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Curriculum Standards: MAFS.K12.MP.6 Attend to precision. - 340833b6-d1c4-44eb-9647-f79f7daf0030 MAFS.6.SP.2.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. - 6a475527-2c2f-42e6-a0c8-cd8bccfb8bcc CCSS.Math.Content.6.EE.B Reason about and solve one-variable equations and inequalities. - 1E746F4A-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-IF.2.6 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. - 1d1f44f9-3b27-4ba9-8a74-8cf374455d45 CCSS.Math.Content.HSF-TF.A.2 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. - 206FEA2C-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSN-RN.A.1 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. - 1F7642B0-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-SSE.2.3.a Factor a quadratic expression to reveal the zeros of the function it defines. - 6e8d693f-acb0-4a9c-a13e-5b0e76b6634c MAFS.912.A-SSE.1.2 Use the structure of an expression to identify ways to rewrite it. - ab53e453-944a-43b3-9178-8443bbd95b16 MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - 74b31224-ff95-4c0d-a7d3-3ed7d443ee48 MAFS.912.S-MD.2.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). - af3d22fc-b1a1-409a-87c2-8b17e6e8e1aa MAFS.912.S-IC.1.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. - 57d6093f-cded-4c3a-b9b3-d6f7c617f46a CCSS.Math.Content.HSA-SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines. - 1FCF76A0-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSG-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. - 20E5E0A6-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.N-CN.3.8 Extend polynomial identities to the complex numbers. - 587d1127-0ea3-41da-b0bb-444d1ec28337 MAFS.912.A-REI.2.4.a Use the method of completing the square to transform any quadratic equation in 𝘹 into an equation of the form (𝘹𝘹 – 𝘹𝘹𝘱)² = 𝘹𝘹𝘱𝘲 that has the same solutions. Derive the quadratic formula from this form. - 2d950d92-7ee9-4947-b5c7-82f4494ada91 MAFS.912.A-SSE.2.4 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. - c28aa5db-7078-471e-9b27-0453d9883e22 MAFS.912.F-TF.1.2 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 CCSS.Math.Content.HSF-IF.B.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. - 202DFCA2-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-IC.1.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. - dffe2ef5-7600-4254-bf7f-9e9f93e780c6 MAFS.912.F-TF.1.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–𝘹𝘹𝘱𝘲𝘹, π+𝘹𝘹𝘱𝘲𝘹𝘹, and 2π–𝘹𝘹𝘱𝘲𝘹𝘹𝘹 in terms of their values for 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹, where 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹 is any real number. - 886f0a51-dddf-44b1-932e-4273174a3189 MAFS.6.RP.1.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. - 94c59a18-9a16-401a-9457-d6a22f3be8a0 MAFS.912.F-TF.2.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. - 06bef262-1b10-4e99-a5e8-0d36cf67dec5 MAFS.912.F-BF.2.4.b Verify by composition that one function is the inverse of another. - 4dc6ff62-3014-4961-b45f-3fd1f4eaf653 CCSS.Math.Content.6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: - 1E9CD886-7053-11DF-8EBF-BE719DFF4B22 MAFS.6.RP.1 Understand ratio concepts and use ratio reasoning to solve problems. - 50458c9e-ed0f-4cba-a28a-f4957022f614 CCSS.Math.Content.HSA-SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients. - 1FC1804A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A Understand ratio concepts and use ratio reasoning to solve problems. - 1E1E82CE-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-SSE.2.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. - 4db017ec-c7d0-4c7c-acc9-b6a3facb0dbe CCSS.Math.Content.HSF-IF.A.1 Understand that 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. If 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧 is a function and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹 is an element of its domain, then 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹) denotes the output of 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧 corresponding to the input 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹. The graph of 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧 is the graph of the equation 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺 = 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹). - 2022443E-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-APR.3.5 Know and apply the Binomial Theorem for the expansion of (𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹 + 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺)ⁿ in powers of 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹 and y for a positive integer 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯, where 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹 and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle. - 4f7f84f2-725d-49ab-ac9d-c416de16267f MAFS.K12.MP.2 Reason abstractly and quantitatively. - 3885dc10-69f7-4a9d-b273-ed83a569094a MAFS.912.N-RN.1.1 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. - 3bf3bf8d-8807-4549-a096-8887e7cfc300 CCSS.Math.Content.HSA-SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions. - 1FD28A34-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning. - A6497ED0-6F89-11DF-BAEE-EA329DFF4B22 MAFS.912.F-IF.3.7.e 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 MAFS.912.S-IC.2.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. - 2cf7cb51-e872-460e-bb8e-ced6b83c68e7 MAFS.6.SP.1.