### N: Number and Quantity

#### N.CN: The Complex Number System

N.CN.2: Represent complex numbers 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.

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

N.CN.4: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

#### N.VM: Vector and Matrix Quantities

N.VM.6: 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).

N.VM.7: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

N.VM.9.a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

N.VM.9.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

N.VM.9.c: Understand vector subtraction v ? w as v + (?w), where ?w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

N.VM.16: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

N.VM.17: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

### A: Algebra

#### A.REI: Reasoning with Equations and Inequalities

A.REI.19: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

### F: Functions

#### F.CS: Conic Sections

F.CS.20: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

F.CS.20.a: Formulate equations of conic sections from their determining characteristics.

#### F.IF: Interpreting Functions

F.IF.21: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

#### F.BF: Building Functions

F.BF.22: Compose functions.

F.BF.23: Determine the inverse of a function and a relation.

F.BF.25: Read values of an inverse function from a graph or a table, given that the function has an inverse.

F.BF.26: Produce an invertible function from a non-invertible function by restricting the domain.

F.BF.27: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

F.BF.28: Compare effects of parameter changes on graphs of transcendental functions.

#### F.TF: Trigonometric Functions

F.TF.29: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses.

F.TF.30: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function.

F.TF.31: Utilize parametric equations by graphing and by converting to rectangular form.

F.TF.31.b: Solve applied problems that include sequences with recurrence relations.

F.TF.32: 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.

F.TF.33: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

F.TF.34: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

F.TF.36: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

### G: Geometry

#### G.GPE: Expressing Geometric Properties with Equations

G.GPE.37: Derive the equation of a parabola given a focus and directrix.

G.GPE.38: 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.

### S: Statistics and Probability

#### S.MD: Using Probability to Make Decisions

S.MD.40: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

S.MD.41: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

S.MD.42: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

S.MD.43: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

S.MD.44: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

S.MD.44.a: Find the expected payoff for a game of chance.

Correlation last revised: 3/17/2015

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