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Prime Number

answer

whole number that has only 2 factors (1 and itself)

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Composite Number

answer

whole number that has factors in addition to 1 and itself

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0 & 1

answer

Neither prime nor composite

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Even Numbers

answer

Composite (because they are all divisible by two)

question

Numbers that end in 5

answer

Composite (because they are all divisible by 5)

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Prime Numbers up to 20

answer

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

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Interval

answer

Connected portion of the real line

question

Closed Interval

answer

Filled in circles & [ ]

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Open Interval

answer

Open circles & ( )

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Rational Number

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Number that can be written as a ratio/fraction Ex: 8 = 8/1 3/4 7,344/123,239 *EVERY WHOLE NUMBER*

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Irrational Number

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Number that can be written as a decimal but not a fraction Ex: pi= 3.141592... square root 2= 1.414213

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Absolute Value

answer

distance from 0 |x| Ex: |3|=3 |-3|=3 *never negative*

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Factors

answer

Numbers you multiply to get another number

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Prime Factorization

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List of prime numbers that are factors of a number Ex: prime fac of 8 = 2X2X2 *Take number and divide it by smallest prime that goes into it*

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Relation

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Relationship between sets of information

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Domain

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set of all starting points; x

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Range

answer

set of all ending points; y

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All functions are _________ but not all ______ are functions.

answer

RELATIONS

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Well-behaved Function

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relation that has only one y when given one x *Can't share * None can not be matched *

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If you can draw a _______________ through two points it is NOT a function

answer

VERTICAL LINE

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Linear Function

answer

f(x)=x D: (-inf, inf) R: (-inf, inf) *Diagonal Line*

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Constant Function

answer

f(x)=c D: (-inf, inf) R: (y|y=c) *Horizontal Line*

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Quadratic Function

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f(x)=x^2 D: (-inf, inf) R: [0, inf) *Smile/Increases Quickly*

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Cubic Function

answer

f(x)=x^3 D: (-inf, inf) R: (-inf, inf) *Mirror Half Quadratic*

question

Square Root Function

answer

f(x)=sq rt x D: [0, inf) R: [0, inf) *Sideways Quadratic*

question

Absolute Value Function

answer

f(x) =|x| D: (-inf, inf) R: [0, inf) *A V*

question

Graphing a Function

answer

1) find at least 4 ordered pair solutions 2) plot points 3) connect

question

X/Y Intercept

answer

Where graph crosses that axis whether it be x or y

question

If no vertical line can be drawn so that it intersects more than once it is a _______.

answer

FUNCTION

question

Increasing

answer

Going up left to right

question

Decreasing

answer

Going down left to right

question

Constant

answer

horizontal

question

Even

answer

Replacing x with -x doesn't change the function

question

Odd

answer

Replacing x with -x changes every sign of every term

question

Greatest Integer Function

answer

Greatest integer that is less than or equal to x; int(x)

question

Function

answer

No duplicate x's in set, all x's go to y's and are different

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Composition

answer

Plus entire function in for x; symbol is o

question

Inverse

answer

Same points just reversed 1) Draw points 2) Draw reflection line (diagonal through 0,0) 3) reflect points

question

Set

answer

Collection of distinct objects *Sets are ONLY EQUAL if they have the SAME EXACT ELEMENTS*

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Membership

answer

One set is an element of another Symbol: sideways U with line in it

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Subset

answer

Every member of one is also a member of the other Symbol: sideways U with line under it

question

Union

answer

All things that are members of EITHER a OR b Symbol: U

question

Intersection

answer

All things that are members of BOTH a AND b Symbol: upside down U

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Complements

answer

All elements of a but NOT b Symbol:

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Cartesian Product

answer

All ordered pairs a=A, b=B Symbol: X Ex: {1,2} X {red,blue} = {1, red}, {1, blue}, {2, red}, {2, blue}

question

Venn Diagram

answer

Illustrates relationships Universe: Entire Square Intersection: Middle portion

question

Truth Table

answer

Tables used to compute truth values of logical expressions

question

Boolean Value

answer

Either true or false

question

Boolean N-Tuple

answer

How many pieces are in a set Ex: 1-tuple: (True); (False).. 2-tuple: (T,T); (F,F)...

question

Propositional Operator

answer

Rule defined by a truth table

question

Negation Operator

answer

Reverses value of input / ALWAYS OPPOSITE OF ORIGINAL Symbol: Sideways L Ex: P: I am happy Neg P: I am not happy

question

Constant True

answer

Always returns true

question

Identity

answer

Always returns original

question

Constant False

answer

Always returns false

question

Conjunction

answer

Combining of statements Symbol: ^ Ex: P: I like milk Q: I like cookies P^Q= I like milk and I like cookies

question

Disjunction

answer

Including and/or to link 2 statements Symbol: V Ex: P: Mary might sneeze, Q: Joe might sneeze PVQ= Mary might sneeze, or Joe might sneeze *PVQ is TRUE when P, Q OR BOTH are TRUE!*

question

Negation

answer

Turns statement opposite Symbol: ~ Ex: P: She is happy ~P: She is not happy *~P is TRUE when P is FALSE* *~P is FALSE when P is TRUE*

question

Implication

answer

Implies Symbol: =; Ex: P: X is in NY Q: X is in USA P=; If X is in NY, then X is in the USA *Q is TRUE when P is TRUE* P Q P=;Q T T T T F F F T T F F F

