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Topic: Mathematics for Advanced Courses 

Common Core Mathematics 9-12

 Cluster  Perform arithmetic operations with complex numbers.
  Grade 9-12
   N.CN.3.(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
 Cluster  Represent complex numbers and their operations on the complex plane.
  Grade 9-12
   N.CN.4.(+) 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.5.(+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (-1 + √ 3i)3 = 8 because (-1 + √ 3i) has modulus 2 and argument 120°.
   N.CN.6.(+) 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.
 Cluster  Represent and model with vector quantities.
  Grade 9-12
   N.VM.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).
   N.VM.2.(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
   N.VM.3.(+) Solve problems involving velocity and other quantities that can be represented by vectors.
 Cluster  Perform operations on vectors.
  Grade 9-12
   N.VM.4.(+) Add and subtract vectors.
   N.VM.4.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.4.b.Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
   N.VM.4.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.5.(+) Multiply a vector by a scalar.
   N.VM.5.a.Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
   N.VM.5.b.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).
 Cluster  Perform operations on matrices and use matrices in applications.
  Grade 9-12
   N.VM.6.(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
   N.VM.7.(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
   N.VM.8.(+) Add, subtract, and multiply matrices of appropriate dimensions.
   N.VM.9.(+) Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
   N.VM.11.(+) 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.12.(+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
 Cluster  Solve systems of equations
  Grade 9-12
   A.REI.8.(+) Represent a system of linear equations as a single matrix equation in a vector variable.
   A.REI.9.(+) 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).
 Cluster  Analyze functions using different representations
  Grade 9-12
   F.IF.7.d.(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
 Cluster  Build a function that models a relationship between two quantities
  Grade 9-12
   F.BF.1.c.(+) Compose functions. For example, 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.