Final Study Guide

Question 1

Describe the rules for Order of Operations

Answer 1

1. Parentheses and other grouping symbols
2. Exponents
3. Multiply and Divide - left to right
4. Add and Subtract - left to right

Question 2

What three things can describe an irrational number?

Answer 2

A decimal with three dots, an imperfect square root, and pi

Question 3

What is meant by “like terms”?

Answer 3

a term with same variables and same exponents

Question 4

Define absolute value

Answer 4

distance of a number from zero- must be positive

Question 5

How does one tell whether an equation has one answer, infinitely many answers, or no answer?

Answer 5

one answer ( x=4 )

infinitely many answers ( 3=3 )

no answer ( 0=4 , 4=3 )

Question 6

What is a conversion factor?

Answer 6

a ratio that is equal to 1, used to convert units of measure

1 KiloG / 1000 G

Question 7

How do we find the percent of increase or decrease?

Answer 7

original - new |
___________________
original

Question 8

Describe what happens when we divide an inequality by a negative number on each side.

Answer 8

the inequality sign flips

Question 9

what two words join compound inequalities?

Answer 9

and, or

Question 10

In an absolute value inequality, < is what type of sentence? > is what type of sentence?

Answer 10

< = and (Land)
> = or

Question 11

An “and” sentence shows ___________ and an “or” sentence shows _________.

Answer 11

intersection ; union

Question 12

Explain how y= |x-2| + 4 is graphed

Answer 12

The parent absolute value graph is shifted to the right 2, and up 4.

Question 13

Tell how to find the domain and range of a relation and how to determine whether it is a function.

Answer 13

domain = all of x's
range = all of y's 

If the x’s do not repeat, it is a function

Question 14

What does f(x), g(x), h(x), etc., represent?

Answer 14

y

Question 15

In order for a sequence to be arithmetic, what must it have?

Answer 15

common difference

Question 16

Tell three ways to describe or show slope.

Answer 16

1. change in y
   _______________
   change in x
2. y_2 - y_1
   ______________
   x_2 - x_1
3. rate of change
4. rise over run

Question 17

What is the slope of a horizontal and vertical line?

Answer 17

zero ; undefined

Question 18

what is slope-intercept form of a line?

Answer 18

y = mx + b

Question 19

what is point-slope form of a line?

Answer 19

y - y₁ = m (x- x₁)

Question 20

what is standard form of a line?

Answer 20

Ax + By = C

A,B, and C must be integers

Question 21

In order to have an equation of a line, what two things must one have?

Answer 21

slope and a point

Question 22

Slopes of parallel lines have _________ slopes, and perpendicular lines have ____________ slopes.

Answer 22

same ; negative reciprocal

Question 23

What does the correlation coefficient or “r” tell is?

Answer 23

how closely the data fits the line of regression

Question 24

how do the lines look in a system of two or more equations with infinitely many answers? in a system with no solution?

Answer 24

lines overlap = infinitely many

lines are parallel = no solution

Question 25

how do we know where to color a linear inequality on a coordinate plane?

Answer 25

< below

> above

Question 26

how do we determine the answer to a system of linear inequalities in the coordinate plane?

Answer 26

intersection of the shaded areas

Question 27

anything raised to the zero power is equal to ________, except for 0 raised to the zero power which is undefined

Answer 27

one

Question 28

how can i make a negative exponent a positive exponent?

Answer 28

put it under a one

Question 29

how can i multiply powers with the same base?

Answer 29

leave the base alone, and add the exponents

Question 30

what happens to exponents when we raise a power to a power?

Answer 30

multiply them

Question 31

what happens with exponents when i divide?

Answer 31

subtract them

Question 32

what equation models exponential growth? exponential decay?

Answer 32

growth) y= a ( 1 + r)⁺

decay) y= a (1-r)⁺

Question 33

describe how to multiply two binomials

Answer 33

use distributive twice

Question 34

give five statements to decide what method one would use to factor a polynomial

Answer 34

1. Try common monomial
2. If two parts, try difference of squares
3. If 3 parts, w/ understood 1, try factor pairs
4. If 3 parts w/o understood 1, trial and error
5. If 4 parts, group

Question 35

what are the five steps of Trial and Error

Answer 35

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.

Question 36

what is the quadratic formula?

Answer 36

x = -b± √ b² - 4ac
___________________
2a

Question 37

If the discriminant is greater than 0, there are ______ ______ solutions

Answer 37

2 real

Question 38

if the discriminant equals 0, there is ________ ________ solution

Answer 38

1 real

Question 39

if the discrimination is less than zero, there are ________ ________ solutions.

Answer 39

2 imag

Question 40

the process of ridding a radical from the denominator of a fraction is called ____________.

Answer 40

rationalization

Question 41

to simplify a rational expression, first one must _______, then state the _________, and then _________ common factors.

Answer 41

factor completely; restrictions; cancel/slash