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.
Math Track
Intermediate
Algebra
by Angel Reyes
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.