College- and Career-Readiness Standards
NQ.1: Express sequences and series using recursive and explicit formulas.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
NQ.2: Evaluate and apply formulas for arithmetic and geometric sequences and series.
Arithmetic Sequences
Geometric Sequences
A.8: Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).
Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Introduction to Functions
Logarithmic Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
A.10: Prove polynomial identities and use them to describe numerical relationships.
A.12: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.
A.15: Determine asymptotes and holes of rational functions, explain how each was found, and relate these behaviors to continuity.
General Form of a Rational Function
A.18: Find the composite of two given functions and find the inverse of a given function. Extend this concept to discuss the identity function f(x) = x.
A.21: Find the zeros of polynomial functions by synthetic division and the Factor Theorem.
Polynomials and Linear Factors
A.22: Graph and solve quadratic inequalities.
F.24: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
General Form of a Rational Function
Rational Functions
F.25: Compose functions.
Function Machines 1 (Functions and Tables)
F.26: Verify by composition that one function is the inverse of another.
F.27: Read values of an inverse function from a graph or a table, given that the function has an inverse.
Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions
F.28: Produce an invertible function from a non-invertible function by restricting the domain.
F.29: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
F.30: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi – x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.
Cosine Function
Sine Function
Sum and Difference Identities for Sine and Cosine
Tangent Function
Translating and Scaling Sine and Cosine Functions
F.31: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions
F.32: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
F.35: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
F.36: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.
Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios
G.37: Graph piecewise defined functions and determine continuity or discontinuities.
Absolute Value with Linear Functions
G.38: Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer).
Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Rational Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game
G.39: Explain the effects of changing the parameters in transformations of functions.
Absolute Value with Linear Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game
G.40: Predict the shapes of graphs of exponential, logarithmic, rational, and piece-wise functions, and verify the prediction with and without technology.
Absolute Value with Linear Functions
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Rational Functions
SP.45: Analyze expressions in summation and factorial notation to solve problems.
Binomial Probabilities
Permutations and Combinations
Correlation last revised: 9/15/2020