Washington+State+College+Readiness+Mathematics+Standards+and+Learning+Outcomes

1.1 Analyze a situation and describe the problem(s) to be solved. a. Extract necessary facts and relationships from the given information. b. Identify and supply additional information needed to solve each problem. || 1.2 Formulate a plan for solving the problem. a. Evaluate the advantages and disadvantages of different strategies, representations, and tools (including various forms of technology) for solving problems. b. Choose concepts, strategies, representations, models, and tools well-suited to solving the problem. || 1.3 Use logical reasoning and math knowledge to obtain and justify correct solutions. a. Correctly execute the plan to solve the problem. b. Evaluate and revise the solution method when it appears unlikely to produce a reasonable or suitably accurate result. c. Evaluate potential solutions for appropriateness, accuracy, and suitability to the context of the original problem. d. Provide oral, written, and/or symbolic explanations of the reasoning used to obtain the solution. e. Make and justify a multi-step mathematical argument providing appropriate evidence at each step. f.Use a variety of approaches – inductive and deductive, estimations, generalizations, formal, and/or informal methods of proof to justify solutions. ||  || 2.1 Summarize and interpret math information which may be in oral or written formulas. a. Summarize and interpret many different types of graphs. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Recognize and explain the meaning of information presented using mathematical notation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Create symbolic representations for situations described in everyday language. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">2.2 Use symbols, diagrams, graphs, and words to clearly communicate math ideas, reasoning and their implications. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Identify the variables and constants used. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Identify units associated with these variables and constants. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Use correct mathematical symbols, terminology, and notation. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">2.3 Produce mathematically valid oral, written, and/or symbolic arguments to support a position or conclusion, using both math and everyday language. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Create explanations that are appropriate to the needs of the and the situation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Use appropriate details or evidence to support the explanation. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">3.1 Use math ideas and strategies to analyze relationships within mathematics and in other disciplines and real life situations. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Compare and contrast the different mathematical concepts and procedures that could be used to complete a particular task. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Recognize patterns and apply mathematical concepts and procedures in other subject areas and real world situations. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">3.2 Understand the importance of math as a language. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Connect mathematical definitions and procedures with underlying math concepts. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Transfer mathematical vocabulary, concepts, and procedures to other disciplinary contexts and the real world. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Construct procedures and concepts from mathematical definitions. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">3.3 Make connections by using multiple representations, e.g. analytic, numeric, and geometric <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Integrate mathematical content areas by using multiple representations. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Use multiple representations to demonstrate understanding of links between math and other disciplines, and real world situations. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">3.4 Abstract math models from word problems, geometric problems, and applications. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Recognize and clarify mathematical structures that are embedded in other context. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Describe geometric objects and shapes algebraically. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Compare and contrast different mathematical models. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4.1 Understand the concept of real numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Explain the meaning of the square root of a number, include why negative numbers have no real square root. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Describe a situation that requires an irrational number and provide an example of an irrational number. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Apply the definition for negative integer exponents of real numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Represent real numbers with rational exponents. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Compare and order real numbers without a calculator using relationships between integers, and the effects of radicals and rational exponents on those <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">relationships. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4.2 Accurately and efficiently compute with real numbers in all forms, including rational exponents and scientific notation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Complete multi-step computations using the order of operations and the properties of operations (associative, commutative, distributive, etc.) in situations <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">involving combinations of real numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Recognize and justify the need for an exact answer in a given situation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Select and justify appropriate strategies and tools to compute the answer in a problem. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4.3 Apply estimation strategies using real numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Recognize and justify the sufficiency of estimating or approximating the result of a calculation involving real numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Use estimation to predict or verify the reasonableness of calculated results. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4.4 // Understand the concept of complex numbers and perform computations with complex numbers. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Add, subtract, multiply and divide complex numbers; express in standard form and explain the properties (i.e. why useful ////<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">; when used) // //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Describe a situation that requires a complex number (include an algebraic example and a graphical example) //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">5.1 Make and test conjectures about 2-D figures (polygons, and circles) and 3-D figures (spheres and right prisms and pyramids, right circular cylinders and cones) or figures constructed from these shapes. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Use physical, symbolic, and technological models to explore conjectures. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">5.2 Present the relevant features of a physical situation using 2-D figures with and without a coordinate system. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Use basic 2-D figures such as circles or polygons to represent objects essential to a situation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Include additional line segments to represent important known or unknown distances. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Introduce a coordinate system when useful for describing the position of objects in a situation. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">5.3 Use properties of and relationships between 2-D and 3-D figures to draw and justify conclusions about a situation represented with such figures with or without a coordinate system. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Inductively generate a conjecture and deductively support it. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Apply and justify the applicability of transformations, congruence, similarity, ratios, and proportions in problem solving situations. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Distinguish between area and perimeter of 2-D figures, surface area and volume of 3-D figures. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Calculate the area and perimeter of circles, triangles, quadrilaterals, and regular polygons. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Use the Pythagorean Theorem (or distance formula) in 2-D and 3-D situations when appropriate to compute unknown distances. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">f. Calculate the volume and surface area of spheres, right rectangular prisms, and right circular cylinders, right prisms, right pyramids, and right cones. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">// g. Graph ellipses and hyperbolas whose axes are parallel to the x and y axes, and demonstrate understanding of the relationship between their standard // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">algebraic form and their graphical characteristics. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">5.4 Recognize and apply the basic right-triangle trigonometric relationships (sine, cosine, and tangent) to solve problems. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Use sine, cosine or tangent to find unknown distances and angles. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Use the inverse of sine, cosine, or tangent to find the measure of a missing angle. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Understand the relationship of cotangent, secant, and cosecant to basic right-triangle ratios. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Use Law of Cosines and Law of Sines to solve problems. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6.1 Use empirical/experimental and theoretical probability to investigate, represent, solve and interpret the solutions to problems involving uncertainty or counting techniques. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Describe and apply the concept of complementary, mutually exclusive, independent and compound events. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Describe and apply procedures for computing and comparing theoretical probabilities and empirical/experimental results. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Describe and apply procedures for counting techniques such as the Fundamental Counting Principle, permutations, and combinations. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6.2 Develop informative tables, plots and graphic displays to accurately represent and study data. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Use and interpret pie charts, bar graphs, histograms, box and whisker plots, scatter plots, stem and leaf, and line graphs. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Analyze data displays to evaluate the reasonableness of claims, reports, studies, and conclusions. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Justify the use of appropriate graphical displays to accurately represent and study data. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Determine trends, predicted values and possible causes of skewed and clustered distributions. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6.3Develop and evaluate inferences and predictions that are based on data. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Use measures of central tendency (mean, median, mode) and spread (range, quartiles) to summarize data, draw inferences, make predictions, and <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">justify conclusions. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Develop and conduct an investigation drawing appropriate conclusions through the use of statistical measures of center, frequency, and spread, <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">combined with graphical displays. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6.4 Create and evaluate the suitability of linear models for a data set. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Create, select, and justify an appropriate linear model for a given set of data. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Use reasonable models to make predictions and justify conclusions. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Recognize when arguments based on data confuse correlation with causation. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7.1 Recognize and use appropriate concepts, procedures, definitions and properties to simplify expressions and solve equations. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Explain the distinction between a factor and a term. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Explain the distinction between an expression and equation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Explain the distinction between simplify and solve. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Know what it means to have a solution to an equation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Use properties of equality to solve an equation through a series of equivalent equations. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">f. Use appropriate properties to simplify an expression resulting in an equivalent expression. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">g. Recognize the equivalence between expressions with rational exponents and radicals. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7.2 Combine and simplify algebraic expressions that contain polynomials, rational expressions, radicals, or rational exponents // and logarithm expressions // .. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Find the sum, difference, or product of two polynomials, then simplify the result. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Factor out the greatest common factor from polynomials of any degree //and from expressions involving rational exponents. // <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Factor quadratic polynomials with integer coefficients into a product of linear terms. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Simplify quotients of polynomials given in factored form, or in a form which can be factored // or determine if irreducible over the real numbers. // <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Add, subtract, multiply and divide two rational expressions of the form where //a//, //b//, and //c// are real numbers such that bx + c ≠ 0 and <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">// and of the form where p(x) and q(x) are polynomials .// <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">f. Simplify products and quotients of single-term expressions with rational exponents (rationalizing denominators is not necessary). <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">// g. Simplify products and quotients of single-term expressions with rational exponents and rationalize denominators when necessary. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">h. Simplify rational expressions that involve complex fractions. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">i. Simplify logarithmic expressions. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">j. Factor polynomials over the complex numbers, if possible, and relate to the Fundamental Theorem of Algebra. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7.3 Solve various types of equations and inequalities numerically, graphically, and algebraically and in the context of the problem distinguish between exact and <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">approximate answers. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Solve linear equations in one variable. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Solve linear inequalities in one variable, including those involving “and” and “or”. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Solve systems of linear // and nonlinear // equations in two variables. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Solve linear inequalities in two variables (graphically only) // and nonlinear inequalities – numerically, graphically and algebraically. // <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Solve absolute value equations of the form. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">f.Use a variety of strategies to solve quadratic equations including those with irrational solutions and recognize when solutions are non-real. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">// Simplify complex solutions and check algebraically.Solve quadratic equations by completing the square and taking roots. // <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">g. Solve equations in one variable containing a single radical // or two radicals. // <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">h. Solve exponential equations in one variable (numerically, graphically // and algebraically ).// <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">i.Solve rational equations in one variable that can be transformed into an equivalent linear or quadratic equation <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">(limited to monomial or binomial denominators). <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">j. Solve literal equations (formulas) for a particular variable. <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">k. //Solve logarithmic equations.// <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">l.//Solve rational equations and inequalities with polynomial denominators.// <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">m. //Solve absolute value and polynomial inequalities and justify the solution.// <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7.4 // Demonstrate an understanding of matrices and their application. // <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">a. //Add, subtract and multiply 2 by 2 matrices.// //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Find the inverse of a 2 by 2 matrix. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Evaluate the determinant of 2 by 2 and 3 by 3 matrices. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Solve 2 by 2and 3 by 3systems of linear equations using matrices or the determinant. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7.5 // Demonstrate an understanding of sequences and series //. <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">a. //Identify a sequence as arithmetic or geometric, write an expression for the general term, and evaluate the sum of a series based upon the sequence.// <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">b. //Construct terms of a series from the general formula and use summation notation.// <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">c.//Use induction to prove theorems about sums of series.// <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8.1 Recognize functional relationships presented in words, tables, graphs, and symbols. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Recognize whether a relationship given in a symbolic, graphical, or tabular form is a function. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Determine the domain // and range // of a function. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Understand and interpret function notation, particularly as it relates to graphic displays of data. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">// d. Demonstrate and understanding of parametric equations. // || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8.2 Represent basic function (linear, quadratic, exponential, and reciprocal) and piecewise-defined functions (varying over subintervals of the domain) using and translating among words, tables, graphs and symbols.Include advanced functions (cubic, quartic, logarithmic, square root, cube root, absolute value, and rational fuctions of the type ). <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Evaluate functions to generate a graph. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Describe relationships between the algebraic features of a function and the features of its graph and/or its tabular representation. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c.Use simple transformations (horizontal and vertical shifts, reflections about axes, //shrinks or stretches//) to create the graphs of new functions using linear, <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">quadratic, and/or absolute value functions, // cubic, quartic, exponential, logarithmic, square root, cube root, absolute value, piecewise, and rational // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">functions of the type //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">, <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">// d. Algebraically construct new functions using addition and subtraction (e.g. profit function) multiplication, division, and composition. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Given an algebraic representation of a rational function, find the intercepts, asymptotes (horizontal, vertical, and slant), and holes (discontinuities), then // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">sketch the graph. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">f.Given a graph or graphical features, including degrees, intercepts, asymptotes, and/or holes (discontinuities), generate an algebraic representation of a // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">polynomial or rational function. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">g.Sketch the graph of a polynomial given the degree, zeros, max/min values, and/or initial conditions. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">h.Graphically/numerically construct new functions using addition, subtraction, and composition. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">i.Identify the components of composite functions (e.g. given find suitable functions f,g, and h) and determine the domain and range // <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;"> <span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;"> //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8.3 Analyze and interpret features of a function. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Describe patterns in the functions rate of change, identifying intervals of increase, decrease, constancy, and, if possible, relate them to the functions <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">description in words or graphically (using graphic calculator). <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Identify y-intercepts and zeros using symbols, graphs, and tables. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Identify extrema and trends using graphs and tables. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">// d. Recognize and sketch, without the use of technology the graphs of the following families of functions: linear, quadratic, cubic, quartic, exponential, // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">logarithmic, square root, cube root, absolute value, and rational functions of the type, using the symmetry of odd and even functions when // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">appropriate. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Understand the relationship between the degree of a polynomial and the number of roots: interpret the multiplicity of roots graphically. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8.4 Model situations and relationships using a variety of basic functions (linear, quadratic, exponential, logarithmic and reciprocal) and piecewise-defined functions. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Choose a function suitable for modeling a real world situation presented using words or data. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Determine and interpret the meaning of rates of change, intercepts, zeros, extrema, and trends. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Abstract mathematical models from word problems and interpret solutions in the context of these source problems. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Identify and justify whether a result obtained from a function model has real world significance. || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8.5 // Recognize, analyze, and interpret inverse functions. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Explain the conceptual meaning of inverse functions using graphs, tables, in words, and arrow diagrams. