ALGEBRA II & HONORS ALGEBRA II PACING GUIDE
Course Description: Algebra 2 and Honors Algebra 2 continues students' study of advanced algebraic concepts including functions, polynomials, rational expressions, systems of functions and inequalities, and matrices. Students will be expected to describe and translate among graphic, algebraic, numeric, tabular, and verbal representations of relations and use those representations to solve problems. Emphasis will be placed on higher order thinking skills that impact practical and increasingly complex applications, modeling, and algebraic proof. Appropriate technology should be used regularly for instruction and assessment.
DAY UNIT NAME Solving Equations and Inequalities 1 – 1 Expressions and Formulas 1 – 2 Properties of Real Numbers 1 – 3 Solving Equations 1 – 4 Solving Absolute Value Equations 1 – 5 Solving Inequalities 1 – 6 Solving Compound and Absolute Value SCS OBJECTIVES 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 2.08 Use equations and inequalities with absolute value to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the context of the problem. ESSENTIAL QUESTION How do you solve absolute value inequalities and equations? What is different about solving absolute value equations which contain a variable outside the absolute value? What do the constants in the absolute value function represent, y = a|x – h| + k? How can inequalities be used to compare phone plans? How are compound inequalities used in medicine? CONTENT Absolute value equations. Absolute value functions. Absolute value inequalities. Vertex, slope, direction of opening, domain and range.
1-5
y = a bx + c + d
Maximum and minimum. Transformations. Conjunction and disjunction. Real-world applications. Parallel and perpendicular lines. Direct variation. Graphing linear equations and inequalities. Scatter plot. Linear regression. Prediction equations. Correlation coefficient. Systems of equations. Systems of inequalities. Matrices. Linear programming. Feasible region. Convex polygon. Real-world applications.
6 – 13
Linear Relations and Functions 2 – 1 Relations and Functions 2 – 2 Linear Equations 2 – 3 Slope 2 – 4 Writing linear Equations 2 – 5 Modeling Real-World Data Using Scatter Plots 2 – 6 Special Functions 2 – 7 Graphing Inequalities Systems of Equations and Inequalities 3 – 1 Solving Systems of Equations by Graphing 3 – 2 Solving Systems of Equations Algebraically 3 – 3 Solving Systems of Inequalities by Graphing 3 – 4 Linear Programming (See Note #1) * 3 – 5 Solving Systems of Equations in Three Variables Matrices 4 – 1 Introduction to Matrices 4 – 2 Operations with Matrices 4 – 3 Multiplying Matrices 4 – 4 Transformation with Matrices 4 – 5 Determinants 4 – 6 Cramer’s Rule 4 – 7 Identity and Inverse Matrices 4 – 8 Using Matrices to Solve Systems of Equations
2.04 Use relations and functions to solve problems. Create, justify, and use best-fit mathematical models of linear, exponential, quadratic, and cubic functions to solve problems involving sets of data. a) Interpret the constants, coefficients, and bases in the context of the data. b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. 2.10 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, algebraic properties, and linear programming.
How do you find the equation of lines either parallel or perpendicular to a given line through a given point? How do you use data tables to make predictions for unknown values? How do you make predictions based upon data tables where the entries appear to vary directly? What is the difference in the graph of a linear equation and a linear inequality? How do you solve systems of equations using matrices on your graphing calculator? Are there any limits to the number of unknowns in a system of equations that restricts the use of matrices on the calculator? What is the relationship between graphing systems of inequalities and making maximum profit predictions in a business? How do you convert data tables to matrices? Can you add and multiply matrices on the graphing calculator? Just what is the calculator doing to solve system of equations using matrices? How are matrices used to make decisions? How can matrices be used in sports statistics? How are transformations used in computer animation?
14- 22
23 – 31
1.04 Operate with matrices to model and solve problems. 2.10 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, algebraic properties, and linear programming.
Dimensions of matrices. Adding matrices. Multiplying matrices. Inverse matrix. Cramer’s Rule. Real-world applications. Matrix equation. Determinant.
32 – 42
Polynomials 5 – 1 Monomials 5 – 2 Polynomials 5 – 3 Dividing Polynomials 5 – 4 Factoring Polynomials 5 – 5 Roots of Real Numbers 5 – 6 Radical Expressions 5 – 7 Rational Exponents 5 – 8 Radical Equations and Inequalities 5 – 9 Complex Numbers
1.01 Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems. 1.02 Define and compute with complex numbers. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 2.07 Use equations with radical expressions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the degree, constants, and coefficients in the context of the problem. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 2.02 Use quadratic functions and inequalities to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. 2.04 Create, justify, and use best-fit mathematical models of linear, exponential, quadratic, and cubic functions to solve problems involving sets of data. a) Interpret the constants, coefficients, and bases in the context of the data. b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 2.01 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 2.06 Use polynomial equations (third degree and higher) to model and solve problems. a) Solve using tables and graphs. b) Interpret constants and coefficients in the context of the problem. 2.07 Use equations with radical expressions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the degree, constants, and coefficients in the context of the problem.
How can polynomials be applied to financial situations? How can you use division of polynomials in manufacturing? How do square roots apply to oceanography? How do radical expressions apply to failing objects? How do rational expressions apply to astronomy? How do rational expressions apply to manufacturing? How do complex numbers apply to polynomial equations? How can income from a rock concert be maximized? How does a quadratic function model a free-fall ride? How is blood pressure related to age? How can the graph of
Operations with polynomials. Radical expressions. Complex numbers. Factoring polynomials. Solving radical equations. Rational exponents. Extraneous solutions. Conjugates.
a + bi
Synthetic division. Graphs. Maximum and minimum. Increasing and decreasing. Domain and range. Real and imaginary roots. Rational and irrational roots.
