Algebra Flashcards
A letter that represents a quantity whose value is unknown
variable
an expression that has one or more variables and can be written as a single term or a sum of terms
algebraic expression examples: 2x y- (1/4) (8)/(n+p)
terms that have the same variable
like terms example: 5z + -z —> 4z
a number that is in front of a variable
coefficient example: 3z —>coefficient is 3
Combine ______ to simplify an expression
like terms example: 2x + 5x= 7 7x = 7
1x and 1x^2 are NOT like terms
true
1x * 1x =
1x^2
Simplify: (x+2)(3x-7)
x(3x) + x(-7) + 2(3x) + 2(-7)= 3x^2 + (-7x) + 6x + (-14)
Simplify: (a + b)^2
(a + b)(a + b) a^2 + ab + ba + b^2 a^2 + 2ab + b^2
Simplify: (a^2 - b^2)
(a + b)(a - b)
Statement of equality between two algebraic expressions
equation
3x + 5= -2 is an example of a _____ equation
linear with one variable
x- 3y= 10 is an example of a ______ equation
linear with two variables
20y^2 + 6y -17 is an example of a _____ equation
quadratic equation with one variable
If x^a = x^b, then
a=b (except if x=1)
If 2^y = 64, what is y?
2^y=64 2^6=64 2^y=2^6 (rule x^a=x^b) then y=6
x^-a is equal to
(1)/(x^a) example: 4^(-3)= (1)/(4^3)
(x^a)(x^b) is equal to
x^(a+b)
x^0 is equal to
1
(x^a)(y^a) is equal to
(xy)^a
(x/y)^a is equal to
(x^a)/(y^a)
(x^a)^b is equal to
x^ab
A linear equation with two variables can be written in the form…
ax + by= c
You can solve equations with two variables in two ways: _______ or _______
substitution or elimination
Substitution method of solving an equation with two variables
one equation is manipulated to express one variable in terms of the other example: 4x + 3y= 13 and x + 2y=2 x= 2-2y, then substitute this in first equation 4(2-2y) + 3y=13 8- 8y + 3y=13 -8y + 3y=5 -5y=5 y=-1; then substitute y in original equation
ax^2 + bx + c is an example of ______
quadratic equation
Quadratic equation must be solved using _____
the quadratic formula
What is the quadratic equation?
A mathematical statement that uses less than, greater than, less than or equal to, greater than or equal to, is
an inequality
An inequality can be solved by…
simplifying the inequality by isolating the variable on one side of the inequality
example:
- 3x + 5 < 17
- 3x < 12 ***
x > -4
****dividing by a NEGATIVE in an inequality reverses the direction of the symbol
Dividing/multiplying in an inequality by a negative number ________
reverses the direction of the inequality
example: -3x > 12 (divide each side by 3)
x < -4
Solve the inequality:
(4x + 9)/(11) < 5
(4x + 9)/ (11) < 5
4x + 9 < 55
4x < 46
x < 11.5
All real numbers less than 11.5
An algebraic expression in one variable can be used to define the ______ of that variable
function f (x)
f (x) = 3x + 5 is an example of
a function
Solve the function f (x) = 3x + 5
x = 1
f (1) = 3(1) + 5
f (1) = 8
The set of all permissible inputs related to a function is…
the domain
V= P (1 + (rt/100) )
P= amount in dollars
r= interest rate in percent
t= time in years
Simple interest equation
Compound interest equation
V= P(1 + (r/100) )t
P= amount invested in dollars
r= annual interest rate
t= time in years
