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The Major Concepts You Need to Understand to Succeed in Math (Algebra 1 & 2, Trig, Calculus)

I'm going to list what I believe are the key concepts that you need to master across different math subjects. These are the tools that I have to use most often in order to solve problems, so you should get very familiar with the theory behind them and very comfortable with applying them.
 
Algebra 1:
  1. order of operation (PEMDAS)
  2. solving equations
  3. slope-intercept form of linear equations
  4. point-slope form of linear equations
  5. systems of linear equations (elimination and substitution methods)
  6. inequalities
  7. domain and range
  8. undefined and imaginary expressions
  9. asymptotes (horizontal and vertical)
  10. discontinuities (removable and non-removable)
  11. rational expressions
  12. factoring
  13. quadratic formula
  14. radical properties
  15. exponent properties
  16. transformations and translations of functions
 
Algebra 2:
 
1. recognizing and factoring the three most common polynomial forms:
  1. quadratic equations
  2. common factor expressions
  3. difference of square expressions
2. synthetic division
3. Descartes's Rule of Signs
4. Rational Zero Theorem
5. Long division of polynomials
6. Factoring by grouping
7. Using the Quadratic Formula
 
Trigonometry:
  1. understanding and using the unit circle
  2. trig identities
  3. definitions of the trig functions "Soh-Cah-Toa"
  4. factoring quadratic equations (using the quadratic formula, etc.)
 
Calculus:
  1. the power rule
  2. the chain rule: du/dx = du/dy*dy/dx
  3. product rule
  4. quotient rule
  5. u-substitution
  6. integration by parts
  7. the disk, washer, and shell methods for finding volumes of solids of revolution
  8. limits
  9. L'Hopital's rule
  10. separation of variables
  11. trig substitution
  12. partial fractions
  13. implicit differentiation
  14. Taylor polynomials
  15. LaGrange remainders
 
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