Analytic Geometry (Georgia)

Unit 1 – Similarity, Congruence, and Proofs
  • G-SRT.1- Verify experimentally the properties of dilations given by a center and a scale …
    • 1.a – A dilation takes a line not passing through the center of the dilation to a parallel …
    • 1.b – The dilation of a line segment is longer or shorter in the ratio given by the scale …
  • G-SRT.2 – Given two figures, use the definition of similarity in terms of similarity …
  • G-SRT.3 – Use the properties of similarity transformations to establish the AA criterion …
  • G-SRT.4 – Prove theorems about triangles. Theorems include: a line parallel to one side of …
  • G-SRT.5 – Use congruence and similarity criteria for triangles to solve problems and to …
  • G.CO.6 – Use geometric descriptions of rigid motions to transform figures and to predict …
  • G.CO.7 – Use the definition of congruence in terms of rigid motions to show that two …
  • G.CO.8 – Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow …
  • G.CO.9 – Prove theorems about lines and angles. Theorems include: vertical angles …
  • G.CO.10 – Prove theorems about triangles. Theorems include: measures …
  • G.CO.11 – Prove theorems about parallelograms. Theorems include: opposite sides …
  • G.CO.12 – Make formal geometric constructions with a variety of tools and methods …
  • G.CO.13 – Construct an equilateral triangle, a square, and a regular hexagon inscribed in …
Unit 2 – Right Triangle Trigonometry
  • G-SRT.6 – Understand that by similarity, side ratios in right triangles are properties of …
  • G-SRT.7 – Explain and use the relationship between the sine and cosine of complementary …
  • G-SRT.8 – Use trigonometric ratios and the Pythagorean Theorem to solve right triangles …
Unit 3 – Circles and Volume
  • G-C.1 – Prove that all circles are similar.
  • G-C.2 – Identify and describe relationships among inscribed angles, radii, and chords.
  • G-C.3 – Construct the inscribed and circumscribed circles of a triangle, and prove …
  • G-C.4 – (+) Construct a tangent line from a point outside a given circle to the circle.
  • G-C.5 – Derive using similarity the fact that the length of the arc intercepted by an angle is …
  • G-GMD.1 – Give an informal argument for the formulas for the circumference of a circle, …
  • G-GMD.2 – (+) Give an informal argument using Cavalieri’s principle for the formulas for …
  • G-GMD.3 – Use volume formulas for cylinders, pyramids, cones, and spheres to solve …
Unit 4 – Extending the Number System
  • N-RN.1 – Explain how the definition of the meaning of rational exponents follows from …
  • N-RN.2 – Rewrite expressions involving radicals and rational exponents using the …
  • N-RN.3 – Explain why the sum or product of two rational numbers is rational; that the …
  • N-CN.1 - Know there is a complex number i such that i2 = –1, and every complex number …
  • N-CN.2 - Use the relation i2 = –1 and the commutative, associative, and distributive …
  • N-CN.3 - (+) Find the conjugate of a complex number; use conjugates to find moduli and …
  • A-APR.1 – Understand that polynomials form a system analogous to the integers, namely, …
Unit 5 – Quadratic Functions
  • N-CN.7 - Solve quadratic equations with real coefficients that have complex solutions.
  • A-SSE.1- Interpret expressions that represent a quantity in terms of its context.★
    • 1.a -Interpret parts of an expression, such as terms, factors, and coefficients.
    • 1.b – Interpret complicated expressions by viewing one or more of their parts as a
  • A-SSE.2 – Use the structure of an expression to identify ways to rewrite it. For example, …
  • A-SSE.3 – Choose and produce an equivalent form of an expression to reveal and explain …
    • 3.a – Factor a quadratic expression to reveal the zeros of the function it defines.
    • 3.b – Complete the square in a quadratic expression to reveal the maximum or …
  • A-CED.1 – Create equations and inequalities in one variable and use them to solve
  • A-CED.2 – Create equations in two or more variables to represent relationships between …
  • A-CED.4 – Rearrange formulas to highlight a quantity of interest, using the same
  • A-REI.4- Solve quadratic equations in one variable.
    • 4.a – Use the method of completing the square to transform any quadratic equation in x
    • 4.b – Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, …
  • A-REI.7 – Solve a simple system consisting of a linear equation and a quadratic equation …
  • F-IF.4 – For a function that models a relationship between two quantities, interpret key …
  • F-IF.5 – Relate the domain of a function to its graph and, where applicable, to the
  • F-IF.6 – Calculate and interpret the average rate of change of a function (presented …
  • F-IF.7- Graph functions expressed symbolically and show key features of the graph, by …
    • 7.a – Graph linear and quadratic functions and show intercepts, maxima, and minima.
  • F-IF.8- Write a function defined by an expression in different but equivalent forms to …
    • 8.a – Use the process of factoring and completing the square in a quadratic function to …
  • F-IF.9 – Compare properties of two functions each represented in a different way …
  • F-BF.1 – Write a function that describes a relationship between two quantities.
    • 1.a – Determine an explicit expression, a recursive process, or steps for calculation from …
    • 1.b – Combine standard function types using arithmetic operations. For example, build …
  • F-BF.3 – Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and
  • F-LE.3 – Observe using graphs and tables that a quantity increasing exponentially …
  • S-ID.6- Represent data on two quantitative variables on a scatter plot, and describe how …
    • 6.a – Fit a function to the data; use functions fitted to data to solve problems in the …
Unit 6 – Modeling Geometry
  • G-GPE.1 – Derive the equation of a circle of given center and radius using the Pythagorean …
  • G-GPE.2 – Derive the equation of a parabola given a focus and directrix.
  • G-GPE.4 – Use coordinates to prove simple geometric theorems algebraically. For …
Unit 7 – Applications of Probability
  • S-CP.1 – Describe events as subsets of a sample space (the set of outcomes) using …
  • S-CP.2 – Understand that two events A and B are independent if the probability of A and B
  • S-CP.3 – Understand the conditional probability of A given B as P(A and B)/P(B), and …
  • S-CP.4 – Construct and interpret two-way frequency tables of data when two categories …
  • S-CP.5 – Recognize and explain the concepts of conditional probability and independence
  • S-CP.6 – Find the conditional probability of A given B as the fraction of B’s outcomes that …
  • S-CP.7 – Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the …

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