NYS Learning Standards Basic Algebra II

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Select the number of each type of objective: (Selecting Random will randomly generate all subtypes) Click on any title to see the free sample worksheet. (only the first few samples are free) (Random) N-RN.A.1-2 Extend the properties of exponents to rational exponents. a. Converting Radicals to Exponents (Rationals) b. Converting Exponents (Rationals) to Radicals (Random) N-CN.A.1-2 Perform arithmetic operations with complex numbers. a. Fixing Radicals into Imaginary Numbers b. Adding Complex Numbers c. Subtracting Complex Numbers d. Multiplying Complex Numbers e. Dividing Complex Numbers f. Simplifying iⁿ (Random) A-SSE.A.1-2 Interpret the structure of expressions. a. Identifying Like Terms b. Classifying Polynomials by the Number of Terms c. Finding and Completing Patterns (from Pictures) d. Finding and Completing Patterns (from Tables) e. Finding and Completing Patterns (from Word Problems) f. Identifying GCFs g. Factoring out Monomials h. Factoring Trinomials with hints i. Factoring Trinomials (a=1) (Grid Factoring Video) j. Factoring Trinomials (a>1) (Grid Factoring Video) k. Factoring Difference of Squares l. Factoring Perfect Square Trinomials (Random) A-SSE.B.3 Write expressions in equivalent forms to reveal their characteristics. a. Multiplying Monomials (includes negative exponents) b. Dividing Monomials (includes negative exponents) c. Dividing Polynomials by a Monomial (no factoring needed) d. Solving for x in Area Problems e. Area Word Problems f. Factoring: Pulling out the GCF g. Factoring Trinomials (a=1) (Grid Factoring Video) h. Factoring Trinomials (a>1) (Grid Factoring Video) i. Factoring: Difference of Squares j. Factoring: Perfect Square Trinomials k. Factoring: Sum and Difference of Cubes l. Factoring: Group Factorable m. Factoring: Combination -- Hard Factorable n. Identifying Trinomial Factors in Difference of Cubes o. Possible Factoring Coefficients (Random) A-APR.B.2-3 Understand the relationship between zeros and factors of polynomials. a. Graphically Finding the Roots and Zeros b. Identifying Zeros of Graphs c. Relating Factors, Zeros and X-Intercepts (Random) A-APR.D.6 Rewrite rational expressions a. Multiplying Rational Expressions (Easier) b. Multiplying Rational Expressions (Harder) (Requires Factoring!) c. Dividing Rational Expressions (Easier) d. Dividing Rational Expressions (Harder) (Requires Factoring!) e. Adding Rational Expressions(Easier) f. Adding Rational Expressions (Harder) (Requires Factoring!) g. Subtracting Rational Expressions(Easier) h. Subtracting Rational Expressions (Harder) (Requires Factoring!) i. Mixed Rational Expressions (Multiple Operations with simplify)(Easier) (Requires Factoring GCF!) j. Mixed Rational Expressions (Multiple Operations with simplify) (Harder) (Requires Factoring!) k. Finding Equations of Vertical Asymptotes of Rational Functions l. Finding Equations of Horizontal Asymptotes of Rational Functions m. Adding/Subtracting Monomials Rational Expressions (Random) A-CED.A.1 Create equations that describe numbers or relationships. a. Identifying the degree of the polynomial b. Reading Graphs for Word Problems c. Linear Word Problems - finding slope d. Linear Word Problems - finding y-intercepts e. Linear Word Problems - finding f(a) f. Linear Word Problems - finding x where f(x) = a g. Quadratic Word Problems - finding max/min h. Quadratic Word Problems - finding y-intercepts i. Quadratic Word Problems - finding x-intercepts j. Quadratic Word Problems - finding f(a) k. Quadratic Word Problems - finding x where f(x) = a (Random) A-REI.A.1-2 Understand solving equations as a process of reasoning and explain the reasoning. a. Filling In Algebraic Proofs (Simplifying Expressions) b. Filling In Algebraic Proofs (Equations) c. Solving Quadratics by Completing the Square d. Solving Quadratics with the Quadratic Formula (Real Solutions) e. Identifying the Number of Solutions of a Quadratic Using the Discriminant f. Solving Quadratics that have Imaginary Solutions g. Solving Quadratics (both imaginary and real solutions) h. Solving Equations with Rational Expressions i. Solving Equations with Radical Expressions j. Word Problems of Radical Expressions k. Finding Zeros of a Polynomial l. Graphing a Polynomial m. Finding zeros of a Polynomial from a Graph n. Finding the X-Intercepts of a Polynomial o. Finding a Polynomial equation from Zeros p. Domain and Range of Radical Functions q. Identifying Field properties (distributive, associative, etc) (Integers) r. Identifying Field properties (Polynomials) s. Identifying Field properties (Complex Numbers) t. Classifying Numbers into Fields (Natural, Whole, Real, etc.) (Random) A-REI.B.4 Solve equations and inequalities in one variable. a. Solving Quadratics By The Square-Root Method b. Solving Quadratics by Graphing c. Solving Quadratics by Factoring d. Solving Quadratic Equations in Vertex form e. Solving Quadratic Equations using the Quadratic Formula f. Verifying Solutions of Quadratic Equations g. Solving Quadratic Based Word Problems (Random) A-REI.C.7 Solve systems of equations. a. Solving Nonlinear Systems of Equations using Linear Combination b. Solving Nonlinear Systems of Equations using Substitution (Random) A-REI.D.11 Represent and solve equations and inequalities graphically. a. Graphing Linear Inequalities b. Writing the Equation of a Linear Graph c. Graphing in Slope-Intercept Form d. Graphing with Point-Slope Form e. Graphing from Standard Form f. Graphing with x and y Intercepts g. Graphically Solving Quadratic Equations h. Factoring to Solve Quadratic Equations (Random) F-IF.A.3 Understand the concept of a function and use function notation. a. Finding and Completing Patterns (from Sequences) b. Identifying Arithmetic/Geometry Sequences (Random) F-IF.B.4,6 Interpret functions that arise in applications in terms of the context. a. Finding where a Rational Function is positive b. Finding where a Radical Function is positive c. Finding where a Linear Function is positive d. Finding where a Quadratic Function is positive e. Finding where a Polynomial Function is positive f. Finding where an Absolute Value Function is positive g. Finding where a Exponential Function is positive h. Finding where a Rational Function is negative i. Finding where a Radical Function is negative j. Finding where a Linear Function is negative k. Finding where a Quadratic Function is negative l. Finding where a Polynomial Function is negative m. Finding where an Absolute Value Function is negative n. Finding where a Exponential Function is negative o. Finding maxima and minima of an Absolute Value Function p. Finding maxima and minima of a Quadratic Function q. Finding maxima and minima of a Polynomial Function r. Finding symmetries of a Rational Function s. Finding symmetries of a Radical Function t. Finding symmetries of an Absolute Value Function u. Finding symmetries of a Linear Function v. Finding symmetries of a Quadratic Function	w. Finding symmetries of a Polynomial Function x. Finding symmetries of a Exponential Function y. Finding end behavior of a Quadratic Function z. Finding end behavior of a Polynomial Function aa. Finding end behavior of an Absolute Value Function bb. Finding end behavior of a Exponential Function cc. Finding the rate of change of a Radical Function dd. Finding the rate of change of an Absolute Value Function ee. Finding the rate of change of a Linear Function ff. Finding the rate of change of a Quadratic Function gg. Finding the rate of change of a Polynomial Function hh. Finding the rate of change of a Exponential Function (Random) F-IF.C.7-9 Analyze functions using different representations. a. Finding Zeros of Functions b. Finding Values of Functions c. Finding areas of Increasing or Decreasing for Functions d. Describing End Behavior of Polynomials e. Finding X and Y-Intercepts of Functions f. Writing the Equation of a Basic Function from a Graph (Parabola, Line, Absolute Value, etc) g. Writing the Equation of a Basic Function from a Table (Parabola, Line, Absolute Value, etc) h. Graphing Piecewise Functions i. Comparing maximum/minimum j. Comparing domain/range k. Finding domain/range of inverse functions (Random) F-BF.A.1-2 Build a function that models a relationship between two quantities. a. Exponential Growth b. Direct Variation Word Problems c. Polynomial Word Problems - finding max/min d. Polynomial Word Problems - finding y-intercepts e. Polynomial Word Problems - finding x-intercepts f. Polynomial Word Problems - finding f(a) g. Exponential Word Problems - finding y-intercepts h. Exponential Word Problems - finding f(a) i. Exponential Word Problems - finding x where f(x) = a j. Rational Word Problems - finding horizontal asymptotes k. Rational Word Problems - finding f(a) l. Rational Word Problems - finding x where f(x) = a m. Radical Word Problems - finding f(a) n. Radical Word Problems - finding x where f(x) = a o. Writing the first n terms of an Arithmetic Sequence p. Defining an Arithmetic Sequence with Recursion q. Writing the first n terms of a Geometric Sequence r. Defining a Geometric Sequence with Recursion (Random) F-BF.B.3-7 Build new functions from existing functions. a. Describing the Transformation of a Basic Function b. Writing the Equation of a Transformed Function c. Finding Inverses of Functions d. Finding Composition of Functions e. Using Composition of Functions to Identify Inverse Functions f. Identifying Equations (from charts, sets, and scatterplots) g. Composition of Function Word Problems h. Identifying