Math Notes for 12th Graders
1. Algebra & Functions
Quadratic Equation:General form: ax^2 + bx + c = 0Roots: x = [-b ± sqrt(b^2-4ac)] / (2a)Functions:- Domain
2. Calculus
Differentiation (Finding the derivative):- Power Rule: d/dx(x^n) = n x^(n-1)- Product Rule: (uv)' = u'v + uv'- Q
3. Trigonometry
Basic Identities:- sin^2(x) + cos^2(x) = 1- tan(x) = sin(x) / cos(x)- 1 + tan^2(x) = sec^2(x)Special Angles:- sin
4. Probability & Statistics
Probability:- P(A) = Number of favorable outcomes / Total outcomes- Addition Rule: P(A or B) = P(A) + P(B
5. Sequences and Series
Arithmetic Sequence: a_n = a_1 + (n-1)dGeometric Sequence: a_n = a_1 * r^(n-1)Sum (Arithmetic): S_n =
TIP:
Practice with lots of problems, memorize basic formulas, and always check your domain/range in functions
1. Algebra & Functions
Quadratic Equation:General form: ax^2 + bx + c = 0Roots: x = [-b ± sqrt(b^2-4ac)] / (2a)Functions:- Domain
2. Calculus
Differentiation (Finding the derivative):- Power Rule: d/dx(x^n) = n x^(n-1)- Product Rule: (uv)' = u'v + uv'- Q
3. Trigonometry
Basic Identities:- sin^2(x) + cos^2(x) = 1- tan(x) = sin(x) / cos(x)- 1 + tan^2(x) = sec^2(x)Special Angles:- sin
4. Probability & Statistics
Probability:- P(A) = Number of favorable outcomes / Total outcomes- Addition Rule: P(A or B) = P(A) + P(B
5. Sequences and Series
Arithmetic Sequence: a_n = a_1 + (n-1)dGeometric Sequence: a_n = a_1 * r^(n-1)Sum (Arithmetic): S_n =
TIP:
Practice with lots of problems, memorize basic formulas, and always check your domain/range in functions
