WAYNESBORO AREA SCHOOL DISTRICT CURRICULUM ALGEBRA II

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1 UNIT: Review of Basic Algebra Skills as Needed SR1 and any Supplemental Materials UNIT : What skills from Algebra I are used in Algebra II? Review Algebra I Skills as Needed SR1 and any additional resources deemed necessary

2 UNIT: Chapter 1 Quadratic Functions and Factoring UNIT : How do you solve and graph a quadratic function? How do you apply quadratic equations to real-life? A CC.2.2.HS.C.2 CC.2.2.HS.C.5 CC.2.2.HS.C.6 CC.2.2.HS.D Graph Quadratic Functions in Standard Form 1.2 Graphing Quadratic Functions in Vertex or Intercept Form How are the values in Standard Form used to graph the quadratic function What are the advantages to have the equation in intercept form when graphing a parabola? Page 10 Graphing Calculator Activity Maximum value Minimum value Vertex Standard Form Parabola Axis of Symmetry Vertex Form Intercept Form 1.3 Solve x 2 + bx + c = 0 by Factoring How can factoring by use to solve quadratic equations? Roots Zeros Monomial Binomial Trinomial Quadratic Equation 1.4 Solve ax 2 + bx + c = 0 by Factoring How do you factor a quadratic equation/expression to reveal the zeros? Monomial 1.5 Solve quadratic Equations by Finding Square Roots How can you use square roots to solve quadratic equations? Square Roots Conjugate Radical Radicand Rationalizing the Denominator

3 A CC.2.2.HS.C.2 CC.2.2.HS.C.5 CC2.2.HS.C.6 CC.2.2.HS.D.7 CC.2.1.HS.F Perform operations with Complex Numbers 1.7 Complete the Square How do you perform operations with Complex Numbers? How is the process of Completing the Square used to solve equations? Only do examples without graphing and absolute value. (Examples 1-5) Page 49 Algebra Tiles Activity Imaginary Number Complex Number Complex Conjugate Completing the Square 1.8 Use the Quadratic Formula and the Discriminant How do you use the Quadratic Formula and the Discriminant? Discriminant Quadratic Formula 1.9 Graph and Solve Quadratic Inequalities How do you solve quadratic inequalities in one variable? Quadratic Inequality One Variable Two Variable

4 UNIT: Chapter 2 Polynomials and Polynomial Functions UNIT : How do you graph polynomial functions? How do perform polynomial operations? How do you solve polynomials? CC.2.2.HS.C.5 CC.2.1.HS.F Use of Properties of Exponents How do you simplify expressions with exponents? Scientific Notation CC.2.2.HS.C.2 CC.2.2.HS.C Evaluate and Graph Polynomial Functions How can you graph a polynomial function? Page 94 End Behavior Activity Page 103 Viewing Window Graphing Calculators End Behavior Polynomial Polynomial Functions Synthetic Substitution CC.2.2.HS.D Add, Subtract, and Multiply Polynomials What are the specific product values for polynomials? Like Terms CC.2.2.HS.D Factor and Solve Polynomial Equations How can you solve a higher degree polynomial equation? Page 118 and 119 Alternative Solution Methods Factor Completely Factor by Grouping Quadratic Form 2.5 Apply the Remainder Factor Theorems If you know one zero of a polynomial equation, how do you know another zero(s)? Polynomial Division Synthetic Division

5 CC.2.2.HS.C.2 CC.2.2.HS.C.6 CC.2.2.HS.D Find Rational Zeroes How can you find all real zeroes when the leading coefficient is 1? Page 126 Use Location Principle Zero Constant Term Leading Coefficient 2.7 Apply the Fundamental Theorem of Algebra How can you determine the number of positive and negative and imaginary zeroes of polynomial functions? Repeated Solutions Irrational Conjugates Complex Conjugates 2.8 Analyze Graphs of Polynomial Functions When does a graph have a local maximum and minimum?

