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Algebra 2

Algebra 2  is high school level math which  deals with higher degree equations, rational expressions, equations  etc. Here is the list of topics and subtopics covered under Algebra 2.

1) Complex  Numbers
(a) Irrational Numbers
    
      Example: $\sqrt 3$, $\frac{1}{\sqrt 2}$
(b) Radical Numbers
      Example: $2 + \sqrt 5$
(c) Imaginary Numbers
      Example: $i$ = $\sqrt -1$, $i^2$ = $-1$.

(d) Complex Numbers in the form 
     $a + \sqrt b$ OR $a + bi$
(e) Adding / Subtracting Complex Numbers
(f) Multiplying / Dividing Complex Numbers 
Example: $(2 - 3 \sqrt 5)\ \times\ \sqrt 3$
(g) Conjugates of Complex Numbers  
Example: Conjugate of $2 + 5i$ is $2 - 5i$
(h) Rationalising Fractions with Complex Numbers in Denominator 
(i) Transcendental Numbers 
Example: e-Euler number, $\pi$

2) Equations and Inequalities

(a) System of Linear Equations 
Example: Solve $3x - y$ = $6$ and $x + y$ = $4$
(b) System of Non Linear Equations 
Example: Solve $x - y$ = $4$ and $x^2 - 2y$ = $7$
(c) Rational Equations 
(e) Solving Radical Equations and Inequality
Example: Solve $5 - \sqrt{(x+3)}$ = $3,\ \sqrt{(x + 3)} \leq 0$

(f) System of Linear Inequalities

             Numerical and Word Problems

     Example: Solve for Region of Inequality for $x \geq 4$  and $y < 3x - 5$

3) Quadratic Functions and  Equations

(a) Solving Quadratic Equation using Quadratic Formula
(b) Factorizing the Quadratic Expression 
      Finding the factors of $x^2 - 6x - 12$
(c) Completing the Square 
      Use the identity $(a+b)^2$ = $a^2 + 2ab + b^2$
(d) Sum and Product of Roots 
(e) Quadratic Functions  
(f) Word Problems
(g) Quadratic Inequalities
4) Exponents and Logarithm

(a) Equivalent Exponential Expressions

(b) Exponential Functions and Equations  
      $A$ = $Pe^{rt}$
(c) Introduction to Logarithm
        (d) Laws of Logarithm
        (e) Simplifying Logarithmic Expressions
(g) Solving Logarithmic Equations
(h) Extraneous Solution of Logarithmic Equation
(i) Real Life Word Problems on Logarithmic Models


5) Exponential Growth and Decay 

(a) $A$ = $P(1 + r)t,\ A$ = $P(1 - r)t$
(b) Solving Exponential Equations
(d) Word Problems on Exponential Functions
      Compound Interest, Population Growth, Half Life Period
6) Rational Expressions and Equations

    Rational expressions are similar to fractions that have variable expressions in numerator and denominator.

(a) Simplifying Rational Expressions using Factorization
(b) Addition/Subtraction, Multiplication/Division of Rational Expressions 
(c) Restrictions/Discontinuity of Rational Functions 
      Example: $\frac{x + 3}{x - 3}$  
      Cannot have the value $x$ = $3$ as it will make the denominator zero and hence the expression undefined.
(d) Solving Rational Equations
(e) Solving Rational Inequality
7) Radical Expressions and Equations

(a) Solving Square Root Equations
(b) Solving Cube Root Equations
(c) $n^{th}$ root, Simplification
(d) Extraneous Solutions of Radical Equations 
      Example: $\sqrt{x + 5}$ = $-3$
              Rationalizing fractions with radicals in denominator 

8) Polynomials

(a) Adding/Subtracting Polynomials
(b) Multiplying Polynomials
(c) Long Division of Polynomials
(d) Synthetic Division of Polynomials

9) Solving Polynomials

(a) Possible Rational Roots
(b) Descartes' Rule of Sign
(c) Factor Theorem 
(d) Remainder Theorem
(e) Factoring Polynomials

             Quadratic Forms

             Grouping 
(f) Special Forms 
      Difference of Squares

              Sum of Cubes

              Difference of Cubes 
      Example: Factorise $(x^2 - 121),\ (8x^3 + 125)$
(g) Binomial theorem to expand $(a + b)n$
        (h) Understanding Binomial Theorem
(i) Binomial Expansion and Combination

Related Calculators
Determinant Calculator 2x2 eigenvalue calculator 2x2
Angle between Two Vectors Calculator Area between Two Curves Calculator
 

More topics in  Algebra 2
Algebra 2 Problems Linear Inequalities
Compound Inequalities Absolute Value Inequalities
Solving Inequalities with Two Variables Rules for Solving Inequalities
Solving Inequalities by Graphing Solving Inequalities with Fractions
Solving Polynomial Inequalities Solving Systems of Inequalities
Linear Equations System of Linear Equations
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