Summary Essential Algebra 1 Cheat Sheet

Essential Algebra 1 Cheat Sheet
Order of Operations Properties of Numbers
P – Parenthesis Commutative Property:
E – Exponents • 𝑎+𝑏 =𝑏+𝑎
M – Multiplication • 𝑎∗𝑏=𝑏∗𝑎
Left to Right
D – Division Associative Property:
A – Addition • (𝑎 + 𝑏) + 𝑐 = 𝑎 + (𝑏 + 𝑐)
Left to Right
S – Subtraction Distributive Property:
• 𝑎(𝑏 + 𝑐 ) = 𝑎𝑏 + 𝑎𝑐
Exponent Rules
Product Rule: 𝑎𝑚 ∗ 𝑎𝑛 = 𝑎𝑚+𝑛 Solving Equations and Inequalities
𝑎𝑚
Quotient Rule: 𝑎𝑛 = 𝑎𝑚−𝑛 𝑎𝑥 + 𝑏 = 𝑐
Power Rule: (𝑎𝑚 )𝑛 = 𝑎𝑚∗𝑛 1. Simplify both sides if needed
2. Isolate the variable (x) by
Solving Quadratics performing operations to both sides
Solve by Factoring:
𝑎𝑥 + 𝑏 > 𝑐 or 𝑎𝑥 + 𝑏 ≤ 𝑐
1. Identify a, b, and c in the quadratic
• Solve like an equation but reverse
expression
the inequality sign when
2. Find two numbers that
multiplying or dividing by a
• Multiply to 𝑎 ∗ 𝑐
negative number.
• Add to b
3. Write factors as (𝑥 ± ∎)(𝑥 ± ∎)
Special Cases Graphing Functions
Difference of Squares: Linear:
• 𝑎2 − 𝑏2 = (𝑎 + 𝑏)(𝑎 − 𝑏) Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏
Perfect Square Trinomial: Point-Slope Form: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
• 𝑎2 + 2𝑎𝑏 + 𝑏 2 = (𝑎 + 𝑏)2 • m: slope (rate of change)
4. Set each factor equal to 0 and • B: y-intercept (where the line
solve. crosses the y-axis)
Solve by Completing the Square: Inequalities:
1. Ensure the standard form, and 1. Solve for y
divide the equation by a. 2. Graph the line
2. Move the constant c to the other • Solid (≤, ≥) or dashed (<, >)
side. 3. Shade the solution region
𝑏 • Above line for > or ≥
3. Add (2)2 to both sides
• Below line for < or ≤
4. Rewrite the left side as a perfect
square. Distance: 𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2
5. Solve for x by taking the square 𝑥 +𝑥 𝑦 +𝑦
Midpoint: 𝑀 = ( 1 2 , 1 2 )
2 2
root. −𝑏±√𝑏2 −4𝑎𝑐
Quadratic: 𝑥 =
2𝑎
𝑦2 −𝑦1
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Slope: 𝑚 =
𝑥2 −𝑥1