Algebra Regents Exam Review

Integers

positive or negative whole numbers

Rational Numbers

All positive and negative integers, fractions and decimal numbers.

Irrational Numbers

Decimals that don't stop or repeat

Union

All elements in the sets

Intersection

Elements common to sets

Complement

Elements not in set X

Empty set

Set with no elements

Commutative Property of Addition

7+1=1+7(Change order)

Commutative Property Of Multiplication

8x2=2x8

Associative Property of Addition

1+(2+3)=(1+2)+3(Always Stays Same Order)

Associative Property of Multiplication

4x(5x6)=(4x5)x6

Distributive Property

x(x+1)=XxX+xx1

Additive Inverse

5+(-5)=0 (Add opposite #)

Additive Identity Property

5+0=5

Multiplicative Inverse

5X1/5=1

Multiplicative identity property

5x1=5

Like Terms

the same variable(s) and the same exponent(s)

Monomial

an expression with ONE term

Binomial

an expression with TWO terms

Trinomial

an expression with THREE terms

Polynomial

an expression one or more terms

Standard Form

highest to lowest degree in abc order

Complement

elements not in the given set

Union

All elements in the sets

Operation of Addition for Polynomials

1. Combine coeffiecients of like terms and keep the exponents the same
2. Write answer in standard form

Operation of Subtraction for Polynomials

1. Distribute -1 to all terms after the minus sign
2. Combine coeffecients of like terms and keep the exponents the same
3. Write answer in standard form
"from comes first

Operation of Multiplication for Polynomials

1. Multiply coeffiecients
2. Add exponents of like bases
3. Write in standard form
Monomial x Polynomial
Binomial x Binomial
Distribute
FOIL

Operation of Division for Polynomials

1. Divide coefficients in numerator by coefficients in denominator
2. Subtract exponents of like bases
3. Write in standard form
example: 24r^5+12r^3
------------------
"Pretzel"
Polynomial /Monomial
6r

GCF

Can have 2 or more terms
Find a GCF that divides into all terms
ex. 5y^3+10y^2

Diff. of Perf. Squares

Only 2 terms
Is a subtraction sign between the 2 terms
Both terms have to be perfect squares
( + )( - ) once factored
ex. m^2-9

UnFOIL

Exactly 3 terms
Find the factors that add to the middle term and multiply to the end right term
ex. X^2-4x-12

Factoring Completely

Need to use a combination of all the factoring methods
ex. y^3-36y

A fraction is undefined when

the denominator is equal to zero

To determine when a fraction is undefined

set denominator = 0
solve for X

To simplify algebraic fractions, we can only cancel

happy couples

happy couples

same binomials
same like terms

Perfect Squares

1,4,9,16,25,36,49,64,81,100,121,144,x^2,x^4

Square roots

1,2,3,4,5,6,7,8,9,10,11,12,x,x^2

Radicals with addition/subtraction

1st simplify then add coefficients don't add the radicands(The numbers inside the check mark)

Radicals with multiplication

1st multiply, then simplify

Pythagorean Theorem

a^2+b^2=c^2

SOH CAH TOA

S O/H C A/H T O/A

A relation is a function when

every x value has exactly 1 y value

Linear Function

LINEar
y=x+2

Quadratic Functions

qUadratic - u shaped
parabola
y=x^2+2

Absolute Value Functions

Absolute Value - v-shaped
y=[x-3]

Exponential

skateboard ramp
y=2^x
x is in the exponents

Line General form

y=mx+b

To graph a line

1. Need y=mxtb form
2. Identify slope and y-intercept
3. Plot first point at y-intercept
4. Use the slope to plot additional points

Slope formula

m= y^2-y^1
-----------
x^2-x^1

Parallel lines have

the same slope
they never intercept

Perpendicular lines have

slopes that are reciprocals
(negative)/flipped and have opposite sign

To write the equation of a line, we need the

Slope and Y-Intercept

Solving linear equations graphically

Get in standard form
Graph the lines
Find the point of intersection

Solving inequalities graphically

Get in=ity in standard form(Y=mx+b)
Determine if line should be solid (greater than or equal to, less than or equal to) or dashed (<,>)
Draw the boundary line (Pretend there is an = sign instead)
Use (0,0) as a test point; plug in x and y to see if in=ity

Quadratic Equation standard form

ax^2+bx+c=0

Factoring Method of solving quad. equations

Will have an x^2 and x term
Set = 0 and factor
Set factors =0(draw the wall)
Solve

The shape of a quadratic is

a parabola "U

Vertex

lowest or highest point
aka the turning point

Axis of symmetry

Vertical line that divides the parabola in 1/2 cuts through the vertex

To find the x-coordinate of the vertex, use

x= -b over 2a

Exponential functions formula

y=a(b)^X

Growth formula

y=a(1+r)^x

Decay Formula

y=a(1-r)^x

area of square formula

A=s^2

perimeter for all shapes except circle

add all of sides

area of triangle

a=1/2 b/h

area of rectangle

a=bh

area of circle

PIr^2

circumference of a circle

c=piD

area of parallelogram

a=bh

area of a trapezoid

a= 1/2h(b1+b2)

Volume of a rectangular prism

v=L x W x H

Volume of a cylinder

Pir^2h

Surf. Area of a rectangular prism

2lw+2wh+2lh

Surf. Area of a cylinder

2pir^2+2pirh

1 foot is equivalent to

12 in

Relative error formula

[MV-TV]
---------
TV

Is over of is equivalent to

Part/whole

Is over of

%/100