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NC.AFM.Advanced Functions and Modeling
Advanced Functions and Modeling
1 The learner will analyze data and apply probability concepts to solve problems.
1.01. Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.
1.01.b. Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.
NC.M1.A-APR. Algebra: Arithmetic with Polynomial Expressions
Perform arithmetic operations on polynomials.
NC.M1.A-APR.1. Build an understanding that operations with polynomials are comparable to operations with integers by adding and subtracting quadratic expressions and by adding, subtracting, and multiplying linear expressions.
Create equations that describe numbers or relationships.
NC.M1.A-CED.1. Create equations and inequalities in one variable that represent linear, exponential, and quadratic relationships and use them to solve problems.
NC.M1.A-REI. Algebra: Reasoning with Equations and Inequalities
Solve systems of equations.
NC.M1.A-REI.5. Explain why replacing one equation in a system of linear equations by the sum of that equation and a multiple of the other produces a system with the same solutions.
NC.M1.A-REI.6. Use tables, graphs, or algebraic methods (substitution and elimination) to find approximate or exact solutions to systems of linear equations and interpret solutions in terms of a context.
Represent and solve equations and inequalities graphically
NC.M1.A-REI.11. Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, and/or quadratic equations y = (x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) and approximate solutions using graphing tec
Quiz, Flash Cards, Worksheet, Game & Study GuideSequences
NC.M1.F-IF. Functions: Interpreting Functions
Interpret functions that arise in applications in terms of the context.
NC.M1.F-IF.4. Interpret key features of graphs, tables, and verbal descriptions in context to describe functions that arise in applications relating two quantities, including: intercepts; intervals where the function is increasing, decreasing, positive, or negative; an
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
NC.M1.F-IF.6. Calculate and interpret the average rate of change over a specified interval for a function presented numerically, graphically, and/or symbolically.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Analyze functions using different representations.
NC.M1.F-IF.7. Analyze linear, exponential, and quadratic functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; rate of change; intercepts; intervals
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
NC.M1.F-IF.8. Use equivalent expressions to reveal and explain different properties of a function.
NC.M1.F-IF.8b. Interpret and explain growth and decay rates for an exponential function.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Understand the concept of a function and use function notation.
NC.M1.F-IF.1. Build an understanding that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range by recognizing that:
NC.M1.F-IF.1a. If f is a function and x is an element of its domain, then (x) denotes the output of f corresponding to the input x.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
NC.MI.F-IF.3. Recognize that recursively and explicitly defined sequences are functions whose domain is a subset of the integers, the terms of an arithmetic sequence are a subset of the range of a linear function, and the terms of a geometric sequence are a subset of t
NC.M1.S-ID. Statistics and Probability: Interpreting Categorical and Quantitative Data
Interpret linear models.
NC.M1.S-ID.8. Analyze patterns and describe relationships between two variables in context. Using technology, determine the correlation coefficient of bivariate data and interpret it as a measure of the strength and direction of a linear relationship. Use a scatter plo
NC.M2.A-APR. Algebra: Arithmetic with Polynomial and Rational Expressions
Perform arithmetic operations on polynomials
NC.M2.A-APR.1. Extend the understanding that operations with polynomials are comparable to operations with integers by adding, subtracting, and multiplying polynomials.
Create equations that describe numbers or relationships.
NC.M2.A-CED.1. Create equations and inequalities in one variable that represent quadratic, square root, inverse variation, and right triangle trigonometric relationships and use them to solve problems.
NC.M2.A-REI. Algebra: Reasoning with Equations and Inequalities
Represent and solve equations and inequalities graphically.
NC.M2.A-REI.11. Extend the understanding that the x-coordinates of the points where the graphs of two square root and/or inverse variation equations y = (x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) and approximate solutions using graphing tech
NC.M2.A-REI.7. Use tables, graphs, and algebraic methods to approximate or find exact solutions of systems of linear and quadratic equations, and interpret the solutions in terms of a context.
Analyze functions using different representations.
NC.M2.F-IF.7. Analyze quadratic, square root, and inverse variation functions by generating different representations, by hand in simple cases and using technology for more complicated cases, to show key features, including: domain and range; intercepts; intervals wher
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
NC.M2.G-CO. Geometry: Congruence
Understand congruence in terms of rigid motions.