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. - 7a07f2a6-b564-40d2-aa66-e48c4fbd09af MAFS.912.F-BF.2.4.a Solve an equation of the form 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹) = 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤 for a simple function 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧 that has an inverse and write an expression for the inverse. - 49b475dd-0964-4f64-a441-8f66f0eccaaf CCSS.Math.Content.HSA-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. - 1FC900FE-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima. - 2031EE3E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSN-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. - 1F78FAA0-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-LE.A.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. - 20641210-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. - 496eb64d-a4b3-4eab-87cc-1468af8f8f00 MAFS.912.A-SSE.1.1 Interpret expressions that represent a quantity in terms of its context. - 5253e510-7b24-44fb-b86e-89bf9576f607 MAFS.K12.MP.3.1 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 MAFS.912.N-Q.1.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. - 4641014a-4a04-42ea-a758-242a7c410bc5 CCSS.Math.Content.HSN-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. - 1F82CF6C-7053-11DF-8EBF-BE719DFF4B22 Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. - 5C561224-7377-11DF-A1E8-223D9DFF4B22 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. - 5C551ED2-7377-11DF-A1E8-223D9DFF4B22 CCSS.Math.Content.6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. - 1E28AC4A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-APR.B.2 Know and apply the Remainder Theorem: For a polynomial 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹) and a number 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢, the remainder on division by 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹 – 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢 is 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢), so 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢) = 0 if and only if (𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹 – 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢) is a factor of 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹). - 1FE14A60-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-IF.3.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima. - 39c4a7bf-37d3-4b65-9448-981cc401c99a MAFS.912.F-IF.2.4 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. - caa1c5ce-9954-4bd4-913c-82f5740ef25c MAFS.6.RP.1.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. - 8d888642-08c1-45e3-8286-0420933ab148 MAFS.912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context. - 3d9245a7-1c9a-4797-80f5-9265839bcc7d CCSS.Math.Content.HSS-IC.B.6 Evaluate reports based on data. - 2136997E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. - 1E331C2A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSS-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. - 212668B0-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-APR.1.1 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 CCSS.Math.Content.6.SP.B.5.a Reporting the number of observations. - 1E9EE9FA-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSN-CN.A.2 Use the relation 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. - 1F89941E-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-LE.1.4 For exponential models, express as a logarithm the solution to 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣 to the 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵 power = 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥 where 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢, 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤, and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥 are numbers and the base 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣 is 2, 10, or 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦; evaluate the logarithm using technology. - 63a09493-0302-452b-87e5-d91fb9c84276 CCSS.Math.Content.HSA-REI.B.4.b Solve quadratic equations by inspection (e.g., for 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹² = 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 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢 ± 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪 for real numbers 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢 and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣. - 200DF4F2-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. - 1E20776E-7053-11DF-8EBF-BE719DFF4B22 MAFS.K12.MP.5 Use appropriate tools strategically. - 7fb94672-da71-44b5-950f-b57258b31b63 CCSS.Math.Content.HSF-BF.B.4.a Solve an equation of the form 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹) = 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤 for a simple function 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧 that has an inverse and write an expression for the inverse. - 20552DCC-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-SSE.1.1.a Interpret parts of an expression, such as terms, factors, and coefficients. - 8f350077-a0f8-40fa-99b2-7f4e0d02815a CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. - A6430F50-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.HSA-REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. - 2010D992-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-APR.B.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. - 1FE3040E-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-LE.1.