### 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

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: 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)

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

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

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

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: 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

T.3.PC.2: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems

#### 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

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

### 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

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

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

### 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]

F.6.PC.3: Read values of an inverse function from a graph or a table given that the function has an inverse

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)

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

#### 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

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

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

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

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

Correlation last revised: 5/8/2018

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