Algebra Flashcards
Commutative Property
Outcome is the same both ways. You can move the numbers around (think commute) to get the same outcome.
[Addition and Multiplication are commutative.]
Associative Property
Parenthesis or groupings create the same outcome in any order. You can “associate” any grouping and get the same outcome. [Addition and Multiplication are associative.]
Distributive Property
Multiplication distributes over addition and subtraction.
Identity Property
Zero is the addition identity operator. A+0=A
One is the multiplicative identity operator. A*1=A
Additive Inverse
The additive inverse of A is -A
A + (-A) = 0
Multiplicative Inverse
The multiplicative inverse of A is the reciprocal.
A (1 / A) = 1
i^2 =
-1
Fundamental Theorem of Algebra
A polynomial of degree “n” has exactly “n” solutions, some of which might be real, some of which might be imaginary, and some of which might have multiplicity more than one.
Vertical Line Test
If a vertical line intersects the graph more than once, the relation is not a function
Projectile Motion
h(t) = g(t^2) + v.t + h. where “g” is -16ft/sec or -4.9 m/sec, “v.” is initial velocity, and “h.” is initial height
Compounded Interest
P = P.(1 + r/n) ^ nt where “P” is amount after time “P.” is initial investment, “r” is rate as a decimal, “n” is number of compoundings per year, and “t” is number of years
Continually Compounded interset
P = P. e ^ rt
Simple growth or decay
P = P. ( 1 + or - r) ^ t
How do you determine the number of positive real roots using Descartes rule of signs?
Count the number of sign changes
How do you determine the number of negative real roots using Descartes rule of signs?
Substitute in -x for x and then count the sign changes
How do you determine the number of imaginary/complex roots?
Look at highest exponent to determine how many roots are needed. Combine values in positive + negative real roots and make them add up to that exponent. (ie: function has X^6 there should be 6 total roots. positive real roots = 4, 2, 0. negative real roots = 0. Thus imaginary roots is 2, 4 & 6).
Rational Zeros Theorem
Take factors of the constant term, divided by factors of the leading coefficient. If there are any factors or any zeros of this polynomial that are rational numbers, they will be on this list. (ie: 2x^3 - 5x^2 - x + 6 would be factors of 6 over factors of 2). Take the results and divide them using synthetic division. When you have a result with a 0 remainder, that is a factor of the polynomial.
Fundamental Theorem of Algebra
Any polynomial of degree “n” has “n” roots which can be real and/or imaginary…. [“n” = highest exponent]
Symmetric Property of Equality
7 =x
and thus
x = 7
Coefficient
If we have 5x, then 5 is the coefficient
Variable
If we have 2y, then y is the variable
Factor
If we have 5x + 2y + 10xy, then the first two terms have 2 factors, and the third term has 3 factors
