# Algebra II Curriculum Guide Dunmore School District Dunmore, PA

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1 Algebra II Dunmore School District Dunmore, PA

2 Algebra II Prerequisite: Successful completion of Geometry This course continues and reinforces the mathematical material learned in Algebra I. It deals with many concepts including equations, inequalities, probability, relations, functions, and complex numbers. The solving of higher level polynomial (higher than degree 2) and radical functions are also covered. Applications of the above are also discussed and completed as part of the course. Algebra II Page 1

3 Year-at-a-glance Subject: Algebra II Grade Level: 11 Date Completed: 5/22/17 1 st Quarter Topic Resources Standards Real Numbers, Algebra, and Problem Solving Chapter 1 (Sections 1-1,1-2,1-3,1-4,1-5,1-6,1-7,1-8) CC.2.1.HS.F.2 CC.2.1.HS.F.1 A and Inequalities Chapter 2 (Sections 2-1,2-2,2-3,2-4,2-5,2-6,2-7) CC.2.2.HS.D.7 A CC.2.2.HS.D.10 A CC.2.2.HS.D.9 A A Relations, Functions, and Graphs Exponential Functions Logarithmic Functions (Common and Natural Logarithms) Chapter 3 (Sections 3-1,3-2,3-3,3-4,3-5,3-6,3-7) Chapter 12 (Sections 12-2,12-3,12-8) CC.2.1.HS.F.3 CC.2.2.HS.C.2 A A CC.2.2.HS.C.5 A A Algebra II Page 2

4 2 nd Quarter Topic Resources Standards Systems of and Problem Solving Chapter 4 (Sections 4-1,4-2,4-3,4-4,4-5,4-6,4-7) CC.2.2.HS.D.7 CC.2.2.HS.D.10 A Polynomials and Polynomial Chapter 5 (Sections 5-1,5-2,5-3,5-4,5-5,5-6,5-7) CC.2.2.HS.D.4 CC.2.2.HS.D.5 CC.2.2.HS.D.3 A Algebra II Page 3

5 3 rd Quarter Topic Resources Standards Rational Expressions and Chapter 6 (Sections 6-1,6-2,6-3,6-4,6-5,6-6,6-7,6-8) CC.2.2.HS.D.1 CC.2.2.HS.D.2 CC.2.2.HS.D.6 CC.2.1.HS.F.4 Powers, Roots, and Complex Numbers Chapter 7 (Sections 7-1,7-2,7-3,7-4,7-5,7-6,7-7,7-8,7-9) CC.2.1.HS.F.6 CC.2.1.HS.F.7 A A A Quadratic Chapter 8 (Sections 8-1,8-2,8-3,8-4,8-5,8-6,8-7) CC.2.2.HS.C.5 A CC.2.2.HS.D.7 CC.2.2.HS.D.9 A A Algebra II Page 4

6 4 th Quarter Quadratic Functions and Transformations of Second Degree Data and Statistics Review and Final Exams Chapter 9 (Sections 9-1,9-2,9-3,9-4,9-5,9-6,9-7) Chapter 10 (Sections 10-1,10-2,10-3,10-4,10-5,10-6,10-7) Chapter 15 (Sections 15-1,15-2,15-3) Review Worksheets CC.2.2.HS.C.4 CC.2.2.HS.C.6 CC.2.1.HS.F.5 A A CC.2.2.HS.C.3 A CC.2.4.HS.B.2 CC.2.2.HS.C.3 CC.2.3.HS.A.10 A A A CC.2.1.HS.F.3 CC.2.4.HS.B.2 CC.2.4.HS.B.3 CC.2.4.HS.B.4 CC.2.4.HS.B.5 CC.2.4.HS.B.6 CC.2.4.HS.B.7 Algebra II Page 5

7 General Topic Anchor Descriptor PA Core Standards Eligible Content, Essential Knowledge, Skills & Vocabulary Real Numbers, Algebra, and Problem Solving A Use Exponents, roots, and/or absolute value to represent equivalent forms or to solve problems. CC.2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems. CC.2.1.HS.F.1 Apply and extend the property of exponents to solve problems. A Use exponential expressions to represent rational numbers. A Simplify/evaluate expressions involving positive and negative exponents and/or roots (may contain all types of real numbers). Algebraic Expressions Commutative Property Associative Property Distributive Property Exponential Notation Order of Operations Resources & Activities Assessments Suggested Time (In Days) Approved textbook Chapter Real Numbers and 1-2 Multiplication and Division 1-3 Algebraic Expressions and Properties of Numbers 1-4 The Distributive Property 1-5 Solving 1-6 Writing 1-7 Exponential Notation 1-8 Properties of Exponents 14 Days Algebra II Page 6

