Algebra 2 | Index

Algebra 2 builds on Algebra 1 with new kinds of functions and equations. It covers transformations and inverses, complex numbers, polynomials, radicals, rational functions, logarithms and series.

It’s for high school Algebra 2 students and anyone preparing for precalculus. Together with Precalculus, it also covers a college algebra course.

What to know first: Algebra 1, especially factoring, quadratic equations and exponent rules. Most students take Geometry before Algebra 2.

Lessons for this course are coming soon. The list below shows every planned lesson in teaching order.

Units in this course

Unit 1: Functions, Transformations and Inverses

  1. Transformations of Functions (coming soon) — shift, stretch and reflect the graphs of parent functions
  2. Absolute Value Functions (coming soon) — graph absolute value functions and their transformations
  3. Piecewise Functions (coming soon) — evaluate and graph functions defined in pieces
  4. Function Operations (coming soon) — add, subtract, multiply and divide functions
  5. Composition of Functions (coming soon) — put one function inside another and evaluate the result
  6. Inverse Functions (coming soon) — find and graph inverses, and check them with composition

Unit 2: Systems in Three Variables

  1. Systems of Equations in Three Variables (coming soon) — solve three equations with three unknowns by elimination
  2. Linear Programming (coming soon) — find the maximum or minimum of a quantity under several limits

Unit 3: Quadratics and Complex Numbers

  1. Complex Numbers (coming soon) — the imaginary unit i and numbers in a + bi form
  2. Operations with Complex Numbers (coming soon) — add, subtract and multiply complex numbers
  3. Dividing Complex Numbers (coming soon) — use complex conjugates to divide
  4. Complex Solutions of Quadratic Equations (coming soon) — solve quadratics whose solutions are not real
  5. Quadratic Inequalities (coming soon) — solve and graph inequalities with a squared term
  6. Nonlinear Systems of Equations (coming soon) — solve systems that include a parabola, circle or other curve

Also see: factoring, completing the square and the quadratic formula in Algebra 1, Unit 9.

Unit 4: Polynomial Functions

  1. End Behavior of Polynomials (coming soon) — use the degree and leading coefficient to describe a graph’s ends
  2. Polynomial Long Division (coming soon) — divide polynomials the way you divide numbers
  3. Synthetic Division (coming soon) — a shortcut for dividing by a linear factor
  4. Remainder and Factor Theorems (coming soon) — use the remainder to test factors and evaluate polynomials
  5. Sum and Difference of Cubes (coming soon) — factor sums and differences of two cubes
  6. Solving Polynomial Equations (coming soon) — solve higher-degree equations by factoring
  7. Rational Root Theorem (coming soon) — list possible rational zeros and test them
  8. Fundamental Theorem of Algebra (coming soon) — count all zeros of a polynomial, including complex and repeated ones
  9. Graphing Polynomial Functions (coming soon) — sketch a graph from its zeros, multiplicity and end behavior

Unit 5: Radicals and Rational Exponents

  1. nth Roots (coming soon) — evaluate and simplify cube roots, fourth roots and other roots
  2. Rational Exponents (coming soon) — rewrite between radicals and fractional exponents and simplify
  3. Radical Functions (coming soon) — graph square root and cube root functions
  4. Solving Radical Equations (coming soon) — isolate the radical, raise both sides to a power and check for extraneous solutions

Unit 6: Rational Expressions and Functions

  1. Inverse Variation (coming soon) — relationships where the product of two quantities stays the same
  2. Simplifying Rational Expressions (coming soon) — factor and cancel, and note the excluded values
  3. Multiplying and Dividing Rational Expressions (coming soon) — factor first, then multiply or divide and simplify
  4. Adding and Subtracting Rational Expressions (coming soon) — find a common denominator with variables
  5. Complex Rational Expressions (coming soon) — simplify fractions that contain rational expressions
  6. Solving Rational Equations (coming soon) — clear the denominators and check for extraneous solutions
  7. Graphing Rational Functions (coming soon) — find vertical and horizontal asymptotes and holes, then graph

Unit 7: Exponential and Logarithmic Functions

  1. The Number e (coming soon) — the natural base e and continuously compounded interest
  2. Logarithms (coming soon) — what a logarithm is and how to switch between log and exponential form
  3. Graphing Logarithmic Functions (coming soon) — graph log functions as inverses of exponential functions
  4. Properties of Logarithms (coming soon) — the product, quotient and power rules and the change of base formula
  5. Solving Exponential Equations (coming soon) — use logarithms when the bases don’t match
  6. Solving Logarithmic Equations (coming soon) — rewrite in exponential form and check for extraneous solutions

Unit 8: Sequences and Series

  1. Sigma Notation (coming soon) — write and evaluate sums with sigma notation
  2. Arithmetic Series (coming soon) — add up the terms of an arithmetic sequence
  3. Geometric Series (coming soon) — add up the terms of a finite geometric sequence
  4. Infinite Geometric Series (coming soon) — decide whether an infinite series has a sum and find it

Also see: arithmetic and geometric sequences in Algebra 1, Units 4 and 6.

For Teachers: Standards Alignment

Lessons follow the Common Core high school Algebra 2 standards. Trig functions (the unit circle, radians and sine and cosine graphs) are taught in Trigonometry. Statistics topics, such as the normal distribution and margin of error, are taught in Statistics.

Previous course: Geometry Index · Next course: Trigonometry Index