Organization: Pearson Product Name: Mathematics III Common Core 2014 Product Version: 1 Source: IMS Online Validator Profile: 1.2.0 Identifier: realize-73bb48c9-a95b-332a-8c1a-bef371df1d47 Timestamp: Tuesday, November 19, 2019 11:28 AM EST 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: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. - E0339DE0-DA22-11E2-95B3-3B359DFF4B22 (+) Extend polynomial identities to the complex numbers. - DF8AEA7E-DA22-11E2-95B3-3B359DFF4B22 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. - C62520C6-96FF-11E0-9509-C03D9DFF4B22 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). - B3E12E02-D959-11E2-9C66-33FC9CFF4B22 Evaluate reports based on data. - E098A73A-DA22-11E2-95B3-3B359DFF4B22 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. - E023ED6E-DA22-11E2-95B3-3B359DFF4B22 Interpret parts of an expression, such as terms, factors, and coefficients. - DF9B3546-DA22-11E2-95B3-3B359DFF4B22 Derive the equation of a parabola given a focus and directrix. - C634F104-96FF-11E0-9509-C03D9DFF4B22 (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. - C600926A-96FF-11E0-9509-C03D9DFF4B22 For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. - E03914AA-DA22-11E2-95B3-3B359DFF4B22 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. - C63891F6-96FF-11E0-9509-C03D9DFF4B22 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. - C5DC44BE-96FF-11E0-9509-C03D9DFF4B22 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x). - DFA30E56-DA22-11E2-95B3-3B359DFF4B22 (+) Compose functions. - C608780E-96FF-11E0-9509-C03D9DFF4B22 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. - C63487AA-96FF-11E0-9509-C03D9DFF4B22 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. - B3DA864C-D959-11E2-9C66-33FC9CFF4B22 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. - B3DA1342-D959-11E2-9C66-33FC9CFF4B22 Understand statistics as a process for making inferences to be made about population parameters based on a random sample from that population. - E090761E-DA22-11E2-95B3-3B359DFF4B22 (+) Prove the Laws of Sines and Cosines and use them to solve problems. - C62E2AF4-96FF-11E0-9509-C03D9DFF4B22 Write a function that describes a relationship between two quantities. - E02F939E-DA22-11E2-95B3-3B359DFF4B22 (+) Find inverse functions. Verify by composition that one function is the inverse of another. - C60D53C4-96FF-11E0-9509-C03D9DFF4B22 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. - E0254970-DA22-11E2-95B3-3B359DFF4B22 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. - DFA44DA2-DA22-11E2-95B3-3B359DFF4B22 Prove the Pythagorean identity sin^2 (theta) + cos^2 (theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle. - C61BF3D4-96FF-11E0-9509-C03D9DFF4B22 (+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascals Triangle. - DFA8A154-DA22-11E2-95B3-3B359DFF4B22 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. - DFA9F1C6-DA22-11E2-95B3-3B359DFF4B22 Determine an explicit expression, a recursive process, or steps for calculation from a context. - C606C52C-96FF-11E0-9509-C03D9DFF4B22 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. - E03D757C-DA22-11E2-95B3-3B359DFF4B22 Define appropriate quantities for the purpose of descriptive modeling. - C5C2BAD0-96FF-11E0-9509-C03D9DFF4B22 Use the properties of exponents to interpret expressions for exponential functions. - C602BCF2-96FF-11E0-9509-C03D9DFF4B22 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. - E02A9D9E-DA22-11E2-95B3-3B359DFF4B22 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. - DFA15D40-DA22-11E2-95B3-3B359DFF4B22 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. - C62D8C70-96FF-11E0-9509-C03D9DFF4B22 Prove that all circles are similar. - C630426C-96FF-11E0-9509-C03D9DFF4B22 Graph linear and quadratic functions and show intercepts, maxima, and minima. - C5FE91F4-96FF-11E0-9509-C03D9DFF4B22 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. - C624849A-96FF-11E0-9509-C03D9DFF4B22 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - DFAF102A-DA22-11E2-95B3-3B359DFF4B22 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. - E02498E0-DA22-11E2-95B3-3B359DFF4B22 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - E02C2C0E-DA22-11E2-95B3-3B359DFF4B22 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). - E06C72E6-DA22-11E2-95B3-3B359DFF4B22 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). - E06B1D88-DA22-11E2-95B3-3B359DFF4B22 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. - C1638E3E-B858-11E2-9705-A41A9DFF4B22 (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. - DF8BD92A-DA22-11E2-95B3-3B359DFF4B22 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. - C5F1AA84-96FF-11E0-9509-C03D9DFF4B22 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. - E03C4EAE-DA22-11E2-95B3-3B359DFF4B22 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. - DFB02D16-DA22-11E2-95B3-3B359DFF4B22 Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. - E035B530-DA22-11E2-95B3-3B359DFF4B22 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). - E06D1A02-DA22-11E2-95B3-3B359DFF4B22 (+) 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. - DFAB3BDA-DA22-11E2-95B3-3B359DFF4B22 Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. - E029F56A-DA22-11E2-95B3-3B359DFF4B22 Use the structure of an expression to identify ways to rewrite it. - DF9CE346-DA22-11E2-95B3-3B359DFF4B22 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. - C6314C16-96FF-11E0-9509-C03D9DFF4B22 (+) Construct a tangent line from a point outside a given circle to the circle. - C631EA86-96FF-11E0-9509-C03D9DFF4B22 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. - DFB53CE8-DA22-11E2-95B3-3B359DFF4B22 Use coordinates to prove simple geometric theorems algebraically. - C6367FC4-96FF-11E0-9509-C03D9DFF4B22 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. - E03FAAAE-DA22-11E2-95B3-3B359DFF4B22 Use the properties of exponents to transform expressions for exponential functions. - C5DE1618-96FF-11E0-9509-C03D9DFF4B22 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. - C5EC5AB6-96FF-11E0-9509-C03D9DFF4B22 (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. - C60DE3FC-96FF-11E0-9509-C03D9DFF4B22 (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. - C60F05CA-96FF-11E0-9509-C03D9DFF4B22 Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - E028485A-DA22-11E2-95B3-3B359DFF4B22 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. - E0687934-DA22-11E2-95B3-3B359DFF4B22 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. - C5C205B8-96FF-11E0-9509-C03D9DFF4B22 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. - C5DEF7B8-96FF-11E0-9509-C03D9DFF4B22 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. - C60236A6-96FF-11E0-9509-C03D9DFF4B22 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. - E094DF60-DA22-11E2-95B3-3B359DFF4B22 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. - DFCC4B22-DA22-11E2-95B3-3B359DFF4B22 Combine standard function types using arithmetic operations. - E0302296-DA22-11E2-95B3-3B359DFF4B22 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. - C630D29A-96FF-11E0-9509-C03D9DFF4B22 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). - C62EBCEE-96FF-11E0-9509-C03D9DFF4B22 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. - DFB20CEE-DA22-11E2-95B3-3B359DFF4B22 Interpret complicated expressions by viewing one or more of their parts as a single entity. - DF9BB8F4-DA22-11E2-95B3-3B359DFF4B22 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. - C5F50576-96FF-11E0-9509-C03D9DFF4B22 List of all Files Validated: imsmanifest.xml I_0030a8c1-f411-3332-b998-61b652f9ffd9_1_R/BasicLTI.xml I_0030a8c1-f411-3332-b998-61b652f9ffd9_3_R/BasicLTI.xml I_006f3269-f572-39e3-8772-43e8c8afd1fc_1_R/BasicLTI.xml I_009f3e73-c760-3d4b-aee2-fc3a63658fe4_R/BasicLTI.xml I_00a15d58-5e02-3c89-b71b-84eb39a23099_1_R/BasicLTI.xml I_00d1203a-2858-389f-8fcd-18bf13c00a5e_1_R/BasicLTI.xml I_01768eed-981b-39b4-852d-2c12f40c35c9_1_R/BasicLTI.xml I_01768eed-981b-39b4-852d-2c12f40c35c9_3_R/BasicLTI.xml I_01768eed-981b-39b4-852d-2c12f40c35c9_5_R/BasicLTI.xml I_01e07229-587b-36da-9ae5-d2678b60f105_1_R/BasicLTI.xml I_0205dbf8-bd5e-3b59-8ccc-6898bc95025f_R/BasicLTI.xml I_0231aa74-b5f5-3ff0-8253-518ee5231810_1_R/BasicLTI.xml I_0236a474-077b-3985-944e-97d84fafe051_1_R/BasicLTI.xml I_0277aaf9-5b83-3b20-8c2b-bb50709ee873_R/BasicLTI.xml 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