ALGEBRA 2

UNIT 1

UNIT TITLE

UNIT LENGTH

Systems of Equations

3 weeks Standards/Benchmarks

NM A.1.5, A.1.7, A.1.8, A.2.3, A.3.4, A.3.4, A.3.5, A.3.8, G.4.8 Topics for further study: Solve 3 by 3 linear systems, Solve and graph equations and inequalities involving absolute value, Determine whether the linear system is inconsistent (no solutions) or consistent with one solution or infinitely many solutions, Solve systems of linear equations and inequalities (in 2 or 3 variables) by substitution, with graphs, and with matrices.

UNIT COMPONENTS Graphing Systems

Solving Systems Algebraically

Linear Programming

Vocabulary

Vocabulary

Vocabulary

Review Systems of 2 variables: • solve graphically without technology • solve graphically with technology

Review Systems of 2 equations: • substitution method • elimination (combination) method • technology (inverse matrix)

Review Systems of inequalities: • solve by graphing (include linear absolute values)

New Concepts Graph a point in 3 dimensions.

New Concepts Solve systems of 3 variables

New Concepts Linear programming

Learner Performance Objectives

Assessments/Evidence

1. Define and use unit vocabulary 2. Graph a point on a 3 dimensional plane 3. Solve systems of 3 variables using the substitution method 4. Solve systems of 3 variables using the elimination method 5. Solve systems of 3 variables using matrices with technology (Inverse matrices & Augmented matrices 6. Implement systems of 3 variables to solve problems that model real world phenomena 7. Given linear equations and constraints, find maximum and minimum values 8. Use linear equations and constraints, solve problems that model real world phenomena

Pre/post test Quiz Vocab notebook or similar activity Homework assignments ACE questions Resources: Text Chapter 3 Text Chapter 4 Sec 7 & Sec 8 Linear programming worksheet

ALGEBRA 2

UNIT 2

UNIT TITLE

UNIT LENGTH

Quadratics

3 Weeks Standards/Benchmarks

NM A.1.2, A.1.5, A.1.6, A.1.7, A.1.9, A.1.13, A.1.14, A.1.16, A.1.18, A.2.3, A.2.5, A.2.8, A.2.10, A.2.11, A. 2.12, A.2.13, A.3.2, G.4.4

UNIT COMPONENTS Graphing Quadratics (Parabolas) Vocabulary vertex form Review Standard form of quadratic equation • Find axis of symmetry • Find vertex • Use leading coefficient to determine if parabola opens up or down • Use discriminant to determine the number of real solutions New Concepts Vertex form Transformations End behavior Focus point/Directrix

Solving Quadratics Vocabulary imaginary number (i) complex numbers Review Solve quadratic equation • Graphing • Factoring • Quadratic formula

New Concepts Complex numbers Completing the square Graph parabola identifying focus pt & directrix

Learner Performance Objectives

Assessments/Evidence

1. Define and use unit vocabulary 2. Convert quadratics from standard form to vertex form (vertex to S.F) 3. Transform parabolas • reflection • stretch/shrink • horizontal/vertical shift 4. Graph with technology/tables/intersection 5. Identify complex numbers 6. Basic operations on complex numbers (conjugates) 7. Solutions to quadratics using complex numbers 8. Solve by completing the square 9. Graph by completing the square (vertex form) 10.Modeling real world situations with quadratics

Pre/post test Quiz Vocab notebook or similar activity Homework assignments ACE questions Project Resources: Text Chapter 5 Text Chapter 10.2

ALGEBRA 2

UNIT 3

UNIT TITLE

UNIT LENGTH

Polynomial Functions

3 Weeks Standards/Benchmarks

NM A.1.1, A.1.3, A1.5, A.1.6, A.1.7, A.1.13, A.1.14, A.1.14, A.1.15, A.1.16, A.2.3, A.2.4, A.2.12, A.2.13, A. 2.15, A.3.2, D.2.10 Topics for Further Study: Factor polynomials of degree higher than two using the fundamental theorem of algebra rational zero theorems and factor and remainder theorems, Perform long division and synthetic division of polynomials

UNIT COMPONENTS Polynomial Functions Vocabulary End behavior Composition Inverse

Graphing Polynomials Vocabulary Local (regional) max and/or min Global(absolute) max and/or min Odd/even function

Review Classifying polynomials • degree • number of terms Standard form Basic operations • add • subtract • multiply • long division Factoring New Concepts Writing polynomial functions Factoring with complex numbers

Review Graphing lines Graphing quadratics

New Concepts Graphing polynomials of degree 3 and higher Composition of functions

Learner Performance Objectives 1. Define and use unit vocabulary 2. Write a polynomial function given its zeros 3. Write a polynomial function using technology regression 4. Find all real solutions using technology 5. Determine end behavior using leading coefficients and odd/even functions 6. Number of possible zeros determined by exponent 7. Max and Min (turning points) 8. Sum and difference of cubes 9. Solve by factoring 10. Synthetic division 11. Rational Root Theorem to solve 12. Imaginary Root Theorem 13. Irrational Root Theorem 14. Fundamental Theorem of Algebra to find all zeros 15. Perform 5th operation (composition of functions) 16. Modeling real world phenomena using polynomial functions

