3124.1: Mathematical Processes

3124.1.1: Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

Biconditional Statements
Conditional Statements
Estimating Population Size

3124.1.2: Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

Estimating Population Size

3124.1.4: Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

Using Algebraic Equations
Using Algebraic Expressions

3124.1.5: Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

Estimating Population Size
Unit Conversions

3124.1.6: Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

Biconditional Statements

3124.2: Number & Operations

3124.2.1: Understand the capabilities and the limitations of calculators and computers in solving problems.

Estimating Population Size

3124.2.2: Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

3124.2.3: Develop the arithmetic and properties of the complex numbers.

Points in the Complex Plane

3124.3: Algebra

3124.3.1: Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist.

Arithmetic Sequences
Geometric Sequences

3124.3.2: Identify or analyze the distinguishing properties of exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations.

Compound Interest
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Rational Functions

3124.3.5: Solve problems by converting the given verbal information into an appropriate mathematical model involving equations or systems of equations; apply appropriate techniques to analyze these mathematical models; and interpret the solution obtained in written form using appropriate units of measurement.

Linear Functions
Solving Equations on the Number Line

3124.3.6: Understand the properties of conic sections whether displayed in equation or graphical form.

Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas

3124.4: Geometry & Measurement

3124.4.1: Understand basic right triangle trigonometry and use it to solve problems.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

3124.4.3: Solve trigonometric equations.

Sine, Cosine, and Tangent Ratios

3124.4.4: Apply trigonometric identities to rewrite expressions and solve equations.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

3124.4.6: Understand the measure of angles and the relationship to the circle; convert between degrees and radians.

Chords and Arcs
Cosine Function
Inscribed Angles
Sine Function
Tangent Function
Triangle Angle Sum

3124.4.7: Develop the measurement of arcs of circles; calculate angular and linear velocity.

Chords and Arcs
Inscribed Angles

3124.5: Data Analysis, Statistics, & Probability

3124.5.1: Create scatter plots, analyze patterns and describe relationships that exist in a set of linear and non-linear paired data to make predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

3124.5.2: Identify and interpret the correlation coefficient for a linear bivariate data set.

Correlation

3124.5.3: Examine all aspects of using regression equations to act as a model for a real world situation, including interpolation, extrapolation and validity of model.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots