precalc

Question 1

Conjuction

Answer 1

Compound Statement joined by AND - true when both are true (^)

Question 2

Disjunction

Answer 2

Compound Statement joined by OR - true when 1 is true (V)

Question 3

Intersection

Answer 3

a SET of elements formed where 2 sets OVERLAP (∩)

Question 4

Union

Answer 4

a SET of elements formed where 2 sets combine (U)

Question 5

Conditional

Answer 5

If p, then q (implies, only if, is sufficient for)

Question 6

Logically Equivalent

Answer 6

statements with the same final values in a truth table

Question 7

Biconditional

Answer 7

“if and only if” - “equivalences” F-F and T-T

Question 8

Converse

Answer 8

switch p and q - If q, then p

Question 9

Principal of Inference

Answer 9

__→T = T then __ is T

Question 10

Principal of Contraposition

Answer 10

__ →F = T then __ is F

Question 11

Principal of Syllogism

Answer 11

p→q = T and q→r =T then p→r is T (p→q→r)

Question 12

Principal of Substitution of Statements

Answer 12

1. Math Teachers are cool.
2. danny is a Math Teacher.
   Therefore, Danny is cool.

Question 13

Disjunctive Inference

Answer 13

F V __ = T then __ = T

Question 14

Equivalence Inference

Answer 14

T ←→ __ = T then __ = T

Question 15

Empty (Null) Set

Answer 15

set which has NO elements {}, ø - proper subset of ALL sets

Question 16

Tautology

Answer 16

True no matter what values are assigned to p and q

Question 17

Contrapositive

Answer 17

p → q becomes q’ → p’

Question 18

Vertex Theorem

Answer 18

Corners of a shaded region - max or min value of f(x,y) = ax+by+c

Question 19

Determinant

Answer 19

in a SQUARE matrix ( detA or |A| ) is -/

Question 20

Multiplying Matricies

Answer 20

must have same inside dimensions when put next to each other
axb x bxc - b have to be the same and axc is product

Question 21

Adding/Subtracting Matricies

Answer 21

Must have same dimensions then add/subtract from same position in both

Question 22

Inverse of a Matrix

Answer 22

[ : : ] - change sign of \
- switch /

Question 23

Dependent system of equations

Answer 23

infinite solutions - same line

Question 24

Independent system of equations

Answer 24

one solution - lines intersect

Question 25

Consistent system of equations

Answer 25

lines that touch - not parallel

Question 26

Inconsistant system of equations

Answer 26

parallel lines

Question 27

Horizontal Asymptote

Answer 27

HA

Question 28

Vertical Asymptote

Answer 28

occurs when denominator has an exponent that doesn't cancel

Question 29

Slant Asymptote

Answer 29

divide numerator by denominator?

Question 30

Hole

Answer 30

occurs when a factor of the denominator cancels

Question 31

Inflection Points

Answer 31

where a curve in a graph changes direction - f"(x)

Question 32

Critical Points

Answer 32

where nature of graph changes - (max / min / inflection) f'(x)

Question 33

Symmetry

Answer 33

Point, origin, line

Question 34

First derivative of a graph

Answer 34

tells the max/min

Question 35

Second derivative of a graph

Answer 35

tells the inflection points - concave up or down

Question 36

GOAL

Answer 36

Greater than - OR Less than - AND Used with absolute value inequalities

Question 37

Even Function

Answer 37

Symmetric to y-axis

Question 38

Odd Function

Answer 38

Symmetric to origin

Question 39

YEOO

Answer 39

Y-axis - even Origin - odd

Question 40

Types of Graph Discontinuity

Answer 40

Infinite (Asymptotes) Jump Point

Question 41

Fundamental Theorem of Algebra

Answer 41

Every polynomial with n degrees has n roots

Question 42

Corollary

Answer 42

describes the relationship between roots and factors - if 2 is a root, (x-2) is a factor

Question 43

Discriminant

Answer 43

"b^2 - 4ac" tells the # and type of roots = positive - 2 real roots = 1 - 1 real rood = neg - 2 imaginary roots

Question 44

Complex Conjugates Theorem

Answer 44

If (a + bi) is a root, then (a - bi) is also a root

Question 45

Remainder Theorem

Answer 45

If a polynomial is divided by (x-r), the remainder is a constant, P(r)

Question 46

Factor Theorem

Answer 46

A binomial (x-r) is a factor of a polynomial if there is NO remainder

Question 47

Location Principal

Answer 47

If you plug 3 and 4 into a function and they are opposite in sign, there is a real ZERO between them

Question 48

Rational Root Theorem

Answer 48

If you set a polynomial equal to 0 8x^3 ... + 15 = 0 , then the rational roots are the last constant over the first constant. L/F

Question 49

Present Value of an Annuity

Answer 49

(Loans) Pn = ... n = total # payments i = interest / # payments per year

Question 50

Future Value of an Annuity

Answer 50

(Savings) Fn = ...

Question 51

Interest Compounded Continuously

Answer 51

A = Pe^rt

Question 52

Inverse of Log Function

Answer 52

Exponential Function

Question 53

Log PRODUCT property

Answer 53

logmn = logm+logn

Question 54

Log QUOTIENT property

Answer 54

logm/n = logm - logn

Question 55

Log POWER property

Answer 55

logm^p = p logm

Question 56

Log EQUALITY property

Answer 56

logm = logn, then n = m

Question 57

Common Log

Answer 57

Log base 10

Question 58

Natural log

Answer 58

Ln Log base e

Question 59

Arithmetic / Geometric

Answer 59

Add / Multiply

Question 60

Convergent Series

Answer 60

infinite series that has a sum / limit Geometric when |r|< 1 (decimal)

Question 61

Divergent Series

Answer 61

infinite series that doesn't have a sum / limit All Arithmetic Geometric when |r|>1

Question 62

Binomial Theorem

Answer 62

choose statement

Question 63

Derivative SUM rule

Answer 63

x' + y' (derive each piece separately)

Question 64

Derivative PRODUCT rule

Answer 64

1st x D2nd + 2nd x D1st

Question 65

Derivative CHAIN rule

Answer 65

D(outer) + D(inner)

Question 66

Derivative QUOTIENT rule

Answer 66

LoDhi minus HiDLo all over the square of whats below

Question 67

Definite Integral

Answer 67

area under f(x) from vertical lines x=a to x=b bound to the x-axis (S with the #s)

Question 68

Indefinite Integral

Answer 68

the general antiderivative of a function (S without the #s)

Question 69

Constant of Integration

Answer 69

+C

Question 70

Fundamental Theorem of Calculus

Answer 70

Integration is the inverse of Differentiation (derivation)

Question 71

Integration CONSTANT Rules

Answer 71

Skdx = kSdx + c (move constant out front)

Question 72

Integration x^-1 rule

Answer 72

Ln |x| + c