Solving Polynomials Vocabulary Conjugate pair

Review Factoring out a monomial Sum & difference of squares Perfect square trinomial Factor by grouping

New Concepts Solve polynomials of degree 3 and higher

Assessments/Evidence Pre/post test Quiz Vocab notebook or similar activity Homework assignments ACE questions Resources: Text Chapter 6 (Sec 1 - 6) Extension Pg. 312 Text Chapter 7.6

ALGEBRA 2

UNIT 4

UNIT TITLE

UNIT LENGTH

Functions (Rational)

3 Weeks Standards/Benchmarks

NM A.1.1, A.1.5, A.1.13, A.1.14, A.1.7, A.1.18, A.2.3, A.2.5, A.2.6 Topics for Further Study: Find and use inverse functions involving ordered pairs, graphs, and explicit statements of a function rule examine and graph piece-wise defined functions, including the use of the properties of continuity and discontinuity graph rational functions and locate zeros and horizontal and vert asymptotes

UNIT COMPONENTS Graphing Vocabulary Discontinuous Asymptotes

Rational Expressions Vocabulary Review Factoring Simplify

Review Inverse Variation New Concepts Graph Rational Functions - with technology - without technology

Rational Equations Vocabulary Review Direct Variation Inverse Variation

New Concepts New Concepts Perform basic operations on rationals Joint Variation Solving Rational Equations

Learner Performance Objectives 1. Define and use unit vocabulary 2. Identify vertical asymptotes 3. Identify points of discontinuity 4. Identify horizontal asymptotes (limits to infinity) 5. Multiple rational expressions 6. Divide rational expressions 7. Add/Subtract rational expressions 8. Solve with cross-products 9. Solve with common denominator 10. Solve with technology 11. Model real world situations with rational equations

Assessments/Evidence Pre/post test Quiz Vocab notebook or similar activity Homework assignments ACE questions Resources: Text Chapter 2 Section 3 Text Chapter 9 Sections 1 - 6 Handout on Limit to Infinity

ALGEBRA 2

UNIT 5

UNIT TITLE

UNIT LENGTH

Probability & Data Analysis

3 Weeks

Standards/Benchmarks NM D.1.1, D.1.2, D.1.3, D.1.4, D.2.2, D.2.3, D.2.4, D.2.5, D.2.6, D.2.7, D.2.13, D.2.14, D.2.15, D.3.1, D.3.2, D. 3.3, D.3.4

UNIT COMPONENTS Probability Vocabulary Conditional probability Addition rule Multiplication rule Expected value Variability

Review Experimental probability Theoretical probability Geometric probability Probability of compound events New Concepts Conditional probability

Data Analysis Vocabulary Univariate Bivariate Review Tree diagrams to solve conditional situations Multiplication Counting Principle Permutations Combinations Box-n-whisker plot Histogram Scatterplot Measures of central tendency New Concepts Probability distributions Standard deviation Normal distribution

Learner Performance Objectives 1. Define and use unit vocabulary 2. Construct frequency table to show probability distributions 3. Analyze applicable measures of central tendency 4. Find standard deviation of a set of values 5. Determine unbiased samples 6. Find margin of error 7. Use standard deviation in real-world situations

Assessments/Evidence Pre/post test Vocab notebook or similar activity Homework assignments ACE questions Resources: Text Chapter 1 Sec 6 Text Chapter 6 Sec 7 Text Chapter 9 Sec 7 Text Chapter 12 Sec 1 - 5, 7

ALGEBRA 2

UNIT 6

UNIT TITLE

UNIT LENGTH

Functions (Radicals)

4 Weeks Standards/Benchmarks

NM A.1.1, A.1.5, A.1.6, A.1.7, A.1.8, A.1.10, A.1.11, A.1.12, A.2.3, A.2.10 Topics for Further Study: Find and use inverse functions involving ordered pairs, graphs, and explicit statements of a function rule examine and graph piece-wise defined functions, including the use of the properties of continuity and discontinuity graph rational functions and locate zeros and horizontal and vert asymptotes

UNIT COMPONENTS Radical Expressions & Rational Exponents

Solving Radical Equations

Graphing Radicals

Vocabulary

Vocabulary

Vocabulary

Review Property of exponents Square Roots • Simplifying radicals • Perform basic operations • Rationalize denominator

Review Solving square root equations Solving quadratics

Review Vertex form of parabola

New Concepts nth Root • Simplify nth roots • Perform basic operations Convert Rational Exponents to and from Radical Form

