Organization: Pearson Education Product Name: Envision Florida Algebra 2 20202 Product Version: 1 Source: IMS Online Validator Profile: 1.2.0 Identifier: realize-ca1f2c4e-0d24-38b4-aaa4-40aacf8db737 Timestamp: Thursday, October 31, 2019 12:01 PM EDT Status: VALID! Conformant: true ----- VALID! ----- Resource Validation Results The document is valid. ----- VALID! ----- Schema Location Results Schema locations are valid. ----- VALID! ----- Schema Validation Results The document is valid. ----- VALID! ----- Schematron Validation Results The document is valid. Curriculum Standards: Describe the rate of change of a function using words. - c69f37dc-f5de-4cc3-88bd-531febed5c09 When solving a multi-step problem, use units to evaluate the appropriateness of the solution. - 3d49f891-55fb-4246-8289-b091c823a246 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. - 1d1f44f9-3b27-4ba9-8a74-8cf374455d45 Understand the conditional probability of 𝘈 given 𝘈𝘉 as 𝘈𝘉𝘗(𝘈𝘉𝘗𝘈 and 𝘈𝘉𝘗𝘈𝘉)/𝘈𝘉𝘗𝘈𝘉𝘗(𝘈𝘉𝘗𝘈𝘉𝘗𝘉), and interpret independence of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈 and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉 as saying that the conditional probability of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈 given 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉 is the same as the probability of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈, and the conditional probability of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉 given 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈 is the same as the probability of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉. - 15e241f3-e466-4c02-9ccd-1e2c64a44542 Factor a quadratic expression to reveal the zeros of the function it defines. - 6e8d693f-acb0-4a9c-a13e-5b0e76b6634c Use the structure of an expression to identify ways to rewrite it. Example: For example, see 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹⁴ – 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺⁴ as (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹²)² – (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺²)², thus recognizing it as a difference of squares that can be factored as (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹² – 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺²)(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹² + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺²). - ab53e453-944a-43b3-9178-8443bbd95b16 Write or select the graph that represents a defined change in the function (e.g., recognize the effect of changing k on the corresponding graph). - 474b6b9a-5fce-4c3f-b2ab-0d9d7978ed3b Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. Example: For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? - 57d6093f-cded-4c3a-b9b3-d6f7c617f46a Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). - af3d22fc-b1a1-409a-87c2-8b17e6e8e1aa Write or select an equivalent form of a function [e.g., y = mx + b, f(x) = y, y - y1 = m(x - x1), Ax + By = C]. - a03d1c29-e08a-4bdf-a0b1-3f46a6812114 Use the method of completing the square to transform any quadratic equation in 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹 into an equation of the form (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹 – 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱)² = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲 that has the same solutions. Derive the quadratic formula from this form. - 2d950d92-7ee9-4947-b5c7-82f4494ada91 (HONORS ONLY) Extend polynomial identities to the complex numbers. Example: For example, rewrite 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹² + 4 as (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹 + 2𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪)(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹 – 2𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪). - 587d1127-0ea3-41da-b0bb-444d1ec28337 Create linear, quadratic, rational, and exponential equations and inequalities in one variable and use them in a contextual situation to solve problems. - f516795e-3f58-4dfa-9059-7653a0fc9bb9 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. Example: For example, calculate mortgage payments. - c28aa5db-7078-471e-9b27-0453d9883e22 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. - c644dec0-b9ac-4687-87da-43e3bcb7e9ed Describe the meaning of the factors and intercepts on linear and exponential functions. - 9e77ef68-ba32-4bac-a9c7-198c68aba2f4 Graph a system of linear inequalities in two variables using at least two coordinate pairs for each inequality. - 4bce082d-cd58-400e-adbc-b93957373622 Rewrite algebraic expressions in different equivalent forms, such as factoring or combining like terms. - 47e437a4-51d0-450c-a4b4-1f94bcdfa2c5 Understand the solution to a system of two linear equations in two variables corresponds to a point(s) of an intersection of their graphs, because the point(s) of intersection satisfies both equations simultaneously. - 99e125fa-bdd5-45f8-9fa7-50d3d10ca505 Decompose expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts. - 33fca141-a135-473f-babc-45b3ca2be4b6 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. - dffe2ef5-7600-4254-bf7f-9e9f93e780c6 Given a graph, describe or select the solution to a system of linear equations. - efe17d35-83a1-4683-85dd-750619b04733 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Example: For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. - 604f911f-7b09-48ad-8ca3-d5dc05924acc Solve quadratic equations by factoring. - 0b86b8bb-82be-4134-8228-8f6cd1fae56d Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. - 06bef262-1b10-4e99-a5e8-0d36cf67dec5 Verify by composition