Muskogee Public Schools Curriculum Map

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1 Muskogee Public Schools Curriculum Map Course: Algebra II Grade Level: 9-12 Nine- 1 st Nine Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers. Use a number line to graph and order real numbers. Identify properties of and use operations with real numbers. Evaluate algebraic expression. Simplify algebraic expressions by combining like terms. Vocabulary: Variable, Values, Variable Expression, Evaluating the expression, Unit Analysis, and Verbal Model. Numerical Expression, Base of a power, Exponent, Power, Algebraic Expression, Mathematical Model, Terms of an Expression, Coefficient, Like Terms, Constant Term, Equivalent Algebraic Expressions, and Identity. Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. 2. Systems of Equations a. Model a situation that can be described by a system of equations or inequalities and use the model to answer questions about the situation. b. Solve systems of linear equations and inequalities using various methods and tools which may include substitution, Solve linear equations. Use linear equations to solve real-life Solve simple inequalities. Solve compound inequalities. Solve absolute value equations and inequalities. Use absolute value equations and inequalities to solve real-life Equation, Linear Equation, Solution of an equation in one variable, Equivalent Equations, Algebraic Model, Linear Inequality in One Variable, Solution of an Inequality in One Variable, Graph of an Inequality, Compound Inequality, and Absolute value of a real number.

2 1 st Nine elimination, matrices, graphing, and graphing calculators. Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. 1. Functions and Function Notation b. Add, subtract, multiply, and divide functions using function notation. d. Use algebraic, interval, and set notations to specify the domain and range of functions of various types. Represent relations and functions. Graph and evaluate linear functions. Use the slope-intercept form of a linear equation to graph linear equations. Use the standard form of a linear equation to graph linear equations. Write Linear Equations. Write direct variation equations. Relation, Domain of a Relation, Range of a Relation, Function, Ordered Pair, Coordinate Plane, Equation in Two Variables, Solution of an Equation in Two Variables, Independent Variable, Dependant Variable, Graph of an Equation in Two Variables, Linear Function, Function Notation, X and Y- intercept, Slope-intercept Form, Standard Form of a Linear Equation, Direct Variation, and Constant of Variation. Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data. 1. Analysis of Collected Data Involving Two Variables a. Interpret data on a scatter plot using a linear, exponential, or quadratic model/equation. b. Identify whether the model/equation is a curve of best fit for the data, using various methods and tools which may include a graphing calculator. Use a scatter plot to identify the correlation shown by a set of data. Approximate the best-fitting line for a set of data. Scatter Plot, Positive, Negative, and Relatively No Correlation, Standard 2: 2 a and b (written above) Graph linear inequalities in two variables. Linear Inequality in Two Variables, Solution of an Inequality in Two

3 1 st Nine Use linear inequalities to solve real-life Variables, and Half-planes. Represent piecewise functions. Use piecewise functions to model reallife quantities. Piecewise Function and Step Function. Represent absolute value functions. Use absolute value functions to model real-life situations. Vertex of an Absolute Value Graph Standard 2: 2 a and b (written above) Graph and solve systems of linear equations in two variables. Use linear systems to solve real-life Use algebraic methods to solve linear systems. Use linear systems to model real-life situations. Graph a system of linear inequalities to find the solutions of the system. Use systems of linear inequalities to solve real-life Solve linear programming Use linear programming to solve reallife problems Graph linear equations in three variables and evaluate linear functions in two variables. Use functions of two variables to model real-life situations. Solve systems of linear equations in three variables. Use linear systems in three variables to System of Two Linear Equations, Solution of a System of Linear Equations, System of linear inequalities in two variables, Solution of a system of linear inequalities, Graph of a system of linear inequalities, Optimization, Linear Programming, Objective Function, Constraints, Feasible Region, Threedimensional coordinate system, Z-axis, Ordered Triple, Octants, Linear Equation in Three Variables, Function of Two Variables, System of Three Linear Equations, and Solution of a System of Three Linear Equations.

4 model real-life situations. 2 nd Nine Add and subtract matrices, multiply a matrix by a scalar, and solve matrix equations. Use matrices in real-life situations. Multiply two matrices. Use matrix multiplication in real-life situations. Evaluate determinants of and matrices. Use Cramer s rule to solve systems of linear equations. Matrix, Dimensions of a Matrix, Entries of a Matrix, Equal Matrices, Scalar, Scalar Multiplication, Determinant, Cramer s Rule, and Coefficient Matrix. Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. 1. Functions and Function Notation a. Recognize the parent graphs of polynomial, exponential, radical, quadratic, and logarithmic functions and predict the effects of transformations on the parent graphs, using various methods and tools which may include graphing calculators. 2. Systems of Equations a. Model a situation that can be described by a system of equations or Graph quadratic functions. Use quadratic functions to solve real-life Quadratic Function, Parabola, Vertex of a Parabola, Axis of Symmetry of a Parabola, and Standard Form.

