Final Study Guide Flashcards
Describe the rules for Order of Operations
- Parentheses and other grouping symbols
- Exponents
- Multiply and Divide - left to right
- Add and Subtract - left to right
What three things can describe an irrational number?
A decimal with three dots, an imperfect square root, and pi
What is meant by “like terms”?
a term with same variables and same exponents
Define absolute value
distance of a number from zero- must be positive
How does one tell whether an equation has one answer, infinitely many answers, or no answer?
one answer ( x=4 )
infinitely many answers ( 3=3 )
no answer ( 0=4 , 4=3 )
What is a conversion factor?
a ratio that is equal to 1, used to convert units of measure
1 KiloG / 1000 G
How do we find the percent of increase or decrease?
original - new |
___________________
original
Describe what happens when we divide an inequality by a negative number on each side.
the inequality sign flips
what two words join compound inequalities?
and, or
In an absolute value inequality, < is what type of sentence? > is what type of sentence?
< = and (Land) > = or
An “and” sentence shows ___________ and an “or” sentence shows _________.
intersection ; union
Explain how y= |x-2| + 4 is graphed
The parent absolute value graph is shifted to the right 2, and up 4.
Tell how to find the domain and range of a relation and how to determine whether it is a function.
domain = all of x's range = all of y's
If the x’s do not repeat, it is a function
What does f(x), g(x), h(x), etc., represent?
y
In order for a sequence to be arithmetic, what must it have?
common difference
Tell three ways to describe or show slope.
- change in y
_______________
change in x - y_2 - y_1
______________
x_2 - x_1 - rate of change
- rise over run
What is the slope of a horizontal and vertical line?
zero ; undefined
what is slope-intercept form of a line?
y = mx + b
what is point-slope form of a line?
y - y₁ = m (x- x₁)
what is standard form of a line?
Ax + By = C
A,B, and C must be integers
In order to have an equation of a line, what two things must one have?
slope and a point
Slopes of parallel lines have _________ slopes, and perpendicular lines have ____________ slopes.
same ; negative reciprocal
What does the correlation coefficient or “r” tell is?
how closely the data fits the line of regression
how do the lines look in a system of two or more equations with infinitely many answers? in a system with no solution?
lines overlap = infinitely many
lines are parallel = no solution
how do we know where to color a linear inequality on a coordinate plane?
< below
> above
how do we determine the answer to a system of linear inequalities in the coordinate plane?
intersection of the shaded areas
anything raised to the zero power is equal to ________, except for 0 raised to the zero power which is undefined
one
how can i make a negative exponent a positive exponent?
put it under a one
how can i multiply powers with the same base?
leave the base alone, and add the exponents
what happens to exponents when we raise a power to a power?
multiply them
what happens with exponents when i divide?
subtract them
what equation models exponential growth? exponential decay?
growth) y= a ( 1 + r)⁺
decay) y= a (1-r)⁺
describe how to multiply two binomials
use distributive twice
give five statements to decide what method one would use to factor a polynomial
- Try common monomial
- If two parts, try difference of squares
- If 3 parts, w/ understood 1, try factor pairs
- If 3 parts w/o understood 1, trial and error
- If 4 parts, group
what are the five steps of Trial and Error
Step 1: Multiply first and last terms
Step 2: Find a factor pair that adds to the middle term
Step 3: Substitute factor pair for middle term
Step 4: Group first two terms and last 2… common monomial
Step 5: Take one of what’s in parentheses, and take what’s left outside in the other set of parentheses.
what is the quadratic formula?
x = -b± √ b² - 4ac
___________________
2a
If the discriminant is greater than 0, there are ______ ______ solutions
2 real
if the discriminant equals 0, there is ________ ________ solution
1 real
if the discrimination is less than zero, there are ________ ________ solutions.
2 imag
the process of ridding a radical from the denominator of a fraction is called ____________.
rationalization
to simplify a rational expression, first one must _______, then state the _________, and then _________ common factors.
factor completely; restrictions; cancel/slash
