ALGEBRA SOL REFERENCE SHEET



ALGEBRA 2 SOL REFERENCE SHEET

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?

• SLOPE!! [pic] 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

X= is a vertical line

Y= is a horizontal line

• Variations can be solved using proportions[pic]

Direct Variation-Where the line goes through the origin. Also uses y=kx, where k is the constant (slope)

Indirect Variation-[pic] Remember this is where you switch the x’s is the proportional setup

Joint Variation- y=kxz

• Systems of equations

3 types of solutions: No solution (parallel lines), ∞ solutions (same line), one solution (where lines cross-each 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.

• FACTOR—Check for GCF first (could be # or variable)

Sign rules for factoring ___ + ___ + ____

Difference of Perfect Squares x2-4 (prefect square) - (perfect square)

Perfect trinomials ( + )2 signs are the same, either + or –

Difference of cubics [pic]= [pic] “alternate signs”

• Quadratics ax2+bx+c=0 **Must show for zero **Can factor or y= key

Maximum Opens Down a0

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 [pic] [pic]

• Point discontinuity (hole)-Where a binomial gets cancelled out.

• Conics—Remember if it is in a parenthesis then the answer is the opposite sign!

Parabola [pic] or [pic]

Circle [pic]

Ellipse [pic] [pic]

Hyperbola [pic] [pic]

• 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 [pic] geometric sequence [pic]

Series (summation)- [pic]

Calculator format sum(seq(formula, variable, start, end, count))

***Foreign Veggies Seem Extremely Crunchy***

• Storing a value for x [pic] the x will remain the same value until you restore

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y-axis

x-axis

If you see (+) Add or (-) subtract the factors to make the middle number

This sign is the result when you add the two factors together

Remember to work out all your problems and read the questions carefully.

The turning point is where the graph turns

Don’t forget the Martinsville method for trinomials with a leading number.

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GOLDEN RULE:

If it is in a parenthesis—DO THE OPPOSITE!!!

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