Organization: Pearson Product Name: Mathematics II Common Core 2014 Product Version: 1 Source: IMS Online Validator Profile: 1.2.0 Identifier: realize-3b461766-9aef-3f86-9140-6a17a38c48af Timestamp: Tuesday, November 19, 2019 11:26 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: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. - G.CO.B.8 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. - F.BF.B.3 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. - G.CO.B.7 Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive the quadratic formula from this form. - A.REI.B.4a Solve quadratic equations by inspection (e.g., for x2 = 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 a +/- bi for real numbers a and b. - A.REI.B.4b 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). - S.CP.A.1 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. - S.CP.A.2 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. - G.CO.D.13 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. - G.CO.D.12 Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models. - S.ID.B.6a 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. - F.IF.B.6 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. - F.IF.B.5 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. - G.CO.B.6 Derive the equation of a parabola given a focus and directrix. - G.GPE.A.2 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. - G.C.A.3 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. - F.IF.B.4 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. - G.C.A.2 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. - A.SSE.B.4 Prove that all circles are similar. - G.C.A.1 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. - G.SRT.C.8 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. - S.CP.B.9 A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. - G.SRT.A.1a Explain and use the relationship between the sine and cosine of complementary angles. - G.SRT.C.7 Find the conditional probability of A given B as the fraction of Bs outcomes that also belong to A, and interpret the answer in terms of the model. - S.CP.B.6 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). - S.MD.B.7 The dilation of a line segment is longer or shorter in the ratio given by the scale factor. - G.SRT.A.1b (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). - S.MD.B.6 Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. - S.CP.B.7 Define appropriate quantities for the purpose of descriptive modeling. - N.Q.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. - G.SRT.A.2 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. - G.SRT.A.3 Combine standard function types using arithmetic operations - F.BF.A.1b Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). - G.GPE.B.5 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). - G.MG.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. - A.APR.A.1 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segments endpoints. - G.CO.C.9 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieris principle, and informal limit arguments. - G.GMD.A.1 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. - A.REI.C.7 (+) Give an informal argument using Cavalieris principle for the formulas for the volume of a sphere and other solid figures. - G.GMD.A.2 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. - G.GMD.A.3 Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. - F.IF.C.7e 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. - F.IF.C.8a Know there is a complex number i such that i^2 = -1, and every complex number has the form a + bi with a and b real. - N.CN.A.1 Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. - N.CN.A.2 Use the properties of exponents to interpret expressions for exponential functions. - F.IF.C.8b Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. - N.CN.A.3 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - F.IF.C.9 Solve quadratic equations with real coefficients that have complex solutions. - N.CN.C.7 Use coordinates to prove simple geometric theorems algebraically. - G.GPE.B.4 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. - A.CED.A.1 Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. - A.CED.A.4 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. - A.CED.A.2 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. - G.C.B.5 Interpret complicated expressions by viewing one or more of their parts as a single entity. - A.SSE.A.1b Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. - G.CO.C.10 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other and its converse, rectangles are parallelograms with congruent diagonals. - G.CO.C.11 Interpret parts of an expression, such as terms, factors, and coefficients. - A.SSE.A.1a Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. - G.SRT.B.5 Use the structure of an expression to identify ways to rewrite it. - A.SSE.A.2 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. - S.CP.A.5 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally and conversely the Pythagorean Theorem proved using triangle similarity. - G.SRT.B.4 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. - A.REI.A.1 Understand the conditional probability of A given B as P (A and B)/P (B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. - S.CP.A.3 Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. - F.IF.C.7b 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. - S.CP.A.4 Graph linear and quadratic functions and show intercepts, maxima, and minima. - F.IF.C.7a 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. - N.RN.A.1 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. - F.LE.A.3 Rewrite expressions involving radicals and rational exponents using the properties of exponents. - N.RN.A.2 Determine an explicit expression, a recursive process, or steps for calculation from a context. - F.BF.A.1a List of all Files Validated: imsmanifest.xml I_002df4e8-5223-385b-82a0-5be8e103f33a_R/BasicLTI.xml 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