WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Algebra II

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1 WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Algebra II (s) ESS Vocabulary AII.4 Absolute Value Equations and Inequalities Absolute Value Equations and Inequalities FIRST QUARTER union, intersection, linear inequality, absolute value, distance, linear equation, compound inequality, absolute value inequality AII.6, AII.7, AII.8 Functions Transformational Graphing Rational Functions: Intercepts, Asymptotes, a Functions: Domain, Range, End Behavior, Incre Inverse Functions Composite of Functions Factors, Zeros, and Solutions transformation, vertex, absolute value, quadratic term, reflection, logarithmic function, exponential function, x-intercept, y-intercept, domain, range, zeros, discontinuous domain, discontinuous range, point of discontinuity, asymptote, increasing function, decreasing function, end behavior, input, output, composition of functions, one-to-one function composite functions, inverse functions, solution, factor, slope, zeros of a function Days Assessed 4.a Solve absolute value equations and inequalities algebraically and graphically. 4.g Apply an appropriate equation to solve a real-world problem. 7.a Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically b Describe restricted/discontinuous domains and ranges. 6.a Recognize graphs of parent functions. (Absolute value, square foot, Cube root, Rational, Polynomial) 6.d Given the graph of a function, identify the parent function. 1

2 Days Assessed 6.b 6.c 6.f 6.e 8.a 7.c Given a transformation of a parent function, identify the graph of the transformed function. Given the equation and using a transformational approach, graph a function. Using a transformational approach, write the equation of a function given its graph. Given the graph of a function, identify the transformations that map the preimage to the image in order to determine the equation of the image. Describe the relationships among solutions of an equation, zeros of a function, x-intercepts of a graph, and factors of a polynomial expression. Given the graph of a function, identify intervals on which the function is increasing and decreasing. 7.e Describe the end behavior of a function. 8.e Given a polynomial equation, determine the number of real solutions and nonreal solutions 8.b Define a polynomial function, given its zeros. 8.c 7.d Determine a factored form of a polynomial expression from the x-intercepts of the graph of its corresponding function. Find the equations of vertical and horizontal asymptotes of functions. 7.f Find the inverse of a function 7.g Graph the inverse of a function as a reflection across the line y = x. 7.j Find the composition of two functions. 7.k Use composition of functions to verify two functions are inverses. 7.h 7.i Common Assessment Investigate exponential and logarithmic functions, using the graphing calculator. Convert between logarithmic and exponential forms of an equation with bases consisting of natural numbers. 2

3 (s) ESS WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Algebra II AII.2 Sequences Series Arithmetic and Geometric Sequences and Series SECOND QUARTER AII.1, AII.4 Radical Expressions Equations Exponents and Radicals Radical Equations AII.10 Variations Types of Variations AII.11 Statistics Normal Distributions Vocabulary recursive formula, explicit formula, sequence, series, arithmetic sequence, arithmetic series, infinite series, geometric sequence, geometric series integer, volume, surface area, index, radicand, radical, square, square root, radical, power, radical algebraic equations, extraneous solution, radicand, index varies directly, direct variation, direct proportion, inverse variation, joint variation, combined variation mean, median, mode, standard deviation, z-score, probability, quartile, normal distribution, normal curve, percentile, area under a curve, probability density function, discrete vs. continuous data Days Assessed 2.a Distinguish between a sequence and a series. 2.b Generalize patterns in a sequence using explicit and recursive formulas. 2.c Use and interpret the notations, n, n th term, and an. 4 2.d 2.e Given the formula, find an (the n th term) for an arithmetic or a geometric sequence. Given formulas, write the first n terms and find the sum, Sn, of the first n terms of an arithmetic or geometric series. 2.f Given the formula, find the sum of a convergent infinite series. 2.g Model real-world situations using sequences and series.

4 Days Assessed 1.d 1.e Simplify radical expressions containing positive rational numbers and variables. Convert from radical notation to exponential notation, and vice versa. 1.f Add and subtract radical expressions. 7 1.g 4.e 4.f Multiply and divide radical expressions not requiring rationalizing the denominators. Solve an equation containing a radical expression algebraically and graphically. Verify possible solutions to an equation containing radical expressions. 4.g Apply an appropriate equation to solve a real-world problem. Common Assessment 10.b Translate y is directly proportional to x as y = kx. 10.c Translate y is inversely proportional to x as y = k x a Translate y varies jointly as x and z as y = kxz. 10.d 10.e Given a situation, determine the value of the constant of proportionality Set up and solve problems, including real-world problems, involving inverse variation, joint variation, and a combination of direct and inverse variations. 11.a Identify the properties of a normal probability distribution. 11.b 11.c 11.d 11.e Benchmark Test Describe how the standard deviation and the mean affect the graph of the normal distribution. Compare two sets of normally distributed data using a standard normal distribution and z-scores. Represent probability as area under the curve of a standard normal probability distribution. Use the graphing calculator or a standard normal probability table to determine probabilities or percentiles based on z-scores. 4

5 (s) ESS Vocabulary THIRD QUARTER WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Algebra II AII. Complex Numbers AII.4 Quadratics Complex Numbers Quadratic Equations real numbers, rational numbers, irrational numbers, integers, whole numbers, natural numbers, commutative, associative, closed, complex numbers, pure imaginary numbers, quadratic, factor, zero, quadratic formula, x- intercepts, solving over the set of complex numbers, nature of solution, conjugate, discriminant, solution, factor, slope, x- intercept, y-intercept, zeros of a function THIRD QUARTER AII.5 Non-Linear Systems Nonlinear Systems of Equations circle, parabola, quadratic, linear, linear system, points of intersection, inverse system, quadratic system, quadratic term, nonlinear system, linearquadratic system, quadratic-quadratic system AII.1, AII.8 Factoring Factoring Factors, Zeros, and Solutions factor, prime, trinomial, composite, greatest common factor, binomial, sum and difference of two cubes, perfect square trinomial, solution, factor, slope, x-intercept, y-intercept, zeros of a function 5

6 Days 10 7 Assessed.a Recognize that the square root of 1 is represented as i..d Simplify powers of i..g Write a real number in a+bi form..h Write a pure imaginary number in a+bi form..c Simplify radical expressions containing negative rational numbers and express in a+bi form. Place the following sets of numbers in a hierarchy of subsets:.f complex, pure imaginary, real, rational, irrational, integers, whole, and natural..b Determine which field properties apply to the complex number system..e Add, subtract, and multiply complex numbers. 4.c Calculate the discriminant of a quadratic equation to determine the number of real and complex solutions. 4.b Solve a quadratic equation over the set of complex numbers using an appropriate strategy. Recognize that the quadratic formula can be derived by applying 4.h the completion of squares to any quadratic equation in standard form. 4.g Apply an appropriate equation to solve a real-world problem. 5.c Solve a quadratic-quadratic system of two equations algebraically and graphically. 5.b Solve a linear-quadratic system of two equations algebraically and graphically. 5.a Predict the number of solutions to a nonlinear system of two equations. Factor polynomials by applying general patterns including 1.h difference of squares, sum and difference of cubes, and perfect square trinomials. 1.j Verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials. 1.i Factor polynomials completely over the integers. 8.d For a function, identify zeros of multiplicity greater than 1 and describe the effect of those zeros on the graph of the function. 6

7 (s) ESS Vocabulary WESTMORELAND COUNTY PUBLIC SCHOOLS Integrated Instructional Pacing Guide and Checklist Algebra II AII.1, AII.4 Rational Expressions Rational Equations Rational Expressions Rational Equations simplify, factor, undefined, rational expression, solution, replacement set, algorithm, numerator, denominator, least common multiple, rational algebraic equations, extraneous solution FOURTH QUARTER AII.9, AII.4 Scatterplots Curve of Best Fit Curve of Best Fit line of best fit, index mathematical model, radical algebraic equations, extraneous solution, radicand AII.12 Permutations and Combinations Combinations and Permutations counting, multiplication counting principle, permutation, combination, factorial Days 10 2 Assessed 7 1.a Add, subtract, multiply, and divide rational algebraic expressions. 1.b Simplify a rational algebraic expression with common monomial or binomial factors. 1.c Recognize a complex algebraic fraction, and simplify it as a quotient or product of simple algebraic fractions. Solve equations containing rational algebraic expressions 4.d with monomial or binomial denominators algebraically and graphically. 4.f Verify possible solutions to an equation containing rational expressions. 9.a Collect and analyze data. 9.b Investigate scatterplots to determine if patterns exist, and then identify the patterns. Find an equation for the curve of best fit for data, using a 9.c graphing calculator. Models will include polynomial, exponential, and logarithmic functions. 9.d Make predictions, using data, scatterplots, or the equation of the curve of best fit.

8 Days 2(con t) Assessed Test 9.e Given a set of data, determine the model that would best describe the data. 4.g Apply an appropriate equation to solve a real-world problem. 12.a Compare and contrast permutations and combinations. 12.b Calculate the number of permutations of n objects taken r at a time. 12.c Calculate the number of combinations of n objects taken r at a time. 12.d Use permutations and combinations as counting techniques to solve real-world problems. 8

Algebra 2 Curriculum Guide Lunenburg County Public Schools June 2014

Algebra 2 Curriculum Guide Lunenburg County Public Schools June 2014 Marking Period: 1 Days: 5 Reporting Category/Strand: Equations & Inequalities SOL AII.4a The student will solve, algebraically and graphically, a) absolute value equations and inequalities Graphing calculars