Academic Standards

P.N-CN.A: Perform arithmetic operations with complex numbers.

P.N-CN.A.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

Points in the Complex Plane

Roots of a Quadratic

P.N-CN.B: Represent complex numbers and their operations on the complex plane.

P.N-CN.B.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.

P.N-CN.B.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

P.N-VM.A: Represent and model with vector quantities.

P.N-VM.A.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.

P.N-VN.B: Perform operations on vectors.

P.N-VM.B.4: Add and subtract vectors.

P.N-VM.B.4a: 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.

P.N-VM.B.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

P.N-VM.B.4c: 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.

P.N-VM.C: Perform operations on matrices and use matrices in applications.

P.N-VM.C.8: Add, subtract, and multiply matrices of appropriate dimensions.

P.N-VM.C.12: Work with 2 x 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

P.A-APR.C: Use polynomial identities to solve problems.

P.A-APR.C.5: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

P.A-REI.C: Solve systems of equations.

P.A-REI.C.8: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

P.A-REI.C.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 x 3 or greater).

Solving Linear Systems (Matrices and Special Solutions)

P.F-IF.C: Analyze functions using different representations.

P.F-IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

Absolute Value with Linear Functions

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

P.F-BF.B: Build new functions from existing functions.

P.F-BF.B.4: Find inverse functions.

P.F-BF.B.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

P.F-BF.B.4d: Produce an invertible function from a non-invertible function by restricting the domain.

P.F-BF.B.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

P.F-TF.A: Extend the domain of trigonometric functions using the unit circle.

P.F-TF.A.3: 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.

Cosine Function

Sine Function

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

P.F-TF.A.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

P.F-TF.C: Apply trigonometric identities.

P.F-TF.C.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Sum and Difference Identities for Sine and Cosine

P.G-GPE.A: Translate between the geometric description and the equation for a conic section.

P.G-GPE.A.2: Derive the equation of a parabola given a focus and directrix.

P.G-GPE.A.3: 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.

P.G-GMD.A: Explain volume formulas and use them to solve problems.

P.G-GMD.A.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Prisms and Cylinders

Pyramids and Cones

P.S-IC.B: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

P.S-IC.B.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City

Polling: Neighborhood

P.S-IC.B.4: Use data from a random sample to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

P.S-IC.B.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Polling: City

Polling: Neighborhood

P.S-IC.B.6: Evaluate reports based on data.

Describing Data Using Statistics

Polling: City

Polling: Neighborhood

Real-Time Histogram

P.S-CP.B: Use the rules of probability to compute probabilities of compound events in a uniform probability model.

P.S-CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

Binomial Probabilities

Permutations and Combinations

P.S-MD.A: Calculate expected values and use them to solve problems.

P.S-MD.A.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.

P.S-MD.A.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

P.S-MD.A.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.

Binomial Probabilities

Geometric Probability

Probability Simulations

Theoretical and Experimental Probability

P.S-MD.A.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically. Find the expected value.

Geometric Probability

Probability Simulations

Theoretical and Experimental Probability

P.S-MD.B: Use probability to evaluate outcomes of decisions.

P.S-MD.B.7: Analyze decisions and strategies using probability concepts.

Estimating Population Size

Probability Simulations

Theoretical and Experimental Probability

Biconditional Statements

Conditional Statements

Estimating Population Size

Conditional Statements

Estimating Population Size

Biconditional Statements

Using Algebraic Expressions

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Correlation last revised: 1/22/2020