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Algebra 1 semester exam Cheat Sheet (DRAFT) by

This is from the first semester of my Algebra 1 class.

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Data Analysis

Five Number Summaries
Minimum (MinX)
the smallest number in the data
1st quartile (Q1)
the median of the lower half of the data
Median (Med)
the middle of the data
3rd quartile (Q3)
median of the upper half of the data
Maximum (MaxX)
the largest number in the data
 
Other Data Analysis Terms
Mean(x̄)
∑x / n (where n is the number of pieces in the data)
Mode
the number that appears the most
Range
the difference between the minimum and the maximum
Standard Deviat­ion(Sx or σx)
1. find the mean (x̄) of the whole data set (∑x/n) 2.subtract each number from the mean and square it. 3.Find the mean of the squared differ­ences. Your σx is the square root of the new mean.
σx
is standard deviation of the whole popula­tion. At the end of calcul­ation, divide by "­n"
Sx
standard deviation of a sample of the data. At the end of calcul­ation, you divide it by "­n-1­"
Mean Absolute Deviation (MAD)
1. Find the mean of the data 2.Find the absolute difference between each value and the mean. Then find the mean of the absolute differ­ences
 
SOCS
Shape
What is the shape of the graph?
SPUGS!
You can find the shape of the graph with a histogram of the data set
1.Symm­etric
the graph is symmet­rical
2. Peaks
unimodal (1 peak), bimodal (2 peaks), or multimodal (3 or more peaks)
3. Uniform
all of the data are the same value
4. Gaps
In a histogram, there is a section that has nothing.
5. Skewness
skewed left: the tail points left skewed right: the tail points right
 
Outliers
Are there any outliers in the data set?
Outliers are more of a yes or no question
find the interq­uartile range, from Q1 to Q3. multiply it by 1.5 and subtra­ct/add from the mean. That is the border­line. Anything greater than the border line is an outlier
 
From now on, it will be separated based on whether or not there is an outlier or not.
a = no outlier
b = outlier
 
Center
What is the center of the data set?
a
mean
b
median
 
Spread
What is the spread of the data set?
a
Standard Deviation
b
IQR, range, and five number summary
 
 
In the end, add an explan­ation to your data set, analyzing using all of the inform­ation
 

Simplified Algebraic Expres­sions

1.) No double signs
3x - 4 not 3x +- 4
2.) Variables are in Alphab­etical order
3a + 8f - 5g not - 5g + 8f + 3a
3.) Exponents are in decreasing order
- 2x5 + 6y3 not 6y3 - 2x 5
4.) No coeffi­cients of 1
y = 7 not 1y = 7
5.) No denomi­nators of 1
x = 9 not x/1 = 9
6.) Variables before constants
x + 5 not 5+x

Tolerances

degree of error
level of accept­ability

3 Types of Linear Equations

Condit­ional Equations
have exactly one solution
Identity Equations
have an infinite amount of solutions
Contra­dictory Equations
have no solutions

Functions

Yes a Function
  
Not a function
x
y
x
y
0
5
0
4
1
4
3
3
2
3
3
8
3
2
7
4
**
  

Frequency Tables

Relative
setting up to what part of wholes (decimals or percents)
Joint Relative Frequency
the section in blue
Marginal Relative Frequency
the section in red
Grand Total
the bottom right corner of the table

Frequency Table Example

Refer to Frequency Tables

7 step Algebraic Method for Word Problems

1.) List all important inform­ation
2.) Assign a variable
3.) Write an expression
4.) Write an equation
5.) Solve the equation

7 step Algebraic Method for Word Problems

1.) List all important inform­ation
2.) Assign a variable
3.) Write an expression
4.) Write an equation
5.) Solve the equation
6.) Check equation
7.) Write the answer as a complete sentence