Free 16-Week Course
Intermediate AlgebraFrom real numbers to logarithms, a complete sequence
A self-paced intermediate algebra course covering 16 weeks of material: real numbers and order of operations, linear equations and inequalities, systems, polynomials, factoring, quadratics, rational and radical expressions, exponentials, and logarithms. Each lesson ships with worked notes and common-mistake callouts.
What you will be able to do
By the end of the 16-week sequence, you will be able to:
- Classify any number into the most specific set among naturals, integers, rationals, irrationals, and reals
- Solve linear equations and inequalities in one variable, including absolute-value and compound forms
- Solve systems of linear equations in two and three variables using substitution, elimination, and matrices
- Operate on polynomials confidently: add, subtract, multiply, divide, and factor with strategy
- Solve quadratic equations by factoring, completing the square, and the quadratic formula, and graph the result
- Simplify and solve rational and radical expressions while tracking domain restrictions
- Work fluently with exponential and logarithmic functions and translate between their forms
- Diagnose your own mistakes through scenario-based quizzes and worked-solution practice problems
Course outline
16 weekly lessons · ~32 hours total · click any lesson to start
- Week 1
Real Numbers & Order of Operations
- Classify any given number into the most specific set among naturals, integers, rationals, and reals
- Evaluate mixed-operator expressions using PEMDAS with zero left-to-right slips
- Distribute positive and negative coefficients across grouped terms while preserving sign integrity
- Week 2
Linear Equations in One Variable
- Solve any single-variable linear equation in 4-6 mechanical steps with a written verification line
- Distribute negative coefficients across grouped terms before combining like terms
- Identify equations with no solution (contradiction) versus infinitely many (identity)
- Week 3
Linear Inequalities & Interval Notation
- Solve a linear inequality and graph the solution set on a number line
- Apply the flip rule whenever multiplying or dividing both sides by a negative
- Translate among inequality, interval, and graph representations without ambiguity
- Week 4
Absolute Value Equations & Inequalities
- Solve absolute-value equations by splitting into the positive and negative cases
- Recognize when an absolute-value equation has no solution because distance cannot be negative
- Convert |expr| <= k into a single bounded interval (intersection)
- Week 5
Systems of Linear Equations (2 Variables)
- Solve a 2-variable system using substitution with one variable already isolated
- Solve a 2-variable system using elimination by aligning opposite coefficients
- Classify a system as one solution, no solution, or infinitely many from its row-reduced form
- Week 6
Systems of 3 Variables & Intro to Matrices
- Solve a 3-variable system by reducing to 2-variable systems via consistent elimination
- Identify the dimensions of a matrix and locate any entry by row and column
- Apply the three legal row operations (swap, scale, add multiple of one row) without changing the solution set
- Week 7
Polynomial Operations
- Add, subtract, and multiply polynomials of degree up to four by hand
- Apply FOIL fluently to any product of two binomials in under thirty seconds
- Memorize and apply the perfect-square and difference-of-squares special products
- Week 8
Factoring Strategies (GCF & Grouping)
- Pull out the greatest common factor from any polynomial as the first step
- Recognize and factor difference-of-squares patterns by inspection
- Recognize and factor perfect-square trinomials in either direction
- Week 9
Factoring Quadratics (Monic & Non-Monic)
- Factor monic quadratics by finding integer pairs whose product is c and sum is b
- Apply the ac method to non-monic quadratics by splitting the middle term
- Compute and interpret the discriminant b^2 - 4ac
- Week 10
Quadratic Functions & Vertex Form
- Convert any standard-form quadratic to vertex form by completing the square
- Compute the vertex using the formula x = -b/(2a) and back-substitute for y
- Predict opening direction from the sign of the leading coefficient
- Week 11
Solving Quadratic Equations
- Solve a quadratic of the form (expr)^2 = k using the square root property
- Solve a factorable quadratic using zero-product property
- Apply the quadratic formula to any quadratic with a clear written setup
- Week 12
Rational Expressions
- State the domain restrictions of any rational expression by setting denominators not equal to zero
- Simplify rational expressions by factoring numerator and denominator and cancelling common factors
- Multiply two rational expressions and simplify the result
- Week 13
Solving Rational Equations
- Solve rational equations by multiplying both sides by the LCD
- Identify and discard extraneous solutions that violate the original domain
- Solve a rational equation that yields a quadratic after clearing denominators
- Week 14
Radicals & Rational Exponents
- Convert between radical and rational-exponent notation in both directions
- Simplify radicals by factoring out perfect powers under the radical
- Solve radical equations and identify extraneous roots from squaring
- Week 15
Exponential Functions
- Evaluate exponential expressions $b^x$ for positive bases and integer or rational exponents
- Sketch the shape of an exponential growth curve and identify its horizontal asymptote
- Sketch the shape of an exponential decay curve as a reflection across the y-axis
- Week 16
Logarithms & Properties
- Convert between logarithmic form and exponential form in both directions
- Apply the product rule, quotient rule, and power rule of logarithms to expand or condense expressions
- Solve exponential equations by taking the log of both sides
Questions about the course?
Reach out on LinkedIn. Happy to answer questions about the curriculum, suggest where to start based on your background, or talk research and instruction.