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Define what it means for a functions to be one-to-one, identify examples and non-examples (algebraic and graphical), and generate examples (algebraic // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">and graphical). // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Find and verify the inverse function algebraically, graphically, and numerically, restrict the domain of a function when necessary ////<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">. // || <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8.6 // Recognize analyze, interpret, and model with trigonometric functions. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">a. Represent and interpret trig functions using the unit circle. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">b. Demonstrate an understanding of radians and degrees by converting between units, finding areas of sectors and determining arc lengths of circles. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">c. Find exact values (without technology) of sine, cosine and tangent for unit circle and for multiples of and ; evaluate trigonometric ratios; and // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">distinguish between exact and approximate values when evaluating trig ratios/functions. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">d. Sketch graphs of sine, cosine, and tangent functions, without technology; identify the domain, range, intercepts, and asymptotes. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">e. Use transformations (horizontal and vertical shifts, reflections about axes, period and amplitude changes) to create new trig functions // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">(algebraic, tabular, and graphical). // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">f. Know and apply the identity and generate related identities; apply sum and half-angle identities. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">g. Solve linear and quadratic equations involving trig functions. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">h. Generate algebraic and graphical representation of inverse trig functions (arcsin, arcos, actan) and determine domain and range. // //<span style="color: #3366ff; font-family: 'Arial','sans-serif'; font-size: 10pt;">i. Use trig and inverse trig functions to solve application problems. //<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Washington ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> State ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> College Readiness Mathematics Standards and Learning Outcomes -page 1 ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc) // Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">1. Reasoning/Problem Solving - Student uses logical reasoning and math knowledge to define and solve problems ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc) // Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">1. Reasoning/Problem Solving - Student uses logical reasoning and math knowledge to define and solve problems ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">1. Reasoning/Problem Solving - Student uses logical reasoning and math knowledge to define and solve problems ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">2. Communication - The student can interpret and communicate math knowledge and relationships in both math and everyday language. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">2. Communication - The student can interpret and communicate math knowledge and relationships in both math and everyday language. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">3. Connections - The student extends math thinking across math content areas, and to other disciplines and real life situations. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">3. Connections - The student extends math thinking across math content areas, and to other disciplines and real life situations. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Washington ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> State ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> College Readiness Mathematics Standards and Learning Outcomes -page 2 ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4. Number Sense - The student accurately describes and applies concepts and procedures related to real and complex numbers. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4. Number Sense - The student accurately describes and applies concepts and procedures related to real and complex numbers. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">4. Number Sense - The student accurately describes and applies concepts and procedures related to real and complex numbers. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">5. Geometry - The student make hypotheses, models situations, draws conclusions, and supports claims using geometric concepts and procedures. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">5. Geometry - The student make hypotheses, models situations, draws conclusions, and supports claims using geometric concepts and procedures. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Washington ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> State ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> College Readiness Mathematics Standards and Learning Outcomes -page 3 ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6. Probability/Statistics - The student accurately describes and applies concepts and procedures from probability and statistics to analyze data ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6. Probability/Statistics - The student accurately describes and applies concepts and procedures from probability and statistics to analyze data ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">6. Probability/Statistics - The student accurately describes and applies concepts and procedures from probability and statistics to analyze data ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Washington ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> State ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> College Readiness Mathematics Standards and Learning Outcomes -page 4 ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7. Algebra - The student accurately describes and applies concepts and procedures from algebra. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7. Algebra - The student accurately describes and applies concepts and procedures from algebra. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7. Algebra - The student accurately describes and applies concepts and procedures from algebra. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Washington ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> State ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> College Readiness Mathematics Standards and Learning Outcomes -page 5 ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7. Algebra (continued) - The student accurately describes and applies concepts and procedures from algebra. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7. Algebra (continued) - The student accurately describes and applies concepts and procedures from algebra. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">7. Algebra (continued) - The student accurately describes and applies concepts and procedures from algebra. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8. Functions - The student accurately describes and applies function concepts and procedures to understand mathematical relationships. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8. Functions - The student accurately describes and applies function concepts and procedures to understand mathematical relationships. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Washington ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> State ****<span style="font-family: 'Arial','sans-serif'; font-size: 10pt;"> College Readiness Mathematics Standards and Learning Outcomes -page 6 ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8. Functions (continued)- The student accurately describes and applies function concepts and procedures to understand mathematical relationships. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">Note: Evidence of learning appears after letters ( a., b., c., etc)// Text in blue italics indicate extra expectations. (STEM) // ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8. Functions (continued)- The student accurately describes and applies function concepts and procedures to understand mathematical relationships. ** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 10pt;">8. Functions (continued)- The student accurately describes and applies function concepts and procedures to understand mathematical relationships. ** ||