Number and Quantity

The Complex Number System; Perform arithmetic operations with complex numbers; Use complex numbers in polynomial identities and equations.

Algebra
Students learn to interpret the structure of polynomial and rational expressions, understanding terms, factors, and coefficients. They derive and use the formula for the sum of a finite geometric series. Arithmetic with polynomials includes understanding the relationship between zeros and factors, applying the Remainder Theorem, and identifying zeros to graph polynomial functions. Key concepts include polynomial identities, Pythagorean triples, and the Binomial Theorem. Students create and solve equations and inequalities in one variable, including those with absolute values, and extend to linear, quadratic, rational, and exponential functions. They also create equations in multiple variables, graph them, represent constraints, and solve these equations and inequalities both algebraically and graphically.

Functions

Students understand the concept of functions and interpret key features of their graphs, such as intercepts, intervals of increase or decrease, positivity or negativity, relative maximums and minimums, symmetries, end behavior, and periodicity. They calculate and interpret the average rate of change of a function from graphs. Students graph square root, cube root, and piecewise-defined functions, including step and absolute value functions, as well as polynomial, exponential, logarithmic, and trigonometric functions, highlighting intercepts, end behavior, period, midline, and amplitude.

They learn to build functions that model relationships between quantities and create new functions from existing ones. Students convert exponential expressions to logarithmic forms, prove simple logarithm laws, translate between logarithms in any base, and use logarithmic properties to simplify expressions and approximate values.

For trigonometric functions, students extend their domain using the unit circle, model periodic phenomena with specified amplitude, frequency, and midline, and prove and apply trigonometric identities.

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Geometry

Translate between the geometric description and the equation for a conic section; use the method for completing the square to put the equation into standard form; identify whether the graph of the equation is a circle, ellipse, parabola, or hyperbola and graph the equation.

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Statistics and Probability

Summarize, represent, and interpret data on a single count or measurement variable; Understand and evaluate random processes underlying statistical experiments; Make inferences and justify conclusions from sample surveys, experiments, and observational studies; Use probability to evaluate outcomes of decisions.