Course of Study
1.1.1: Represent complex numbers and their operations on the complex plane.
N-CN.1: Students will: 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.2: Students will: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
N-CN.3: Students will: 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.
1.5.1: Represent and model with vector quantities.
N-VM.5: Students will: 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.6: Students will: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
N-VM.7: Students will: Solve problems involving velocity and other quantities that can be represented by vectors.
1.5.2: Perform operations on vectors.
N-VM.8: Students will: 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.
N-VM.8.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
N-VM.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.
N-VM.9: Students will: 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 ??(???, ?? subscript ??) = (?????, ???? subscript ??).
N-VM.9.b: Compute the magnitude of a scalar multiple ???? using ||????|| = |??|??. Compute the direction of ???? knowing that when |??|?? ? 0, the direction of ???? is either along ?? (for ?? > 0) or against ?? (for ?? < 0).
1.5.3: Perform operations on matrices and use matrices in applications.
N-VM.11: Students will: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
2.2.1: Use polynomial identities to solve problems.
A-APR.13: Students will: 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.
2.3.1: Solve systems of equations.
A-REI.14: Students will: Represent a system of linear equations as a single matrix equation in a vector variable.
2.4.1: Understand the graphs and equations of conic sections.
A-CS.15: Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.
A-CS.15.a: Formulate equations of conic sections from their determining characteristics.
3.1.1: Interpret functions that arise in applications in terms of the context.
F-IF.16: Students will: 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.
F-IF.17: Students will: 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.
3.1.2: Analyze functions using different representations.
F-IF.18: Students will: 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.
F-IF.18.b: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
F-IF.18.c: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
F-IF.18.d: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
3.2.1: Build a function that models a relationship between two quantities.
F-BF.19: Students will: Compose functions.
3.2.2: Build new functions from existing functions.
F-BF.20: Students will: Determine the inverse of a function and a relation.
F-BF.21: Students will: Verify by composition that one function is the inverse of another.
F-BF.22: Students will: Read values of an inverse function from a graph or a table, given that the function has an inverse.
F-BF.23: Students will: Produce an invertible function from a non-invertible function by restricting the domain.
F-BF.24: Students will: Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents.
F-BF.25: Students will: Compare effects of parameter changes on graphs of transcendental functions.
3.3.1: Recognize attributes of trigonometric functions and solve problems involving trigonometry.
F-TF.26: Students will: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses.
F-TF.27: Students will: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function.
F-TF.28: Students will: Utilize parametric equations by graphing and by converting to rectangular form.
F-TF.28.b: Solve applied problems that include sequences with recurrence relations.
3.3.2: Extend the domain of trigonometric functions using the unit circle.
F-TF.29: Students will: Use special triangles to determine geometrically the values of sine, cosine, and 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.
F-TF.30: Students will: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
3.3.4: Prove and apply trigonometric identities.
F-TF.33: Students will: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1, and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.
F-TF.34: Students will: Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems.
4.2.1: Translate between the geometric description and the equation for a conic section.
G-GPE.36: Students will: Derive the equation of a parabola given a focus and directrix.
G-GPE.37: Students will: 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.
4.2.2: Explain volume formulas and use them to solve problems.
G-GPE.38: Students will: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
5.1.1: Summarize, represent, and interpret data on a single count or measurement variable.
S-ID.39: Students will: 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.
S-ID.40: Students will: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
S-ID.41: Students will: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
5.1.2: Interpret linear models.
S-ID.42: Students will: Compute (using technology) and interpret the correlation coefficient of a linear fit.
S-ID.43: Students will: Distinguish between correlation and causation.
5.2.1: Understand and evaluate random processes underlying statistical experiments.
S-IC.44: Students will: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
S-IC.45: Students will: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
5.2.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
S-IC.46: Students will: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
S-IC.47: Students will: 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.
S-IC.48: Students will: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
S-IC.49: Students will: Evaluate reports based on data.
5.3.1: Calculate expected values and use them to solve problems.
S-MD.50: Students will: 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.
S-MD.51: Students will: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
S-MD.52: Students will: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
S-MD.53: Students will: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
5.3.2: Use probability to evaluate outcomes of decisions.
S-MD.54: Students will: 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.
S-MD.54.b: Evaluate and compare strategies on the basis of expected values.
Correlation last revised: 9/15/2020