Academic Standards
AII.CNE.1: Know there is an imaginary number, i, such that i^2 = -1, and every complex number can be written in the form a + bi, with a and b real. Use the relation i^2=–1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Points in the Complex Plane
Roots of a Quadratic
AII.CNE.2: Translate expressions between radical and exponent form and simplify them using the laws of exponents.
Exponents and Power Rules
Simplifying Radical Expressions
AII.F.1: Determine whether a relation represented by a table, graph, or equation is a function.
Introduction to Functions
Linear Functions
Points, Lines, and Equations
AII.F.3: Understand that an inverse function can be obtained by expressing the dependent variable of one function as the independent variable of another, as f and g are inverse functions if and only if f(x)=y and g(y)=x, for all values of x in the domain of f and all values of y in the domain of g. Find the inverse of a function that has an inverse.
AII.F.4: 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.
Absolute Value with Linear Functions
Introduction to Exponential Functions
Logarithmic Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
AII.F.5: Describe the effect on the graph of f(x) by replacing f(x) with f(x) + k, k f(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
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game
AII.SEII.2: Solve systems of two or three linear equations in two or three variables algebraically and using technology.
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
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.
AII.Q.2: Use completing the square to rewrite quadratic functions into the form y = a(x + h)^2 + k, and graph these functions with and without technology. Identify intercepts, zeros, domain and range, and lines of symmetry. Understand the relationship between completing the square and the quadratic formula.
Quadratics in Vertex Form
Roots of a Quadratic
AII.Q.3: Use the discriminant to determine the number and type of solutions of a quadratic equation in one variable with real coefficients; find all solutions and write complex solutions in the form of a ± bi for real numbers a and b.
Points in the Complex Plane
Roots of a Quadratic
AII.EL.1: Write arithmetic and geometric sequences both recursively and with an explicit formula; use them to model situations and translate between the two forms.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
AII.EL.2: Graph exponential functions with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, and asymptotic and end behavior.
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
AII.EL.3: Identify the percent rate of change in exponential functions written as equations, such as y = (1.02)^t, y = (0.97)^t, y = (1.01)12^t, y = (1.2)^t/10, and classify them as representing exponential growth or decay.
Compound Interest
Introduction to Exponential Functions
AII.EL.4: Use the properties of exponents to transform expressions for exponential functions (e.g., the express ion 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%)
Dividing Exponential Expressions
Exponents and Power Rules
AII.EL.5: Know that the inverse of an exponential function is a logarithm. Represent exponential and logarithmic functions using graphing technology and describe their inverse relationship.
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
AII.PR.2: Graph relations and functions including polynomial, square root, and piecewise-defined functions (including step functions and absolute value functions) with and without technology. Identify and describe features, such as intercepts, zeros, domain and range, end behavior, and lines of symmetry.
Absolute Value with Linear Functions
Graphs of Polynomial Functions
Introduction to Functions
Linear Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Radical Functions
Translating and Scaling Functions
AII.PR.3: Solve real-world and other mathematical problems involving rational and radical equations, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise.
AII.DSP.1: Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Correlation
Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Real-Time Histogram
AII.DSP.2: Use technology to find a linear, quadratic, or exponential function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient.
Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
AII.DSP.3: Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, inter-quartile range, standard deviation, percentiles, and variance). Understand the effects of outliers on the statistical summary of the data.
Box-and-Whisker Plots
Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode
Populations and Samples
Real-Time Histogram
Stem-and-Leaf Plots
AII.DSP.4: Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models.
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
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 multiplication counting principle, permutations, and combinations; apply these concepts to calculate probabilities.
Binomial Probabilities
Permutations and Combinations
Correlation last revised: 11/9/2021