NQ: Number and Quantity

NQ.1: Students will use complex numbers and determine how polar and rectangular coordinates are related.

NQ.1.PC.1: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers

 Points in the Complex Plane
 Roots of a Quadratic

NQ.1.PC.2: Represent complex numbers and their operations on the complex plane in rectangular and polar form, including real and imaginary numbers, and explain why the rectangular and polar forms of a given complex number represent the same number

 Points in the Complex Plane

NQ.1.PC.3: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation

 Points in the Complex Plane

NQ.2: Students will perform operations with vectors and use those skills to solve problems.

NQ.2.PC.1: Recognize vector quantities as having both magnitude and direction; represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v)

 Vectors

NQ.2.PC.3: Perform operations on vectors in component form:

NQ.2.PC.3.3: vector addition and subtraction

 Adding Vectors
 Vectors

NQ.2.PC.4: Represent and perform vector operations geometrically

NQ.2.PC.4.2: vector addition (triangle and parallelogram models)

 Adding Vectors
 Vectors

NQ.2.PC.4.3: vector subtraction (adding a negative vector, missing addend model)

 Adding Vectors
 Vectors

NQ.2.PC.5: Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v; compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v(for c > 0) or against v (for c < 0)

 Vectors

T: Trigonometry

T.3: Students will develop and apply the definitions of the six trigonometric functions and use the definitions to solve problems and verify identities.

T.3.PC.1: Use special triangles to determine geometrically the values of sine, cosine, and tangent for 𝜋/3, 𝜋/4 and 𝜋/6; use the unit circle to express the values of sine, cosine, and tangent for 𝑥, 𝜋 + 𝑥, and 2𝜋 − 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

T.3.PC.2: 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

T.4: Students will solve trigonometric equations and sketch the graph of periodic trigonometric functions.

T.4.PC.1: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions

 Cosine Function
 Sine Function
 Tangent Function

T.4.PC.5: Use trigonometric functions to model physical situations (e.g., harmonic motion, circular motion, area of polygons)

 Sine, Cosine, and Tangent Ratios
 Translating and Scaling Sine and Cosine Functions

CS: Conic Sections

CS.5: Students will identify, analyze, and sketch the graphs of the conic sections and relate their equations and graphs.

CS.5.PC.1: Derive the equations of ellipses and hyperbolas given the foci using the fact that the sum or difference of distances from the foci is constant

 Ellipses
 Hyperbolas

CS.5.PC.2: Find the equations for the asymptotes of a hyperbola

 Hyperbolas
 Rational Functions

CS.5.PC.3: Complete the square in order to generate an equivalent form of an equation for a conic section; use that equivalent form to identify key characteristics of the conic section

 Circles

CS.5.PC.4: Identify, graph, write, and analyze equations of each type of conic section, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and using technology when appropriate

 Addition and Subtraction of Functions
 Circles
 Ellipses
 Hyperbolas
 Linear Inequalities in Two Variables
 Parabolas
 Roots of a Quadratic

CS.5.PC.5: Solve systems of equations and inequalities involving conics and other types of equations, with and without appropriate technology

 Linear Programming
 Solving Equations by Graphing Each Side

F: Functions

F.6: Students will be able to find the inverse of functions and use composition of functions to prove that two functions are inverses.

F.6.PC.1: Compose functions [e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time]

 Function Machines 1 (Functions and Tables)

F.6.PC.3: 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.6.PC.5: Combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model)

 Function Machines 1 (Functions and Tables)

F.6.PC.6: Understand the inverse relationship between exponents and logarithms; use this relationship to solve problems involving logarithms and exponents

 Logarithmic Functions

F.7: Students will be able to interpret different types of functions and their key characteristics including polynomial, exponential, logarithmic, power, trigonometric, rational, and other types of functions.

F.7.PC.1: Graph rational functions identifying zeros and asymptotes when suitable factorizations are available and show end behavior

 General Form of a Rational Function
 Rational Functions

F.7.PC.2: Analyze and interpret power and polynomial functions numerically, graphically, and algebraically, identifying key characteristics such as intercepts, end behavior, domain and range, relative and absolute maximum and minimum, as well as intervals over which the function increases and decreases

 Graphs of Polynomial Functions
 Polynomials and Linear Factors
 Quadratics in Factored Form

F.7.PC.3: Analyze and interpret rational functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes (vertical, horizontal, and slant), domain and range, end behavior, point discontinuities, and intercepts

 General Form of a Rational Function
 Rational Functions

F.7.PC.4: Analyze and interpret exponential functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, domain and range, end behavior, and intercepts

 Exponential Functions
 Introduction to Exponential Functions
 Logarithmic Functions

F.7.PC.5: Analyze and interpret logarithmic functions numerically, graphically, and algebraically, identifying key characteristics such as asymptotes, domain and range, end behavior, and intercepts

 Logarithmic Functions

F.7.PC.6: Analyze and interpret trigonometric functions numerically, graphically, and algebraically, identifying key characteristics such as period, midline, domain and range, amplitude, phase shift, and asymptotes

 Cosine Function
 Sine Function
 Tangent Function
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions

Correlation last revised: 1/19/2017

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