Algebra II Objectives & Standards
A2…1.1…Exploring Transformations
Ø Apply transformations to points and sets of points.
Ø Interpret transformations of real-world data.
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A2…1.2…Introduction to Parent Functions
Ø Identify parent functions from graphs and equations.
Ø Use parent functions to model real world data and make estimates for unknown values.
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A2…1.3…Transforming Linear Functions
Ø Transform linear functions.
Ø Solve problems involving linear transformations.
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A2…1.4…Curve Fitting with Linear Models
Ø Fit scatter plot data using linear models with and without technology.
Ø Use linear models to make predictions.
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A2…2.1…Using Transformations to Graph Quadratic Functions
Ø Transform quadratic functions.
Ø Describe the effects of changes in the coefficients of y=a(x – h)2 + k.
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A2…2.2…Properties of Quadratic Functions in Standard Form
Ø Define, identify, and graph quadratic functions.
Ø Identify and use maximums and minimums of quadratic functions to solve problems.
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A2…2.3…Solving Quadratic Equations by Graphing and Factoring
Ø Solve quadratic equations by graphing or factoring.
Ø Determine a quadratic function from its roots.
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A2…2.4…Completing the Square
Ø Solve quadratic equations by completing the square.
Ø Write quadratic equations in vertex form.
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A2…2.5…Complex Numbers and Roots
Ø Define and use imaginary and complex numbers.
Ø Solve quadratic equations with complex roots.
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A2…2.6…The Quadratic Formula
Ø Solve quadratic equations using the Quadratic Formula.
Ø Classify roots using the discriminant.
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A2…2.7…Solving Quadratic Inequalities
Ø Solve quadratic inequalities by using tables and graphs.
Ø Solve quadratic inequalities by using algebra.
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A2…2.8…Curve Fitting with Quadratic Models
Ø Use quadratic functions to model data.
Ø Use quadratic models to analyze and predict.
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A2…2.9…Operations with Complex Numbers
Ø Perform operations with complex numbers.
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A2…3.1…Polynomials
Ø Identify, evaluate, add, and subtract polynomials.
Ø Classify and graph polynomials.
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A2…3.2…Multiplying Polynomials
Ø Multiply polynomials.
Ø Use binomial expansion to expand binomial expressions that are raided to positive integer powers.
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A2…3.3…Dividing Polynomials
Ø Use long division and synthetic division to divide polynomials.
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A2…3.4…Factoring Polynomials
Ø Use the Factor Theorem to determine factors of a polynomial.
Ø Factor the sum and difference of two cubes.
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A2…3.5…Finding Real Roots of Polynomial Equations
Ø Identify the multiplicity of roots.
Ø Use the Rational Root Thm. and the Irrational Root Thm. to solve polynomial equations.
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A2…3.6…Fundamental Thm. of Algebra
Ø Use the Fundamental Thm. of Algebra & its corollary to write a polynomial equation of least degree with given roots.
Ø Identify all of the roots of a polynomial equation.
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A2…3.7…Investigating Graphs of Polynomial Functions
Ø Use properties of end behavior to analyze, describe, and graph polynomial functions.
Ø Identify and use maxima & minima of polynomial functions to solve problems.
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A2…3.8…Transforming Polynomial Functions
Ø Transform polynomial functions.
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A2…3.9…Curve Fitting with Polynomial Models
Ø Use finite differences to determine the degree of a polynomial that will fit a given set of data.
Ø Use technology to find polynomial models for a given set of data.
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A2…4.1…Exponential Functions, Growth, and Decay
Ø Write and evaluate exponential expressions to model growth and decay situations.
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A2…4.2…Inverses of Relations and Functions
Ø Graph and recognize inverses of relations and functions.
Ø Find inverses of functions.
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A2…4.3…Logarithmic Functions
Ø Write equivalent forms for exponential and logarithmic functions.
Ø Write, evaluate, and graph logarithmic functions.
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A2…4.4…Properties of Logarithms
Ø Use properties to simplify logarithmic expressions.
Ø Translate between logarithms in any base.