8 and Inequalities A Use Exponents, roots, and/or absolute value to represent equivalent forms or to solve problems. A Describe and/or determine change. CC.2.2.HS.D.8 Apply inverse operations to solve equations and formulas for a given variable. CC.2.2.HS.D 9 Use reasoning to solve equations and justify the solution. A Simplify/evaluate expressions involving multiplying with exponents, powers of powers, and powers of products. A Use algebraic processes to solve a formula for a given variable. A Write and/or solve a simple exponential or logarithmic equation. A Write, solve, and/or apply linear or exponential growth and decay. 2-1 More on Solving 2-2 Using 2-3 Solving Formulas 2-4 Solving Inequalities 2-5 Using Inequalities 2-6 Compound Inequalities 2-7 Absolute Value 14 Days CC.2.2.HS.D.7 Create and graph equations or inequalities to describe numbers or relationships. CC.2.2.HS.D.9 Use reasoning to solve equations, and justify the solution method. Principle of Zero Products Guidelines to Solve Word Problems Solution Sets Compound Inequality Conjunctions Disjunctions Absolute Value Number Line Algebra II Page 7

9 Relations, Functions, and Graphs Exponential Functions Logarithmic Functions A Use exponents, roots, and/or absolute values to represent equivalent forms or to solve problems. A Create, interpret, and/or use polynomial, exponential, and/or logarithmic functions and their equations, graphs, or tables CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.2.HS.C.2 Graph and analyze functions and use their properties to make connections between the different representations. CC.2.2.HS.C.1 Use the concept and notation of functions to interpret and apply them in terms of their context. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. A Determine the domain, range, or inverse function. A Create, interpret, and/or use the equation, graph, or table of a polynomial function. A Create, interpret, and/or use the equation, graph, or table of exponential functions. A Determine, use, and/or interpret minimum and maximum values over a specified interval of a graph of a polynomial. Cartesian Product Domain and Range Vertical Line Test Function Notation x-intercept y-intercept Slope Point-Slope Form Slope-Intercept Form Parallel Lines Perpendicular Lines Composite Functions 3-1 Relations and Ordered Pairs 3-2 Graphs (Guidelines) 3-3 Functions 3-4 Graphs of Linear 3-5 Slope 3-6 More of Lines 3-7 Parallel and Perpendicular 3-9 Composition of Function 12-2 Exponential and Logarithmic Functions 12-4 Properties of Logarithms 20 Days Algebra II Page 8

10 A Simplify or evaluate Expressions involving logarithms and exponents. A Draw, identify, find, interpret, and/or write an equation for regression model for a scatter plot. A Make predictions using the equations or graphs of regression models of scatter plots. Exponential Functions (Growth and Decay) Logarithms (Natural and Common) A Identify and/or determine the characteristics of an exponential, quadratic, or polynomial function Vocabulary Line of best fit Scatter plots Systems of and Inequalities and Problem Solving A Describe and/or determine change. CC.2.2 HS. D.7 Create and graph equations or inequalities to describe numbers and relationships. A Determine how a change in one variable relates to a change in the second variable. Substitution Method Linear Combinations Ordered Triple 4-1 Systems of I Two Variables 4-2 Solving a System of 4-3 Using a System of Two 20 Days Algebra II Page 9

11 Polynomials and Polynomial CC.2.2.HS.D.10 Represent, solve and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically. A Simplify expressions involving polynomials. CC.2.2.HS.D.4 Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs. CC.2.2.HS.D.5 Use polynomial identities to solve problems. CC.2.2.HS.D.3 Extend the knowledge of arithmetic operations and apply to polynomials. Consistent System Dependent System A Factor algebraic expressions, including difference of squares and trinomials. ( In the form ax 2 + bx + c where (a) is not equal to zero). A Simplify rational algebraic expressions. Monomial Binomial Trinomial Additive Inverses F.O.I.L. Factoring Principle of Zero Products Factoring (3-1 and 2-2 grouping) 4-4 Systems of in Three 4-5 Using a System of Three Variables 4-6 Consistent and Dependent Systems 4-7 Systems of Inequalities 5-1 Polynomials and Functions 5-2 Addition and Subtraction of Polynomials 5-3 Multiplication of Polynomials 5-4 Factoring 5-5 More Factoring 5-6 Factoring (A General Strategy) 5-7 Solving by Factoring 20 Days Algebra II Page 10

12 Factoring (Sum and Difference of two cubes) Rational Expressions and A Simplify expressions involving polynomials. A Write and/or solve non-linear equations using various methods. CC.2.2.HS.D.1 Interpret the structure of expressions to represent a quantity in terms of its context. CC.2.2.HS.D.2 Write expressions in equivalent forms to solve problems. CC.2.2.HS.D.6 Extend the knowledge of rational functions to rewrite in equivalent forms. CC.2.1.HS.F.4 Use units as a way to understand problems and guide the solution of multi-step problems. A Simplify rational expressions. A Solve equations involving rational and/or radical expressions. Reciprocals Common Denominator Least Common Multiple Complex Rational Expression Algorithm Rational Equation Distance Direct Variation Synthetic Division 6-1 Multiplying and Simplifying 6-2Addition and Subtraction 6-3 Complex Rational Expressions 6-4 Division of Polynomials 6-5 Synthetic Division 6-6 Solving Rational 6-8 Formulas 20 Days Algebra II Page 11