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. - 5bd8b229-eab1-4a8f-ae0b-d54e832a0ed8 MAFS.912.F-IF.3.7.d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. - cfa65496-45b0-4a5f-8a62-ddfbfc42a87a MAFS.912.S-ID.1.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). - 5c4a6eb4-8864-4748-a2b3-9f905af11859 CCSS.Math.Content.HSA-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. - 1FFDCE7E-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-APR.A.1 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. - 1FDDE172-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-IC.2.6 Evaluate reports based on data. - 66c1992f-d334-40ac-8ee1-b2161e34a661 MAFS.912.F-BF.2.4.d Produce an invertible function from a non-invertible function by restricting the domain. - d0d39548-4500-42f2-beea-e91b256d6b2e MAFS.912.A-APR.2.2 Know and apply the Remainder Theorem: For a polynomial 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹) and a number 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢, the remainder on division by 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹 – 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢 is 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢), so 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢) = 0 if and only if (𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹 – 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢) is a factor of 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹). - dd06b50d-5364-4b96-9f62-93fda1f14cfb MAFS.6.RP.1.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. - c49ed342-fc0a-4f9d-a8f0-8428508960be MAFS.912.F-IF.1.2 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 MAFS.K12.MP.6.1 Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. - cc88d0e7-1375-41f3-89ff-b0557b54b359 CCSS.Math.Content.HSN-CN.C.8 Extend polynomial identities to the complex numbers. - 1F95DB2A-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-CP.1.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). - 365e2305-0416-4ba3-8680-d56ec4c87bda CCSS.Math.Content.HSS-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). - 213B2728-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. - A630F7A2-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.HSA-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. - 1FF53976-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP7 Look for and make use of structure. - A648672A-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.HSF-LE.A.4 For exponential models, express as a logarithm the solution to 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣 to the 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵 power = 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥 where 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢, 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤, and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥 are numbers and the base 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣 is 2, 10, or 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦; evaluate the logarithm using technology. - 206840D8-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. - 3ff81b1a-0429-4077-b975-7bf3ef39b19b CCSS.Math.Content.HSF-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. - 202B0812-7053-11DF-8EBF-BE719DFF4B22 MAFS.K12.MP.2.1 Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. - 0331111e-4349-473a-ae23-5b4b6572bb0c MAFS.912.N-CN.1.1 Know there is a complex number 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪 such that 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪² = –1, and every complex number has the form 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢 + 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪 with 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢 and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣 real. - f3a17aba-a5f4-43e1-b9e4-f9ee1137b55d MAFS.912.F-BF.2.a Use the change of base formula. - 6568997c-442b-4325-9a4b-5c80bc2a8788 MAFS.912.F-TF.3.8 Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to calculate trigonometric ratios. - 19f08ed7-6a29-40db-83d9-1cd879026b9f CCSS.Math.Content.HSA-REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. - 201D5924-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context. - 206AD910-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-IF.3.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - 08878758-8098-43fd-9f51-ced6566042b4 MAFS.912.A-APR.2.3 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. - 92e6f323-be53-4506-86e4-350312f8a433 MAFS.912.A-APR.4.7 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 MAFS.912.F-BF.1.1.b Combine standard function types using arithmetic operations. - 2b53cd9d-2997-422d-90f1-057cd438db7a MAFS.912.F-BF.2.4.c Read values of an inverse function from a graph or a table, given that the function has an inverse. - 58d366b5-0df6-4494-adba-d67270412506 CCSS.Math.Content.HSF-IF.C.8.a 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. - 203A6D70-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-CED.1.2 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 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. - 5C54A65A-7377-11DF-A1E8-223D9DFF4B22 CCSS.Math.Content.HSA-APR.D.6 Rewrite simple rational expressions in different forms; write 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹)/𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹) in the form 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹) + 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹)/𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹), where 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹), 