# MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators*

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1 Content Standard 1.0 (HS) Patterns, Algebra and Functions Students will algebraically represent, model, analyze, and solve mathematical and real-world problems involving functional patterns and relationships. Category 1.1 Functional Representations 1.1.A2.1 write a polynomial function given its real zeros or a graph with real 1.1.PC.1 write a rational function or expression in an equivalent form. zeros. 1.1.A2.2 write a polynomial function given its real or complex zeros. 1.1.PC.2 write a rational function or expression in an equivalent form, including partial fractions. 1.1.A2.3 write a radical function or expression as an equivalent power function or expression. 1.1.PC.3 write an exponential function or expression in an equivalent form using laws of exponents 1.1.A2.4 write a rational function or expression in the form 1 n x as an 1.1.PC.4 write equivalent forms for rectangular and polar equations. equivalent power function or expression. 1.1.A2.5 write the equation and describe the characteristics of a circle, ellipse, and hyperbola centered at the origin, and parabola with 1.1.PC.5 write equivalent equations for functions and relations in parametric and rectangular form. vertex at the origin given its graph. 1.1.A2.6 write the equation and describe the characteristics of a conic 1.1.PC.6 write a vector equation of a line in 2-space. section given its graph. 1.1.A2.7 represent exponential functions, including base e, numerically, 1.1.PC.7 write an equation of a line or plane in 3-space. algebraically, and 1.1.A2.8 represent logarithmic functions, including base e, numerically, algebraically, and 1.1.PC.8 represent a piece-wise function numerically, algebraically and 1.1.A2.9 represent radical functions numerically, algebraically and 1.1.PC.9 represent parametric functions and relations numerically, algebraically, and 1.1.A2.10 represent piece-wise functions involving linear, absolute value, and step functions numerically, algebraically, and 1.1.PC.10 represent a series using summation notation. 1.1.A2.11 represent a system of two or more linear equations in matrix form. 1.1.PC.11 graph rational functions and describe their properties. 1.1.A2.12 represent arithmetic and geometric sequences explicitly and 1.1.PC.12 recursively. graph rational functions and describe their properties, including limit theory as it applies to determining their asymptotes and removable discontinuities. 1

2 1.1.A2.13 represent circles, ellipses, and hyperbolas centered at the origin, 1.1.PC.13 graph polar equations and describe their properties. and parabolas with vertex at the origin algebraically and 1.1.A2.14 represent conic sections algebraically and 1.1.PC.14 graph a point, line, or plane in 3-space. 1.1.A2.15 graph rational functions with numerators and/or denominators that are linear polynomials and describe their properties. 1.1.PC.15 determine the period, amplitude, phase shift, and/or vertical shift of a trigonometric function represented graphically or algebraically. 1.1.A2.16 determine the sum and n th term of an arithmetic or geometric series. 1.1.PC.16 determine the sum, if it exists, of an infinite geometric series. 1.1.PC.17 apply the fundamental trigonometric identities. 1.1.PC.18 expand and evaluate a series written in summation notation. 2

3 Category 1.2 Properties of Functions and Relations MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators* 1.2.A2.1 describe functions using domain and range, one-to-one, increasing, decreasing, continuous, maximum and minimum values, and 1.2.PC.1 describe the properties of rational functions, including domain, range, continuity, end behavior, horizontal and vertical asymptotes. symmetry. 1.2.A2.2 describe and compare the characteristics of polynomial functions, 1.2.PC.2 describe oblique asymptotes of rational functions. given numerical, graphical, and algebraic representations including domain and range, increasing, decreasing, continuous, maximum and minimum values, end behaviors, symmetry, zeroes and their multiplicity, and turning points. 1.2.A2.3 describe the properties of exponential functions including domain and range, increasing, decreasing, continuous, maximum and minimum values, end behaviors, symmetry, asymptotes, and zeros. 1.2.PC.3 describe the properties of linear, quadratic, power, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions 1.2.A2.4 describe the properties of logarithmic functions including domain 1.2.PC.4 describe the properties of a piece-wise function. and range, increasing, decreasing, continuous, maximum and minimum values, end behaviors, symmetry, asymptotes, and zeros. 1.2.A2.5 describe the inverse relationship between exponential and logarithmic functions numerically, graphically, and algebraically. 1.2.PC.5 describe the inverse relationship between trigonometric and inverse trigonometric functions, numerically, algebraically and 1.2.A2.6 describe the properties of radical functions. 1.2.PC.6 identify and distinguish between the graphs of linear, quadratic, power, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions. 1.2.A2.7 describe the properties of a piece-wise function involving linear, absolute value, and step functions. 1.2.A2.8 describe the properties of rational functions with numerators and/or denominators that are linear polynomials, including domain, range, continuity, end behavior, horizontal asymptotes, and vertical asymptotes. 1.2.A2.9 describe the properties of circles, ellipses, and hyperbolas centered at the origin and parabolas with vertex at the origin. 1.2.A2.10 describe the properties of circles, ellipses, hyperbolas, and parabolas. 1.2.A2.11 apply finite differences to find the degree of polynomial functions. 3