question

Conditional Statements

answer

If - Then Statements

question

Converse

answer

Reversal of the parts Ex: P-;Q, converse is Q-;P P-;Q Q-;P T T F T T F T T

question

Contraposition

answer

Inverted and flipped *THIS IS SAME AS ORIGINAL!* *If ORIGINAL is TRUE, CONTRAPOSITIVE is TRUE* *If ORIGINAL is FALSE, CONTRAPOSITIVE is FALSE*

question

Counterexample

answer

disproves a universal statement

question

Logical Consequence

answer

relationship between statements that holds true when every sentence in the set is true

question

Inverse

answer

same points as original function, but x's & y's are switched Ex: {(1,0), (-3,5), (0,4)} Inverse: {(0,1), (5,-3), (4,0)}

question

Factorial

answer

Symbol: ! Multiply number by every number less than that Ex: 5!= (5)(4)(3)(2)(1)

question

Permutation

answer

Number of ways you can arrange something *ORDER IS IMPORTANT* n!/(n-r)! N= Number of Objects R= Number of Ranks

question

0!

answer

1

question

Combination

answer

Number of ways you can arrange somethign Order isn't important n!/(n-r)!r!

question

Mean

answer

Average

question

Median

answer

Middle number

question

Mode

answer

Number that occurs most often

question

Range

answer

Difference between highest and lowest numbers

question

Experiment

answer

act for which the outcome is uncertain

question

Sample Space

answer

set of all possible outcomes of the experiment

question

Event

answer

any subset (E) of a sample space

question

Empirical Probability

answer

Finding probability of an empirical event # of times it occurs/total # of observed occurrences

question

Equiprobable Space

answer

all events are EQUALLY LIKELY to occur Ex: Tossing a coin

question

Theoretical Probability

answer

Finding probability of events in an equiprobable sample # of outcomes in event/number of outcomes in set

question

Mutually Exclusive

answer

Events that have NO ELEMENTS IN COMMON

question

Properties of Probability

answer

1) 0< P(E)< 1 : Probability will NEVER EXCEED 1 2) P (not E) = 1-P(E) : It either IS or ISN'T in E 3) P (E) =1-P(not E) : It either ISN'T or IS in E 4) P(E or F) = P(E)+P(F) : Only for mutually exclusive 5) P(E or F) =P(E)+P(F)-P(E and F) : For not mut. exc

question

Independent Events

answer

outcome of 1 event DOESN'T affect outcome of the other event P(E and F)= P(E)P(F)

question

Standard Deviation

answer

How spread out number are Symbol: Theta 1) Find mean 2) Subtract each number from mean and square it 3) average all squared differences

question

Logarithm

answer

Opposite/Inverse of Exponentials; Undo Exponentials Ex: y=b^x= logb(y)=x

question

Pythagorean Theorem

answer

a^2+b^2=c^2 2 legs squared are equal to hypotenuse squared

question

Area of Triangle

answer

1/2 (b*h) OR 1/2b(c*sinA) 1/2a(c*sinB) 1/2a(b*sinC)

question

Perimeter of Triangle

answer

a+b+c

question

Perimeter of Rectangle

answer

2L+2W

question

Area of Rectangle

answer

L*W

question

Perimeter of Parallelogram

answer

B*H

question

Area of Trapezoid

answer

1/2 (A+B)*H

question

Circumference of Circe

answer

2*pi*R

question

Area of Circle

answer

pi*R^2

question

Arc Length of Circular Sector

answer

s=rt

question

Area of Circular Sector

answer

1/2(R^2*T)

question

Volume of Sphere

answer

4/3*pi*R^3

question

Surface Area of Sphere

answer

4*pi*R^2

question

Volume of Cylinder

answer

pi*R^2*H

question

Surface Area of Cylinder

answer

2*pi*R*H

question

Volume of Cone

answer

1/3*pi*R^2*H

question

Surface Area of Cone

answer

pi*r*sq rt r^2+h^2

question

Fundamental Theorem of Algebra

answer

Using complex numbers, all polynomials can be factored

question

Imaginary Unit

answer

i= square root of -1 i^2=-1 *SIMPLIFY SQUARE ROOT OF -1 as i* *SIMPLIFY i^2 as -1*

question

Complex Number

answer

a+bi *a+bi=c+di if a=c and b=d* *2 complex numbers are EQUAL if REAL ; IMAGINARY numbers MATCH* *THEN THEY CAN BE ADDED AND SUBTRACTED!*

question

Adding/Subtracting Complex Numbers

answer

1) Add/Subtract real number parts 2) Do same for imaginary parts 3) Write in standard form (a+bi) Ex: (7+2i) + (9-5i) (7+9) + (2-5)i 16-3i

question

Multiplying Complex Numbers

answer

1) Simplify *WHENEVER IT IS i^2 REPLACE with -1* 2) Write answer in standard form (a+bi) Ex: -2i(5+31) -10i-6i^2 -10i-6(-1) -10+6 6-10i

question

Dividing Complex Numbers

answer

1) Find conjugate of denominator (Change sign) 2) Multiply 3) Simplify *REPLACE -i^2 with -1* 4) Write answer in standard form (a+bi)

question

Square root of a negative is _____

answer

i

question

Square Root Complex Numbers

answer

Sq Rt(-b)= i Sq Rt (b)

question

Square Roots with Negative Numbers

answer

Express in terms of i (Sq Rt(-b)= i Sq Rt(b)

question

Remainder Theorem

answer

Divide polynomial by linear factor *REMAINDER HAS TO BE SMALLER THAN WHAT IT WAS DIVIDED BY*

question

Factor Theorem

answer

Divide polynomial by a factor of that polynomial and there is a 0 remainder *REVERSE OF REMAINDER THEOREM*

CLEP College Mathematics

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