Algebra Review Flashcards
Coefficient
Number that is multiplied by a variable (ex. 2 in 2x)
Constant
Term with no variable
Identity
Statement of equality between two algebraic expressions that is true for all possible variables involved
Equation
Statement of equality between two algebraic expressions that is true for only certain values of the variables involved
x^-a
1/(x^a)
(x^a)(x^b) =
x^(a+b)
(x^a)/(x^b) =
x^(a-b)
x^0 =
1
(x^a)(y^a) =
(xy)^a
(x/y)^a =
(x^a)/(y^a)
(x^a)^b =
x^ab
(x+y)/a =
(x/a) + (y/a)
When dividing an inequality by a negative number, the direction of the inequality is…
Reversed.
When dividing an inequality by a positive number, the direction of the inequality is…
Preserved.
Domain (function)
Set of all permissible inputs of that function
Simple interest
Based on the initial deposit, or principal (which serves as the amount on which interest is computed)
V = P (1+(rt/100))
Where r is the interest rate (ex 6%, r=0.06) and t is time in years (ex 6 months, t=0.5)
Compound interest
Interest added to the principal (initial deposit) at some time interval (annually, quarterly, or monthly). Interest is then earned on each new principal
V = P (1+(r/100))^t
Compound interest at an annual interest rate of r percent, compounded n times per year
V = P ( 1 + (r/100n))^nt
To find the distance between two points on a graph…
Construct a right triangle and use Pythagorean theory to find hypotenuse
Linear equation (graphing)
y = mx + b m = slope b = y-intercept
Slope
Rise over run
X2-X1
Two lines are perpendicular if…
Slopes are negative reciprocal of one another
Ex. y=2x+5 and y=-1/2x +9
Finding y-intercept
Insert (x,y) point into equation if you know slope. Then solve for b
Equation system solution result:
Point at which the two lines intersect