A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
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1 | Algebra II | |||||||||||||||||||||||||

2 | A.APR.3 | Arithmetic With Polynomials And Rational Expressions | Understand The Relationship Between Zeros And Factors Of Polynomials | Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. | ||||||||||||||||||||||

3 | A.APR.4 | Arithmetic With Polynomials And Rational Expressions | Use Polynomial Identities To Solve Problems | Prove polynomial identities and use them to describe numerical relationships. | ||||||||||||||||||||||

4 | A.REI.11 | Reasoning With Equations And Inequalities | Represent And Solve Equations And Inequalities Graphically | Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g. using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★ | ||||||||||||||||||||||

5 | A.REI.12 | Reasoning With Equations And Inequalities | Represent And Solve Equations And Inequalities Graphically | Graph the solutions to a linear inequality in two variables as a half- plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. | ||||||||||||||||||||||

6 | A.REI.2 | Reasoning With Equations And Inequalities | Understand Solving Equations As A Process Of Reasoning And Explain The Reasoning | Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. | ||||||||||||||||||||||

7 | A.REI.4.a | Reasoning With Equations And Inequalities | Solve Equations And Inequalities In One Variable | Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. | ||||||||||||||||||||||

8 | A.REI.5 | Reasoning With Equations And Inequalities | Solve Systems Of Equations | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. | ||||||||||||||||||||||

9 | A.REI.6 | Reasoning With Equations And Inequalities | Solve Systems Of Equations | Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables. | ||||||||||||||||||||||

10 | A.REI.7 | Reasoning With Equations And Inequalities | Solve Systems Of Equations | Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. | ||||||||||||||||||||||

11 | A.SSE.3.b | Seeing Structure In Expressions | Write Expressions In Equivalent Forms To Solve Problems | Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. | ||||||||||||||||||||||

12 | A.SSE.3.c | Seeing Structure In Expressions | Write Expressions In Equivalent Forms To Solve Problems | Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. | ||||||||||||||||||||||

13 | A.SSE.4 | Seeing Structure In Expressions | Write Expressions In Equivalent Forms To Solve Problems | Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. | ||||||||||||||||||||||

14 | F.BF.1 | Building Functions | Build A Function That Models A Relationship Between Two Quantities | Write a function that describes a relationship between two quantities. | ||||||||||||||||||||||

15 | F.BF.1.a | Building Functions | Build A Function That Models A Relationship Between Two Quantities | Determine an explicit expression, a recursive process, or steps for calculation from a context. | ||||||||||||||||||||||

16 | F.BF.1.b | Building Functions | Build A Function That Models A Relationship Between Two Quantities | Combine standard function types using arithmetic operations. | ||||||||||||||||||||||

17 | F.BF.2 | Building Functions | Build A Function That Models A Relationship Between Two Quantities | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★ | ||||||||||||||||||||||

18 | F.BF.3 | Building Functions | Build New Functions From Existing Functions | Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. | ||||||||||||||||||||||

19 | F.BF.4 | Building Functions | Build New Functions From Existing Functions | Find inverse functions. | ||||||||||||||||||||||

20 | F.BF.4.a | Building Functions | Build New Functions From Existing Functions | Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. | ||||||||||||||||||||||

21 | F.IF.3 | Interpreting Functions | Understand The Concept Of A Function And Use Function Notation | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. | ||||||||||||||||||||||

22 | F.IF.4 | Interpreting Functions | Interpret Functions That Arise In Applications In Terms Of The Context | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★ | ||||||||||||||||||||||

23 | F.IF.6 | Interpreting Functions | Interpret Functions That Arise In Applications In Terms Of The Context | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ | ||||||||||||||||||||||

24 | F.IF.7.b | Interpreting Functions | Analyze Functions Using Different Representations | Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. | ||||||||||||||||||||||

25 | F.IF.7.c | Interpreting Functions | Analyze Functions Using Different Representations | Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. | ||||||||||||||||||||||

26 | F.IF.7.e | Interpreting Functions | Analyze Functions Using Different Representations | Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. | ||||||||||||||||||||||

27 | F.IF.8 | Interpreting Functions | Analyze Functions Using Different Representations | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | ||||||||||||||||||||||

28 | F.IF.8.a | Interpreting Functions | Analyze Functions Using Different Representations | Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. | ||||||||||||||||||||||

29 | F.IF.8.b | Interpreting Functions | Analyze Functions Using Different Representations | Use the properties of exponents to interpret expressions for exponential functions. | ||||||||||||||||||||||

30 | F.IF.9 | Interpreting Functions | Analyze Functions Using Different Representations | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | ||||||||||||||||||||||

31 | F.LE.1 | Linear, Quadratic, And Exponential Models★ | Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems | Distinguish between situations that can be modeled with linear functions and with exponential functions. | ||||||||||||||||||||||

32 | F.LE.1.a | Linear, Quadratic, And Exponential Models★ | Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems | Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. | ||||||||||||||||||||||

33 | F.LE.1.b | Linear, Quadratic, And Exponential Models★ | Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems | Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. | ||||||||||||||||||||||

34 | F.LE.1.c | Linear, Quadratic, And Exponential Models★ | Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems | Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. | ||||||||||||||||||||||

35 | F.LE.2 | Linear, Quadratic, And Exponential Models★ | Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). | ||||||||||||||||||||||

36 | F.LE.3 | Linear, Quadratic, And Exponential Models★ | Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems | Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. | ||||||||||||||||||||||

