Algebra II Unit Breakdown (Curriculum Map Outline)

Transcription

1 QUARTER 1 Unit 1 (Arithmetic and Geometric Sequences) A. Sequences as Functions 1. Identify finite and infinite sequences 2. Identify an arithmetic sequence and its parts 3. Identify a geometric sequence and its parts 4. Identify a sequence as arithmetic, geometric or neither 5. Write recursive and explicit formulas for sequences B. Arithmetic Sequences and series 2. Define a formula to find the nth term of an arithmetic sequence 3. Calculate the arithmetic mean 4. Find the sum of an arithmetic series 5. Write an arithmetic series in summation notation C. Geometric Sequences and series 1. Define formula to find the nth term of a geometric sequence 2. Calculate the geometric mean 3. Find the sum of a finite geometric series D. Infinite Geometric Series 1. Determine whether an infinite geometric series diverges or converges 2. Find the sum of an infinite geometric series E. Modeling 1. Apply an arithmetic sequence 2. Apply a geometric sequence 3. Apply an arithmetic series 4. Apply a geometric series Unit 2 Unit 3 (Quadratic Relations and Equations) A. The Square Root Property and Completing the Square 1. Solve quadratic equations using the square root property 2. Solve quadratic equations by completing the square 3. Solve quadratic equations with solutions that are not real numbers* B. The Quadratic Formula 1. Solve quadratic equations by using the quadratic formula 2. Use the discriminant to determine the number and type of solutions 3. Solve quadratic equations with solutions that are not real numbers 4. Determine which method applies, and then solve the equation C. Graphs of Quadratic Functions 1. Graph parabolas with horizontal and vertical shifts 2. Identify the vertex of a parabola 3. Predict the shape and directions of a parabola 4. Graph a parabola using the focus and directrix D. Modeling with Quadratic Functions 1. Find a quadratic function to model data, and use it to answer questions 2. Solve problems involving maximum or minimum values 3. Find the equation of a parabola through three ordered pairs, using a system of 3 equations 4. Graph quadratic inequalities (Polynomial Functions and Equations) A. Operations on Polynomials 1. Add and subtract polynomials

2 QUARTER 2 Unit 4 2. Multiply polynomials 3. Divide polynomials using synthetic division 4. Divide polynomials using polynomial long division B. Graphs of Polynomial Functions 1. Determine end behavior of a polynomial function 2. Describe the graph of a polynomial function 3. Determine if a function is even or odd 4. Find the relative maximum and relative minimum of the graph of a function 5. Locate zeros on a graph C. Solving Polynomonial Equations 1. Factor polynomials (include sum and difference of cubes) 2. Find all real roots of polynomial equations algebraically and by graphing 3. Find all complex roots of a polynomial equation D. Remainder and Factor Theorems 1. Apply the remainder theorem* 2. Use synthetic substitution to find polynomial values 2. Use the factor theorem to find remaining factors E. Modeling Functions 1. Write a polynomial function from its zeros 2. Graph a polynomial model (Rational Functions and Equations) A. Inverse Variation 1. Recognize and use inverse variation 2. Use joint and other variations B. Rational Functions and their Graphs 1. Identify properties of rational functions 2. Find the domain of a rational function 3. Graph rational functions 4. Find removable and non-removable points of discontinuity C. Rational expressions 1. Simplify rational expressions 2. Multiply or divide rational expressions 3. Adding and Subtracting Rational Expressions 1. FInd the least common multiple 2. Simplify complex fractions E. Solving Rational Equations 1. Solve rational equations* 2. Use rational equations to solve problems F. Modeling Functions 1. Graph inequlaities Unit 5 (Radical Functions and Equations) A. Radical Graphs 1. Graph radical functions 2. Find domain and range of radical functions B. Rational Exponents 1. Use exponential notation for nth roots 2. Convert expressions with rational exponents to radicals

