What Is Algebra 2? Problems, Topics, Formulas - Cuemath

Algebra 2

Algebra 2 is a higher standard branch of mathematics that includes the secondary level topics studied in the modern elementary Algebra course. In pre-algebra and algebra-1 we study the arithmetic operations which consist of numbers with operators such as +, -, x, ÷, and variables like x, y, z, along with mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression. Algebra 2 helps in the representation of different situations or problems as mathematical expressions. Let us learn about the curriculum that covers Algebra 2.

1.	What is Algebra 2?
2.	Algebra 2 Topics
3.	Algebra 2 Formulas
4.	Difference between Algebra 2 and Algebra 1
5.	FAQs on Algebra 2

What is Algebra 2?

Algebra 2 is the advanced level of pre-algebra and Algebra 1. It introduces higher grades topics such as evaluating equations and inequalities, matrices, vectors, functions, quadratic equations, complex numbers, relations, inverse operations, and various other properties. In algebra 2, we will also be incorporating a bit of geometry and coordinate geometry along with calculus to calculate the area, volume, and perimeters of shapes using algebraic expressions instead of numbers.

Algebra 2 or elementary algebra deals with long-form algebraic expressions such as ax + b = c, ax + by + c = 0, ax + by + cz + d = 0 and a general form of representation of a quadratic equation is ax2 + bx + c = 0, and for a polynomial equation, it is axn + bxn-1+ cxn-2+ .....k = 0.

Algebra 2 Topics

Algebra is divided into numerous topics to help for a detailed study. Algebra 2 is divided into approximately 13 chapters and each chapter is divided into several lessons. These 12 chapters in Algebra 2 are given as:

Chapter 1: Linear Equations and Inequalities

• Variable expressions
• Linear Equations
• Linear Inequalities

Chapter 2: Functions

• What Are Functions?
• Composition of Functions
• Inverse Functions
• Arithmetic and Geometric Progressions
• Types of Functions
• Transformation of Functions
• Graphing Functions

Chapter 3: Relations

• Equivalence Relation
• Reflexive Relation
• Symmetric Relations
• Inverse Relation
• Types Of Relations

Chapter 4: Cartesian and Coordinate System

• Graphing linear equations
• Cartesian Coordinate System

Chapter 5: Sequence

• Geometric Sequence
• Arithmetic Sequence
• Arithmetic Sequence Formula
• Geometric Sequence Formulas

Chapter 6: Solving Matrices

• Matrices
• Matrix Operations
• Transformation Matrix
• Properties of Matrices
• Determinant of Matrix

Chapter 7: Vector

• Vector Algebra
• Scalar Product
• Product of Vectors
• Dot Product
• Cross Product

Chapter 8: Polynomials

• Polynomials
• Types of Polynomials
• Polynomial Function
• Polynomial Equations

Chapter 9: Factoring and Solving by Factorization

• Factorization of Algebraic Expressions
• Factorization of Quadratic Equations
• Factoring Polynomials

Chapter 10: Exponents And Exponential Functions

• Exponents
• Exponential Functions
• Irrational Exponents
• Operations on Exponential Terms

Chapter 11: Radical Expressions and Equations

• Surds
• Square and Square Root
• Rationalization
• Rationalize the Denominator

Chapter 12: Solving Quadratic Equations

• Quadratic Equations
• Roots of Quadratic Equation
• Graphing Quadratic Functions
• Complex Numbers

Chapter 13: Data Analysis And Probability

• Data Handling
• Statistics
• Categorical Data
• Permutation and Combination

Chapter 14: Sets

• Sets
• Types of Sets
• Set Operations
• Finite and Infinite Sets

Chapter 15: Logarithms

• Introduction to Logarithms
• Properties of Logarithms
• Logarithmic Functions

Chapter 16: Conic Sections

• Circles
• Ellipse
• Parabola
• Hyperbola

Chapter 17: Trigonometry

• Trigonometric Ratios
• Trigonometric Functions
• Trigonometric Chart
• Trigonometric Identities

Algebra 2 Formulas

Here are the list of formulas that are very useful in solving Algebra 2 problems.

• Function Formulas: (f + g)(x) = f(x) + g(x) (f - g)(x) = f(x) - g(x) (αf)(x) = αf(x) (fg)(x) = f(x).g(x) (f/g)(x)  = f(x)/g(x) (fog)(x) = f(g(x)) (gof)-1(x) = f-1og-1(x)
• Arithmetic Sequence Formulas: nth term of arithmetic sequence, an=a1+(n−1)d Sum of arithmetic sequence = n/2 [2a + (n - 1) d] (OR) n/2 [a1 + an]
• Geometric Sequence Formulas: The nth term of the geometric sequence is, an = a · rn - 1. Sum of n terms of geometric sequence, Sn = a (rn - 1) / (r - 1) Sum of infinite terms of geometric sequence, S = a / (1 - r)
• Vector Formulas: a · b = |a| |b| cos θ a × b = |a| |b| sin θ \(\hat{n}\) If a = x i + y j + z k then |a| = √ (x2+y2+z2) 
• Polynomials Formulas: Remainder Theorem: f(a) gives the remainder when the polynomial f(x) is divided by (x - a). Factor Theorem: If f(a) = 0 then (x - a) is a factor of f(x).  Rational Root Theorem: A rational zero of a polynomial p(x) is of the form p/q where p is a factor of the constant and q is a factor of the leading coefficient.
• Quadratic Formula: The roots of a quadratic equation ax2 + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.
• Log Rules: log xy = log x + log y log x/y = log x - log y log am = m log a logba = (log a)/(log b)
• Trigonometry Formulas sin θ = Perpendicular/Hypotenuse cos θ = Base/Hypotenuse tan θ = Perpendicular/Base sec θ = Hypotenuse/Base cosec θ = Hypotenuse/Perpendicular cot θ = Base/Perpendicular
• For conic sections formulas, click here.

Difference Between Algebra 2 and Algebra 1

Algebra 2 and Algebra 1 can be distinguished based on the complexity and use of algebraic expressions. The following table explains the important differences between Algebra 2 and Algebra 1.

Algebra 2	Algebra 1
Algebra 2 is much more advanced. It is also much more miscellaneous and complex. In this, we learn about logarithms, functions, relations, sequences, complex numbers, and the advanced fundamental theorem of Algebra.	In Algebra 1 we study variables, expressions, simplification of expressions with two variables, etc.
Algebra 2 increases complexity. It is a plus one level and advanced version of the topics learned in Algebra 1.	Algebra 1 helps students to have the basic command of Algebra 2 topics.
Algebra 2 concentrates on additional types of equations, such as exponential and logarithmic equations.	Algebra 1 is concentrated on creating a basic understanding of solving equations and inequalities.
Algebra 2 is essential for understanding concepts coming on Calculus.	Algebra 1 is essential for understanding Algebra 2.