Centerville High School Curriculum Mapping Algebra 2 Semester 1

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1 Unit/Section Indiana Standard(s) Unit 1 1-1/1-3 NA Evaluate the expression. Solve the equation. 3-1/3-2 AII.SE.1, A.II.SE AII.SE.1, A.II.SE.2 Applications AII.SE.3 of Systems Centerville High School Curriculum Mapping Algebra 2 Semester 1 Key Questions/Concepts Resources/Activities Vocabulary Assessments Solve the system of equations involving two variables. Write systems equations involving real world problems and solve them. Solve systems of equations with three variables. Solve systems of equations with two or three variables. Write systems of equations involving real world problems. Solve systems of equations with lines, circles, and parabolas. Unit 2 2-1/2-2 AII.F.1 What is a relation? What is a function? Determine whether the set of ordered pairs, table, mapping, or graph represents a function. List the domain and range of the relation/function. Find values of functions at given inputs. Determine whether the function is linear. 2-6 AII.PR.2, AII.PR AII.PR.2, AII.PR.3, AII.F.5 Graph the absolute value function or piecewise function. List the domain and range of the functions. Describe the transformation of the parent function. Graph the function using transformations. Expression, Equation, Evaluate, Solve, Solution Systems of Equations Systems of Equations Linear equation, parabola, circle Relation, Function, Domain, Range, Vertical Line Test, Function Notation, Linear Function Absolute Value, Piecewise Function, Domain, Range Parent Function, Transformation (Vertical Shift, Horizontal Shift, Stretch/Compress) Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, 1

2 Unit 3 4-1/4-2 AII.Q.1 Identify the Axis of Symmetry and Vertex of the Parabola. Determine whether the vertex is a maximum or minimum. Graph the quadratic function. Determine the solutions of the quadratic equation by graphing. 4-3 AII.Q.1 Factor the polynomial. Factor the quadratic expression. Solve the quadratic equation by factoring. 4-4 AII.CNE.1 What is i? What is a complex number? Perform various operations with i. Simplify expressions with i. 4-5 AII.Q.1, AII.Q AII.Q.1, AII.Q AII.Q.1, AII.Q.3 Identify perfect square trinomials. Find the value of c such that the trinomial is a perfect square. Complete the square. Solve the quadratic equation by completing the square. Identify the vertex of the parabola given vertex form. Graph the parabola from vertex form. Re-write the quadratic equation in vertex form. Solve the quadratic equation using the quadratic formula. Identify the number and type of solutions to the quadratic equation using the discriminant. Unit AII.CNE.3 Add, Subtract, and Multiply Polynomial Expressions. Divide polynomials by a monomial Days AII.CNE.3, AII.CNE.5 Divide a polynomial by a binomial using Long Division and Synthetic Division 5-3/5-4 AII.PR.2 Identify the Domain, Range, Maximums, Minimums, Intercepts, and End Behavior of the function. Analyze major points (listed above) in the context of a real-world situation. Quadratic Equation/Function, Parabola, Axis of Symmetry, Vertex, Maximum, Minimum, Solutions Polynomial, Factor Imaginary Unit, Complex Number, Complex Conjugate Perfect Square Trinomial, Completing the Square Vertex Form, Completing the Square Quadratic Formula, Discriminant Polynomial Long Division, Synthetic Division Domain, Range, Maximums, Minimums, Intercepts, and End Behavior Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, Quizzes, 2

3 5-6 AII.CNE.3, AII.CNE AII.CNE.1, AII.CNE.2, AII.CNE AII.CNE.1, AII.CNE.2, AII.CNE.5 What is the Remainder Theorem? Use Synthetic Substitution to find function values at given inputs. What is the Factor Theorem? Find all factors of a polynomial given one of its factors. What is the Fundamental Theorem of Algebra? State the possible number of positive and negative roots using Descartes Rule of Signs. Determine a polynomial given its roots and using the Complex Conjugate Theorem. List all possible real roots of a polynomial. Find all roots of the polynomial Remainder Theorem, Synthetic Substitution, Factor Theorem Fundamental Theorem of Algebra, Descartes Rule of Signs, Complex Conjugate Theorem Rational Zero Theorem, Synthetic Substitution Quizzes, Quizzes, Quizzes, 3

4 Unit/Section Indiana Standard(s) Unit AII.F.2 Add, Subtract, Multiply, and Divide functions. Compose Functions 6-2 AII.F.2, AII.F.3, AII.F.4 Curriculum Mapping Algebra 2 Semester 2 Key Questions/Concepts Resources/Activities Vocabulary Assessments Find the inverse of a function. Graph a function and its inverse. Determine whether the functions are inverses. 6-3 AII.PR.2 Graph the square root function. Determine the domain and range of the function. 6-4 AII.CNE.2 What is a radical expression? Determine the nth root of a number. Simplify radical expressions. 6-5 AII.CNE.2 Add, Subtract, Multiply, and Divide Radical Expressions. Use the Conjugate to simplify. 6-6 AII.CNE.2 Re-Write radical expressions using rational exponents. Evaluate with rational exponents. Simplify rational expressions using properties of exponents. 6-7 AII.PR.3 Solve radical equations Unit AII.EL.2 Graph the exponential function. Determine the Domain, Range, and Horizontal Asymptote. 7-2 AII.EL.7 Re-write the number in terms of a smaller base. Solve the exponential equation. Find Compound interest, and values of exponential growth and decay. Function, Composition of Functions Inverse Relation/Function Square Root Function Radical Expression, nth root (cube, fourth, etc.) Conjugate Rational Exponent Radical Equation Exponential Function, Domain, Range, Asymptote Base, Exponent, Power, Compound Interest, Exponential Growth/Decay, Growth/Decay Factor 4

