AII.DSP: Data Analysis, Statistics, and Probability
AII.DSP.1: Distinguish between random and non-random sampling methods, identify possible sources of bias in sampling, describe how such bias can be controlled and reduced, evaluate the characteristics of a good survey and well-designed experiment, design simple experiments or investigations to collect data to answer questions of interest, and make inferences from sample results.
Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Histograms
Polling: City
Polling: Neighborhood
Sight vs. Sound Reactions
Stem-and-Leaf Plots
AII.DSP.2: Interpret and compare univariate data using measures of center (mean and median) and spread (range, inter-quartile range, standard deviation, and variance). Understand the effects of outliers on the statistical summary of the data.
Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Mean, Median, and Mode
Polling: City
Populations and Samples
Stem-and-Leaf Plots
AII.DSP.3: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; Interpret the correlation coefficient for linear models.
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
AII.DSP.4: Using the results of a simulation, decide if a specified model is consistent to those results. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models.
Lucky Duck (Expected Value)
AII.DSP.5: Understand dependent and independent events, and conditional probability; apply these concepts to calculate probabilities.
Binomial Probabilities
Independent and Dependent Events
AII.DSP.6: Understand the Fundamental Counting Principle, permutations, and combinations; apply these concepts to calculate probabilities.
Permutations and Combinations
AII.ASE: Arithmetic and Structure of Expressions
AII.ASE.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Simplifying Radical Expressions
AII.ASE.4: Rewrite rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x).
Dividing Polynomials Using Synthetic Division
AII.F: Functions
AII.F.2: Define and find the inverse of a function. Verify functions are inverses algebraically and graphically.
Logarithmic Functions
Radical Functions
AII.F.3: Understand that if the graph of a function contains a point (a, b), then the graph of the inverse relation of the function contains the point (b, a); the inverse is a reflection over the line y = x.
Logarithmic Functions
Radical Functions
AII.F.4: Explore and describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative) with and without technology. Find the value of k given the graph of f(x) and the graph of f(x) + k, k f(x), f(kx), or f(x + k).
Absolute Value with Linear Functions
Exponential Functions
Logarithmic Functions: Translating and Scaling
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Zap It! Game
AII.SEI: Systems of Equations and Inequalities
AII.SEI.2: Represent and solve real-world systems of linear equations and inequalities in two or three variables algebraically and using technology. Interpret the solution set and determine whether it is reasonable.
Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)
AII.Q: Quadratic Equations and Functions
AII.Q.1: Represent real-world problems that can be modeled with quadratic functions using tables, graphs, and equations; translate fluently among these representations. Solve such problems with and without technology. Interpret the solutions and determine whether they are reasonable.
Quadratics in Polynomial Form
Roots of a Quadratic
AII.Q.2: Use completing the square to rewrite quadratic functions in vertex form and graph these functions with and without technology.
Quadratics in Vertex Form
AII.Q.3: Understand that different forms of a quadratic equation can provide different information. Use and translate quadratic functions between standard, vertex, and intercept form to graph and identify key features, including intercepts, vertex, line of symmetry, end behavior, and domain and range.
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game
AII.Q.4: Use the discriminant to determine the number and type of solutions of a quadratic equation. Find all solutions and write complex solutions in the form of a ± bi for real numbers a and b.
Roots of a Quadratic
AII.EL: Exponential and Logarithmic Equations and Functions
AII.EL.1: Graph exponential and logarithmic functions with and without technology. Identify and describe key features, such as intercepts, domain and range, asymptotes and end behavior. Know that the inverse of an exponential function is a logarithmic function.
Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
AII.EL.2: Identify the percent rate of change in exponential functions. Classify them as representing exponential growth or decay.
Compound Interest
Exponential Growth and Decay
AII.EL.3: Use the properties of exponents to rewrite expressions to describe transformations of exponential functions.
Exponential Functions
Introduction to Exponential Functions
AII.EL.4: Use the properties of exponents to derive the properties of logarithms. Evaluate exponential and logarithmic expressions.
Logarithmic Functions
AII.EL.5: Solve exponential and logarithmic equations in one variable.
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
AII.EL.6: Represent real-world problems using exponential and logarithmic functions and solve such problems with technology. Interpret the solutions and determine whether they are reasonable.
Compound Interest
Exponential Functions
Exponential Growth and Decay
Logarithmic Functions: Translating and Scaling
AII.PR: Polynomial, Rational, and Other Equations and Functions
AII.PR.1: Solve real-world and other mathematical problems involving polynomial equations with and without technology. Interpret the solutions and determine whether the solutions are reasonable.
Graphs of Polynomial Functions
Polynomials and Linear Factors
AII.PR.2.i: Graph mathematical functions including: with technology.
AII.PR.2.a: polynomial functions;
Graphs of Polynomial Functions
Polynomials and Linear Factors
AII.PR.2.b: rational functions;
General Form of a Rational Function
Rational Functions
AII.PR.2.c: square root functions;
Radical Functions
AII.PR.2.d: absolute value functions; and,
Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Translating and Scaling Functions
AII.PR.2.e: piecewise-defined functions
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
AII.PR.2.ii: Identify and describe features, such as intercepts, domain and range, end behavior, and lines of symmetry.
Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Polynomials and Linear Factors
Radical Functions
Rational Functions
AII.PR.3: Solve real-world and other mathematical problems involving radical and rational equations. Give examples showing how extraneous solutions may arise.
Direct and Inverse Variation
Radical Functions
AII.PR.4: Solve absolute value linear equations and inequalities in one variable.
Absolute Value Equations and Inequalities
Correlation last revised: 11/9/2021