6 UNIT 3: Rational Exponents and Radical Functions UNIT : How do you simplify expressions with rational exponents? How do you perform and find operation of inverse functions? How do graph and solve radical equations? CC.2.2.HS.D.6 CC.2.1.HS.F.1 CC.2.1.HS.F Evaluate nth Roots and use rational exponents What is the relationship between nth root and rational exponents? Index nth root of a 3.2 Apply properties of rational exponents How are the properties of rational exponents related to the integer properties of exponent? Simplest form of radicals Like radicals CC.2.2.HS.C.1 CC.2.2.HS.C Perform function operations and compositions What operations can be performed on a function to obtain a third function? Page 187 Use operations with functions activity Composition Power Function CC.2.2.HS.C Use Inverse Functions How do you find the inverse relation of a given function? Inverse Relation Inverse Function CC.2.2.HS.C Graph Square Root and Cube Root Functions What do the square root and cube root functions look like? Radical Function Parent Function

7 CC.2.2.HS.C.1 CC.2.2.HS.C.5 CC.2.2.HS.C Solve Radical Equations Why is it necessary to check your solution in a radical equation? Page Alternative Methods Page Solve Radical Inequalities Extension Radical Equation Extraneous Solution

8 UNIT 4 : Chapter 4 Exponential and Logarithmic Functions UNIT : How do you graph and solve exponential and log equations? How do you write exponential and power functions? CC.2.2.HS.C.2 CC.2.2.HS.C.5 CC.2.2.HS.C Graph Exponential Growth Functions What does the graph of an exponential function look like? Growth Factor Exponential Function Exponential Growth Exponential Decay Asymptote 4.2 Graph Exponential Decay Functions What does the graph of an exponential decay function look like? Page 242 Transform Expressions of Exponential Functions Extension Exponential Decay Function Exponential Decay Factor Transformations CC.2.2.HS.C.1 CC.2.2.HS.C Use Functions Involving e When is the natural base e useful? Natural Base e CC.2.2HS.C Evaluate Logarithms and Graph Logarithmic Functions What is the relationship between logarithmic and exponential functions? Logarithm of y with base b Common Log Natural Log 4.5 Apply properties of logarithms How can you simplify log expressions/equations with log properties? Page 266 Graph Logarithmic Functions Activity Base

9 CC.2.2.HS.C.1 CC.2.2.HS.C.2 CC.2.2.HS.C Solve Exponential and Log Equations Why do log equations sometimes have extraneous solutions? Extraneous Solutions Exponential Equation Log Equation

10 UNIT: Chapter 5 Rational Functions UNIT : How can the student solve and graph rational equations? How can you perform operations with rational expressions? CC.2.2.HS.C Model Inverse and Joint Variation What are the differences between direct, inverse, and joint variation? Inverse variation Constant of variation Joint variation CC.2.2.HS.D.6 CC2.2.HS.D Graph Simple Rational Functions What does the graph of a rational function look like? p. 317 extension rewrite rational expressions Rational function Domain Range Asymptote 5.3 Graph General Rational Functions What are the steps for graphing a general rational function? End behavior Asymptote Rational function CC2.2.HS.E Multiply and Divide rational expressions What are the steps for multiplying and dividing rational expressions? Simplified form of rational expression Reciprocal 5.5 Add and Subtract rational expressions What are the steps for adding or subtracting rational expressions with different denominators? Complex fraction

11 CC2.2.HS.E.6 CC2.2.HS.E Solve rational Equations What are the steps for solving rational equations? p alternative methods Cross multiplying Extraneous solution CC.2.2.HS.E Describe and compare function characteristics How do you compare functions represented in different ways? Increasing and decreasing Odd function Even function

