Algebra Flashcards
Variable
A placeholder for a number whose value may vary. (X, y, z, a, b)
Constant
A numerical quantity whose value does not change
Numerical expression
Any constant or combination of two or more constants joined by explicit or implied operational symbols
Algebraic expression
A symbol or combination of symbols that represent a number.
Consist of one or more variables joined by one or more operations with it without constants explicitly included.
Juxtaposition
When constants and variables or two or more variables are written side by side, they are products.
Terms (in algebraic expression)
The parts of the expression that are connected to the other parts by plus or minus symbols.
Monomial
A term that when simplified is a constant or a product of one or more variables raised to non-negative integer powers, with it without and explicit coefficient.
Coefficient
The product of the other factors in a term.
Ex, the coefficient of y in 5y(x+2) is 5(x+2)
Degree of a monomial
The sum of the exponents of its variables
Like terms
Monomial terms that only differ in their numerical coefficients
Numerical coefficient
The constant number in a term with a variable
Polynomial
An algebraic expression composed of one or more monomials.
A monomial Is polynomial with only one term.
Binomial
Polynomial with exactly two terms
Ex, 8xy+5
Trinomial
A polynomial with exactly three terms
Ex, 16x+8x+1
FOIL
First terms, Outer Terms, Inner terms, Last terms.
Used to obtain the product of two binomials.
Ex, (2x-3)(x+4)
Perfect trinomial square
(X+/-y) squared
Difference of two squares
(X+y)(x-y)
Perfect cube
(X+/- y) cubed
Rational expression
An algebraic fraction in which both the numerator and denominator are polynomials
Complex fraction
A fraction that has fractions in its numerator, denominator or both
Equation
A statement that two mathematicians expressions are equal
Open sentence
An equation containing one or more variables
Ex, x+2=3 or x+2y=8
Formula
An equation that expresses the relationship between two or more variables
Literal equation
An equation with no numbers, only letters
Fractional equation
One in which a variable appears in the denominator of one or more terms
Ex, 1/2+1/x = 5/6
Can be converted to a quadratic equation by multiplying both sides by the lcm of the equations fractions.
Radical equation
One in which the variable appears in a radical (square root)
Exponential equation
One in which the variable appears in a exponent
System
A set of equations with the same set of variables and are all considered simultaneously.
Consistent system
A system that has a solution
Inconsistent system
One without a solution
Ordered pair
An x-value paired with a corresponding y-values
X, y
Three possibilities of a system of equations
- Exactly one solution. Lines intersect at the solution.
- Infinitely many solutions. Lines have all points in common (two identical lines overlapped)
- No solution. Lines are parallel
Positive slope
When a line slopes upward to the right.
Negative slope
When a line slopes downward to the right
Horizontal line equation
Y=k (m=0)
K stands for any constant
Vertical line equation
X=h (undefined slope)
H stands for any constant
Percentage change formula
Percent change=(new value-old value)/old value • 100%
