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precalc Flashcards

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1
Q

Conjuction

A

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

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2
Q

Disjunction

A

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

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3
Q

Intersection

A

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

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4
Q

Union

A

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

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5
Q

Conditional

A

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

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6
Q

Logically Equivalent

A

statements with the same final values in a truth table

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7
Q

Biconditional

A

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

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8
Q

Converse

A

switch p and q - If q, then p

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9
Q

Principal of Inference

A

__→T = T then __ is T

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10
Q

Principal of Contraposition

A

__ →F = T then __ is F

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11
Q

Principal of Syllogism

A

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

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12
Q

Principal of Substitution of Statements

A
  1. Math Teachers are cool.
  2. danny is a Math Teacher.
    Therefore, Danny is cool.
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13
Q

Disjunctive Inference

A

F V __ = T then __ = T

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14
Q

Equivalence Inference

A

T ←→ __ = T then __ = T

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15
Q

Empty (Null) Set

A

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

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16
Q

Tautology

A

True no matter what values are assigned to p and q

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17
Q

Contrapositive

A

p → q becomes q’ → p’

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18
Q

Vertex Theorem

A

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

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19
Q

Determinant

A

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

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20
Q

Multiplying Matricies

A

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

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21
Q

Adding/Subtracting Matricies

A

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

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22
Q

Inverse of a Matrix

A

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

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23
Q

Dependent system of equations

A

infinite solutions - same line

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24
Q

Independent system of equations

A

one solution - lines intersect

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25
Q

Consistent system of equations

A

lines that touch - not parallel

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26
Q

Inconsistant system of equations

A

parallel lines

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27
Q

Horizontal Asymptote

A

HA

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28
Q

Vertical Asymptote

A

occurs when denominator has an exponent that doesn’t cancel

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29
Q

Slant Asymptote

A

divide numerator by denominator?

30
Q

Hole

A

occurs when a factor of the denominator cancels

31
Q

Inflection Points

A

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

32
Q

Critical Points

A

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

33
Q

Symmetry

A

Point, origin, line

34
Q

First derivative of a graph

A

tells the max/min

35
Q

Second derivative of a graph

A

tells the inflection points
- concave up or down

36
Q

GOAL

A

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

37
Q

Even Function

A

Symmetric to y-axis

38
Q

Odd Function

A

Symmetric to origin

39
Q

YEOO

A

Y-axis - even
Origin - odd

40
Q

Types of Graph Discontinuity

A

Infinite (Asymptotes)
Jump
Point

41
Q

Fundamental Theorem of Algebra

A

Every polynomial with n degrees has n roots

42
Q

Corollary

A

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

43
Q

Discriminant

A

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

44
Q

Complex Conjugates Theorem

A

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

45
Q

Remainder Theorem

A

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

46
Q

Factor Theorem

A

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

47
Q

Location Principal

A

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

48
Q

Rational Root Theorem

A

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

49
Q

Present Value of an Annuity

A

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

50
Q

Future Value of an Annuity

A

(Savings) Fn = …

51
Q

Interest Compounded Continuously

A

A = Pe^rt

52
Q

Inverse of Log Function

A

Exponential Function

53
Q

Log PRODUCT property

A

logmn = logm+logn

54
Q

Log QUOTIENT property

A

logm/n = logm - logn

55
Q

Log POWER property

A

logm^p = p logm

56
Q

Log EQUALITY property

A

logm = logn, then n = m

57
Q

Common Log

A

Log base 10

58
Q

Natural log

A

Ln
Log base e

59
Q

Arithmetic / Geometric

A

Add / Multiply

60
Q

Convergent Series

A

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

61
Q

Divergent Series

A

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

62
Q

Binomial Theorem

A

choose statement

63
Q

Derivative SUM rule

A

x’ + y’ (derive each piece separately)

64
Q

Derivative PRODUCT rule

A

1st x D2nd + 2nd x D1st

65
Q

Derivative CHAIN rule

A

D(outer) + D(inner)

66
Q

Derivative QUOTIENT rule

A

LoDhi minus HiDLo all over the square of whats below

67
Q

Definite Integral

A

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

68
Q

Indefinite Integral

A

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

69
Q

Constant of Integration

A

+C

70
Q

Fundamental Theorem of Calculus

A

Integration is the inverse of Differentiation (derivation)

71
Q

Integration CONSTANT Rules

A

Skdx = kSdx + c
(move constant out front)

72
Q

Integration x^-1 rule

A

Ln |x| + c

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