount of another.

12:28 = 6:14 = 3:7

x/100

$20 *.85 = $17

Ratio

The amount of one object compared to the amount of another.

For every 40 games a baseball team pla…

12:28 = 6:14 = 3:7

Percent

Percent Increase

Percent Decrease

common multiple of 2 numbers

part = percent X whole

Amount of Increase/Original Whole X 100%

amount of decrease/original whole X 100%

prime factor both numbers; multiply each factor the greatest…

Percent

part = percent X whole

Percent Increase

Amount of Increase/Original Whole X 100%

Perfect Squares 1-15

How to recognize if a # is a multiple…

How to recognize a # as a multiple of 9

Slope given 2 points

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits it a multiple of 3 and the last two dig…

The sum of the digits is a multiple of 9.

m= (Y1-Y2)/(X1-X2)

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

How to recognize if a # is a multiple…

The sum of the digits it a multiple of 3 and the last two dig…

Perfect Squares 1-15

How to recognize if a # is a multiple…

Area of a rectangle

How to recognize a # as a multiple of 9

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits it a multiple of 3 and the last two dig…

A = length x width

The sum of the digits is a multiple of 9.

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

How to recognize if a # is a multiple…

The sum of the digits it a multiple of 3 and the last two dig…

Supplementary Angles

Complimentary Angles

Corresponding Angles

Vertical Angles

Add up to 180 degrees

Add up to 90 degrees

2 parallel lines cut by transverse line, labeled angles are e…

2 parallel lines cut by transverse line, labeled angles are e…

Supplementary Angles

Add up to 180 degrees

Complimentary Angles

Add up to 90 degrees

Perfect Squares 1-15

How to recognize if a # is a multiple…

Area of a rectangle

How to recognize a # as a multiple of 9

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits it a multiple of 3 and the last two dig…

A = length x width

The sum of the digits is a multiple of 9.

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

How to recognize if a # is a multiple…

The sum of the digits it a multiple of 3 and the last two dig…

Perfect Squares 1-15

Number is multiple of 12

Number is a multiple of 9

Slope given 2 points

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits is a multiple of 3; the last two digits…

sum of the digits is a multiple of 9.

m= (Y2-Y1)/(X2-X1)... ex: (1,3); (5,6)... m = (6-3) / 5-1) = 3/4

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Number is multiple of 12

The sum of the digits is a multiple of 3; the last two digits…

Primes

Pythagorean triples

Greatest Common Factor/divisor

Area of a parallelogram

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

(3, 4, 5)... (5, 12, 13)... (8, 15, 17)... (7, 24, 25)

biggest factor shared by 2 numbers -- easiest way to find is…

A=bh

Primes

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

Pythagorean triples

(3, 4, 5)... (5, 12, 13)... (8, 15, 17)... (7, 24, 25)

Perfect Squares 1-15

How to recognize if a # is a multiple…

Area of a rectangle

How to recognize a # as a multiple of 9

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits it a multiple of 3 and the last two dig…

A = length x width

The sum of the digits is a multiple of 9.

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

How to recognize if a # is a multiple…

The sum of the digits it a multiple of 3 and the last two dig…

integers

factor

multiple

multiples of non-zero integers

numbers 1, 2, 3..., with their negatives and 0

a number multiplied by another number (another factor) to giv…

opposite of a factor; a number that is the product of certain…

every non-zero integer has infinitely many multiples

integers

numbers 1, 2, 3..., with their negatives and 0

factor

a number multiplied by another number (another factor) to giv…

Perfect Squares 1-15

Number is multiple of 12

Number is a multiple of 9

Slope given 2 points

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits is a multiple of 3; the last two digits…

sum of the digits is a multiple of 9.

m= (Y2-Y1)/(X2-X1)... ex: (1,3); (5,6)... m = (6-3) / 5-1) = 3/4

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Number is multiple of 12

The sum of the digits is a multiple of 3; the last two digits…

Perfect Squares 1-15

How to recognize if a # is a multiple…

Area of a rectangle

How to recognize a # as a multiple of 9

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits it a multiple of 3 and the last two dig…

A = length x width

The sum of the digits is a multiple of 9.

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

How to recognize if a # is a multiple…

The sum of the digits it a multiple of 3 and the last two dig…

30°-60°-90° right triangle

45°-45°-90° right triangle

The sum of any two sides of a triangle…

If we know the lengths of two sides of…

1-2-√3

1-1-√2

GREATER than the third side

Difference of other two sides < third side < Sum of other two…

30°-60°-90° right triangle

1-2-√3

45°-45°-90° right triangle

1-1-√2

Perfect Squares 1-15

How to recognize if a # is a multiple…

Area of a rectangle

How to recognize a # as a multiple of 9

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits it a multiple of 3 and the last two dig…

A = length x width

The sum of the digits is a multiple of 9.