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A2…4.5…Exponential and Logarithmic Equations and Inequalities
Ø Solve exponential and logarithmic equations and inequalities.
Ø Solve problems involving exponential and logarithmic equations.
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A2…4.6…The Natural Base, e
Ø Use the number e to write and graph exponential functions representing real-world situations.
Ø Solve equations and problems involving e or natural logarithms.
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A2…4.7…Transforming Exponential and Logarithmic Functions
Ø Transform exponential and logarithmic functions by changing parameters.
Ø Describe the effects of changes in the coefficients of exponential and logarithmic functions.
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A2…4.8…Curve Fitting with Exponential and Logarithmic Functions
Ø Model data by using exponential and logarithmic functions.
Ø Use exponential and logarithmic models to analyze and predict.
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A2…5.1…Variation Functions
Ø Solve problems involving direct, inverse, joint, and combined variation.
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A2…5.2…Multiplying and Dividing Rational Expressions
Ø Simplify rational expressions.
Ø Multiply and divide rational expressions.
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A2…5.3…Adding and Subtracting Rational Expressions
Ø Add and subtract rational expressions.
Ø Simplify complex fractions.
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A2…5.4…Rational Functions
Ø Graph rational functions.
Ø Transform rational functions by changing parameters.
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A2…5.5…Solving Rational Equations and Inequalities
Ø Solve rational equations and inequalities.
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A2…5.6…Radical Expressions and Rational Exponents
Ø Rewrite radical expressions by using rational exponents.
Ø Simplify and evaluate radical expressions containing rational exponents.
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A2…5.7…Radical Functions
Ø Graph radical functions and inequalities.
Ø Transform radical functions by changing parameters.
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A2…5.8…Solving Radical Equations and Inequalities
Ø Solve radical equations and inequalities.
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A2…6.1…Multiple Representations of Functions
Ø Translate between the various representations of functions.
Ø Solve problems by using the various representations of functions.
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A2…6.2…Comparing Functions
Ø Compare properties of two functions.
Ø Estimate and compare rates of change.
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A2…6.3…Piecewise Functions
Ø Write and graph piecewise functions.
Ø Use piecewise functions to describe real-world situations.
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A2…6.4…Transforming Functions
Ø Transform functions.
Ø Recognize transformations of functions.
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A2…6.5…Operations with Functions
Ø Add, subtract, multiply, and divide functions.
Ø Write and evaluate composite functions.
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A2…6.6…Functions and Their Inverses
Ø Determine whether the inverse of a function is a function.
Ø Write rules for the inverses of functions.
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A2…6.7…Modeling Real-World Data
Ø Apply functions to problem situations.
Ø Use mathematical models to make predictions.
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A2…7.1…Permutations and Combinations
Ø Solve problems involving the Fundamental Counting Principle.
Ø Solve problems involving permutations and combinations.
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A2…7.2…Theoretical and Experimental Probability
Ø Find the theoretical probability of an event.
Ø Find the experimental probability of an event.
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A2…7.3…Independent and Dependent Events
Ø Determine whether events are independent or dependent.
Ø Find the probability of independent and dependent events.
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A2…7.4…Two-Way Tables
Ø Construct and interpret two-way tables of data when two categories are associated with each object being classified.
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A2…7.5…Compound Events
Ø Find the probability of mutually exclusive events.
Ø Find the probability of inclusive events.
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A2…8.1…Measures of Central Tendency and Variation
Ø Find measures of central tendency of dispersion for statistical data.
Ø Examine the effects of outliers on statistical data.
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A2…8.2…Data Gathering
Ø Explain how random samples can be used to make inferences about a population.
Ø Use probability to analyze decisions and strategies.
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A2…8.3…Surveys, Experiments, and Observational Studies
Ø Focus on the commonalities and differences between surveys, experiments, and observational studies.
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A2…8.4…Significance of Experimental Results
Ø Use simulations and hypothesis testing to compare treatments from a randomized experiment.
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A2…8.5…Sampling Distributions
Ø Estimate population means and proportions and develop margin of error from simulations involving random sampling.