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹), 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹), and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹) are polynomials with the degree of 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹) less than the degree of 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣(𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. - 1FEDFDB4-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-REI.2.4.b Solve quadratic equations by inspection (e.g., for 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘹² = 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 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘹𝘢 ± 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘹𝘢𝘣𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘹𝘢𝘣𝘪 for real numbers 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘹𝘢𝘣𝘪𝘢 and 𝘹𝘹𝘱𝘲𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘹𝘺𝘹𝘯𝘹𝘺𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘪𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘹𝘢𝘣𝘪𝘢𝘣𝘧𝘹𝘤𝘧𝘱𝘹𝘢𝘹𝘢𝘱𝘢𝘱𝘢𝘹𝘢𝘱𝘹𝘢𝘣𝘤𝘵𝘥𝘢𝘤𝘥𝘣𝘦𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘹𝘢𝘣𝘪𝘢𝘣. - 5b718173-1711-4db7-912f-2629db1814fb MAFS.K12.MP.3 Construct viable arguments and critique the reasoning of others. - 0ab2c4e3-2b87-4dd9-a12b-353a486762fa CCSS.Math.Content.HSF-TF.C.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. - 207B22CA-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSS-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. - 2124F836-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-BF.1.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - 6dd64416-2b83-4d29-af53-77be3b9c8693 CCSS.Math.Content.6.SP.A Develop understanding of statistical variability. - 1E8FD2DA-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-IC.2.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. - e54367f2-9d49-472a-ae58-482f0c0b72d4 Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. - 5C53AC00-7377-11DF-A1E8-223D9DFF4B22 CCSS.Math.Content.HSA-REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). - 201A8BE0-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-ID.2.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. - 7408e735-5c56-4fdf-81fd-4973e4b6d11a CCSS.Math.Content.6.SP.B.5.c Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. - 1EA3F940-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Practice.MP6 Attend to precision. - A647016E-6F89-11DF-BAEE-EA329DFF4B22 CCSS.Math.Content.HSF-BF.A.1.b Combine standard function types using arithmetic operations. - 20491316-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-APR.C.5 Know and apply the Binomial Theorem for the expansion of (34𝘹 + 34𝘹𝘺)ⁿ in powers of 34𝘹𝘺𝘹 and y for a positive integer 34𝘹𝘺𝘹𝘯, where 34𝘹𝘺𝘹𝘯𝘹 and 34𝘹𝘺𝘹𝘯𝘹𝘺 are any numbers, with coefficients determined for example by Pascal’s Triangle. - 1FEA73F6-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.G-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. - 313f2846-7fe7-4707-b21e-d95e6904380f CCSS.Math.Content.HSN-CN.C.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. - 1F98D762-7053-11DF-8EBF-BE719DFF4B22 MAFS.6.SP.2.5.a Reporting the number of observations. - c3a58735-2dd0-4744-9076-860065f28f35 CCSS.Math.Content.HSA-SSE.A.1 Interpret expressions that represent a quantity in terms of its context. - 1FC6D040-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. - 204F7382-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-REI.A.1 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. - 200598A2-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-APR.D.7 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. - 1FF0311A-7053-11DF-8EBF-BE719DFF4B22 MAFS.6.SP.1 Develop understanding of statistical variability. - c82cdde6-0186-4a24-b01e-324e0ab1302d MAFS.912.N-Q.1.2 Define appropriate quantities for the purpose of descriptive modeling. - ea155e2f-c077-4a91-b6c9-3415d50c5e5b CCSS.Math.Content.HSA-REI.B.4 Solve quadratic equations in one variable. - 200B3AAA-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. - 206E8C72-7053-11DF-8EBF-BE719DFF4B22 MAFS.K12.MP.1.1 Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. - db656dba-3ee7-423e-9020-626812d8c8d3 MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - 604f911f-7b09-48ad-8ca3-d5dc05924acc MAFS.912.F-BF.2.4 Find inverse functions. - be7cab76-def7-40ea-8f21-ac539ab72a8a CCSS.Math.Content.HSF-TF.A.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–34𝘹, π+34𝘹𝘹, and 2π–34𝘹𝘹𝘹 in terms of their values for 34𝘹𝘹𝘹𝘹, where 34𝘹𝘹𝘹𝘹𝘹 is any real number. - 20710358-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-IF.C.8.b Use the properties of exponents to interpret expressions for exponential functions. - 203BE466-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSS-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. - 21328E9C-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSS-IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. - 212E0304-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles. - f133b6ed-fc63-41e5-a15e-aa0517226554 MAFS.912.A-REI.3.