New Concepts Solving radical equations with rational exponents

Learner Performance Objectives 1. Define nth roots 2. Inverse property of nth roots (text p. 370) 3. Determine number of possible real roots 4. Add/Sub Radicals 5. Mult/Divide Radicals 6. Multiplying Binomial Radical Exponents 7. Convert Rational Exponents to Radical Form 8. Convert Radical Form to Rational Exponents 9. Solve radical equation by raising to a reciprocal power 10. Solve radical equations using technology 11. Check for extraneous solutions 12. Find the inverse of a relation with table and/or graph 13. Find the inverse given an equation 14. Composition of inverse functions 15. Graph square root functions 16. Graph cube root functions 17. Restrict domain 18. Modeling real world phenomena using radical functions

New Concepts Graph inverse relations Graph inverse functions Graph families of radical functions

Assessments/Evidence Pre/post test Vocab notebook or similar activity Quiz Homework assignments ACE questions Resources: Exercises Pg. 368 Text Chapter 7 Sec 1 - 5, 7 & 8

ALGEBRA 2

UNIT 7

UNIT TITLE

UNIT LENGTH

Exponential & Logarithmic Functions

4 Weeks

Standards/Benchmarks NM A.1.1, A.1.5, A.1.7, A.1.12, A.1.19, A.2.3, A.3.3 Topics for Further Study: Operate with logs and exponential functions on the basis of their inverse relationship, Identify the concept of e, Use exponential functions and common and natural logs to understand real-life situations, Use logs and exponents to solve equations

UNIT COMPONENTS Properties of Exponential Functions & Logarithms Vocabulary Common logarithm Natural logarithm

Graphing Exponential Equations Vocabulary Half life Doubling time

Solving Exponential & Logarithmic Equations Vocabulary Review

Review Properties of exponents Exponential functions • Modeling growth • Modeling decay Simple & compound interest formula New Concepts Logarithms Relationships between exponents & logarithms

Review Graph • exponential growth functions • exponential decay functions

New Concepts Solve • exponential equations • logarithmic equations

New Concepts Graph families of exponential functions

Learner Performance Objectives 1. Define and use unit vocabulary 2. Evaluating logarithms 3. Write an exponential function given two points 4. Use technology to find the exponential function for set of data 5. Use continuously compounded interest formula 6. Graph exponential functions/identifying horizontal asymptotes 7. Identify the role of parameter changes in graphing expo function 8. Write exponential equations in logarithmic form 9. Write logarithmic equations in exponential form 10. Solve exponential equation by taking the log of each side 11. Solve exponential equation by graphing with technology 12. Solve logarithmic equation by rewriting in exponential form 13. Model real-world phenomena using expo and log equations

Assessments/Evidence Pre/post tests Quiz Vocab notebook or similar activity Homework assignments ACE questions Project Resources: Text Chapter 8: Sec 1, 2, 3 (not do include graphing logs) Sec 5 (Solving exponential equations & solving logarithmic equations that do not require simplifying or expanding logs) Sec 6 (Solving natural log equations that do not require simplifying or expanding logs)

ALGEBRA 2

UNIT 8

UNIT TITLE

UNIT LENGTH

Trigonometry

6 Weeks Standards/Benchmarks

NM G.4.4, G.4.5, G.4.6, G.4.7 Topics for Further Study: Demonstrate an understanding of trig functions as circular functions using symmetry, Solve trig equations, Verify trig identities, Apply trig functions to solve physical problems including the use of the law of sines and cosines

UNIT COMPONENTS Unit Circle Vocabulary radians Review Special right triangles Angles in standard position Basic trig functions of angles New Concepts Unit circle Arc length in terms of radians

Graphing Trig Functions

Solving Trig Equations

Vocabulary

Vocabulary Law of Sines Law of Cosines

Review

Review

New Concepts Trig functions • Cosine • Sine • Tangent

Learner Performance Objectives 1. Define and use unit vocabulary 2. Find coordinates of points (related to spec triangles) on unit circle 3. Convert radians to degrees 4. Convert degrees to radians 5. Find the length of an intercepted arc 6. Evaluate trig functions with/without technology 7. Graph cosine function with/without technology and recognize relationship with unit circle 8. Graph sine function with/without technology and recognize relationship with unit circle 9. Graph tangent function with/without technology 10. Graph basic trig functions with multiple translations 11. Write trig equation given periodic data and/or graph 12. Use basic trig functions to model real-world situations 13. Evaluate reciprocal trig functions with/without technology 14. Verify trig identities 15. Solve trig equations using reciprocal trig functions 16. Solve trig equations using inverses 17. Use Law of Sines to find area, side, and/or angle of a triangle 18. Use Law of Cosines to find sides and/or angles of a triangle

New Concepts Trigonometric identities Reciprocal trig functions

Assessments/Evidence Pre/post test Vocab notebook or similar activity Homework assignments ACE questions Resources: Text Pg. 717 (Spec Rt. Triangles) WS (Special Right Triangles) Text Chapter 13 Text Chapter 14 Sec 1 - 5