MA 12.1: Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.1.1.a: Graph complex numbers on the complex plane.

Points in the Complex Plane

MA 12.1.1.f: Derive and use the formulas for the general term and summation of finite arithmetic and geometric series.

Arithmetic Sequences

MA 12.1.2: Students will compute with matrices.

MA 12.1.2.b: Add, subtract, and multiply matrices of appropriate dimensions.

Translations

MA 12.2: Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.2.1: Students will demonstrate, represent, and show relationships with non-linear and trigonometric functions.

MA 12.2.1.a: Analyze and graph non-linear functions (e.g., quadratic, trigonometric, square root, logarithmic, rational, higher-order polynomials, exponential, absolute value, piecewise, and sinusoidal).

Absolute Value with Linear Functions
Quadratics in Vertex Form
Zap It! Game

MA 12.2.1.b: Use the unit circle to define the trigonometric functions on all real numbers.

Cosine Function
Sine Function
Tangent Function

MA 12.2.1.c: Evaluate sine, cosine, and tangent functions at positive and negative multiples of 30, and 45 degrees.

Cosine Function
Sine Function
Tangent Function

MA 12.2.1.d: Create new functions out of existing functions using addition, subtraction, multiplication, division, translation, dilation, and composition.

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

MA 12.2.1.g: Convert between radian and degree measures of an angle.

Cosine Function
Sine Function
Tangent Function

MA 12.2.2: Students will apply the identities when evaluating and solving trigonometric equations.

MA 12.2.2.d: Find the period, amplitude, and midline of a trigonometric function of the form y=A + Bsin (Cx), where A, B, and C are parameters, and identify these properties on a graph of the function.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

MA 12.3: Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.3.2: Students will determine location, orientation, and relationships on the coordinate plane.

MA 12.3.2.a: Identify features of a function (e.g., local and global maxima and minima, concavity, approximate locations of points of inflection and vertical and horizontal asymptotes) from its graph.

Absolute Value with Linear Functions
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Vertex Form
Radical Functions

MA 12.3.2.b: Identify symmetry properties of a function (e.g., axis of symmetry of a parabola) and know the connection between its symmetry properties and specific transformations.

Absolute Value with Linear Functions
Parabolas

MA 12.3.2.c: Recognize that vector quantities have both magnitude and direction and can be represented by directed line segments.

Adding Vectors
Vectors

MA 12.3.2.d: Add and subtract vectors graphically and algebraically.

Adding Vectors
Vectors

MA 12.3.2.f: Derive the equations of parabolas, ellipses, and hyperbolas from a graph or given parameters.

Ellipses
Hyperbolas
Quadratics in Vertex Form
Translating and Scaling Functions

MA 12.3.3: Students will perform and compare measurements and apply formulas.

MA 12.3.3.a: Use Cavalieri?s Principle to determine the volume of a sphere and other solid figures.

Prisms and Cylinders

MA 12.3.3.b: Determine the tolerance interval and percent of error in measurement.

Real-Time Histogram

MA 12.4: Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.4.2: Analysis & Applications: Students will analyze data to address the situation.

MA 12.4.2.a: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Real-Time Histogram

MA 12.4.3: Probability: Students will interpret and apply concepts of probability.

MA 12.4.3.a: Calculate the expected value of a random variable and interpret it as the mean of a probability distribution.

Polling: City

MA 12.4.3.b: Determine possible outcomes of a decision by assigning probabilities to outcome values and finding expected values.

Binomial Probabilities
Probability Simulations
Theoretical and Experimental Probability

MA 12.4.3.d: Analyze decisions and strategies using probability concepts (e.g., medical testing and product testing).

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability