North Carolina SCOS Advanced Functions and Modeling

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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) 1.01 Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems. a. Finding best fit for scatterplots of a Linear Function b. Finding best fit for scatterplots of a Quadratic Function c. Finding best fit for scatterplots of a Polynomial Function d. Finding best fit for scatterplots of a Exponential Function e. Finding best fit for scatterplots of a Logarithmic Function f. Finding the Best Fit Line from a Data Set or a Scatterplot g. Identifying the Best Fit Equation type from a Data Set or a Scatterplot h. Finding the Best Fit Curve from a Data Set i. Explaining Slope and Intercepts of Graphs in Word Problems (Random) 1.02 Summarize and analyze univariate data to solve problems. a. Census b. Sample Survey c. Experiment d. Observational Study e. Center and Spread f. Measuring Center: Median, Mean g. Measuring Spread: Range, Interquartile Range, Standard Deviation h. Properties of Normal Distribution i. Using Tables of the Normal Distribution j. The Normal Distribution as a Model for Measures (Random) 1.03 Use theoretical and experimental probability to model and solve problems. 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 g. Identifying Permutations and Combinations h. Calculating Permutations (And other cases where order matters) i. Calculating Combinations j. Calculating Rearrangements of Words k. Using Formulas l. Discrete vs. Continuous Random Variables m. Probability Distributions n. Mean of a Discrete Random Variable o. Variance and Standard Deviation of a Discrete Random Variable p. Definition of a Binomial Probability Distribution q. Mean and Standard Deviation of Binomial Distributions (Random) 2.01 Use logarithmic (common, natural) functions to model and solve problems; justify results. a. Writing Logarithmic Functions from Graphs b. Writing Logarithmic Functions from Words c. Writing Logarithmic Functions from Sets/Tables d. Solving for the domain of a Logarithmic Function given an element of the range e. Find the value of a Logarithmic Function f. Find the x-intercepts of a Logarithmic Function g. Find the y-intercepts of a Logarithmic Function h. Finding the rate of change of a Logarithmic Function i. Logarithmic Word Problems - finding f(a) j. Logarithmic Word Problems - finding x where f(x) = a	(Random) 2.02 Use piecewise-defined functions to model and solve problems; justify results. a. Finding Domain of Piecewise Functions b. Finding Range of Piecewise Functions c. Evaluating Piecewise Functions d. Graphing Piecewise Functions e. Graphing Linear Piecewise Functions (Random) 2.03 Use power functions to model and solve problems; justify results a. Writing Power Functions from Graphs b. Writing Power Functions from Words c. Writing Power Functions from Sets/Tables d. Solving for the domain of a Power Function given an element of the range e. Find the value of a Power Function f. Find the x-intercepts of a Power Function g. Find the y-intercepts of a Power Function h. Power Word Problems - finding f(a) i. Power Word Problems - finding x where f(x) = a (Random) 2.04 Use trigonometric (sine, cosine) functions to model and solve problems; justify results. a. Graphing Cos/Sin by Chart b. Basic Facts and Graphs of parent Trigonometric Functions c. Determining Amplitude in Graph and Equation d. Writing Equations of Amplitude and Vertical Stretch Changes e. Sketching Graphs with Amplitude Changes, Vertical Stretches, and Vertical Flips f. Determining Period in Graph and Equation g. Writing Equations of Period Changes h. Sketching Graphs with Period Changes i. Determining Phase Shift in Graph and Equation j. Writing Equations of Phase Shift Changes k. Sketching Graphs with Phase Shift Changes l. Determining Vertical Shift in Graph and Equation m. Writing Equations of Vertical Shift Changes n. Sketching Graphs with Vertical Shift Changes o. Sketch the Graph of a Trigonometric Function p. Writing Equations of Trigonometric Functions From Graphs q. Graphing Sec/Csc by Chart r. Graphing Tan/Cot by Chart s. Finding key values in Compound Trigonometric Functions t. Inverse Trigonometric Functions (Random) 2.05 Use recursively-defined functions to model and solve problems. a. Identifying Arithmetic/Geometry Sequences b. Writing the first n terms of an Arithmetic Sequence c. Defining an Arithmetic Sequence with Recursion d. Finding the n^th term formula for an Arithmetic Sequence e. Finding Arithmetic Means f. Evaluating Summations of Arithmetic Series (Number Arches Video) g. Writing the first n terms of a Geometric Sequence h. Defining a Geometric Sequence with Recursion i. Finding the n^th term formula for a Geometric Sequence j. Finding Geometric Means k. Evaluating Finite Summations of Geometric Series l. Evaluating Infinite Summations of Geometric Series
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