the Base i. Logarithmic to Exponential j. Exponential to Logarithmic k. Evaluating Logs (by hand) l. Evaluating Summations of Arithmetic Series (Number Arches Video) m. Evaluating Finite Summations of Geometric Series n. Evaluating Infinite Summations of Geometric Series (Random) F-LE.A.2,4 Construct and compare linear, quadratic, and exponential models and solve problems. a. Writing Linear Functions from Graphs b. Writing Linear Functions from Words c. Writing Linear Functions from Sets/Tables d. Writing Linear Functions from Sequences e. Writing Exponential Functions from Graphs f. Writing Exponential Functions from Words g. Writing Exponential Functions from Sets/Tables h. Writing Exponential Functions from Sequences i. Completing Ordered Pairs for Linear Equations j. Checking Points for Solutions in Linear Equations k. Expanding Expressions (easier) l. Expanding Expressions (harder) m. Contracting Expressions (easier) n. Contracting Expressions (harder) o. Solving Equations with Logs p. Evaluating Logs using the Change of Base Formula q. Finding Inverses (Random) F-LE.B.5 Interpret expressions for functions in terms of the situation they model. a. Solving Word Problems (Systems of Linear Equations) b. Identifying the function graph (exponential / logarithmic / polynomial / absolute value / etc) c. Recognizing the Equations and Graphs of Absolute Value, Greatest Integer, and Exponential Functions d. Triangle Sum Word Problems e. Basic Growth And Decay Problems f. Multiple Bank Account Word Problems (Random) F-TF.A.1-2,4 Extend the domain of trigonometric functions using the unit circle. a. Recognize and draw an angle in standard position. b. Using the Unit Circle and Arc Length to see Radians. c. Finding the Reference Angle d. Converting from Radians to Degrees e. Converting from Degrees to Radians f. Converting from Degrees Minutes and Seconds to Degrees g. Converting from Degrees to Degrees Minutes and Seconds h. Determining Odd/Even Functions i. Applying the Unit Circle to find Domain/Range Even/Odd Period (Random) F-TF.B.5 Model periodic phenomena with trigonometric functions. a. Basic Facts and Graphs of parent Trigonometric Functions b. Determining Amplitude in Graph and Equation c. Writing Equations of Amplitude and Vertical Stretch Changes d. Sketching Graphs with Amplitude Changes, Vertical Stretches, and Vertical Flips (Random) F-TF.C.8 Prove and apply trigonometric identities. a. Define the six triangular trigonometric functions of an angle in a right triangle. b. Define the six circular trigonometric functions of an angle in standard position. c. Make the connection between the triangular and circular trigonometric functions. d. Given one trigonometric function value, find the other five trigonometric function values. e. Simplifying Pythagorean Identities f. Verifying Pythagorean Identities (Random) S-ID.A.4 Summarize, represent, and interpret data on a single count or measurement variable. a. Finding Mean, Median and Mode b. Identifying the Meaning of Mean, Median and Mode c. Finding Standard Deviation (s) d. Finding Standard Deviation (σ) e. Comparing Two Normal Curves (with Z-Scores) f. Properties of Normal and Standard Normal Distributions g. Using Tables of the Normal Distribution (given a sample piece of data) h. Using Tables of the Normal Distribution (given probability) (Random) S-ID.B.6 Summarize, represent, and interpret data on two categorical and quantitative variables. a. Finding the Line of Best Fit from a Table or Scatter Plot b. Predicting with the Line of Best Fit c. Finding the Curve of Best Fit d. Displaying Data using Frequency Distribution Chart e. Reading Frequency Distribution Chart (Random) S-IC.A.2 Understand and evaluate random processes underlying statistical experiments. a. Properties of Normal and Standard Normal Distributions and the Empirical Rule 68-95-99.7 b. Finding the Z-Score c. Using Tables of the Normal Distribution (given z-score) d. Using Tables of the Normal Distribution (given a sample piece of data) e. Using Tables of the Normal Distribution (given probability) (Random) S-IC.B.3,4,6 Make inferences and justify conclusions from sample surveys, experiments, and observational studies. a. Census b. Sample Survey c. Experiment d. Observational Study (Random) S-CP.A.1,4 Understand independence and conditional probability and use them to interpret data. a. Empirical vs. Theoretical vs. Subjective Probability b. Law of Large Numbers c. Finding Sample Space d. Mutually Exclusive and Basic Probabilities e. Finding Probability of Independent Events f. Finding Probability of Dependent Events (Random) S-CP.B.7 Use the rules of probability to compute probabilities of compound events in a uniform probability model. a. Addition Rule
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