43 – 51
Quadratic Functions and Inequalities 6 – 1 Graphing Quadratic Functions 6 – 2 Solving Quadratic Equations by Graphing 6 – 3 Solving Quadratic Equations by Factoring 6 – 4 Completing the Square 6 – 5 The Quadratic Formula and the Discriminant 6 – 6 Analyzing Graphs of Quadratic Functions 6 – 7 Graphing and Solving Quadratic Inequalities
y = x 2 be used to graph
any quadratic function?
f ( x) = ax 2 + bx + c
Intercepts and zeroes.
y = a ( x ! h) 2 + k
Where are polynomial functions found in nature? How can graphs of polynomial functions show trends in data? How can you use the Remainder Theorem to evaluate polynomials? How can the Rational Root Theorem solve problems involving large numbers? How are square roots used in bridge design? Quadratic regression. Scatter plot. Zeros Graphs. Left and right endbehavior. Intercepts. Possible rational roots. Possible number of positive and negative real roots.
52 – 61
Polynomial Functions 7 – 1 Polynomial Functions (See Note #2) 7 – 2 Graphing Polynomial Functions 7 – 3 Solving Equations Using Quadratic Techniques 7 – 4 The Remainder and Factor Theorem 7 – 5 Roots and Zeros 7 – 6 Rational Root Theorem 7 – 7 Operations on Functions 7 – 8 Inverse Functions and Relations 7 – 9 Square Root Functions and Inequalities
f ( g ( x))
Index. Transformations. Domain and range. Independent and dependent.
62 – 69
Conic Section 8 – 1 Midpoint and Distance Formulas 8 – 2 Parabolas 8 – 3 Circles 8 – 4 Ellipses (See Note #1) * 8 – 5 Hyperbolas (See Note #1) * 8 – 6 Conic Sections 8 – 7 Solving Quadratic Systems
1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 2.09 Identify, compare, and construct the conic sections to model and solve problems; justify results. a) Precisely describe parabolas and circles algebraically according to definitions, characteristics, and constituent parts. b) Interpret the constants and coefficients of parabolas and circles in the context of the problem. c) Identify and distinguish among the conic sections using tables, graphs, and algebraic properties. 2.10 Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, algebraic properties, and linear programming. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems. 2.05 Use rational equations to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants and coefficients in the context of the problem. c) Identify the asymptotes and intercepts graphically and algebraically. 1.01 Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems. 2.01 Use the composition and inverse of functions to model and solve problems; justify results. 2.03 Use exponential functions to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties. b) Interpret the constants, coefficients, and bases in the context of the problem. 2.04 Create, justify, and use best-fit mathematical models of linear, exponential, quadratic, and cubic functions to solve problems involving sets of data. a) Interpret the constants, coefficients, and bases in the context of the data. b) Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions. 1.03 Operate with algebraic expressions (polynomial, rational, complex fractions) to solve problems.
How are Midpoint and Distance Formulas used in emergency medicine? How are parabolas used in manufacturing? How are circles important in air traffic control? How are hyperbolas different from parabolas? How can you use a flashlight to make a conic section? How do systems of equations apply to video games?
Conics. Vertex and focus. Axis of symmetry. Completing the square. Real-world applications. Center and radius. Major and minor axis. Direction of opening. Loci. Directrix. Transverse axis.
70 – 76
Rational Expressions and Equations 9 – 1 Multiplying and Dividing Rational Expressions 9 – 2 Adding and Subtracting Rational Expressions 9 – 3 Graphing Rational Functions 9 – 4 Direct, Joint, and Inverse Variation 9 – 5 Classes of Functions 9 – 6 Solving Rational Equations and Inequalities Exponential and Logarithmic Relations 10 – 1 Exponential Functions 10 – 2 Logarithms and Logarithmic Functions 10 – 3 Properties of Logarithms 10 – 4 Common Logarithms 10 – 5 Base e and Natural Logarithms 10 – 6 Exponential Growth and Decay
How are rational expressions used in mixtures? How is subtraction of rational expressions used in photography? How are rational expressions used to solve problems involving unit price?
Extraneous roots. Graphs. Domain and range. Asymptotes. Discontinuity. Intercepts. Zeros.
77 – 82
What is the relationship between exponential and logarithmic functions? How does an exponential function describe tournament play? Why is a logarithmic scale used to measure sound? How are properties of exponents and logarithms related? Why is a logarithmic scale used to measure acidity? How is the natural base e used in banking? How can you determine the current value of your car?
Inverse relationships. Law of Exponents. Laws of Logarithms. Common logarithms. Natural logarithms. e
f !1 f ( x) = ab x + c
Graphs Domain and range of exponential and logarithmic functions. Coefficient Base Binomial Theorem
83 – 86
Sequences and Series 11 - 1 Through 11 – 5 Sequences & Series (See Note #1) (Optional) ** 11 – 6 Recursion and Special Sequences 11 – 7 The Binomial Theorem
How does a power of a binomial describe the number of boys and girls in a family? How is the Fibonacci sequence illustrated in nature?
87 – 90
Exam Review and Exam
*NOTE #1 HONORS ALGEBRA II ONLY. **NOTE #2 LIMIT POLYNOMIAL FUNCTIONS TO THIRD DEGREE FOR ALGEBRA II.