Download ALGEBRA SOL REFERENCE SHEET

GOLDEN RULE:
ALGEBRA 2 SOL REFERENCE SHEET
If it is in a parenthesis—DO THE OPPOSITE!!!
This you need to memorize for the SOL test.
 Properties
Commutative Property 3+5=5+3 3*5=5*3 (change order)
Associative property (3+4) +5 = 3+ (4+5) same for multiplication (grouping)
Identity Property a*1= a
a+0=a
Distributive Property 3(a+8) = 3a+24
Multiplicative Property of Zero x*0=0
Reflexive property ab=ab (the same on both sides)
Symmetry property ab=ba (flipped)
Key words: sum, product, difference, twice, less than, greater than, etc.
 Matrices: rows by columns
[2 3 5 6] would be 1x 4
When adding or subtract match the elements (same location)
Scalar Multiplication is just distributive property for matrices.
System of equations with matrices—[A]-1 * [B] Matrix A is the coefficients, Matrix B is the answer
column
 FUNCTIONS!!!
The x coordinates cannot be the same to be a function (2,3) (3,5) is a function.
Vertical line test
One x to any y
Function Families: Quadratic (u), Linear (line), Absolute value (V), Rational , exponential (lazy J)
f(x)= x +3 f(4) just replace x with the 4***Use parentheses around new values***
Odd degree
Even degree
 Zero of function---what would x equal to make the function equal zero
Where does the graph cross the x-axis?

y2  y1
x2  x1
SLOPE!!
Change of y over x RISE OVER RUN
y=mx+b m equals slope and b is the y-intercept(were line crosses the y-axis)
Remember positive lines go up and negative lines go down
Horizontal line is a zero slope and vertical lines are undefined slopes
y-axis
X= is a vertical line
Y= is a horizontal line
x-axis

Variations can be solved using proportions
y y

x x
Direct Variation-Where the line goes through the origin. Also uses y=kx, where k is the constant (slope)
Indirect Variation- y 
k
Remember this is where you switch the x’s is the proportional setup
x
Joint Variation- y=kxz
 Systems of equations
3 types of solutions: No solution (parallel lines), ∞ solutions (same line), one solution (where lines crosseach other, it’s a coordinate)
4 ways to solve: Graph (solve for y) Substitution method, elimination method, matrices
 Polynomials Standard form ax2+bx+c=0 highest degree 1st
Degree of polynomial is the largest exponent.
Don’t forget the Martinsville method
for trinomials with a leading number.

FACTOR—Check for GCF first (could be # or variable)
Sign rules for factoring ___ + ___ + ____
This sign is the result when you
add the two factors together
If you see (+) Add or (-) subtract the
factors to make the middle number
Difference of Perfect Squares x2-4 (prefect square) - (perfect square)
Perfect trinomials ( + )2 signs are the same, either + or –
Difference of cubics x3  8 = ( x  2)( x 2  4 x  4) “alternate signs”
 Quadratics ax2+bx+c=0 **Must show for zero **Can factor or y= key
I’m a
pothole
The
turning
point is
where the
graph turns
Maximum Opens Down a<0
Minimum Opens up a>0
If a=0 then it’s a linear equation not a parabola (u shaped)
Vertex ( , ) where the min and max is located. Go to y= then graph, 2nd trace choose max or min then
hit enter, enter, enter.
 Axis of symmetry always is x=(the first coordinate of the vertex)

Asymptotes-where the graph cannot have a number is the denominator

Point discontinuity (hole)-Where a binomial gets cancelled out.
1
x2
 x  2
 Conics—Remember if it is in a parenthesis then the answer is the opposite sign!
Parabola y  a( x  h)2  k
or x  a( y  k )2  h
Circle  x  h    y  k   r 2
2
Ellipse
 x  h
2
2
a2
Hyperbola
y k

b2
 x  h
2
a2
 x  h
2
1
y k

b2
2
b2
2
1
 y k
a2
y k

2
a2
2
 x  h

b2
1
2
1
 The following all mean the same thing—Find where the graph crosses the x-axis
-Zero of the function
-Factors
-Real solutions
-x-intercepts
-Roots


Scatter plots or best fit of line-go to STAT EDIT CAL 4 ENTER
Rational Functions-Must have like denominators to add the numerators. Sometimes you have to
factor to see the new denominator.
Remember: What you see is what you need for the LCD!!
 Sequences and Series
Arithmetic sequence an  a1  (n  1)d
geometric sequence an  a1  r n 1
end
Series (summation)-
 formula
start
Calculator format sum(seq(formula, variable, start, end, count))
***Foreign Veggies Seem Extremely Crunchy***
sto  X
 Storing a value for x number 
the x will remain the same value until you restore
Remember to work out all your problems and read the questions carefully.