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. - 8ff0f22d-117f-49bc-a3b3-c068e87e737c MAFS.912.F-IF.3.8.a 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 CCSS.Math.Content.HSF-BF.B.3 Identify the effect on the graph of replacing 34𝘹𝘹𝘹𝘹𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹) by 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹) + 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬, 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹), 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹), and 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹 + 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬) for specific values of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬 (both positive and negative); find the value of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. - 2051CA1A-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹) by 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹) + 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬, 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹), 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹), and 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹 + 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬) for specific values of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬 (both positive and negative); find the value of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. - 6b38a99d-560c-4cab-81a9-84c58508eb20 CCSS.Math.Content.HSS-ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. - 211C3D22-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. - 20D81638-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.N-CN.1.2 Use the relation 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. - 0e6955ff-4575-4299-bafd-82217823ce46 MAFS.912.F-TF.3.9 Prove the addition and subtraction, half-angle, and double-angle formulas for sine, cosine, and tangent and use these formulas to solve problems. - 8650c9b2-acf2-4eb2-a045-0d34f04539e2 CCSS.Math.Content.HSA-SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity. - 1FC38598-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. - 75d55b82-83c7-43ca-ab1f-998a20e958f4 CCSS.Math.Content.HSF-IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - 20334950-7053-11DF-8EBF-BE719DFF4B22 Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. - 5C5422D4-7377-11DF-A1E8-223D9DFF4B22 MAFS.6.SP.2.5 Summarize numerical data sets in relation to their context, such as by: - d5388c0c-2589-43b6-ad5e-739cd6c3e753 MAFS.912.A-SSE.1.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity. - 0374dc6c-a25f-460b-8fb4-fd72200c73f1 CCSS.Math.Content.HSN-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions. - 1F94A462-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). - 2065846A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-IF.C.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. - 203752B6-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. - 20256704-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-TF.B.7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. - 207725D0-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-APR.4.6 Rewrite simple rational expressions in different forms; write 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹)/34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹) in the form 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹) + 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹)/34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹), where 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹), 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹), 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹), and 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹) are polynomials with the degree of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹) less than the degree of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹), using inspection, long division, or, for the more complicated examples, a computer algebra system. - 37c1428a-15f3-47ec-88cd-141f70720584 MAFS.K12.MP.7 Look for and make use of structure. - 4b6d6fc7-f9ff-4e3c-89c9-3642b61650a0 MAFS.912.A-CED.1.3 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. - 3940bed0-00a3-49dc-9b74-172f6db23b03 CCSS.Math.Content.HSA-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - 1FF7725E-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-REI.3.6 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 CCSS.Math.Content.HSS-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. - 212C3E02-7053-11DF-8EBF-BE719DFF4B22 MAFS.K12.MP.1 Make sense of problems and persevere in solving them. - efdcc5ef-fe77-460b-b67c-303a7528d39d CCSS.Math.Content.HSA-SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. - 1FD11118-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSG-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles. - 20D9571E-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-IF.3.8.b Use the properties of exponents to interpret expressions for exponential functions. - 64d18729-b3c5-42f4-9ec3-d505f13a292c CCSS.Math.Content.HSN-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. - 1F819E58-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-IF.1.1 Understand that 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. If 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧 is a function and 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹 is an element of its domain, then 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹) denotes the output of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧 corresponding to the input 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹. The graph of 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧 is the graph of the equation 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺 = 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹). - 3b9e7038-0e8e-4ad9-b588-f99932d41bed CCSS.Math.Content.HSA-APR.C.4 Prove polynomial identities and use them to describe numerical relationships. - 1FE68F2A-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. - 20072668-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-SSE.2.3.c Use the properties of exponents to transform expressions for exponential functions. - cdb48175-78dd-4251-88e8-121f0ab727a6 MAFS.912.S-ID.1.