12 UNIT: Chapter 6 Data analysis and statistics UNIT : CC.2.4.HS.B Use combinations and the binomial theorem How can you determine the number of ways a certain number of objects can be taken from a larger set? Regular don t do binomial theorem Combination Pascal s triangle Binomial theorem CC.2.4.HS.B Use Normal Distributions What are values that occur on normal distribution curve? Generalize Normal Distribution Standard normal distribution CC.2.4.HS.B Select and draw conclusions from samples What should be true of the sample when you construct a survey? Population Sample Unbiased sample Biased sample Margin of error CC.2.4.HS.B Compare survey s, experiments, and observational studies How do you collect data that accurately represent a population? Biased questions Experiment Observational study Controlled experiment Control group Treatment group Randomized comparative experiment

13 UNIT: Chapter 7 Sequences and Series UNIT : How do you analyze and find sums of sequences and series? CC.2.2.HS.D.1 CC.2.2.HS.D.2 CC.2.2.HS.C.1 CC.2.2.HS.C Define and use sequences and series 7.2 Analyze arithmetic sequences and series How can you write an expression from a sequence? How can you tell that a sequence is arithmetic? Sequence Terms of a sequence Series Summation notation Sigma notation Arithmetic sequence Common difference Arithmetic series 7.3 Analyze geometric sequences and series How can you find the sum of the terms of a geometric series? Geometric sequence Common ratio Geometric series 7.4 Find sums of infinite geometric series When does an infinite geometric series have a sum, and when does it not have a sum? Accelerated only Partial sum 7.5 Use recursive rules with sequences and functions How do you write a recursive rule for an arithmetic sequence and for a geometric sequence? Accelerated only Extension: Translate between recursive and explicit rule for sequences Explicit rule Recursive rule iteration

14 UNIT: Chapter 8 Quadratic Relations and conic sections UNIT : How will the student write and graph conic sections? CC.2.3.HS.A Apply the distance and midpoint formulas If you are given the coordinates of the endpoints of the diameter of a circle, how can you find the center and radius of the circle? Distance formula Midpoint formula CC.2.2.HS.A Graph and write equations and parabolas Which two features of a parabola are equidistant from its vertex? Accelerated only focus DirectX Parabola Vertex CC.2.2.HS.A Graph and write equations and circles What information do you need to write the equation of a circle with center (0,0)? Center Circle radius CC.2.2.HS.A Graph and write equations and ellipses What points do you need to write an equation of an ellipse? Ellipse Foci Vertices Major axis Center Co-vertices Minor axis

15 CC.2.2.HS.A Graph and write equations of hyperbolas What kind of figure can be used to locate the vertices and asymptotes of a hyperbola? Hyperbola Foci Vertices Transverse axis Center CC.2.2.HS.D.1 CC.2.2.HS.D.2 CC.2.2.HS.D Solve quadratic systems How can you identify the points of intersection of two distinct conics? Extension p Quadratic system

16 UNIT: chapter 9 10Trigonometric ratios and functions UNIT : How will the student use and apply trig functions? CC.2.3.HS.A.7 CC.2.2.HS.C.7 CC2.2.HS.C Use trigonometry with right triangles How are trigonometric functions used in right triangles? Sine Cosine Tangent Cosecant Secant Cotangent 9.2 Define General angles and use radian measure What is radian measure? Initial side Terminal side Standard position Coterminal Radian Sector Central angle 9.3 evaluate trigonometric functions of any angle How can you evaluate trigonometric functions of any angle? Unit circle Quadrantal angle Reference angle 9.4 Evaluate inverse trigonometric functions How are inverse trigonometric functions used? Accelerated Only Inverse sine Inverse cosine Inverse tangent

17 CC.2.3.HS.A.7 CC.2.2.HS.C.7 CC2.2.HS.C Apply the law of Sines When can the law of sines be used to solve a triangle? Law of sines 9.6 Apply the law of Cosines In which cases can the law of cosines be used to solve a triangle? Law of cosines 10.1 Graph sine, cosine, and tangent functions Compare the graphs of the trig functions? Amplitude Periodic function Cycle Period Frequency 10.4 Solve Trigonometric Equations How can you write the general solution of a trigonometric equation? Extraneous solution

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