5 7-3 AII.EL.5 Re-write the exponential expression as a logarithm. Evaluate the logarithm. Graph the Logarithmic Function. Determine the Domain and Range. 7-4 AII.EL.6 Solve the logarithmic equation. 7-5 AII.EL.6 Simplify the logarithm. Re-write the logarithmic expression as a single logarithm using properties of logs. Solve the logarithmic equation. 7-6 AII.EL.6 What is the Common Log? Use the Change of Base Formula to evaluate logs of different bases. Use Common Log to solve exponential equations. 7-7 AII.EL.6 What are e and ln? Simplify expressions with e and ln. Solve equations using e and ln. Use the continuous interest formula. 7-8 AII.EL.7 Use e and ln to solve real world problems involving exponential growth and decay. Unit AII.CNE.3, AII.CNE AII.CNE.3, AII.CNE AII.CNE.3, AII.CNE.4 What is a rational expression? Determine the undefined values of a rational expression. Multiply/divide the rational expressions. Simplify the complex fraction. Add/Subtract the rational expressions. Solve the equation/inequality containing rational expressions. 8-3 AII.PR.2 Graph the reciprocal function. Determine the asymptotes, domain and range. 8-5 AII.PR.3 Use Direct, Joint, and Inverse variations to find unknown values. Logarithm, Inverse, Logarithmic Function, Domain, Range Logarithm Logarithm; Addition, Subtraction, multiplication, division, and power rules for logarithms Common Log, Change of Base Formula Natural Base, Natural Logarithm, Continuous Interest Formula Exponential Growth/Decay Formulas Rational Expression, Undefined, Multiplication/Division rules for fractions, Complex Fraction Rational Expression, Addition/Subtraction Rules for Fractions Rational Expression, Common Denominator, Undefined Values Reciprocal Function, Asymptote, Domain, Range Direct, Joint, and Inverse Variations 5

6 Unit ALL.CNE.6 Determine whether a sequence is arithmetic or geometric. Find values of a sequence given terms in the sequence. Write a linear or exponential equation to represent a(n) arithmetic or geometric sequence respectively AII.CNE.6, AII.EL AII.CNE.6, AII.EL.1 Find terms (first, last, nth) in an arithmetic sequence. Find the common difference of a sequence. Use the Arithmetic Equation to write an equation for a given sequence. Find partial sum of an arithmetic series. Write an arithmetic series in sigma notation. Find terms (first, last, nth) in a geometric sequence. Find the common ratio of a sequence. Use the Geometric Equation to write an equation for a given sequence. Find partial sum of a geometric series. Write a geometric series in sigma notation N/A Determine whether the infinite geometric series converges or diverges. Find the sum of an infinite geometric series AII.EL.1 Evaluate terms of recursive sequences. Write recursive formulas for arithmetic and geometric sequences. Use recursion in a real-world context. Unit AII.DSP.1 Create and analyze scatter plots. Find lines of regression. Make predictions based on a line of regression. Sequence, Arithmetic Sequence, Geometric Sequence. Arithmetic Sequence, Common Difference, Arithmetic Equation, Series, Partial Sum, Sigma Notation Geometric Sequence, Common Ratio, Geometric Equation, Series, Partial Sum, Sigma Notation Converge, Diverge, Infinite Geometric Series Recursion 6

7 11-1 AII.DSP.2 Identify different forms of studies and when they are appropriate for data collection. Design a study and collect data to be analyzed AII.DSP.3, AII.DSP AII.DSP.3, AII.DSP.4 Identify types of distributions of data. Create and analyze box and whisker plots and histograms. What is a discrete random variable? What is a continuous random variable? What is a probability distribution? What is the Law of Large Numbers? Calculate the Expected Value. Calculate the standard deviation. 0-4 AII.DSP.6 Use the Fundamental Counting Principle to find the number of possible outcomes. Identify Permutations and Combinations. Evaluate Permutations and Combinations 0-6 AII.DSP.5 Find probabilities of independent and dependent events. Find conditional Probabilities. Study, Sample Spaces, Bias Negatively Skewed, Symmetrically Skewed, Positively Skewed Distributions, Box and Whisker Plots, Histograms, Discrete random variable, Continuous random variable, probability distribution, Law of Large Numbers, Expected Value, Standard Deviation Findamental Counting Principle, Permutation, Combination Independent/ Dependent Events, Conditional Probability 7

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