Algebra

Question 1

Commutative Property

Answer 1

Outcome is the same both ways. You can move the numbers around (think commute) to get the same outcome.
[Addition and Multiplication are commutative.]

Question 2

Associative Property

Answer 2

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.]

Question 3

Distributive Property

Answer 3

Multiplication distributes over addition and subtraction.

Question 4

Identity Property

Answer 4

Zero is the addition identity operator. A+0=A

One is the multiplicative identity operator. A*1=A

Question 5

Additive Inverse

Answer 5

The additive inverse of A is -A

A + (-A) = 0

Question 6

Multiplicative Inverse

Answer 6

The multiplicative inverse of A is the reciprocal.

A (1 / A) = 1

Question 7

i^2 =

Answer 7

-1

Question 8

Fundamental Theorem of Algebra

Answer 8

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.

Question 9

Vertical Line Test

Answer 9

If a vertical line intersects the graph more than once, the relation is not a function

Question 10

Projectile Motion

Answer 10

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

Question 11

Compounded Interest

Answer 11

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

Question 12

Continually Compounded interset

Answer 12

P = P. e ^ rt

Question 13

Simple growth or decay

Answer 13

P = P. ( 1 + or - r) ^ t

Question 14

How do you determine the number of positive real roots using Descartes rule of signs?

Answer 14

Count the number of sign changes

Question 15

How do you determine the number of negative real roots using Descartes rule of signs?

Answer 15

Substitute in -x for x and then count the sign changes

Question 16

How do you determine the number of imaginary/complex roots?

Answer 16

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).

Question 17

Rational Zeros Theorem

Answer 17

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.

Question 18

Fundamental Theorem of Algebra

Answer 18

Any polynomial of degree “n” has “n” roots which can be real and/or imaginary…. [“n” = highest exponent]

Question 19

Symmetric Property of Equality

Answer 19

7 =x
and thus
x = 7

Question 20

Coefficient

Answer 20

If we have 5x, then 5 is the coefficient

Question 21

Variable

Answer 21

If we have 2y, then y is the variable

Question 22

Factor

Answer 22

If we have 5x + 2y + 10xy, then the first two terms have 2 factors, and the third term has 3 factors