4 Category 1.3 Operations and Transformations on Functions 1.3.A2.1 describe the effect of transformations on the graph of f( x ), including a ( fx), f( x h),and f( x) + k. MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators* 1.3.PC.1 describe the effect of single or multiple transformations on the graph of ( ) a fx, f x h, f x, including ( ) ( ) f ( x) k, f ( ax), f x,and f x. 1.3.A2.2 describe the effect of transformations on graphs of exponential 1.3.PC.2 describe the effect of transformations on graphs of exponential x h functions, f( x) = ab ( ) + k. cx functions, f( x) = ab ( ). 1.3.A2.3 describe the effect of transformations on the graphs of radical 1.3.PC.3 describe the effect of transformations on graphs of logarithmic functions, f ( x) = n ( x h) + k. functions. 1.3.A2.4 perform operations on functions, including determining the 1.3.PC.4 describe the effect of transformations on the graphs of trigonometric composition of two functions. functions. 1.3.A2.5 determine the domain of the composition of two functions. 1.3.PC.5 describe the effect of transformations on a function with a restricted domain. 1.3.A2.6 determine whether two functions are inverses analytically and 1.3.A2.7 determine the inverse of a function. 1.3.A2.8 determine the standard form for conics. 1.3.A2.9 modify the domain of a function so that its inverse is a function. + ( ) ( ) 4

5 Category 1.4 Represent and Solve Real-World Problems The student will use numerical, algebraic, and graphical representations of functions and relations in order to solve real world problems. Indicators for Precalculus and Precalculus with Analysis 1.4.A2.1 solve polynomial equations using graphs, the factor theorem, rational root theorem, and the quadratic formula. 1.4.PC.1 solve exponential equations, including base e, using various methods including laws of logarithms. 1.4.A2.2 solve exponential equations using graphs, the laws of exponents, or the inverse relationship with logarithms. 1.4.PC.2 solve logarithmic equations, including base e, using laws of logarithms and exponents 1.4.A2.3 solve logarithmic equations using graphs and the inverse 1.4.PC.3 solve rational equations numerically, graphically, or algebraically. relationship with exponents. 1.4.A2.4 solve rational equations with linear denominators graphically, 1.4.PC.4 solve rational inequalities using a numeric method. numerically, and algebraically. 1.4.A2.5 solve radical equations graphically or algebraically, and check for 1.4.PC.5 solve trigonometric equations. extraneous roots. 1.4.A2.6 solve systems of two or more linear equations using a variety of 1.4.PC.6 solve systems of equations in polar form. methods. 1.4.A2.7 solve polynomial inequalities using the graph of the related 1.4.PC.7 interpret and solve problems involving exponential functions. polynomial function. 1.4.A2.8 solve polynomial inequalities of degree 2 algebraically. 1.4.PC.8 interpret and solve problems involving logarithmic functions. 1.4.A2.9 solve polynomial inequalities of degree greater than PC.9 interpret and solve problems involving piece-wise functions. algebraically. 1.4.A2.10 solve quadratic systems of equations and inequalities. 1.4.PC.10 interpret and solve problems involving trigonometric functions. 1.4.A2.11 interpret and solve problems involving polynomial functions. 1.4.PC.11 interpret and solve problems involving parametric functions and relations. 1.4.A2.12 interpret and solve problems involving exponential functions. 1.4.PC.12 make predictions using trigonometric or power mathematical models given a set of data. 1.4.A2.13 interpret and solve problems involving rational equations, including inverse and combined variation. 1.4.A2.14 interpret and solve problems involving radical functions. 1.4.A2.15 interpret and solve problems involving piece-wise functions including linear, absolute value, and step functions. 1.4.A2.16 make predictions using quadratic, exponential, or logarithmic mathematical models given a set of data. 1.4.A2.17 choose appropriate models, quadratic, exponential, or logarithmic, based on an analysis of the patterns of change in data. 1.4.A2.18 apply the Fundamental Theorem of Algebra. 5

