A2.N: Number Sense and Operations

A2.N.1: Evaluate numerical expressions with negative and/or fractional exponents, without the aid of a calculator (when the answers are rational numbers)

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A2.N.5: Rationalize a denominator containing a radical expression

Simplifying Radical Expressions

A2.N.7: Simplify powers of i

Points in the Complex Plane

A2.N.8: Determine the conjugate of a complex number

Points in the Complex Plane
Roots of a Quadratic

A2.A: Algebra

A2.A.1: Solve absolute value equations and inequalities involving linear expressions in one variable

Compound Inequalities

A2.A.2: Use the discriminant to determine the nature of the roots of a quadratic equation

Roots of a Quadratic

A2.A.4: Solve quadratic inequalities in one and two variables, algebraically and graphically

Quadratic Inequalities

A2.A.5: Use direct and inverse variation to solve for unknown values

Determining a Spring Constant
Direct and Inverse Variation

A2.A.6: Solve an application which results in an exponential function

Compound Interest
Introduction to Exponential Functions

A2.A.7: Factor polynomial expressions completely, using any combination of the following techniques: common factor extraction, difference of two perfect squares, quadratic trinomials

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A2.A.8: Apply the rules of exponents to simplify expressions involving negative and/or fractional exponents

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A2.A.9: Rewrite algebraic expressions that contain negative exponents using only positive exponents

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A2.A.13: Simplify radical expressions

Operations with Radical Expressions
Simplifying Radical Expressions

A2.A.15: Rationalize denominators involving algebraic radical expressions

Simplifying Radical Expressions

A2.A.20: Determine the sum and product of the roots of a quadratic equation by examining its coefficients

Roots of a Quadratic

A2.A.22: Solve radical equations

Operations with Radical Expressions
Radical Functions

A2.A.24: Know and apply the technique of completing the square

Roots of a Quadratic

A2.A.25: Solve quadratic equations, using the quadratic formula

Roots of a Quadratic

A2.A.26: Find the solution to polynomial equations of higher degree that can be solved using factoring and/or the quadratic formula

Modeling the Factorization of x²+bx+c

A2.A.27: Solve exponential equations with and without common bases

Exponential Functions

A2.A.29: Identify an arithmetic or geometric sequence and find the formula for its nth term

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.A.30: Determine the common difference in an arithmetic sequence

Arithmetic Sequences
Arithmetic and Geometric Sequences

A2.A.31: Determine the common ratio in a geometric sequence

Arithmetic and Geometric Sequences
Geometric Sequences

A2.A.32: Determine a specified term of an arithmetic or geometric sequence

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.A.33: Specify terms of a sequence, given its recursive definition

Arithmetic Sequences
Geometric Sequences

A2.A.37: Define a relation and function

Points, Lines, and Equations

A2.A.38: Determine when a relation is a function

Introduction to Functions
Linear Functions

A2.A.39: Determine the domain and range of a function from its equation

Introduction to Functions
Logarithmic Functions
Radical Functions

A2.A.43: Determine if a function is one-to-one, onto, or both

Introduction to Functions
Linear Functions

A2.A.44: Define the inverse of a function

Logarithmic Functions

A2.A.45: Determine the inverse of a function and use composition to justify the result

Logarithmic Functions

A2.A.46: Perform transformations with functions and relations: f(x + a), f(x) + a, f(-x), -f(x), af(x)

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

A2.A.47: Determine the center-radius form for the equation of a circle in standard form

Circles

A2.A.49: Write the equation of a circle from its graph

Circles
Ellipses

A2.A.51: Determine the domain and range of a function from its graph

Exponential Functions
Introduction to Functions
Logarithmic Functions
Radical Functions

A2.A.52: Identify relations and functions, using graphs

Absolute Value with Linear Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form

A2.A.54: Graph logarithmic functions, using the inverse of the related exponential function

Logarithmic Functions

A2.A.55: Express and apply the six trigonometric functions as ratios of the sides of a right triangle

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

A2.A.57: Sketch and use the reference angle for angles in standard position

Cosine Function
Sine Function
Tangent Function

A2.A.58: Know and apply the co-function and reciprocal relationships between trigonometric ratios

Tangent Function

A2.A.60: Sketch the unit circle and represent angles in standard position

Cosine Function
Sine Function
Tangent Function

A2.A.61: Determine the length of an arc of a circle, given its radius and the measure of its central angle

Inscribed Angles

A2.A.62: Find the value of trigonometric functions, if given a point on the terminal side of angle theta

Cosine Function
Sine Function
Tangent Function

A2.A.65: Sketch the graph of the inverses of the sine, cosine, and tangent functions

Tangent Function

A2.A.69: Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

A2.A.70: Sketch and recognize one cycle of a function of the form y = AsinBx = or y = AcosBx

Cosine Function
Sine Function
Translating and Scaling Sine and Cosine Functions

A2.A.71: Sketch and recognize the graphs of the functions y = sec(x), y = csc(x), y = tan(x), and y = cot(x)

Tangent Function

A2.A.72: Write the trigonometric function that is represented by a given periodic graph

Translating and Scaling Sine and Cosine Functions

A2.M: Measurement

A2.M.2: Convert between radian and degree measures

Cosine Function
Sine Function
Tangent Function

A2.S: Statistics and Probability

A2.S.1: Understand the differences among various kinds of studies (e.g., survey, observation, controlled experiment)

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

A2.S.2: Determine factors which may affect the outcome of a survey

Correlation
Polling: City
Polling: Neighborhood

A2.S.3: Calculate measures of central tendency with group frequency distributions

Describing Data Using Statistics
Polling: City
Populations and Samples

A2.S.4: Calculate measures of dispersion (range, quartiles, interquartile range, standard deviation, variance) for both samples and populations

Describing Data Using Statistics
Polling: City
Real-Time Histogram

A2.S.5: Know and apply the characteristics of the normal distribution

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

A2.S.6: Determine from a scatter plot whether a linear, logarithmic, exponential, or power regression model is most appropriate

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

A2.S.8: Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

A2.S.10: Calculate the number of possible permutations (n P r) of n items taken r at a time

Permutations and Combinations

A2.S.11: Calculate the number of possible combinations(n C r) of n items taken r at a time

Binomial Probabilities
Permutations and Combinations

A2.S.12: Use permutations, combinations, and the Fundamental Principle of Counting to determine the number of elements in a sample space and a specific subset (event)

Binomial Probabilities
Permutations and Combinations

A2.S.13: Calculate theoretical probabilities, including geometric applications

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

A2.S.14: Calculate empirical probabilities

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

A2.S.15: Know and apply the binomial probability formula to events involving the terms exactly, at least, and at most

Binomial Probabilities