that one function is the inverse of another. - 4dc6ff62-3014-4961-b45f-3fd1f4eaf653 Determine and interpret appropriate quantities when using descriptive modeling. - 53130ce8-3654-420d-8dbf-adf1358322bb Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. - d88fd899-f951-4e74-a8f5-cccd3347b4ba Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Example: For example, find the points of intersection between the line 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺 = –3𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹 and the circle 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹² + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺² = 3. - 8ff0f22d-117f-49bc-a3b3-c068e87e737c Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. - 4db017ec-c7d0-4c7c-acc9-b6a3facb0dbe Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. - b4324bcf-6bee-49d9-aac5-f2767d2d9a92 Identify the effect on the graph of replacing 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹) by 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹) + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬, 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹), 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹), and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹 + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬) for specific values of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬 (both positive and negative); find the value of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. - 6b38a99d-560c-4cab-81a9-84c58508eb20 Convert from radical representation to using rational exponents and vice versa. - 4fabf9f2-00ce-42ec-a866-7ba87ba58eeb (HONORS ONLY) Know and apply the Binomial Theorem for the expansion of (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹 + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺)ⁿ in powers of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹 and y for a positive integer 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯, where 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹 and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle. - 4f7f84f2-725d-49ab-ac9d-c416de16267f Recognize and interpret the key features of a function. - fb792cd6-8318-44dd-892b-4580c9c9e438 Given a quadratic function, explain the meaning of the zeros of the function (e.g., if f(x) = (x - c) (x - a) then f(a) = 0 and f(c) = 0). - 9105ae41-4874-4c65-99c3-bc85f3af2897 Use the relation 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. - 0e6955ff-4575-4299-bafd-82217823ce46 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Example: For example, we define 5 to the 1/3 power to be the cube root of 5 because we want (5 to the 1/3 power)³ = (5 to the 1/3 power)³ to hold, so (5 to the 1/3 power)³ must equal 5. - 3bf3bf8d-8807-4549-a096-8887e7cfc300 (HONORS ONLY) Use permutations and combinations to compute probabilities of compound events and solve problems. - c0c384a2-4fc8-426a-8c3b-03dbf808fbb8 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift. - e5b40fc6-d095-4429-804f-6a10cbac51ee Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. - 2cf7cb51-e872-460e-bb8e-ced6b83c68e7 Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. - 9a9afa20-1326-4b2b-adce-30513f018bab Solve an equation of the form 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹) = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤 for a simple function 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧 that has an inverse and write an expression for the inverse. Example: For example, 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹) =2 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹³ or 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹) = (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹+1)/(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹–1) for 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹 ≠ 1. - 49b475dd-0964-4f64-a441-8f66f0eccaaf Write expressions in equivalent forms by completing the square to convey the vertex form, to find the maximum or minimum value of a quadratic function, and to explain the meaning of the vertex. - 6e8e6d55-1f83-4826-9cd6-d78eef7370c3 Find the conditional probability of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈 given 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉 as the fraction of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉’s outcomes that also belong to 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈, and interpret the answer in terms of the model. - 1d933095-b158-4d60-923c-5472150d0da2 Choose and interpret both the scale and the origin in graphs and data displays. - a8c544ca-bed3-4567-b1ca-4c35ab23409c Understand the concepts of combining like terms and closure. - f51e09ec-e597-4c8f-b313-c5f844c2f02c Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - 78332818-27d5-4b06-9369-fd35deb0af11 Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. - 9a40d419-ee6e-4423-a2c0-36141274aea2 Use properties of exponents (such as power of a power, product of powers, power of a product, and rational exponents, etc.) to write an equivalent form of an exponential function to reveal and explain specific information about its approximate rate of growth or decay. - 06253520-5db9-40bb-9bb7-bb5ca1a7b2e8 Understand that the denominator of the rational exponent is the root index and the numerator is the exponent of the radicand (e.g., 51/2 = 5). - 42d708a1-7744-4603-a914-c8096b7f787a Rewrite simple rational expressions in different forms; write 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹)/𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹) in the form 