Algebra 2 Honors

Algebra 2 Honors Curriculum Map 

Unit 1: Foundations and Review

Topics:

• Real numbers, sets, and intervals

• Operations with polynomials

• Factoring techniques (GCF, trinomials, difference of squares, sum/difference of cubes)

• Rational expressions and equations

• Advanced: absolute value equations, inequalities in multiple variables

Skills:

• Simplify, factor, and perform operations with polynomials

• Solve linear, quadratic, and higher-order rational equations

• Solve absolute value and compound inequalities

• Analyze errors and justify algebraic steps

Advanced Skills:

• Explore patterns in polynomials (e.g., symmetry, divisibility)

• Manipulate complex numbers in equations

Real-world applications:

• Budgeting problems with constraints

• Analyzing patterns in data and optimization scenarios

Unit 2: Functions and Graphs

Topics:

• Function notation, evaluation, composition, and inverses

• Domain and range, including piecewise-defined functions

• Types of functions: linear, quadratic, exponential, absolute value, reciprocal

• Transformations (translations, reflections, stretches, compressions)

• Advanced: function operations, functional equations

Skills:

• Identify, evaluate, compose, and invert functions

• Graph functions with transformations

• Analyze piecewise-defined functions

Advanced Skills:

• Investigate function families and behavior of transformations

• Compare growth rates of functions

• Determine algebraically and graphically where functions intersect

Real-world applications:

• Modeling profits, population growth, and tiered tax structures

• Optimizing function outputs

Unit 3: Quadratic Functions

Topics:

• Standard, vertex, and factored forms

• Completing the square

• Quadratic formula and discriminant analysis

• Complex roots and conjugates

• Graphing parabolas

• Advanced: analyzing maxima/minima, quadratic inequalities

Skills:

• Solve quadratics by multiple methods

• Analyze properties of parabolas

Advanced Skills:

• Determine effects of parameters on graph shape and position

• Solve real-world optimization problems

• Use discriminant to predict root types

Real-world applications:

• Projectile motion, maximizing area or profit

• Engineering curve optimization

Unit 4: Radical Functions

Topics:

• Simplifying radical expressions, rational exponents

• Operations with radicals

• Solving radical equations

• Graphing square root and cube root functions

• Advanced: compositions and inverses of radical functions

Skills:

• Simplify and manipulate radicals

• Solve equations involving radicals

• Graph radical functions

Advanced Skills:

• Apply radicals to function transformations and inverses

• Explore domains and ranges of composite radical functions

Real-world applications:

• Physics: speed, energy, and distance formulas

• Geometry: Pythagorean theorem in multiple dimensions

Unit 5: Polynomial Functions

Topics:

• End behavior, degree, and leading coefficient

• Zeros and multiplicity

• Factoring higher-degree polynomials

• Long and synthetic division

• Rational root theorem and Fundamental Theorem of Algebra

• Advanced: graphing and analyzing local maxima/minima

Skills:

• Solve and graph polynomial functions

• Determine number and type of roots

Advanced Skills:

• Analyze turning points and inflection behavior

• Use remainder and factor theorems to solve complex polynomials

Real-world applications:

• Population trends, engineering curves, and physics models
  
  

Unit 6: Rational Functions

Topics:

• Simplifying and multiplying/dividing rational expressions

• Adding/subtracting rational expressions

• Solving rational equations

• Asymptotes and discontinuities

• Graphing rational functions

• Advanced: partial fraction decomposition, slant asymptotes

Skills:

• Analyze behavior near asymptotes

• Solve real-world problems involving rational functions

Advanced Skills:

• Apply rational functions to complex modeling

• Decompose complex rational expressions

• Predict long-term behavior

Real-world applications:

• Rates and ratios problems

• Speed/distance/time calculations

Unit 7: Exponential and Logarithmic Functions

Topics:

• Laws of exponents

• Exponential growth and decay

• Logarithms and properties

• Solving exponential and logarithmic equations

• Advanced: compound interest with varying periods, logarithmic scales, natural logarithms

Skills:

• Convert between exponential and logarithmic form

• Solve real-world exponential/logarithmic equations

Advanced Skills:

• Solve multi-step logarithmic and exponential equations

• Compare different growth models

• Model real-world phenomena using exponential/logarithmic functions

Real-world applications:

• Compound interest

• Radioactive decay

• Population growth and sound intensity (decibels)

Unit 8: Systems of Equations and Inequalities

Topics:

• Linear systems in two and three variables

• Substitution, elimination, and matrices

• Nonlinear systems

• Linear and nonlinear inequalities

• Advanced: parametric systems, optimization problems

Skills:

• Solve systems algebraically and graphically

• Represent solutions with inequalities

Advanced Skills:

• Apply Cramer’s Rule for systems

• Solve real-world optimization problems with constraints

• Analyze systems with no solution, infinite solutions, or dependent solutions

Real-world applications:

• Mixture problems

• Optimization in production and resource allocation
  
  

Unit 9: Matrices

Topics:

• Matrix operations (addition, subtraction, multiplication)

• Determinants and inverses

• Solving systems using matrices (row reduction, inverse method)

• Applications of matrices

• Advanced: matrix transformations, eigenvalues (introductory)

Skills:

• Perform operations on matrices

• Solve systems of equations using matrices

• Apply matrices to model real-world problems

Advanced Skills:

• Use matrices for transformations and geometric applications

• Explore properties of square and diagonal matrices

• Understand basic eigenvector concepts

Real-world applications:

• Computer graphics and transformations

• Network analysis, scheduling, and linear programming

• Data organization

*This is a lengthy list.  While I would LOVE to cover all of these topics, it's simply not realistic.  We will do what we can!