Download NxG Trigonometry-Precalculus CSO List.xlsx

NxG Trigonometry/Precalculus CSOs
Building Relationships among Complex Numbers, Vectors, and Matrices
M.TPC.CVM.1 find conjugate of complex number; use conjugates to find moduli & quotients of complex numbers
M.TPC.CVM.2 represent complex numbers on complex plane in rectangular & polar form & explain
M.TPC.CVM.3 represent addition, subtraction, multiplication & conjugation of complex numbers geometrically on
complex plane; use properties of this representation for computation.
M.TPC.CVM.4 calculate distance between numbers in complex plane as modulus of difference & midpoint of
segment as average of numbers at its endpoints
M.TPC.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
M.TPC.CVM.6 find components of vector by subtracting coordinates of initial point terminal point
M.TPC.CVM.7 solve problems involving velocity and other quantities that can be represented by vectors.
M.TPC.CVM.8 add and subtract vectors.
M.TPC.CVM.9 multiply a vector by a scalar.
M.TPC.CVM.10 use matrices to represent & manipulate data
M.TPC.CVM.11 multiply matrices by scalars to produce new matrices
M.TPC.CVM.12 add, subtract and multiply matrices of appropriate dimensions.
M.TPC.CVM.13 understand matrix multiplication for square matrices is not a commutative operation
M.TPC.CVM.14 understand that the zero & identity matrices play a role in matrix addition & multiplication similar to
role of 0 and 1 in real numbers-determinant of square matrix is nonzero only if matrix has multiplicative inverse
M.TPC.CVM.15 multiply a vector by matrix of suitable dimensions to produce another vector. Work with matrices
M.TPC.CVM.16 work with 2 matrices as transformations of plane & interpret absolute value of determinant area
M.TPC.CVM.17 represent a system of linear equations as a single matrix equation in a vector variable.
M.TPC.CVM.18 find the inverse of a matrix if it exists and use it to solve systems of linear equations
Analysis and Synthesis of Functions
M.TPC.ASF.1 graph functions expressed symbolically & show features, by hand & technology for more complicated
M.TPC.ASF.2 write function that describes relationship between two quantities
M.TPC.ASF.3 find inverse functions.
M.TPC.ASF.4 understand the inverse relationship between exponents and logarithms and use this relationship to
solve problems involving logarithms and exponents.
Trigonometric and Inverse Trigonometric Functions of Real Numbers
M.TPC.TF.1 use special triangles to determine geometrically values of sine, cosine, tangent for p/3, p/4 and p/6, and
use unit circle to express values of sine, cosine, & tangent for p–x, p+x, & 2p–x in terms of values for x
M.TPC.TF.2 use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
M.TPC.TF.3 understand that restricting a trigonometric function to a domain on which it is always increasing or
always decreasing allows its inverse to be constructed.
M.TPC.TF.4 use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the
solutions using technology, and interpret them in terms of the context.
M.TPC.TF.5 solve more general trigonometric equations.
M.TPC.TF.6 prove addition and subtraction formulas for sine, cosine, & tangent and use them to solve problems.
M.TPC.TF.7 graph trigonometric functions showing key features, including phase shift.
Derivations in Analytic Geometry
M.TPC.AG.1 derive equations of ellipses & hyperbolas given foci, sum or difference of distances from foci is
constant
M.TPC.AG.2
give informal argument using Cavalieri’s principle for formulas for volume of sphere and other solids
Modeling with Probability
M.TPC.MP.1 define random variable for quantity of interest by assigning numerical value to each event in sample
space; graph corresponding probability distribution using the same graphical displays as for data distributions.
M.TPC.MP.2 calculate expected value of a random variable; interpret it as the mean of the probability distribution.
M.TPC.MP.3 develop a probability distribution for a random variable defined for a sample space in which theoretical
probabilities can be calculated; find the expected value.
M.TPC.MP.4 develop probability distribution for random variable defined for sample space; find expected value
M.TPC.MP.5 weigh possible outcomes of decision by assigning probabilities and finding expected values
Series and Informal Limits
M.TPC.SL.1 develop sigma notation and use it to write series in equivalent form.
M.TPC.SL.2 apply the method of mathematical induction to prove summation formulas.
M.TPC.SL.3 develop intuitively that sum of infinite series of positive numbers can converge & derive formula for sum
M.TPC.SL.4 apply infinite geometric series models.