Mid-Term 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
Order of Operations- Parenthesis- ()
Acronym- Please Excuse My Dear Aunt Sally
Examples: 7^2 – (3^3-4x5)
7^2 – (27 – 20)
7^2 – 7
49 – 7
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) - 18-y > 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.
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.
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
- 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.
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 a-4 l=3 l a-4 l= -3
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
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
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(1-r)^t
Compound Interest- A= P(1+r/n)^nt
P= principal (initial amount)
R= rate as a decimal
N= number of times compounded
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 ^ (n-1)
Examples: Find 6th term
a1= 3 r= -5 an= 3 x -5^(6-1)
an= -15^5 an= -759,375
Geometric Mean- plug in 1st 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
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