3 3. Simplify radicals by first converting to rational exponents 4. Use the rules for exponents with rational exponents C. Simplifying Radical Expressions 1. Use the product and quotient rules for radicals 2. Simplify radicals 3. Simplify products and quotients of radicals with different indexes D. Operations with Radicals 1. Simplify radical expressions involving addition and subtraction 2. Multiply radicals 3. Rationalize denominators 4. Write radical quotients in lowest terms F. Solving Equations with Radicals 1. Solve radical equations using the power rule* 2. Use the power rule to solve a formula for a specified variable. Unit 6 (Inverse, Exponential and Logarithmic Functions and Equations) A. Inverse Functions and Function Compositions 1. Decide whether a function is one-to-one and, if it is, find its inverse 2. Graph inverse functions B. Exponential Functions 1. Graph an exponential functions 2. Solve exponential equations by finding a common base C. Logarithmic Functions 1. Convert between exponential and logarithmic forms 2. Solve logarithmic equations 3. Define and graph logarithmic functions 4. Solve exponential equations using logarithms D. Properties of Logarithms 1. Write logarithms as sum or difference of logarithms, or as a single number if possible 2. Write an expression as a single logarithm 3. Use properties to evaluate logarithms E. Common and Natural Logarithms 1. Evaluate common and natural logarithms 2. Use the change-of-base rule F. Applications of Exponential and Logarithmic Functions 1. Solving applications involving exponential growth and decay. 2. Use common and natural logarithms in applications 3. Solve applications of compound interest QUARTER 3 Unit 7 (Trigonometric Functions) A. Radian Measure 1. Interpret Radians as a new unit of Measurement 2. Find the length of an arc B. Angles and the Unit Circle 1. Convert Degree Measure to Radian, and Radian to Degree 2. Angles in Standard Position 3. Identify Coterminal Angles

4 4. Find Cosines and Sines of Angles C. Sine and Cosine Functions 1. Find Period and Amplitude 2. Graph Sine and Cosine Curves D. Tangent Functions 1. Find the Period and Asymptotes of a tangent graph 2. Graph a Tangent Function E. Translating Sine and Cosine Functions 1. Identifying Phase Shifts 2. Graph Translations 3. Graph a Combined Translation F. Trigonometric Identities 1. Verify Trigonometric Identities 2. Simplify Trigonometric Expressions 3. Express one Trigonometric function in terms of another G. Applications and Modeling 1. Exploring Periodic Data 2. Identify Periodic Functions in Real World Applications Unit 8 Unit 9 (Choosing a Function Model) A. Regression equations 1. Draw from knowledge of parent functions to find an appropriate regression equation 2. Use the model to make predictions in the context of the situation 3. Find correlation coefficient to determine strength of a model B. Optimization 1. Analyze problem situation 2. Model the situation with a function 3. Find local maximum or minimum values of that function 4. Interpret their solutions in the context of the problem C. Applications 1. Use problem solving techniques and knowledge of various function families to solve a variety of application problems 2. Use geometric relationships, numerical relationships and combinations of functions in various real-world applications. (Probability) A. Theoretical vs Empirical Methods B. Conditional Probability 1. Independent Probability 2. Dependent Probability 3. Identify concepts of Independent and Conditional Probability in everyday situations C. Compound Probability 1. Overlapping Events using the Addition Rule 2. Disjoint Events 3. Probability of the Complement of an Event Unit 10 (The Design of Statistical Studies) A. Sampling and Surveys, How to Sample Badly, How to Sample Well: Random Samples B. Inference for Sampling, Sample Surveys: What Can Go Wrong? 1. How undercoverage, nonresponse, and question wording can lead to bias in an SRS C. Observational Studies vs. Experiments, The Language of Experiments

5 1. Distinguish between an observational study and an experiment. 2. Explain how a lurking variable in an observational study can lead to confounding 3. Identify the experimental units or subjects, explanatory variables (factors), treatments, and response variables in an experiment D. How to Experiment Well, Three Principles of Experimental Design 1. Control of Outside Variables 2. Randomization 3. Replication E. Inference for Experiments 1. Explain in context what statistically significant means F. Scope of Inference, the Challenges of Establishing Causation 1. Determine the scope of inference for a statistical study QUARTER 4 Unit 11 (Gathering Data, making inferences, and justifying conclusions) A. Measuring Position: Percentiles, Cumulative Relative Frequency Graphs, Measuring Position: z-scores B. Transforming Data, Density Curves C. Normal Distributions, The Rule, The Standard Normal Distribution D. Normal Distribution Calculations E. Assessing Normality F. Simulation G. Probability Models H. Margin of Error