GA--Standards of Excellence
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.
Points in the Complex Plane
Roots of a Quadratic
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.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.
MGSE9-12.N.VM.4: Add and subtract 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.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.N.VM.7: Multiply matrices by scalars to produce new matrices.
MGSE9-12.A.REI.8: Represent a system of linear equations as a single matrix equation in a vector variable.
Solving Linear Systems (Matrices and Special Solutions)
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.
Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Slope-Intercept Form of a Line
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.
Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions
MGSE9-12.F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
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.
Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios
MGSE9-12.F.TF.9: Prove addition, subtraction, double, and half-angle formulas for sine, cosine, and tangent and use them to solve problems.
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine
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.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.
Independent and Dependent Events
MGSE9-12.S.CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.
Binomial Probabilities
Permutations and Combinations
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.
Independent and Dependent Events
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability
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.
Geometric Probability
Independent and Dependent Events
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability
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: 9/16/2020