Escalera de Matemáticas · Secundaria · Grado 11

Álgebra 2

Las funciones y sus familias: polinómicas, racionales, radicales, exponenciales y logarítmicas, además de números complejos y sucesiones.

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67 temas en 7 unidades. Se apoya en Álgebra 1 y Geometría. Lleva a Precálculo y Trigonometría, Probabilidad y Estadística y Matemática Discreta. ¿No estás seguro de que sea el curso adecuado? Encuentra tu peldaño.

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Unidad 1 Functions and Their Graphs

9 temas

Combine, compose and invert functions, and use the graphs of the parent functions.

  1. Parent Functions
  2. Combining Transformations
  3. Even and Odd Functions
  4. Adding, Subtracting, Multiplying and Dividing Functions
  5. Composition of Functions
  6. Inverse Functions
  7. Checking Inverses by Composition
  8. Restricting a Domain for an Inverse
  9. Ramps: Building Bent-Line Graphs from ReLU

Unidad 2 Quadratics and Complex Numbers

9 temas

Extend quadratics with complex numbers, inequalities and new systems.

  1. The Vertex Formula
  2. Writing Quadratics from Points
  3. The Imaginary Unit i
  4. Adding and Multiplying Complex Numbers
  5. Dividing Complex Numbers
  6. Quadratics with Complex Solutions
  7. Quadratic Inequalities
  8. Systems in Three Variables
  9. Nonlinear Systems

Unidad 3 Polynomial Functions

16 temas

Divide and factor polynomials, find their zeros, and sketch their graphs.

  1. Seeing Structure in Expressions
  2. End Behavior of Polynomials
  3. Zeros and Multiplicity
  4. Polynomial Long Division
  5. Synthetic Division
  6. The Remainder and Factor Theorems
  7. Sums and Differences of Cubes
  8. Factoring Quadratic-Type Polynomials
  9. The Rational Root Theorem
  10. Solving Polynomial Equations
  11. The Fundamental Theorem of Algebra
  12. Writing a Polynomial from Its Zeros
  13. Sketching Polynomial Graphs
  14. Polynomial Identities
  15. The Binomial Theorem
  16. Polynomial and Rational Inequalities

Unidad 4 Rational Expressions and Functions

10 temas

Simplify and combine rational expressions, solve rational equations, and graph rational functions.

  1. Simplifying Rational Expressions
  2. Multiplying and Dividing Rational Expressions
  3. Adding and Subtracting Rational Expressions
  4. Complex Fractions
  5. Rational Equations
  6. Work-Rate and Average-Cost Models
  7. Direct, Inverse and Joint Variation
  8. Asymptotes and Holes
  9. Graphing Rational Functions
  10. Slant Asymptotes

Unidad 5 Radical Functions and Equations

4 temas

Work with nth roots, rationalize denominators, graph radical functions, and solve radical equations.

  1. nth Roots
  2. Simplifying and Rationalizing Radicals
  3. Square Root and Cube Root Functions
  4. Radical Equations

Unidad 6 Exponential and Logarithmic Functions

14 temas

Use e and compound interest, understand logarithms, and solve exponential and log equations.

  1. Graphs of Exponential Functions
  2. Exponential Equations with a Common Base
  3. Compound Interest
  4. The Number e and Continuous Growth
  5. What a Logarithm Is
  6. Switching Between Log and Exponential Form
  7. Properties of Logarithms
  8. Change of Base
  9. Graphs of Logarithmic Functions
  10. Logarithmic Scales
  11. Solving Exponential Equations with Logs
  12. Solving Logarithmic Equations
  13. Exponential and Logarithmic Models
  14. Choosing a Function Model

Unidad 7 Sequences and Series

5 temas

Write sequences recursively, use sigma notation, and sum arithmetic and geometric series.

  1. Recursive Formulas
  2. Sigma Notation
  3. Arithmetic Series
  4. Finite Geometric Series
  5. Infinite Geometric Series