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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

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 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 Interest
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