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: 9/16/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.