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. - ef092516-4307-497b-8ffb-f57bfe6d5100 MAFS.912.N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions. - 1774db36-d9ac-476e-b6b1-13e43681aba9 CCSS.Math.Content.HSA-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. - 20098A98-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-BF.1.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context. - 1ae9b1ba-954d-42ee-8b3d-ce806d59fe78 CCSS.Math.Content.6.SP.B Summarize and describe distributions. - 1E99E8E2-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. - 18186a04-0947-4402-bdac-f6aba4c9e901 MAFS.912.A-REI.1.1 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 MAFS.6.EE.2 Reason about and solve one-variable equations and inequalities. - a971566c-0f10-4450-8b7c-8c0e1e160ab5 MAFS.912.F-TF.1.1 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 CCSS.Math.Content.HSS-IC.B.4 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. - 2133C8D4-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-ID.3.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. - f30051bf-3298-4ca0-90c8-d33d533a9bfc CCSS.Math.Content.HSS-ID.A.4 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. - 21192718-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSN-CN.A.1 Know there is a complex number 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪 such that 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪² = –1, and every complex number has the form 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢 + 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪 with 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢 and 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣 real. - 1F884F0A-7053-11DF-8EBF-BE719DFF4B22 MAFS.K12.MP.4 Model with mathematics. - f68eaa41-9ef2-4f61-941b-e67b099f9c02 CCSS.Math.Content.HSF-IF.B.4 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. - 2029EA4A-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. - 3cba67ec-19a0-405c-8b9c-e48dbaf918ca CCSS.Math.Content.HSS-MD.B.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). - 21C4A7FA-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-REI.1.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. - 43c9f03d-deaa-4f60-8bb7-c09c5c1068b2 CCSS.Math.Content.HSF-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. - 2023EA78-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-ID.1.4 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 CCSS.Math.Content.HSF-IF.C.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. - 2034CEF6-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-REI.4.11 Explain why the 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹-coordinates of the points where the graphs of the equations 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺 = 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹) and 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺 = 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹) intersect are the solutions of the equation 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹) = 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹) and/or 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. - 8747c55b-cbc9-4ef6-b38a-95fde44f15c3 CCSS.Math.Practice.MP4 Model with mathematics. - A6446404-6F89-11DF-BAEE-EA329DFF4B22 MAFS.K12.MP.4.1 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 CCSS.Math.Content.HSF-TF.C.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle. - 17227D98-93AF-11DF-B5CC-4EF79CFF4B22 CCSS.Math.Content.HSF-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. - 20748370-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-REI.4.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). - a764f529-16f8-4fa9-b5cd-3d0831349fe3 CCSS.Math.Content.HSA-SSE.B.4 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. - 1FD5EAEE-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSA-REI.D.11 Explain why the 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹-coordinates of the points where the graphs of the equations 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺 = 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹) and 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺 = 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹) intersect are the solutions of the equation 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹) = 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹) and/or 34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔(34𝘹𝘹𝘹𝘹𝘹𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘧𝘹𝘧𝘹𝘬𝘬𝘧𝘹𝘧𝘬𝘹𝘧𝘹𝘬𝘬𝘬𝘪𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘣𝘹𝘢𝘹𝘣𝘹𝘲𝘹𝘳𝘹𝘳𝘹𝘣𝘹𝘧𝘹𝘧𝘹𝘧𝘹𝘧𝘺𝘧𝘹𝘪𝘪𝘢𝘣𝘪𝘢𝘣𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹𝘹𝘺𝘧𝘹𝘺𝑔𝘹𝘧𝘹𝑔𝘹𝘧𝘹𝑔𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. - 201C0FBA-7053-11DF-8EBF-BE719DFF4B22 CCSS.Math.Content.HSF-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - 203F6C30-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.S-MD.2.7 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 CCSS.Math.Content.HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). - 21148EA6-7053-11DF-8EBF-BE719DFF4B22 MAFS.912.A-CED.1.1 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 MAFS.912.F-IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. - 46d77c7e-5843-4183-950c-b7ba0a8c2f3f CCSS.Math.Content.6.SP.A.3 Recognize that a measure of center for