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹) + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹)/𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹), where 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹), 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹), 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹), and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹) are polynomials with the degree of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹) less than the degree of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. - 37c1428a-15f3-47ec-88cd-141f70720584 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Example: For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. - 3940bed0-00a3-49dc-9b74-172f6db23b03 Compare the properties of two functions. - 30bbec0a-9c1c-4a59-aa12-04cfe0452585 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. - caec55d0-18be-4e92-a8b1-8d8a3677f8b6 Choose the appropriate units for a specific formula and interpret the meaning of the unit in that context. - 1860f45b-3b24-4bcc-8881-02599bcad7b7 Graph linear and quadratic functions and show intercepts, maxima, and minima. - 39c4a7bf-37d3-4b65-9448-981cc401c99a Given a quadratic expression, explain the meaning of the zeros graphically (e.g., for an expression (x - a) (x - c), a and c correspond to the x-intercepts (if a and c are real)). - 8ce50f6e-257b-480d-8f3a-eba602ebae37 Identify and graph the solutions (ordered pairs) on a graph of an equation in two variables. - 8c41e8d5-2ca2-498b-a64c-3b1198a5fc99 Use the properties of exponents to interpret expressions for exponential functions. Example: For example, identify percent rate of change in functions such as y = (1.02) to the 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵 power, 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺 = (0.97) to the 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵 power, 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺 = (1.01) to the 12𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵 power, 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺 = (1.2) to the 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵/10 power, and classify them as representing exponential growth or decay. - 64d18729-b3c5-42f4-9ec3-d505f13a292c English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. - 61EB17D7-11AC-43F1-8B9B-D315C6E267D2 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. - caa1c5ce-9954-4bd4-913c-82f5740ef25c Select a graph of a function that displays its symbolic representation (e.g., f(x) = 3x + 5). - eb68fb17-55fb-4272-aafa-4fa01a8b570e Describe the accuracy of measurement when reporting quantities (you can lessen your limitations by measuring precisely). - c42588ae-ba2e-46d7-b498-bcf772394434 Interpret the parameters in a linear or exponential function in terms of a context. - 3d9245a7-1c9a-4797-80f5-9265839bcc7d Find the sum of two equations. - 45f34c21-383c-40cc-83b2-578bb74fcb4a Use the properties of exponents to transform expressions for exponential functions. Example: For example the expression 1.15 to the 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵 power can be rewritten as ((1.15 to the 1/12 power) to the 12𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵 power) is approximately equal to (1.012 to the 12𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵 power) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. - cdb48175-78dd-4251-88e8-121f0ab727a6 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. - 789fc7d6-8cae-495f-9e63-c14fb1c4dfd6 Describe the rate of change of a function using numbers. - 6e922cdc-2a08-4610-ab72-0475e8101248 For exponential models, express as a logarithm the solution to 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣 to the 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵 power = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥 where 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢, 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤, and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥 are numbers and the base 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣 is 2, 10, or 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦; evaluate the logarithm using technology. - 63a09493-0302-452b-87e5-d91fb9c84276 Determine an explicit expression, a recursive process, or steps for calculation from a context. - 1ae9b1ba-954d-42ee-8b3d-ce806d59fe78 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Example: For example, rearrange Ohm’s law 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝 = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙 to highlight resistance 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙. - 18186a04-0947-4402-bdac-f6aba4c9e901 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. - cb1cbbc6-8b32-4339-bc18-7439326ebb04 English language learners communicate for social and instructional purposes within the school setting. - D7BEB0F4-C962-45CD-A245-6DF8AED7773D Select a function that describes a relationship between two quantities (e.g., relationship between inches and centimeters, Celsius Fahrenheit, distance = rate x time, recipe for peanut butter and jelly- relationship of peanut butter to jelly f(x)=2x, where x is the quantity of jelly, and f(x) is peanut butter). - 57b1356c-e08b-4304-9fe9-42ae9435d20b (HONORS ONLY) Apply the Addition Rule, 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈 or 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉) = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈) + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉) – 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈 and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉), and interpret the answer in terms of the model. - 6427d00f-ad6e-4455-9421-b19c8a2232d0 Compose functions. Example: For example, if 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺) is the temperature in the atmosphere as a function of height, and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵) is the height of a weather balloon as a function of time, then 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵)) is the temperature at the location of the weather balloon as a function of time. - 8d2c080b-7ebb-45cb-ab26-f80ed10c6ef0 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. - 58884854-41ae-4a67-9f44-0d60b8d2a193 Identify and interpret the solution of a system of linear equations from a real-world context that has been graphed. - 4232009b-ab8f-4dd1-adbf-9db9ac36bfa1 Solve quadratic equations by completing the square. - 41a632ea-55aa-4a5b-af6b-9f11462e3656 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; Convert between degrees and radians. - e531a284-d239-40f8-bf50-5d08bdf1d102 Understand and apply the remainder theorem. - a1eed755-9a59-4255-a2fc-6e1afde0926c Interpret parts of an expression, such as terms, factors, and coefficients. - 8f350077-a0f8-40fa-99b2-7f4e0d02815a Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. Example: For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. - 07e659dc-92c0-41d5-b63e-da5d04dfaf66 Select the graph that matches the description of the relationship between two quantities in the function. - adf6937f-b4ef-4a29-a2ac-3810a177bedf Use the zeros of a function to sketch a graph of the function. - 26361f76-a5e1-4d81-9c84-6caa5646c152 Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. - cfa65496-45b0-4a5f-8a62-ddfbfc42a87a Map elements of the domain sets to the corresponding range sets of functions and determine the rules in the relationship. - 288d82e8-8fc0-4b0c-971d-a806453485d3 Represent data with plots on the real number line (dot plots, histograms, and box plots). - 5c4a6eb4-8864-4748-a2b3-9f905af11859 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Example: For example, if the function 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯) gives the number of person-hours it takes to assemble 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯 engines in a factory, then the positive integers would be an appropriate domain for the function. - 3cba67ec-19a0-405c-8b9c-e48dbaf918ca Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. - 43c9f03d-deaa-4f60-8bb7-c09c5c1068b2 Evaluate reports based on data. - 66c1992f-d334-40ac-8ee1-b2161e34a661 Produce an invertible function from a non-invertible function by restricting the domain. - d0d39548-4500-42f2-beea-e91b256d6b2e Know and apply the Remainder Theorem: For a polynomial 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹) and a number 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢, the remainder on division by 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹 – 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢 is 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢), so 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢) = 0 if and only if (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹 – 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢) is a factor of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹). - dd06b50d-5364-4b96-9f62-93fda1f14cfb Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. - 96d80795-c716-44aa-b1fa-28ba14d290c0 Identify the different parts of the expression and explain their meaning within the context of a problem. - 86f66ac4-52de-4b01-b0bd-64b9d1722add Create a multiple of a linear equation showing that they are equivalent (e.g., x + y = 6 is equivalent to 2x + 2y = 12). - 458eb193-8bc0-4657-85c3-a4b617316015 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. - d759abab-27e2-481c-9921-907efa5d74be Write arguments focused on discipline-specific content. a. Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence. b. Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. c. Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. e. Provide a concluding statement or section that follows from or supports the argument presented. - 202825df-c3a2-43e4-948c-3429f9f3d77d Explain why the 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹-coordinates of the points where the graphs of the equations 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺 = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹) and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺 = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹) intersect are the solutions of the equation 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹) = 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹) and/or 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔(𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. - 8747c55b-cbc9-4ef6-b38a-95fde44f15c3 Pair the rate of change with its graph. - d03ec69d-986b-4199-a078-d1be7c49195a Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. - e779da50-d12e-4314-966c-08e1656d94a3 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. - 1cc1fb51-16ed-4934-ae76-87698c73367c Understand that a is a root of a polynomial function if and only if x-a is a factor of the function. - 85aaf90d-097a-455b-b3a2-3b29f9244158 Find the zeros of a polynomial when the polynomial is factored (e.g., If given the polynomial equation y = x ² + 5x + 6, factor the polynomial as y = (x + 3)(x + 2). Then find the zeros of y by setting each factor equal to zero and solving. x = -2 and x = -3 are the two zeroes of y.). - 379be92a-3dac-425d-9359-4bae30c7fb12 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. - e3897065-ef41-4286-880b-2070c9ddb24d Locate the key features of linear and quadratic equations. - f8a502e6-916b-4a60-88a8-ecd687e98d4c Graph equations in two or more variables on coordinate axes with labels and scales. - 7a4aa91b-c778-429d-ad50-346529b9816d Demonstrate that to be a function, from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. - 470f61e3-5bd1-47e2-a139-740035813e91 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). - b551a069-e77a-4830-97c4-f82209c14f6b Understand that two events 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈 and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉 are independent if the probability of 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈 and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉 occurring together is the product of their probabilities, and use this characterization to determine if they are independent. - 7fda3047-95b7-4b43-b537-70f69e6e0338 Derive the equation of a parabola given a focus and directrix. - 3c35b595-e855-489b-9ea9-5217bf140b81 Write expressions in equivalent forms by factoring to find the zeros of a quadratic function and explain the meaning of the zeros. - 80c302a6-c77d-4877-bf8f-c5687a46ed2b Extend the properties of exponents to justify that (51/2)2=5. - 849c1265-fe8c-4957-8650-12abeb37ae2a Solve simple rational and radical equations in one variable. - 64c5bca0-1420-43f3-9286-813ec5ed052c Interpret units in the context of the problem. - 41961540-0e42-46a5-b66e-696c83e8edcb Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions. - 0895ac3a-a4af-48a4-adee-700e9bf4b6b7 Understand the definition of a polynomial. - f68b0506-3ae4-49f7-9b23-509dc19980ab Use the change of base formula. - 6568997c-442b-4325-9a4b-5c80bc2a8788 Know there is a complex number 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪 such that 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪² = –1, and every complex number has the form 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢 + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪 with 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢 and 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣 real. - f3a17aba-a5f4-43e1-b9e4-f9ee1137b55d Simplify expressions including combining like terms, using the distributive property, and other operations with polynomials. - 19cfcf55-311e-46ae-8119-82b61dc71bb3 Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to calculate trigonometric ratios. - 19f08ed7-6a29-40db-83d9-1cd879026b9f Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. - 7d111c6b-17f8-47af-a1ba-eeb71253561d (HONORS ONLY) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. - 2fe9c17e-51f3-49c8-bfc0-1efdc0763d6e Graph a linear inequality in two variables using at least two coordinate pairs that are solutions. - 33375461-533b-4b5d-8c60-32316702a80c 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. - 9bfc5d94-e597-4db8-8a06-1936719a6b65 Use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely. - b5a6d825-102b-4c95-a199-29073ebdc75b Solve systems of nonlinear equations using substitution. - 65b3bc77-7cc5-455d-8f81-07a6e15c8379 Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. a. Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed. c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions. d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented. - 39b2240a-0c67-426e-99bb-c1a880e6c4b8 Describe the properties of a function (e.g., rate of change, maximum, minimum, etc.). - 80018ccd-3b6c-4e32-b983-2694670b2ae2 Prove polynomial identities and use them to describe numerical relationships. Example: For example, the polynomial identity (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹² + 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺²)² = (𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘹² – 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘹𝘺²)² + (2𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘹𝘺𝘹𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘹𝘺𝘹𝘺)² can be used to generate Pythagorean triples. - f414f786-5e26-45a2-a1c4-330764ca685d Solve quadratic equations by using the quadratic formula. - a686f336-08fc-4917-becf-487d5d9d05bb Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - 08878758-8098-43fd-9f51-ced6566042b4 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. - 92e6f323-be53-4506-86e4-350312f8a433 (HONORS ONLY) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. - dd139e52-ad26-4156-bb19-bac0476df671 Combine standard function types using arithmetic operations. Example: For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. - 2b53cd9d-2997-422d-90f1-057cd438db7a Given the graph of a function, determine the domain. - 5f266b29-4721-43d7-a700-11f6fa0e0918 Read values of an inverse function from a graph or a table, given that the function has an inverse. - 58d366b5-0df6-4494-adba-d67270412506 Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. - 85786a83-8e8e-4f2c-9ee5-c473a733533a Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - 8cd34c46-8d1f-4227-bedb-e17c417a5e44 Solve quadratic equations by inspection (e.g., for 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘹𝘺𝘹𝘺𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘹𝘺𝘹𝘯𝘹𝘺𝘪𝘧𝘹𝘤𝘧𝘧𝘹𝘹𝘧𝘹𝘹𝘹𝘹𝘈𝘉𝘉𝘈𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘵𝘺𝘵𝘺𝘵𝘺𝘵𝘵𝘵𝘵𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘝𝘭𝘙𝘙𝘗𝘈𝘉𝘗𝘈𝘗𝘉𝘗𝘈𝘉𝘛𝘺𝘩𝘵𝘛𝘩𝘵𝘩𝘯𝘯𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘈𝘉𝘈𝘉𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘢 ± 𝘈𝘉𝘗𝘈𝘉𝘗𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘈𝘉𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘺𝘹𝘹𝘱𝘲𝘹𝘹𝘪𝘹𝘪𝘺𝘹𝘹𝘺𝘧𝘹𝘧𝘹𝘬