11-12. Represent complex numbers and their operations on the complex plane.
11-12.M.4HS.CVM.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.
11-12. Represent and model with vector quantities.
11-12.M.4HS.CVM.5 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).
11-12.M.4HS.CVM.8.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.
11-12.M.4HS.CVM.9.b Compute the magnitude of a scalar multiple cv using ||cv|| = |c|·||v||. Compute the direction of cv knowing that when |c|v is not equal to 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
11-12.M.4HS.CVM.13 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
11-12.M.4HS.CVM.14 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
11-12.M.4HS.TF Trigonometric and Inverse Trigonometric Functions of Real Numbers
11-12. Extend the domain of trigonometric functions using the unit circle
11-12.M.4HS.TF.1 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.
11-12. Explain volume formulas and use them to solve problems
11-12.M.4HS.AG.2 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
11-12.M.4HS.MP Modeling with Probability
11-12. Calculate expected values and use them to solve problems
11-12.M.4HS.MP.1 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.