NC.M2.G-CO.6. Determine whether two figures are congruent by specifying a rigid motion or sequence of rigid motions that will transform one figure onto the other.
NC.M2.G-CO.2. Experiment with transformations in the plane.
NC.M2.G-CO.2b. Compare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both distance and angle measure (e.g. stretches, dilations).
NC.M2.G-CO.3. Given a triangle, quadrilateral, or regular polygon, describe any reflection or rotation symmetry i.e., actions that carry the figure onto itself. Identify center and angle(s) of rotation symmetry. Identify line(s) of reflection symmetry.
NC.M2.G-CO.4. Verify experimentally properties of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
NC.M2.G-CO.5. Given a geometric figure and a rigid motion, find the image of the figure. Given a geometric figure and its image, specify a rigid motion or sequence of rigid motions that will transform the pre-image to its image.
NC.M2.G-SRT. Geometry: Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations.
NC.M2.G-SRT.1. Verify experimentally the properties of dilations with given center and scale factor:
NC.M2.G-SRT.1a. When a line segment passes through the center of dilation, the line segment and its image lie on the same line. When a line segment does not pass through the center of dilation, the line segment and its image are parallel.
NC.M2.G-SRT.1c. The distance between the center of a dilation and any point on the image is equal to the scale factor multiplied by the distance between the dilation center and the corresponding point on the pre-image.
NC.M2.G-SRT.2b. Use the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent.
NC.M2.S-CP. Statistics and Probability: Conditional Probability and the Rules for Probability
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
NC.M2.S-CP.8. Apply the general Multiplication Rule P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in context. Include the case where A and B are independent: P(A and B) = P(A) P(B).
Understand independence and conditional probability and use them to interpret data.
NC.M2.S-CP.3. Develop and understand independence and conditional probability.
NC.M2.S-CP.3b. Understand that event A is independent from event B if the probability of event A does not change in response to the occurrence of event B. That is P(A|B)=P(A).
NC.M2.S-CP.4. Represent data on two categorical variables by constructing a two-way frequency table of data. Interpret the two-way table as a sample space to calculate conditional, joint and marginal probabilities. Use the table to decide if events are independent.
Create equations that describe numbers or relationships.
NC.M3.A-CED.1. Create equations and inequalities in one variable that represent absolute value, polynomial, exponential, and rational relationships and use them to solve problems algebraically and graphically.
NC.M3.A-CED.2. Create and graph equations in two variables to represent absolute value, polynomial, exponential and rational relationships between quantities.
NC.M3.A-REI. Algebra: Reasoning with Equations and Inequalities
Represent and solve equations and inequalities graphically.
NC.M3.A-REI.11. Extend an understanding that the x-coordinates of the points where the graphs of two equations y = (x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) and approximate solutions using a graphing technology or successive approximations
NC.M3.A-SSE. Algebra: Seeing Structure in Expressions
Write expressions in equivalent forms to solve problems.
NC.M3.A-SSE.3c. Write an equivalent form of an exponential expression by using the properties of exponents to transform expressions to reveal rates based on different intervals of the domain.
Build a function that models a relationship between two quantities.
NC.M3.F-BF.1. Write a function that describes a relationship between two quantities.
NC.M3.F-BF.1a. Build polynomial and exponential functions with real solution(s) given a graph, a description of a relationship, or ordered pairs (include reading these from a table).
Analyze functions using different representations.
NC.M3.F-IF.7. Analyze piecewise, absolute value, polynomials, exponential, rational, and trigonometric functions (sine and cosine) using different representations to show key features of the graph, by hand in simple cases and using technology for more complicated cases
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
NC.M3.S-IC. Statistics and Probability: Making Inference and Justifying Conclusions
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
NC.M3.S-IC.3. Recognize the purposes of and differences between sample surveys, experiments, and observational studies and understand how randomization should be used in each.
2 The learner will use relations and functions to solve problems.
2.01. Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.
2.01.b. Interpret the constants, coefficients, and bases in the context of the problem.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions