A2.1: Solving Problems

A2.1.A: Select and justify functions and equations to model and solve problems.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line

A2.1.B: Solve problems that can be represented by systems of equations and inequalities.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

A2.1.D: Solve problems that can be represented by exponential and logarithmic functions and equations.

Compound Interest
Exponential Functions
Introduction to Exponential Functions

A2.1.E: Solve problems that can be represented by inverse variations of the forms f(x) = a/x + b, f(x) = a/ x² + b, and f(x) = a/(bx + c)

Direct and Inverse Variation

A2.1.F: Solve problems involving combinations and permutations.

Permutations and Combinations

A2.2: Numbers, expressions, and operations

A2.2.A: Explain how whole, integer, rational, real, and complex numbers are related, and identify the number system(s) within which a given algebraic equation can be solved.

Points in the Complex Plane
Solving Algebraic Equations II
Solving Equations on the Number Line

A2.2.C: Add, subtract, multiply, divide, and simplify rational and more general algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Using Algebraic Equations

A2.3: Quadratic functions and equations

A2.3.B: Determine the number and nature of the roots of a quadratic function.

Roots of a Quadratic

A2.3.C: Solve quadratic equations and inequalities, including equations with complex roots.

Quadratic Inequalities
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic

A2.4: Exponential and logarithmic functions and equations

A2.4.A: Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

A2.4.B: Graph an exponential function of the form f(x) = abx and its inverse logarithmic function.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

A2.4.C: Solve exponential and logarithmic equations.

Exponential Functions

A2.5: Additional functions and equations

A2.5.A: Construct new functions using the transformations f(x - h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

A2.5.B: Plot points, sketch, and describe the graphs of functions of the form f (x) = a times the square root of x - c + d , and solve related equations.

Radical Functions

A2.5.C: Plot points, sketch, and describe the graphs of functions of the form (x) = a/x + b, f(x) = a/x² + b, and f(x) = a/(bx + c), and solve related equations.

Compound Interest
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Logarithmic Functions
Rational Functions

A2.5.D: Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.

Graphs of Polynomial Functions
Translating and Scaling Functions

A2.6: Probability, data, and distributions

A2.6.B: Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.

Theoretical and Experimental Probability

A2.6.C: Compute permutations and combinations, and use the results to calculate probabilities.

Binomial Probabilities
Permutations and Combinations

A2.6.F: Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

A2.6.G: Calculate and interpret margin of error and confidence intervals for population proportions.

Polling: City
Polling: Neighborhood