HS.A-APR.A Arithmetic with Polynomials & Rational Expressions: Perform arithmetic operations on polynomials.
HS.A-APR.A.1 Explain 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.
HS.A-APR.B Arithmetic with Polynomials & Rational Expressions: Understand the relationship between zeros and factors of polynomials.
HS.A-APR.B.2 Know and apply the Remainder Theorem. For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). (Students need not apply the Remainder Theorem to polynomials of degree greater than 4.)
HS.A-APR.C.5 Know and apply the Binomial Theorem for the expansion of 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. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)
HS.A-APR.D Arithmetic with Polynomials & Rational Expressions: Rewrite rational expressions.
HS.A-APR.D.6 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.
HS.A-APR.D.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expressions; add, subtract, multiply, and divide rational expressions.
HS.A-CED.A Creating Equations: Create equations that describe numbers or relationships.
HS.A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
HS.A-REI.D Reasoning with Equations & Inequalities: Represent and solve equations and inequalities graphically.
HS.A-REI.D.11 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.
HS.F-IF.B Interpreting Functions: Interpret functions that arise in applications in terms of the context.
HS.F-IF.B.4 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
HS.F-BF.B Building Functions: Build new functions from existing functions.
HS.F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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.
HS.F-TF.A.2 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.
HS.S-ID.A Interpreting Categorical & Quantitative Data: Summarize, represent, and interpret data on a single count or measurement variable.
HS.S-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages and identify data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.