Assessment 1 Reviewer

{ } or ∅

null set or empty set

{x} or x

unit set, which contains exactly one element

P

set of all prime numbers

N

set of all natural numbers

Z

the set of all integers

Q

the set of all rational numbers

R

the set of all real numbers

C

the set of all complex numbers

H

denotes the set of all quaternions

Absolute Complement

U\A or U-A

Relative Complement

A\B or A-B or A only

A or B

Union or A U B

A and B

Intersection or A ∩ B

2 Types of Subsets

Proper and Improper Subset

⊆ is a symbol for?

Improper Subset

⊂ is a symbol for?

Proper Subset

P(A)

Power Set

a set that contains all subsets of a given set including empty set and the set itself

Power Set

Formula for the Cardinality of a Power Set

n(P(A)) = 2^n

Principle of Inclusion and Exclusion Formula for A U B

A U B = A + B - A∩B

Principle of Inclusion and Exclusion Formula for A U B U C

A U B U C = A + B + C - A∩B - B∩A - A∩C + A∩B∩C

Velocity Formula

V = d/t

Veff for Object-Environment with Same Direction

V1 + V2

Veff for Object-Environment with Opposite Direction

V1 - V2

Veff for Object-Object with Same Direction

V1 - V2

Veff for Object-Object with Opposite Direction

V1 + V2

Work Formulas

Rate = Work Done/Time or j = rt

Work Load Formula

Work Load = (# of people)(Duration)

Direct Variation Formula

y = kx

Inverse Variation Formula

y = k/x

Joint Variation Formula

y = kxz

Combined Variation Formula

y = kx/z

Arithmetic Progression nth Term Formulas

an = a1 + (n-1)d or an = am + (n-m)d

Arithmetic Series Sn Formulas

Sn = (n/2)(a1 + an) or Sn = (n/2)(2a1 + (n-1)d)

Arithmetic Progression and Series Calctech

Explain Mode 3-2, syntax: y = A + Bx

Sum of Interior Angles Formula

180(n - 2)

Geometric Progression nth Term Formula

an = a1r^(n-1)

Geometric Series Sn Formula for Finite

Sn = (a1(1-r^n))/(1-r)

Geometric Series Sn Formula for Infinite

S = a1/(1-r)

Geometric Series for Sum of Distance Travelled by an Infinitely Bouncing Ball

S = a1 + (2a2)/(1-r)

Calctech for Geometric Progression and Series

Explain M-3-6 application; Syntax:

Arithmetic Mean Formula

AM = (x+y)/2

Harmonic Mean Formula

HM = (2xy)/(x+y)

Geometric Mean

GM = √(xy)

Relationship between AM, HM, and GM Formula

GM² = HM x AM

Sexagesimal System Conversion Factors

1 rev = 360°

1° = 60’

1’ = 60"

Centesimal System Conversion Factors

1 rev = 400^g

1^g = 100’

1’ = 100”

Circular or Natural System Conversion Factors

1 rev = 2pi rad

Military or NATO Mils System

1 rev = 6400 mils or NATO mils

What is zero angle?

exactly 0°

What is acute angle?

between 0° and 90°

What is right angle?

exactly 90°

What is obtuse angle?

between 90° and 180°

What is straight angle?

exactly 180°

What is reflex angle?

between 180° and 360°

What is full angle?

exactly 360°

Complementary Angles

sum of two angles is 90°

Supplementary Angles

sum of two angles is 180°

Explementary Angles

sum of two angles is 360°

Conjugate Angles

sum of two angles is 360°

Trigonometric Functions

SOHCAHTOA-CAOSHACHO

Trigo Pytha Identities

Memorize all three.

Sum and Difference Trigo Identities

Memorize all three.

Cofunctions

Memorize all 6.

Double Angle Trigo Identity

sin2theta = 2sinthetacostheta

Wave Characteristics Syntax

y = A trig (Bx + C) + D

Amplitude Formula

Amplitude = | A |

Period Formula

T = (To)/B

To for sin, cos, and tan?

2pi for sin and cos, pi for tan

Amplitude for tan?

none or undefined

Frequency Formula

F = 1/T

Phase Shift Formula

PS = -C/B

Vertical Shift Formula

VS = D

Sine Law

Define.

Cosine Law and Calctech

Memorize formula.

Quadratic Equation Calctech and Syntax

syntax: ax2 + bx + c = 0

Colon Calctech

Explain mechanism.

Polar Coordinates Formulas and Calctech

x, y, r², tan theta

Polar Calctech

Explain

Polygon with 3 Sides

Trigon/Triangle

Polygon with 4 Sides

tetragon/quadrilateral

Polygon with 5 Sides

pentagon

Polygon with 6 Sides

hexagon

Polygon with 7 Sides

heptagon

Polygon with 8 Sides

octagon

Polygon with 9 Sides

nonagon/enneagon

Polygon with 10 Sides

decagon

Polygon with 11 Sides

hendecagon

Polygon with 12 Sides

dodecagon

Sum of Central and Exterior Angles

360°

Central and Exterior Angle Formula for Regular Polygons

360°/n

Interior Angle Formula for Regular Polygon

[180(n-2)]/n

Sum of Interior Angles of Polygons

180(n-2)

Diagonals Formula for Polygons and Calctech

[n(n-3)]/2 ; M-3-3, syntax: y=A+Bx+Cx²

Area of Polygons Formula

A = (ns²)/[4tan(180/n)]

Semi-Perimeter Formula

S = P/2

Area of Triangle 3 Formulas

A = (bh)/2

A = (1/2)absintheta

√[s(s-a)(s-b)(s-c)]

Quadrilaterals 2 Formulas

A = (1/2)d1d2

A = √{(s-a)(s-b)(s-c)(s-d)-abcd[cos(E/2)]²}

Circumference Formula

C = 2pi*r

Circle Area Formula

A = pi*r²