Theory Concepts Flashcards
The two main operations in mathematics are ____ and ____.
addition; multiplication
When solving equations with rational components, double-check your answer in the original equation to check for ____.
extraneous solutions
A bunch of things added are called ____.
terms
A bunch of things multiplied are called ____.
factors
In layman’s terms, the identity is what you do under a given operation to get ____.
yourself
The additive identity is always ____.
0
The multiplicative identity is always ____.
1
Math is about “doing” and “undoing.” The mathematical word for the process of “undoing” is ____.
inverse
In layman’s terms, the inverse is what you do under a given operation to get ____.
the identity
Given the number 8, state its additive identity ____ and additive inverse ____
0; -8
Given the number 8, state its multiplicative identity ____ and multiplicative inverse ____.
1; 1/8
The identity for every function is the line: ____
y = x
The graphs of a function and its inverse are ____ of each other over the line y = x.
mirror images
We ____ expressions (no math verb), but we ____ equations (math verb).
simplify; solve
The “mathematical” process for turning TERMS into FACTORS is called: ____
factoring
Speaking of factoring, the difference of two squares factors into ____
conjugates
Speaking of factoring, the sum of two squares factors into ____
prime
Speaking of factoring, the sum of cubes A^3 + B^3 factors into ____
(A + B)(A^2 - AB + B^2)
Speaking of factoring, the difference of cubes A^3 - B^3 factors into ____
(A - B)(A^2 + AB + B^2)
Speaking of factoring, a perfect square trinomial factors into ____
a binomial squared
Given the words “fish” and “frog”, form a PST: ____
fish^2 - 2fish * frog + frog^2
Conjugates multiply to be ____
the difference of squares
A binomial squared multiplies to be ____
a perfect square trinomial (PST)
Finish this statement [formal definition]. A number is rational if it can be written as the ____ of two integers where the denominator ____
ratio; is not zero
When solving an equation, if a true statement is generated at the last step, then the solution is ____.
all real numbers
When solving an equation, if a false statement is generated at the last step, then the solution is ____.
no solution