5 2 nd Nine inequalities and use the model to answer questions about the situation. 3. Quadratic Equations and Functions a. Solve quadratic equations by graphing, factoring, completing the square and quadratic formula. Factor quadratic expressions and solve quadratic equations by factoring. Find zeros of quadratic functions. Solve quadratic equations by finding square roots. Use quadratic equations to solve real-life Binomial, Trinomial, Factoring, Monomial, Quadratic Equation in One Variable, Zero of a Function, Square Root, Radical Sign, Radicand, Radical, Rationalizing the Denominator Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers. 3. Complex Numbers *a. Recognize that to solve certain problems and equations, number systems need to be extended from real numbers to complex numbers. Note: Asterisks (*) have been used to identify standards and objectives that must be assessed by the local school district. All other skills may be assessed by the Oklahoma School Testing Program (OSTP). b. Add, subtract, multiply, divide, and simplify expressions involving complex numbers. Solve quadratic equations with complex solutions and perform operations with complex numbers. Apply complex numbers to fractal geometry. Imaginary Unit i, Complex Number, Standard Form of a complex number, Imaginary Number, Pure Imaginary Number, Complex Plane, Complex Conjugates, and Absolute Value of a Complex Number Standard 2: 3 a (written above) b. Graph a quadratic function and Solve quadratic equations by completing equations the square. Completing the Square

6 identify the x- and y-intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator. c. Model a situation that can be described by a quadratic function and use the model to answer questions about the situation. Use completing the square to write quadratic functions in vertex form. Solve quadratic equations using the quadratic formula. Use the quadratic formula in real-life situations. Graph quadratic inequalities in two variables. Solve quadratic inequalities in one variable. Discriminant of a Quadratic Equation, Quadratic Inequality in Two Variables, and Quadratic Inequality in One Variable. Write quadratic functions given characteristics of their graphs. Use technology to find quadratic models for real-life data. Best-fitting Quadratic Model Use properties of exponents to evaluate and simplify expressions involving powers. Use exponents and scientific notation to solve real-life Scientific Notation 3 rd Nine Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers. 2. Polynomial and Rational Expressions a. Divide polynomial expressions by lower degree polynomials. Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, Evaluate a polynomial function. Graph a polynomial function. Add, subtract, and multiply polynomials. Use polynomial operations in real-life Factor polynomial expressions. Use factoring to solve polynomial equations. Divide polynomials and relate the result to the remainder theorem and the factor theorem. Use polynomial division in real-life Polynomial Function, Leading Coefficient, Constant Term, Degree, Standard Form of a Polynomial Function, End Behavior, Factor by Grouping, Quadratic Form, Polynomial Long Division, and Synthetic Division.

7 3 rd Nine zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. 6. Polynomial Equations and Functions a. Solve polynomial equations using various methods and tools which may include factoring and synthetic division. Find the rational zeros of a polynomial function. Use polynomial equations to solve reallife Use the fundamental theorem of algebra to determine the number of zeros of a polynomial function. Use technology to approximate the real zeros of a polynomial function. Repeated solution c. Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools which may include a graphing calculator. Analyze the graph of a polynomial function. Use the graph of a polynomial function to answer questions about real-life situations. Local Maximum and Minimum. Use finite differences to determine the degree of a polynomial function that will fit a set of data. Use technology to find polynomial models for real-life data. Finite Differences Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers. Evaluate nth roots of real numbers using both radical notation and rational exponent notation. Use nth roots to solve real-life Use properties of rational exponents to evaluate and simplify expressions. Nth Root of A, Index of a Radical, Simplest Form of Radical, and Like Radicals.

