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.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

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Linear Functions

Logarithmic Functions

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

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.

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.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

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

Probability Simulations

Theoretical and Experimental Probability

Correlation last revised: 4/4/2018