How this course works
The chapters and lessons below are the fixed course structure. When you start, LearnLive teaches each lesson interactively and adapts examples, pacing, and questions to you.
Complete syllabus
Every chapter and lesson
- 01
Chapter 1 · 3 lessons
Foundations
- 1.1
Real numbers & expressions
8 min · Quick check
Lesson goal: By the end you can identify and classify real numbers and understand mathematical expressions.
- Define real numbers and their subsets (natural, whole, integers, rational, and irrational numbers).
- Explain mathematical expressions and their components (terms, coefficients, variables).
- Differentiate between expressions and equations.
- 1.2
Exponents & polynomials
9 min · Quick check
Lesson goal: By the end you can apply the rules of exponents and work with polynomial expressions.
- Define exponents and their properties (product, quotient, power of a power).
- Introduce polynomials and their standard form (degree, leading coefficient).
- Perform operations with polynomials (addition, subtraction, multiplication).
- 1.3
Factoring
9 min · Quick check
Lesson goal: By the end you can factor common polynomial forms and verify a factorization by multiplication.
- Identify and factor out the greatest common factor before using another method.
- Factor trinomials by finding terms whose product and sum match the polynomial.
- Recognize and factor special products such as differences of squares and perfect-square trinomials.
- Verify a factorization by multiplying the factors to recover the original polynomial.
- 1.1
- 02
Chapter 2 · 3 lessons
Equations & Inequalities
- 2.1
Linear equations
8 min · Quick check
Lesson goal: By the end you can solve linear equations and understand their properties.
- Define linear equations and their standard form.
- Identify the components of a linear equation.
- Solve linear equations using various methods such as graphing and substitution.
- 2.2
Quadratic equations
9 min · Quick check
Lesson goal: By the end you can solve quadratic equations and apply the quadratic formula.
- Define quadratic equations and their standard form.
- Identify the components of a quadratic equation.
- Solve quadratic equations using factoring, completing the square, and the quadratic formula.
- 2.3
Inequalities & absolute value
8 min · Quick check
Lesson goal: By the end you can solve inequalities and understand absolute value.
- Define inequalities and absolute value.
- Graph inequalities on a number line.
- Solve absolute value equations and inequalities.
- 2.1
- 03
Chapter 3 · 3 lessons
Functions
- 3.1
Functions & graphs
9 min · Quick check
Lesson goal: By the end you can define functions and understand their graphical representations.
- Define a function and its notation.
- Identify the domain and range of a function.
- Understand the concept of a graph as a visual representation of a function.
- 3.2
Linear & quadratic functions
8 min · Quick check
Lesson goal: By the end you can analyze and apply linear and quadratic functions.
- Define linear and quadratic functions and their standard forms.
- Identify key features of linear and quadratic functions, such as slope and vertex.
- Graph linear and quadratic functions and interpret their characteristics.
- 3.3
Transformations & composition
8 min · Quick check
Lesson goal: By the end you can perform transformations and compositions of functions.
- Define transformations of functions, including translations, reflections, and stretches.
- Understand the composition of functions and how to compute it.
- Apply transformations and compositions to given functions.
- 3.1
- 04
Chapter 4 · 3 lessons
Polynomial & Rational Functions
- 4.1
Polynomial functions
8 min · Quick check
Lesson goal: By the end you can define polynomial functions and identify their characteristics.
- Understand the definition of polynomial functions.
- Identify the degree and leading coefficient of a polynomial.
- Recognize the standard form of a polynomial function.
- 4.2
Rational functions
9 min · Quick check
Lesson goal: By the end you can define rational functions and analyze their properties.
- Understand the definition of rational functions.
- Identify the numerator and denominator of a rational function.
- Analyze the domain and asymptotes of rational functions.
- 4.3
Zeros & the factor theorem
8 min · Quick check
Lesson goal: By the end you can apply the factor theorem to find zeros of polynomial functions.
- Understand the factor theorem and its significance.
- Identify zeros of polynomial functions using the factor theorem.
- Apply the factor theorem to factor polynomials.
- 4.1
- 05
Chapter 5 · 3 lessons
Exponential & Logarithmic Functions
- 5.1
Exponential functions
8 min · Quick check
Lesson goal: By the end you can define exponential functions and identify their characteristics.
- Understand the definition of an exponential function.
- Identify the base and exponent in exponential expressions.
- Recognize the general form of an exponential function: f(x) = a * .
- Explore the properties of exponential growth and decay.
- 5.2
Logarithmic functions
9 min · Quick check
Lesson goal: By the end you can define logarithmic functions and understand their relationship to exponential functions.
- Understand the definition of a logarithmic function.
- Identify the base and argument in logarithmic expressions.
- Recognize the general form of a logarithmic function: f(x) = log_b(x).
- Explore the properties of logarithms, including the product, quotient, and power rules.
- 5.3
Exponential & log equations
8 min · Quick check
Lesson goal: By the end you can solve exponential and logarithmic equations.
- Understand how to set up exponential equations for solving.
- Learn to convert between exponential and logarithmic forms.
- Apply properties of logarithms to simplify and solve equations.
- Practice solving real-world problems involving exponential and logarithmic equations.
- 5.1