13 Powers, Roots, and Complex Numbers A Represent and/or use imaginary numbers in equivalent forms (e.g., square roots and exponents). A Apply the order of operations in computation and in problem solving situations. CC.2.1.HS.F.6 Extend the knowledge of arithmetic operations and apply to complex numbers. CC.2.1.HS.F.7 Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems. A Simplify/write square roots in terms of i. A Simplify/evaluate expressions involving powers of i. A Add and subtract complex numbers. A Multiply and divide complex numbers. Radicand Radical Expression Cube Root Even and Odd Roots Rationalize Extraneous Roots Imaginary Numbers Complex Numbers Rational Exponents 7-1 Radical Expressions 7-2 Multiplying and Simplifying 7-3 Operations with Radical Expressions 7-4 More Operations with Radical Expressions 7-5 Rational Numbers as Exponents 7-6 Solving radical 7-7 Imaginary and Complex Numbers 7-8 Complex Numbers and Graphing 7-9 More About Complex Numbers 20 Days Algebra II Page 12

14 Quadratic A Write and/or solve non-linear equations using various methods. CC.2.2.HS.C.5 Construct and compare linear, quadratic, and exponential models to solve problems. A Write/ and or solve quadratic equations 9Including factoring and using the Quadratic Formula). Standard Form Pythagorean Theorem The Quadratic Function Discriminant Quadratic Form Formulas Direct Quadratic Variation 8-1 Introduction to Quadratic 8-2 Using Quadratic 8-3 The Quadratic Equation 8-4 Solutions of Quadratic 8-5 Reducible to Quadratic Form 8-6 Formulas and Problem Solving 20 Days Quadratic Functions and Transformations A Analyze and/or use patterns or relations. CC.2.2.HS.C.4 Interpret the effects transformations have on functions and find the inverses of functions. CC.2.2.HS.C.6 Interpret functions in terms of the situation they model. A Analyze a set of data for the existence of a pattern, and represent the pattern with a rule algebraically and/or graphically. A Identify or describe the effect of changing parameters within a family of functions. 9-1 Symmetry 9-2 Transformations 9-3 Sketching and Shrinking 9-4 Graphs of Quadratic Functions 9-5 Graphs of f(x) = a(x h)^2 + k 9-6 Standard Form for Quadratic Functions 14 Days Algebra II Page 13

15 Conic Sections Data and Statistics CC.2.1.HS.F.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. A Create, interpret, and/or use polynomial, exponential, and/or logarithmic functions and their equations, graphs, or tables. A Analyze and/or use patterns or relations. CC.2.2.HS.C.3 Write functions or sequences that model Relationships between two quantities. CC.2.2.HS.C.3 Write functions Symmetry Axis of Symmetry Even Function Odd Function Transformation Translation Horizontal Vertical Vertex Minimum Maximum Standard Form A Create, interpret, and/or use the equation, or table of a polynomial function (including circles, ellipses, parabola, and hyperbolas). A Identify and/or extend a pattern as either arithmetic or geometric sequence. A Use combinations, permutations, and the fundamental counting principle to solve problems involving probability Coordinate Geometry 10-2 Conic Sections: Circles 10-3 Ellipses 10-4 Hyperbolas 10-5 Parabolas 14-1 Sequence and Series 14-2 Arithmetic Series 15-1 Counting and Permutations 10 Days Algebra II Page 14

16 CC.2.3.HS.A.10 Translate between The geometric description and the equation for a conic section. CC.2.1.HS.F.3 Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays. CC.2.4.HS.B.2 Summarize, represent, and interpret data on two categorical and quantitative variables. CC.2.4.HS.B.3 Analyze linear models to make interpretations based on the data. A Use odds to find probability and/or use probability to find odds. A Use probability for independent, dependent, or compound events to predict outcomes. Parabolas, determine the focus and directrix. Arithmetic Sequences and Series Combinations and Permutations Independent/Dependent Events CC.2.4.HS.B.4 Recognize and evaluate random processes underlying statistical experiments. CC.2.4.HS.B.5 Make interferences and justify conclusions based on sample surveys, experiments, and observational studies. Algebra II Page 15

17 Review and Final Exams CC.2.4.HS.B.6 Use the concepts of independence and conditional probability to interpret data. CC.2.4.HS.B.7 Apply the rules of probability to compute probabilities of compound events in a uniform probability model. 8 Days Algebra II Page 16

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