N-CN: The Complex Number System

N-CN.1: 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.

Points in the Complex Plane

N-VM: Vector and Matrix Quantities

N-VM.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).

Vectors

N-VM.6: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

Vectors

N-VM.7: Solve problems involving velocity and other quantities that can be represented by vectors.

2D Collisions
Golf Range

N-VM.8: Add and subtract vectors.

N-VM.8.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.

Adding Vectors
Vectors

N-VM.8.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

Adding Vectors
Vectors

N-VM.9: Multiply a vector by a scalar.

N-VM.9.a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as 𝘤(𝘷ₓ, 𝘷 subscript 𝘺) = (𝘤𝘷ₓ, 𝘤𝘷 subscript 𝘺).

Dilations

A-APR: Arithmetic with Polynomials and Rational Expressions

A-APR.13: 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.

Binomial Probabilities

A-REI: Reasoning with Equations and Inequalities

A-REI.14: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

F-CS: Conic Sections

F-CS.15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

F-CS.15.a: Formulate equations of conic sections from their determining characteristics.

Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas

F-IF: Interpreting Functions

F-IF.16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

F-IF.17: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

F-IF.18: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.18.a: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions

F-IF.18.b: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game

F-IF.18.c: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function
Rational Functions

F-IF.18.d: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function
Exponential Functions
Exponential Growth and Decay
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

F-BF: Building Functions

F-BF.20: Determine the inverse of a function and a relation.

Logarithmic Functions

F-BF.21: Verify by composition that one function is the inverse of another.

Logarithmic Functions

F-BF.22: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

F-BF.24: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

F-TF: Trigonometric Functions

F-TF.26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

F-TF.27: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function.

Sum and Difference Identities for Sine and Cosine

F-TF.28: Utilize parametric equations by graphing and by converting to rectangular form.

F-TF.28.b: Solve applied problems that include sequences with recurrence relations.

Arithmetic Sequences
Geometric Sequences

F-TF.34: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

G-GPE: Expressing Geometric Properties with Equations

G-GPE.36: Derive the equation of a parabola given a focus and directrix.

Parabolas

G-GPE.37: 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.

Ellipses
Hyperbolas

S-ID: Interpreting Categorical and Quantitative Data

S-ID.39: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Box-and-Whisker Plots
Describing Data Using Statistics
Real-Time Histogram
Sight vs. Sound Reactions

S-ID.40: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Mean, Median, and Mode
Reaction Time 2 (Graphs and Statistics)

S-ID.42: Compute (using technology) and interpret the correlation coefficient of a linear fit.

Correlation

S-IC: Making Inferences and Justifying Conclusions

S-IC.47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Estimating Population Size
Polling: City
Polling: Neighborhood

S-IC.48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Real-Time Histogram
Sight vs. Sound Reactions

S-MD: Using Probability to Make Decisions

S-MD.51: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Lucky Duck (Expected Value)

S-MD.52: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

Independent and Dependent Events
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

S-MD.53: 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
Independent and Dependent Events
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

S-MD.54: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

S-MD.54.a: Find the expected payoff for a game of chance.

Lucky Duck (Expected Value)

S-MD.54.b: Evaluate and compare strategies on the basis of expected values.

Lucky Duck (Expected Value)