Curriculum Framework

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

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

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)

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

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

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

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

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

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)

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.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.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

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

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

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.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

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

Quadratics in Vertex 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

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: 5/8/2018