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Algebra
Algebra Regents Exam Review
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Terms in this set (80)
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 is true
True-shade to include the point(shade towards)
False-don't include the point in the shading(shade away from)
Repeat steps for second in=ity
Label overlap of shaded areas with an "S"(Solution area)
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
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