6 Content Standard 2.0 (HS) Geometry and Measurement Students will apply the properties of one-, two-, and three-dimensional geometric figures to describe, reason, and solve problems about shape, size, position, and motion of objects, and students will identify attributes, units, and systems of measurements and apply a variety of techniques, formulas, tools, and technology for determining measurements. Category 2.1 Relationships Between Geometric Figures 2.1.A2.1 describe circles, ellipses, parabolas, and hyperbolas as a locus of points. Category 2.2 Measurement Applications 2.1.PC.1 write equivalent rectangular and polar forms of points on the coordinate plane. 2.1.PC.2 represent a vector in 2-space by its magnitude and direction, its initial and terminal point, and its component form. 2.1.PC.3 represent a vector in 3-space by its magnitude and direction, its initial and terminal point, and its component form. 2.1.PC.4 describe and apply the relationship between the trigonometry of the right triangle and the unit circle. 2.1.PC.5 describe and apply the relationship between the radian measure of a central angle of a circle and its intercepted arc. 2.1.PC.6 determine multiple polar form representations of a point. 2.1.PC.7 identify the pole and the polar axis, and plot points given in polar form. 2.1.PC.8 define and graph the six circular functions. 2.2.PC.1 write the value of an inverse trigonometric expression in radians. 2.2.PC.2 determine the distance from a point to a line in 2-space. 2.2.PC.3 determine the distance from a point to a plane in 3-space. 2.2.PC.4 determine the angular and linear velocities of an object moving at a constant speed on a circular path. 2.2.PC.5 evaluate a trigonometric expression using radian measure. 2.2.PC.6 convert degree measure to radian measure. 2.2.PC.7 measure indirectly using trigonometric relationships. 6

7 Content Standard 4.0 (HS) Number Relationships and Computation MCPS Algebra 2 and Precalculus Standards, Categories, and Indicators* Category 4.1 Number Relationships and Representations 4.1.A2.1 write equivalent forms for exponential and logarithmic expressions and equations. 4.1.A2.2 write equivalent expressions involving radicals and exponents, including negative exponents. 4.1.A2.3 represent complex numbers numerically and 4.1.A2.4 determine the magnitude of complex numbers. 4.1.A2.5 determine whether a square matrix has a multiplicative inverse. 4.1.A2.6 identify numbers as real or complex, and distinguish among rational, irrational, imaginary, and complex numbers. 4.1.PC.1 write equivalent rectangular and polar forms for complex numbers. 4.1.PC.2 represent complex numbers in polar form numerically and Category 4.2 Estimation and Computation 4.2.A2.1 perform operations on complex numbers. 4.2.PC.1 determine the product or quotient of two complex numbers in polar form. 4.2.A2.2 perform operations on matrices. 4.2.PC.2 determine a power or the roots of a complex number using DeMoivre s Theorem. 4.2.A2.3 evaluate logarithmic expressions. 4.2.PC.3 determine the sum, difference, scalar product, and dot product of vectors in 2-space. 4.2.A2.4 evaluate expressions involving radicals and exponents. 4.2.PC.4 determine the sum, difference, scalar product, dot product, and cross product of vectors in 3-space. 4.2.PC.5 evaluate a logarithm using the change of base rule. 4.2.PC.6 expand powers of binomials applying the binomial theorem, factorials, and combinatorics. 7

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