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Algebra 1 Notes Sheet
Number Operations
Order of Operations (PEMDAS or GEMS)
Grouping ( ), [ ]
Exponents 5²
Multiply & divide
Subract & add
Distributive Property: 5 (2x – 7) = 10x – 35 Multiply the number outside by everything inside.
**Every point looks like (x, y)
Linear (y = mx + b) m: slope or rate of change
b: start value or y-intercept
Slope-intercept form: y = mx + b
Point-Slope form:
y – y1 = m (x – x1) * Use when you are given a point and a slope.
Example: write the equation of a line through (-4, 2) with a slope of 3
y – 2 = 3 (x + 4)
y
= 3x + 12 + 2
y
= 3x + 14
Finding Slope:
rise
run
Four types of slope:
m=
y 2  y1
x 2  x1
Positive
m=
y  change
x  change
Negative
1
m=
3
m=5
Undefined
Zero
4
m=
0
m=
0
10
*Parallel lines have the SAME slope!
Solving Proportions: Use cross-multiplication (the fish method)
Example:
x 3

5 10
Percents %
_is_ =
of
%_
100
15
x
10
x  1 .5
Mean: Average
Median: The middle number
Solving Inequalities: use the same steps as you do for solving an equation.
 FLIP the sign when you multiply or divide by a negative number.
Examples: x + 2 > 15
12< 3x < 24
x > 13
3
3
3
4<x <8
Mode: Number that shows up most
Graphs:
Greater than (x >___)
Less than (x < ____)
Greater than or Equal to (x > )
Greater than or Equal to (x > )
Dot
Open (o)
Open (o)
Closed 
Closed 
Absolute Value: The distance from 0. Example:
Arrow
---
-----
---
x 8
x is 8 away from 0. x = -8 and x = 8
Exponential
y  A(1  r ) t
Exponent Rules:
Multiplication
Add Exponents
A: Start value r: rate % (change to decimal) t: time
Division
Subtract Exponents
Power to a Power
Multiply Exponents
4x5
 2x 4
1
2x
(5 x 5 ) 2  25 x10
x 3 ( x11 )  x14
Scientific Notation: A decimal times 10 to a power.
Example: 456,320,000 =
4.5632 x10 8
0.000213 = 2.13 x 10
4
y  ax 2  bx  c
Quadratics
Combine Like Terms: Only things with the same variable (letter) and exponent (little number) can go together.
Example:
(2 x 2  9 x  10)  (5 x 2  2 x  4)
7 x 2  11x  6
*Distribute Negatives! (2x + 4) – (4x – 8) =
2x + 4 – 4x + 8
Multiplying Binomials (FOIL): Multiply the First, Outside, Inside, and Last Terms
(x + 4) (x – 2)
x 2  2x  4x  8
x 2  2x  8
Factor the quadratic expressions (un-FOIL): BOX METHODWhat numbers multiply to be the last term and add to be the middle term?
x 2  2x  8
4(-2) = -8
4 + (-2) = 2
(x + 4) (x – 2)
The quadratic formula is
2
 b  b  4ac
x
2a
Probability =
number of favorable outcomes
total outcomes
Odds =
number of favorable
number of unfavorabl e
*Multiply your number of choices and the probabilities of individual events in order to find totals.
Example: What is the probability of rolling a 3 then rolling an odd number? Solution:
13 3
1

 
6  6  36 12