37 | F.LE.4 | Linear, Quadratic, And Exponential Models★ | Construct And Compare Linear, Quadratic, And Exponential Models And Solve Problems | For exponential models, express as a logarithm the solution to abct =dwherea,c,anddarenumbersandthebasebis2,10,ore; evaluate the logarithm using technology. | ||||||||||||||||||||||

38 | F.LE.5 | Linear, Quadratic, And Exponential Models★ | Interpret Expressions For Functions In Terms Of The Situation They Model | Interpret the parameters in a linear or exponential function in terms of a context. | ||||||||||||||||||||||

39 | F.TF.1 | Trigonometric Functions | Extend The Domain Of Trigonometric Functions Using The Unit Circle | Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. | ||||||||||||||||||||||

40 | F.TF.2 | Trigonometric Functions | Extend The Domain Of Trigonometric Functions Using The Unit Circle | Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. | ||||||||||||||||||||||

41 | F.TF.5 | Trigonometric Functions | Model Periodic Phenomena With Trigonometric Functions | Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.★ | ||||||||||||||||||||||

42 | F.TF.8 | Trigonometric Functions | Prove And Apply Trigonometric Identities | Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to calculate trigonometric ratios. | ||||||||||||||||||||||

43 | G.GPE.2 | Expressing Geometric Properties With Equations | Translate Between The Geometric Description And The Equation For A Conic Section | Derive the equation of a parabola given a focus and directrix. | ||||||||||||||||||||||

44 | N.CN.1 | The Complex Number System | Perform Arithmetic Operations With Complex Numbers. | Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real. | ||||||||||||||||||||||

45 | N.CN.2 | The Complex Number System | Perform Arithmetic Operations With Complex Numbers. | Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. | ||||||||||||||||||||||

46 | N.CN.7 | The Complex Number System | Use Complex Numbers In Polynomial Identities And Equations. | Solve quadratic equations with real coefficients that have complex solutions. | ||||||||||||||||||||||

47 | N.Q .1 | Quantities | Reason Quantitatively And Use Units To Solve Problems. | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. | ||||||||||||||||||||||

48 | N.RN.1 | The Real Number System | Extend The Properties Of Exponents To Rational Exponents. | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. | ||||||||||||||||||||||

49 | N.RN.2 | The Real Number System | Extend The Properties Of Exponents To Rational Exponents. | Rewrite expressions involving radicals and rational exponents using the properties of exponents. | ||||||||||||||||||||||

50 | N.RN.3 | The Real Number System | Use Properties Of Rational And Irrational Numbers. | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. | ||||||||||||||||||||||

51 | N.VM.4.a | Vector And Matrix Quantities | Perform Operations On Vectors. | Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. | ||||||||||||||||||||||

52 | N.VM.4.b | Vector And Matrix Quantities | Perform Operations On Vectors. | Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. | ||||||||||||||||||||||

53 | N.VM.4.c | Vector And Matrix Quantities | Perform Operations On Vectors. | Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. | ||||||||||||||||||||||

54 | N.VM.5.a | Vector And Matrix Quantities | Perform Operations On Vectors. | Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g. as c(vx, vy) = (cvx, cvy). | ||||||||||||||||||||||

55 | N.VM.5.b | Vector And Matrix Quantities | Perform Operations On Vectors. | Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). | ||||||||||||||||||||||

56 | S.CP.1 | Conditional Probability And The Rules Of Probability | Understand Independence And Conditional Probability And Use Them To Interpret Data | Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). | ||||||||||||||||||||||

57 | S.CP.3 | Conditional Probability And The Rules Of Probability | Understand Independence And Conditional Probability And Use Them To Interpret Data | Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. | ||||||||||||||||||||||

58 | S.CP.4 | Conditional Probability And The Rules Of Probability | Understand Independence And Conditional Probability And Use Them To Interpret Data | Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. | ||||||||||||||||||||||

59 | S.CP.6 | Conditional Probability And The Rules Of Probability | Use The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability Model | Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model. | ||||||||||||||||||||||

60 | S.CP.7 | Conditional Probability And The Rules Of Probability | Use The Rules Of Probability To Compute Probabilities Of Compound Events In A Uniform Probability Model | Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. | ||||||||||||||||||||||

61 | S.IC.2 | Making Inferences And Justifying Conclusions | Understand And Evaluate Random Processes Underlying Statistical Experiments | Decide if a specified model is consistent with results from a given data-generating process, e.g. using simulation. | ||||||||||||||||||||||

62 | S.IC.3 | Making Inferences And Justifying Conclusions | Make Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational Studies | Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. | ||||||||||||||||||||||

63 | S.IC.4 | Making Inferences And Justifying Conclusions | Make Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational Studies | Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. | ||||||||||||||||||||||

64 | S.IC.5 | Making Inferences And Justifying Conclusions | Make Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational Studies | Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. | ||||||||||||||||||||||

65 | S.IC.6 | Making Inferences And Justifying Conclusions | Make Inferences And Justify Conclusions From Sample Surveys, Experiments, And Observational Studies | Evaluate reports based on data. | ||||||||||||||||||||||

66 | S.ID.5 | Interpreting Categorical And Quantitative Data | Summarize, Represent, And Interpret Data On Two Categorical And Quantitative Variables | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. | ||||||||||||||||||||||

67 | S.ID.6.a | Interpreting Categorical And Quantitative Data | Summarize, Represent, And Interpret Data On Two Categorical And Quantitative Variables | Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. | ||||||||||||||||||||||

68 | S.MD.5.b | Using Probability To Make Decisions | Use Probability To Evaluate Outcomes Of Decisions | Evaluate and compare strategies on the basis of expected values. | ||||||||||||||||||||||

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