MidTerm Study Guide
Verbal Expression to write how you say it with words
Algebraic Expressions numbers and variables
Examples: verbal the sum of j and 13
algebraic j+13
Order of Operations Parenthesis ()
Exponents 2^2
Multiplication 3x6
Division 10/5
Addition 2+4
Subtraction 62
Acronym Please Excuse My Dear Aunt Sally
Examples: 7^2 – (3^34x5)
7^2 – (27 – 20)
7^2 – 7
49 – 7
42
Equation one solution / has equal sign
Inequality multiple solutions / has less than, greater than, less than or equal to, greater than or equal to sign
With inequalities if you multiply or divide by a negative you reverse the sign.
Examples: Equation 6x3=18
Inequality 10+x > 2
Inequality (reverse the sign)  18y > 10
Hint: You would have to multiply both sides by 1 and would reverse the sign to <
Distributive Property taking what’s outside of the equation and multiplying it to every term inside.
Examples: 3(x+2x)
3x+6x
9x
Function a relationship between an x and a y.
X is the domain
Y is the range
In order for a graph, ordered pair, or table to be a function each x can only occur once.
A graph can be a function if it passes the vertical line test.
Examples: Function:
Not a Function:
6 Groups of Numbers
Rational Numbers fractions or any number that can be turned into a fraction
Irrational Numbers any number that cannot be turned into a fraction
Whole Numbers 0 – infinity
Natural Numbers 1 – infinity
Integers positive and negative whole numbers
Real Numbers every number
Infinite Solution when both sides of the equation are equal or the same
Examples: 2x+5 = 2x+5
Proportion One ratio set equal to the other.
You use cross products to solve.
Hint: Extremes x Means
Inequalities on a Number Line
Less than shade to left open circle
Greater than shade to right open circle
Less than or equal to shade to left closed circle
Greater than or equal to shade to right closed circle
5 Laws of Exponents
 When multiplying with like bases ADD the powers.
 : p^10 x p^3= p^13
 When dividing with like bases SUBTRACT the powers.
 : a^10 / a^5= a^5
 Anything to the zero power is ONE.
 : 101^0= 1
r^0= 1
 Never leave a negative exponent. You must REWRITE. You rewrite by putting one over the base to the positive power.
 : y^5

 When raising the power of a power; multiply the exponents.
Examples: (2^3)^4
2^12
Absolute Value with Equations and Inequalities
Absolute Value the distance a number is from zero
When solving absolute value equations and inequalities there are two solutions. One positive and one negative.
Examples: l a4 l=3 l a4 l= 3
a=7 a=1
Hint: When solving an absolute value inequality, when you set one inequality equal to the negative number, be sure to reverse your sign.
Standard Form ax+by=c
 x and y on the same side (x value positive).
 No fractions
 GCF of a,b,c is 1
 x intercept is where graph or line crosses the x axis
 y intercept is where graph or line crosses the y axis
Slope Intercept Form get y by itself; y= mx+b
Examples: 10= 5x+y
y= 5x+10
Parallel Lines have the same slope
Perpendicular Lines have slope whose product is 1. (Multiply by opposite reciprocal to get the slope).
Examples: Parallel Perpendicular
y= 1/2x+4 y=1/2x+3
y= 1/2x+9 y= 2x+2
Graphing Inequalities
No Bar dashed line
Bar solid line
Less than shade below line
Greater than shade above the line
*Not a solution if lands on dashed line
Exponential Functions the x is to a power
Examples: y= x^2
To graph a table of values you pick x value and solve for y
Exponential Behavior is if x values have regular intervals and y values have a common factor.
Positive Growth a > 1
Negative Growth a < 1
Growth, Decay, and Compound Interest Formulas
Growth y= c(1+r)^t
Decay y= c(1r)^t
Compound Interest A= P(1+r/n)^nt
A= amount
P= principal (initial amount)
R= rate as a decimal
N= number of times compounded
T= time
Geometric Sequences patterns that use multiplication to get the next term in the pattern
Examples: 4, 8, 16
(you’re multiplying by 2)
Formula for finding nth term in a geometric sequence:
an= a1 x r ^ (n1)
Examples: Find 6^{th} term
a1= 3 r= 5 an= 3 x 5^(61)
an= 15^5 an= 759,375
Geometric Mean plug in 1^{st} term, a1
plug in last term an
will always be r^2
solve for r
that is the rate of change not the answer
Examples: 7___112 a1=7 an=112
112= 7 x r^2
112/7=16
16=r^2
Then you do the square root of 16 which equals 4
You are not done yet!!!
7 x 4= 28
The answer is 28
Created By: Tiffany Bickett, and Elizabeth Hughes