GA--Standards of Excellence

MGSE9-12.N.CN.1: Understand there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 where 𝘢 and 𝘣 are real numbers.

Points in the Complex Plane

Roots of a Quadratic

MGSE9-12.N.CN.2: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

MGSE9-12.N.CN.3: Find the conjugate of a complex number; use the conjugate to find the quotient of complex numbers.

Points in the Complex Plane

Roots of a Quadratic

MGSE9-12.N.CN.7: Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square roots, completing the square, and the quadratic formula.

Points in the Complex Plane

Roots of a Quadratic

MGSE9-12.N.CN.9: Use the Fundamental Theorem of Algebra to find all roots of a polynomial equation.

Polynomials and Linear Factors

MGSE9-12.A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

MGSE9-12.A.SSE.1a: Interpret parts of an expression, such as terms, factors, and coefficients, in context.

Compound Interest

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

MGSE9-12.A.SSE.1b: Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

MGSE9-12.A.SSE.2: Use the structure of an expression to rewrite it in different equivalent forms.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Expressions

MGSE9-12.A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

MGSE9-12.A.SSE.3c.3c: Use the properties of exponents to transform expressions for exponential functions.

MGSE9-12.A.APR.1: Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *x*^{2}+*bx*+*c*

MGSE9-12.A.APR.2: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

MGSE9-12.A.APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Polynomials and Linear Factors

Quadratics in Factored Form

MGSE9-12.A.APR.5: Know and apply that the Binomial Theorem gives 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 using Pascal’s Triangle.

MGSE9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Exploring Linear Inequalities in One Variable

Geometric Sequences

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

MGSE9-12.A.CED.2: Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.)

Point-Slope Form of a Line

Points, Lines, and Equations

Solving Equations by Graphing Each Side

Standard Form of a Line

MGSE9-12.A.CED.3: Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a nonsolution) under the established constraints.

Linear Inequalities in Two Variables

Linear Programming

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

MGSE9-12.A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solving Formulas for any Variable

MGSE9-12.A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

MGSE9-12.A.REI.4: Solve quadratic equations in one variable.

MGSE9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation.

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

MGSE9-12.A.REI.11: Using graphs, tables, or successive approximations, show that the solution to the equation 𝘧(𝘹) = 𝑔(𝘹) is the 𝘹-value where the 𝑦-values of 𝘧(𝘹) and 𝑔(𝘹) are the same.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Circles

Exponential Functions

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Solving Equations on the Number Line

Standard Form of a Line

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 and end behavior.

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.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function

Introduction to Functions

Radical Functions

Rational Functions

MGSE9-12.F.IF.6: 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

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.7b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions

Radical Functions

MGSE9-12.F.IF.7c: 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

MGSE9-12.F.IF.7d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function

Rational Functions

MGSE9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

MGSE9-12.F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest

Exponential Growth and Decay

MGSE9-12.F.BF.1: Write a function that describes a relationship between two quantities.

MGSE9-12.F.BF.1b: Combine standard function types using arithmetic operations in contextual situations. (Adding, subtracting, and multiplying functions of different types).

Addition and Subtraction of Functions

MGSE9-12.F.BF.3: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Exponential Functions

Logarithmic Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Zap It! Game

MGSE9-12.F.BF.4: Find inverse functions.

MGSE9-12.F.BF.4b: Verify by composition that one function is the inverse of another.

MGSE9-12.F.BF.4c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

MGSE9-12.F.BF.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

MGSE9-12.F.LE.4: For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology.

MGSE9-12.G.C.2: Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Chords and Arcs

Circumference and Area of Circles

Inscribed Angles

MGSE9-12.G.C.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

MGSE9-12.G.GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Circles

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

MGSE9-12.G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

MGSE9-12.G.GMD.1: Give informal arguments for geometric formulas.

MGSE9-12.G.GMD.1a: Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

Circumference and Area of Circles

MGSE9-12.G.GMD.1b: Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

Prisms and Cylinders

Pyramids and Cones

MGSE9-12.G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Prisms and Cylinders

Pyramids and Cones

MGSE9-12.S.CP.1: Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

Independent and Dependent Events

MGSE9-12.S.CP.2: Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

Independent and Dependent Events

MGSE9-12.S.CP.3: Understand the conditional probability of A given B as P (A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is, the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

Independent and Dependent Events

MGSE9-12.S.CP.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in context.

Independent and Dependent Events

Correlation last revised: 4/4/2018

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