8 3 rd Nine 1. Rational Exponents a. Convert expressions from radical notations to rational exponents and vice versa. b. Add, subtract, multiply, divide, and simplify radical expressions and expressions containing rational exponents. Use properties of rational exponents to solve real-life Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. 1. Functions and Function Notation b. Add, subtract, multiply, and divide functions using function notation. c. Combine functions by composition. e. Find and graph the inverse of a function, if it exists. Perform operations with functions including power functions. Use power functions and function operations to solve real-life Power Function, Composition, Inverse Relation, and Inverse Functions Graph square root and cube root functions. Use square root and cube root functions to find real-life quantities. Radical Function Standard 1:1 a and b (written above) Solve equations that contain radicals or rational exponents. Use radical equations to solve real-life Extraneous Solution Standard 3: Data Analysis and Use measures of central tendency and Statistics, Mean, Median, Mode,

9 Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data. * 2. Measures of Central Tendency and Variability a. Analyze and synthesize data from a sample using appropriate measures of central tendency (mean, median, mode, weighted average). b. Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation). measures of dispersion to describe data sets. Use box-and-whisker plots and histograms to represent data graphically. Measures of Dispersion, Range of Data Values, Standard Deviation, Box-and- Whisker Plot, Lower and Upper Quartile, Histogram, Frequency of Data Values, and Frequency Distribution. Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. 5. Exponential and Logarithmic Functions a. Graph exponential and logarithmic functions. Graph exponential growth functions. Use exponential growth functions to model real-life situations. Graph exponential decay functions. Use exponential decay functions to model real-life situations. Use the number e as the base of exponential functions. Use the natural base e in real-life situations. Evaluate logarithmic functions. Graph logarithmic functions. Use properties of logarithms. Use properties of logarithms to solve real-life Exponent Function, Asymptote, Exponential Growth Function, Growth Factor, Exponential Decay Function, Decay Factor, Common and Natural Logarithm

10 4 th Nine Standard 1: Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers. 1. Rational Exponents a. Convert expressions from radical notations to rational exponents and vice versa. b. Add, subtract, multiply, divide, and simplify radical expressions and expressions containing rational exponents. 2. Polynomial and Rational Expressions a. Divide polynomial expressions by lower degree polynomials. b. Add, subtract, multiply, divide, and simplify rational expressions, including complex fractions. 3. Complex Numbers *a. Recognize that to solve certain problems and equations, number systems need to be extended from real numbers to complex numbers. Note: Asterisks (*) have been used to identify standards and objectives that must be assessed by the local school district. All other skills may be assessed by the Oklahoma School Testing

11 4 th Nine Program (OSTP). b. Add, subtract, multiply, divide, and simplify expressions involving complex numbers. Standard 2: Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions. 1. Functions and Function Notation a. Recognize the parent graphs of polynomial, exponential, radical, quadratic, and logarithmic functions and predict the effects of transformations on the parent graphs, using various methods and tools which may include graphing calculators. b. Add, subtract, multiply, and divide functions using function notation. c. Combine functions by composition. d. Use algebraic, interval, and set notations to specify the domain and range of functions of various types. e. Find and graph the inverse of a function, if it exists. 2. Systems of Equations a. Model a situation that can be described by a system of equations or inequalities and use the model to answer questions about the situation. b. Solve systems of linear equations and

12 inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators. *c. Use either one quadratic equation and one linear equation or two quadratic equations to solve 3. Quadratic Equations and Functions a. Solve quadratic equations by graphing, factoring, completing the square and quadratic formula. b. Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator. c. Model a situation that can be described by a quadratic function and use the model to answer questions about the situation. 4. Identify, graph, and write the equations of the conic sections (circle, ellipse, parabola, and hyperbola). 5. Exponential and Logarithmic Functions a. Graph exponential and logarithmic functions. b. Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another. c. Model a situation that can be described by an exponential or logarithmic function and use the model

13 to answer questions about the situation. 6. Polynomial Equations and Functions a. Solve polynomial equations using various methods and tools which may include factoring and synthetic division. b. Sketch the graph of a polynomial function. c. Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools which may include a graphing calculator. d. Model a situation that can be described by a polynomial function and use the model to answer questions about the situation. 7. Rational Equations and Functions a. Solve rational equations. b. Sketch the graph of a rational function. c. Given the graph of a rational function, identify the x- and y-intercepts, vertical asymptotes, using various methods and tools which may include a graphing calculator. d. Model a situation that can be described by a rational function and use the model to answer questions about the situation. Standard 3: Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of

14 data. 1. Analysis of Collected Data Involving Two Variables a. Interpret data on a scatter plot using a linear, exponential, or quadratic model/equation. b. Identify whether the model/equation is a curve of best fit for the data, using various methods and tools which may include a graphing calculator. * 2. Measures of Central Tendency and Variability a. Analyze and synthesize data from a sample using appropriate measures of central tendency (mean, median, mode, weighted average). b. Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation). c. Use the characteristics of the Gaussian normal distribution (bell-shaped curve) to solve d. Identify how given outliers affect representations of data. 3. Identify and use arithmetic and geometric sequences and series to solve

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