10-11.M.3HS.IC Inferences and Conclusions from Data
10-11. Summarize, represent, and interpret data on a single count or measurement variable
10-11.M.3HS.IC.1 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
10-11. Understand and evaluate random processes underlying statistical experiments
10-11.M.3HS.IC.2 understand that statistics allows inferences to be made about population parameters based on a random sample from that population.
10-11.M.3HS.IC.3 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
10-11. Make inferences and justify conclusions from sample surveys, experiments, and observational studies
10-11.M.3HS.IC.4 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
10-11.M.3HS.IC.5 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.
10-11. Write expressions in equivalent forms to solve problems
10-11.M.3HS.PR.5 derive the formula for the sum of a geometric series (when the common ratio is not 1), and use the formula to solve problems.
10-11. Perform arithmetic operations on polynomials
10-11.M.3HS.PR.6 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
10-11.M.3HS.PR.10 Know and apply the Binomial Theorem for the expansion of (x + y) to the n power in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
10-11.M.3HS.PR.11 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
10-11.M.3HS.PR.12 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
10-11. Represent and solve equations and inequalities graphically
10-11.M.3HS.PR.14 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.
10-11. Analyze functions using different representations
10-11.M.3HS.PR.15 graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.
10-11.M.3HS.TF Trigonometry of General Triangles and Trigonometric Functions
10-11. Apply trigonometry to general triangles
10-11.M.3HS.TF.1 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
10-11.M.3HS.TF.5 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.
10-11. Interpret functions that arise in applications in terms of the context
10-11.M.3HS.MM.5 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.
10-11.M.3HS.MM.9 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
10-11.M.3HS.MM.10 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
10-11. Build a function that models a relationship between two quantities
10-11.M.3HS.MM.11 write a function that describes a relationship between two quantities. Combine standard function types using arithmetic operations.
10-11. Build new functions from existing functions
10-11.M.3HS.MM.12 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.
10-11.M.3HS.MM.13 find inverse 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.
10-11. Construct and compare linear, quadratic, and exponential models and solve problems
10-11.M.3HS.MM.14 For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
10-11.M.3HS.MM.17 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
10-11.M.3HS.MM.18 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).