Intermediate Algebra
Intermediate Algebra is a comprehensive course designed to bridge the gap between elementary algebra and college-level mathematics. It is tailored for learners with diverse mathematical backgrounds who want to strengthen their algebraic foundations and develop the ability to think more abstractly and analytically. The curriculum covers essential topics including linear equations and inequalities, polynomials, rational expressions, radicals, quadratic functions, exponential and logarithmic functions, conic sections, and sequences.
Through a supportive and practice-oriented learning approach, students build confidence in solving mathematical problems step by step while understanding how algebra applies to real-world situations. By the end of the course, learners will have developed strong problem-solving and critical-thinking skills, along with the mathematical readiness needed for future studies in STEM and non-STEM disciplines.
Adaptive
Varies by mastery
4 domains
How the course works
A session is a short study-and-practice checkpoint, not a fixed class meeting. The course can move faster when material is already familiar and slow down when a topic needs more practice.
Study a focused page
Read a small prerequisite-ordered set that gives the context for the next practice step.
Check understanding
Answer linked questions so the system can tell what is already strong and what needs review.
Keep moving
Unlock the next set after the current material is understood, with review scheduled as needed.
Who this course is for
This course is designed for students taking a intermediate algebra course, serving as a critical bridge between elementary algebra and college-level mathematics such as College Algebra, Statistics, or finite mathematics. It is structured for learners with varied mathematical backgrounds and learning styles who need to strengthen their algebraic skills. The content is designed to transition students from concrete algebraic manipulation to more abstract mathematical reasoning, building the competency and confidence needed for subsequent STEM or non-STEM college pathways.
Objectives
- Evaluate and simplify algebraic expressions by applying the properties of real numbers.
- Solve linear equations, formula manipulations, and compound and absolute value inequalities.
- Graph linear equations in two variables, determine the equations of lines, and utilize function notation to represent mathematical relations.
- Solve systems of linear equations in two and three variables using graphing, substitution, and elimination methods, and graph systems of linear inequalities.
- Perform arithmetic operations on polynomials and apply the properties of exponents, including scientific notation.
- Factor polynomials using multiple strategies, including common factors, grouping, and special products, to solve quadratic equations.
- Simplify, add, subtract, multiply, and divide rational expressions, and solve rational equations involving real-world applications.
- Simplify and perform operations on radical expressions and rational exponents, solve radical equations, and perform basic operations with complex numbers.
- Solve quadratic equations utilizing the square root property, completing the square, and the Quadratic Formula, and graph quadratic functions.
- Evaluate and graph composite, inverse, exponential, and logarithmic functions, and solve related equations using properties of logarithms.
- Analyze and graph conic sections, including circles, parabolas, ellipses, and hyperbolas, and solve systems of nonlinear equations.
- Formulate and analyze arithmetic and geometric sequences and series, and apply the Binomial Theorem.
Syllabus
Use a General Strategy to Solve Linear Equations
Use a Problem Solving Strategy
Solve a Formula for a Specific Variable
Solve Mixture and Uniform Motion Applications
Solve Linear Inequalities
Solve Compound Inequalities
Solve Absolute Value Inequalities
Graph Linear Equations in Two Variables
Slope of a Line
Find the Equation of a Line
Graph Linear Inequalities in Two Variables
Relations and Functions
Graphs of Functions
Solve Systems of Linear Equations with Two Variables
Solve Applications with Systems of Equations
Solve Mixture Applications with Systems of Equations
Solve Systems of Equations with Three Variables
Solve Systems of Equations Using Matrices
Solve Systems of Equations Using Determinants
Graphing Systems of Linear Inequalities
Add and Subtract Polynomials
Properties of Exponents and Scientific Notation
Multiply Polynomials
Dividing Polynomials
Greatest Common Factor and Factor by Grouping
Factor Trinomials
Factor Special Products
General Strategy for Factoring Polynomials
Polynomial Equations
Multiply and Divide Rational Expressions
Add and Subtract Rational Expressions
Simplify Complex Rational Expressions
Solve Rational Equations
Solve Applications with Rational Equations
Solve Rational Inequalities
Simplify Expressions with Roots
Simplify Radical Expressions
Simplify Rational Exponents
Add, Subtract, and Multiply Radical Expressions
Divide Radical Expressions
Solve Radical Equations
Use Radicals in Functions
Use the Complex Number System
Solve Quadratic Equations Using the Square Root Property
Solve Quadratic Equations by Completing the Square
Solve Quadratic Equations Using the Quadratic Formula
Solve Equations in Quadratic Form
Solve Applications of Quadratic Equations
Graph Quadratic Functions Using Properties
Graph Quadratic Functions Using Transformations
Solve Quadratic Inequalities
Finding Composite and Inverse Functions
Evaluate and Graph Exponential Functions
Evaluate and Graph Logarithmic Functions
Use the Properties of Logarithms
Solve Exponential and Logarithmic Equations
Distance and Midpoint Formulas; Circles
Parabolas
Ellipses
Hyperbolas
Solve Systems of Nonlinear Equations
Sequences
Arithmetic Sequences
Geometric Sequences and Series
Binomial Theorem
References
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