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Epublishing #1

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

                 algebraic- j+13

 

Order of Operations-      Parenthesis- ()

                                  Exponents- 2^2

                                  Multiplication- 3x6

                                  Division- 10/5

                                  Addition- 2+4

                                  Subtraction- 6-2

 

Acronym- Please Excuse My Dear Aunt Sally

Examples:  7^2 – (3^3-4x5)

                    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) - 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.

 

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:

x

y

3

7

4

8

5

9

                    

                   Not a Function:                                                                                                                                                                                                          

x

y

1

5

1

4

2

3

 

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 a-4 l=3             l a-4 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(1-r)^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 ^ (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

       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