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

How to recognize if a # is a multiple…

The sum of the digits it a multiple of 3 and the last two dig…

Perfect Squares 1-15

Number is multiple of 12

Number is a multiple of 9

Slope given 2 points

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

The sum of the digits is a multiple of 3; the last two digits…

sum of the digits is a multiple of 9.

m= (Y2-Y1)/(X2-X1)... ex: (1,3); (5,6)... m = (6-3) / 5-1) = 3/4

Perfect Squares 1-15

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Number is multiple of 12

The sum of the digits is a multiple of 3; the last two digits…

Integers

Zero

Even or Odd

Factor

-NUMBERS THAT HAVE NO FRACTIONAL OR DECIMAL PARTS

1) Neither positive or negative... 2) 0 is even ... 3) You can not…

1) Only integers possess the property of being even or odd... 2)…

-number that will divide evenly into the integer in question

Integers

-NUMBERS THAT HAVE NO FRACTIONAL OR DECIMAL PARTS

Zero

1) Neither positive or negative... 2) 0 is even ... 3) You can not…

Always reduce big fractions before doi…

To add or subtract fractions, you must…

To add or subtract fractions, you can…

To multiply fractions, you just ______…

common denominator

Bowtie method

multiply straight across

Always reduce big fractions before doi…

To add or subtract fractions, you must…

common denominator

Arithmetic Mean

Average

Chord

Composite Number

the mean obtained by adding several quantities together and d…

a quantity, rating, or the like that represents or approximat…

Geometry. the line segment between two points on a given curve.

Natural number that has more than two factors. Example: 6, 1•…

Arithmetic Mean

the mean obtained by adding several quantities together and d…

Average

a quantity, rating, or the like that represents or approximat…

Counting factors of large numbers

Find factors of odd numbers

Find even factors

list of Squares of integers (perfect s…

Steps:... 1) prime factorization of number ... 2) create list of ex…

1) same method ... 2) ignore exponent factors of 2!... Done!

1) same method as counting large factors ... 2) find odd factors…

1x1=1... 2x2=4... 3x3=9... 4x4=16... 5x5=25... 6x6=36... 7x7=49... 8x8=64... 9x9=81... 1…

Counting factors of large numbers

Steps:... 1) prime factorization of number ... 2) create list of ex…

Find factors of odd numbers

1) same method ... 2) ignore exponent factors of 2!... Done!

Standard Identities :(A-B)^3

Quadratic Formula

Basic Rules of Exponents I

Basic Rules of exponents II

A^3 - 3A^2b + 3AB^2 - B^3

When the bases are the same and the exponents differ, the bas…

When the bases differ and the exponents are the same, the bas…

Standard Identities :(A-B)^3

A^3 - 3A^2b + 3AB^2 - B^3

Quadratic Formula

Primes

Pythagorean triples

Greatest Common Factor/divisor

Area of a parallelogram

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

(3, 4, 5)... (5, 12, 13)... (8, 15, 17)... (7, 24, 25)

biggest factor shared by 2 numbers -- easiest way to find is…

A=bh

Primes

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

Pythagorean triples

(3, 4, 5)... (5, 12, 13)... (8, 15, 17)... (7, 24, 25)

Isosceles triangle

3-4-5 Isosceles triangle

5-12-13 Isosceles triangle

30-60-90 right triangle

2 sides and their angles are the same length

Ratio: Legs = 3,4, hypotenuse = 5

Ratio: Legs = 5,12, hypotenuse = 13

Ratio: Legs = 1,√3, hypotenuse = 2... *equilateral triangle divi…

Isosceles triangle

2 sides and their angles are the same length

3-4-5 Isosceles triangle

Ratio: Legs = 3,4, hypotenuse = 5

Volume of a sphere with radius r = ?

If events A and B are **not** independen…

If events A and B are independent, wha…

If events A and B are independent, wha…

(4/3) πr^3

P(A and B) = P(B) x P(A|B)... P(A and B) = P(A) x P(B|A)

P(A or B) = P(A) + P(B) - P(A) x P(B)

P(A and B) = P(A) x P(B)

Volume of a sphere with radius r = ?

(4/3) πr^3

If events A and B are **not** independen…

P(A and B) = P(B) x P(A|B)... P(A and B) = P(A) x P(B|A)

Simplifying Square Roots

Median, good way to think about it is ..

Prime Numbers

When subtracting or adding exponents i…

√28 = √4×7 which equals 2√7 and √175 = √25*7 which equals 5√7…

it's the 50th percentile or the middle of a list.

Only two whole number factors are 1 and itself. ie 1, 2, 3, 5…

You have to factor when possible. For example= 4⁶-4⁵ can be f…

Simplifying Square Roots

√28 = √4×7 which equals 2√7 and √175 = √25*7 which equals 5√7…

Median, good way to think about it is ..

it's the 50th percentile or the middle of a list.