Ø Analyze surveys, experiments, and observational studies to judge the validity of the conclusion.
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A2…8.6…Binomial Distributions
Ø Use the Binomial Theorem to expand a binomial raised to a power.
Ø Find binomial probabilities and test hypotheses.
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A2…8.7…Fitting to a Normal Distribution
Ø Use tables to estimate areas under normal curves.
Ø Recognize data sets that are not normal.
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A2…8.8…Analyzing Decisions
Ø Explain that probability can be used to help determine if good decisions are made.
Ø Use probabilities to analyze decisions and strategies.
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A2…9.1…Introduction to Sequences
Ø Find the nth term of a sequence.
Ø Write the rules for sequences.
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A2…9.2…Series and Summation Notation
Ø Evaluate the sum of a series expressed in sigma notation.
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A2…9.3…Arithmetic Sequence and Series
Ø Find the indicated terms of an arithmetic sequence.
Ø Find the sums of arithmetic series.
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A2…9.4…Geometric Sequence and Series
Ø Find terms of a geometric sequence, including geometric means.
Ø Find the sums of geometric series.
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A2…9.5…Mathematical Induction and Infinite Geometric Series
Ø Find sums of infinite geometric series.
Ø Use mathematical induction to prove statements.
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A2…10.1…Right-Angle Trigonometry
Ø Understand and use trig relationships of acute angles in triangles.
Ø Determine side lengths of right triangles by using trig functions.
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A2…10.2…Angles of Rotation
Ø Draw angles in standard position.
Ø Determine the values of the trig functions for an angle in standard position.
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A2…10.3…The Unit Circle
Ø Convert angle measures between degrees and radians.
Ø Find the values of trig functions on the unit circle.
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A2…10.4…Inverses of Trigonometric Functions
Ø Evaluate inverse trig functions.
Ø Use trig equations and inverse trig functions to solve problems.
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A2…10.5…The Law of Sines
Ø Determine the area of a triangle given side-angle-side information.
Ø Use the Law of Sines to find the side lengths and angle measures of a triangle.
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A2…10.6…The Law of Cosines
Ø Use the Law of Cosines to find the side lengths and angle measures of a triangle.
Ø Use Heron’s Formula to find the area of a triangle.
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A2…11.1…Graphs of Sine and Cosine
Ø Recognize and graph periodic and trig functions.
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A2…11.2…Graphs of Other Trig Functions
Ø Recognize and graph trig functions.
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A2…11.3…Fundamental Trig Identities
Ø Use fundamental trig identities to simplify and rewrite expressions and to verify other identities.
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A2…11.4…Sum and Difference Identities
Ø Evaluate trig expressions by using sum and difference identities.
Ø Use matrix multiplication with sum and difference identities to perform rotations.
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A2…11.5…Double-Angle and Half-
Angle Identities
Ø Evaluate and simplify expressions by using double-angle and half-angle identities.
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A2…11.6…Solving Trig Equations
Ø Solve equations involving trig functions.
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A2…12.1…Introduction to Conic Sections
Ø Recognize conic sections as intersections of planes and cones.
Ø Use the distance and midpoint formulas to solve problems.
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A2…12.2…Circles
Ø Write an equation for a circle.
Ø Graph a circle, and identify its center and radius.
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A2…12.3…Ellipses
Ø Write the standard equation for an ellipse.
Ø Graph an ellipse, and identify its center, vertices, co-vertices, and foci.
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A2…12.4…Hyperbolas
Ø Write the standard equation for a hyperbola.
Ø Graph a hyperbola, and identify its vertices, co-vertices, center, foci, and asymptotes.
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A2…12.5…Parabolas
Ø Write the standard equation for a parabola and its axis of symmetry.
Ø Graph a parabola, and identify its focus, directrix, and axis of symmetry.
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A2…12.6…Identifying Conic Sections
Ø Identify and transform conic sections.
Ø Use the method of completing the square to identify and graph conic sections.
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A2…12.7…Solving Nonlinear Systems
Ø Solve systems of equations in two variables that contain at least one second-degree equation.
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