### MGSE9-12.N.CN: The Complex Number System

#### 1.1: Use properties of rational and irrational numbers.

MGSE9-12.N.CN.3: Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.

#### 1.2: Represent complex numbers and their operations on the complex plane.

MGSE9-12.N.CN.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.

### MGSE9-12.N.VM: Vector and Matrix Quantities

#### 2.1: Represent and model with vector quantities.

MGSE9-12.N.VM.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 (e.g., 𝙫, |𝙫|, ||𝙫||, 𝘷).

MGSE9-12.N.VM.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

MGSE9-12.N.VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.

#### 2.2: Perform operations on vectors.

MGSE9-12.N.VM.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.

MGSE9-12.N.VM.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

MGSE9-12.N.VM.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.

MGSE9-12.N.VM.5: Multiply a vector by a scalar.

MGSE9-12.N.VM.5a: 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).

### MGSE9-12.A.REI: Reasoning with Equations and Inequalities

#### 3.1: Solve systems of equations

MGSE9-12.A.REI.8: Represent a system of linear equations as a single matrix equation in a vector variable.

### MGSE9-12.F.IF: Interpreting Functions

#### 4.1: Interpret functions that arise in applications in terms of the context

MGSE9-12.F.IF.4: Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

#### 4.2: Analyze functions using different representations

MGSE9-12.F.IF.7: Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

MGSE9-12.F.IF.7e: Graph trigonometric functions, showing period, midline, and amplitude.

### MGSE9-12.F.TF: Trigonometric Functions

#### 6.2: Model periodic phenomena with trigonometric functions

MGSE9-12.F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

#### 6.3: Prove and apply trigonometric identities

MGSE9-12.F.TF.8: Prove the Pythagorean identity (sin A)² + (cos A)² = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.

MGSE9-12.F.TF.9: Prove addition, subtraction, double, and half-angle formulas for sine, cosine, and tangent and use them to solve problems.

### MGSE9-12.G.GPE: Expressing Geometric Properties with Equations

#### 8.1: Translate between the geometric description and the equation for a conic section

MGSE9-12.G.GPE.2: Derive the equation of a parabola given a focus and directrix.

MGSE9-12.G.GPE.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.

### MGSE9-12.S.ID: Interpreting Categorical and Quantitative Data

#### 9.1: Summarize, represent, and interpret data on a single count or measurement variable

MGSE9-12.S.ID.2: 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.

### MGSE9-12.S.IC: Making Inferences and Justifying Conclusions

#### 10.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

MGSE9-12.S.IC.4: 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.

MGSE9-12.S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

### MGSE9-12.S.CP: Conditional Probability and the Rules of Probability

#### 11.1: Use the rules of probability to compute probabilities of compound events in a uniform probability model

MGSE9-12.S.CP.8: Apply the general Multiplication Rule in a uniform probability model, 𝘗(𝘈 and 𝘉) = [𝘗(𝘈)x[𝘗(𝘉|𝘈)] = [𝘗(𝘉)]x[𝘗(𝘈|𝘉]), and interpret the answer in terms of the model.

MGSE9-12.S.CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

### MGSE9-12.S.MD: Using Probability to Make Decisions

#### 12.1: Calculate expected values and use them to solve problems

MGSE9-12.S.MD.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

MGSE9-12.S.MD.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.

MGSE9-12.S.MD.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

#### 12.2: Use probability to evaluate outcomes of decisions

MGSE9-12.S.MD.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

MGSE9-12.S.MD.5a: Find the expected payoff for a game of chance.

MGSE9-12.S.MD.5b: Evaluate and compare strategies on the basis of expected values.

MGSE9-12.S.MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

MGSE9-12.S.MD.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Correlation last revised: 9/24/2019

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.