NQ: Number and Quantity

1.1: Explore and illustrate the characteristics and operations connecting sequences and series

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: Algebra

2.1: Analyze and manipulate functions

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

2.2: Use polynomial identities to solve problems

A.10: Prove polynomial identities and use them to describe numerical relationships.

Factoring Special Products

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.

Binomial Probabilities

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

2.3: Perform operations on expressions, equations, inequalities and polynomials

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.

Logarithmic Functions

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.

Quadratic Inequalities

F: Functions

3.3: Build new functions from existing functions

F.27: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

F.28: Produce an invertible function from a non-invertible function by restricting the domain.

Logarithmic Functions

F.29: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

3.4: Extend the domain of trigonometric functions using the unit circle

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

3.5: Model periodic phenomena with trigonometric 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

3.6: Prove and apply trigonometric identities

F.35: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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: Geometry

4.1: Recognize, sketch, and transform graphs of functions

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: Statistics and Probability

5.1: Explore and apply fundamental principles of probability.

SP.45: Analyze expressions in summation and factorial notation to solve problems.

Binomial Probabilities
Permutations and Combinations

Correlation last revised: 5/20/2019

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