Functions and Graphs
Explore domain and range, symmetry, intercepts, asymptotes and continuity of functions. Work with inverses of functions and function composition.
Polynomials and Rational Functions
Divide polynomials, and explore the connections between polynomials and rational expressions. Investigate rational functions and three different types of asymptotes.
Logs and Exponents
Use properties of exponents and logarithms, and apply exponential, logarithmic, and logistic functions to real world situations.
Basic Triangle Trigonometry
Find missing sides and angles of both right and non-right triangles using trigonometric ratios, the Law of Sines, and the Law of Cosines. Use the sine ratio to develop a new formula for the area of a triangle.
Extend the concept of trigonometric ratios to trigonometric functions. Investigate amplitude, frequency, period, and phase shift of trigonometric functions.
Use and prove trigonometric identities, sum and difference identities, Pythagorean identities, and double and half angle identities. Solve trigonometric equations.
Add and subtract vectors, find the product of vectors, find the angle between two vectors, and use vector projection to solve problems.
Systems and Matrices
Represent data with matrices, find determinants and inverses of matrices, and use matrices to solve systems of equations.
Investigate and use parabolas, circles, ellipses, and hyperbolas, as well as degenerate conics.
Polar and Parametric Equations
Translate between polar and rectangular coordinates and equations. Use parametric equations to represent an object in flight.
Add, subtract, multiply, and divide complex numbers. Find roots and powers of complex numbers using De Moivre's Theorem.
Use arithmetic and geometric sequences as well as arithmetic and geometric series. Solve basic counting and probability problems using combinations and permutations. Begin to explore induction proofs.
Calculate simple, compound, and continuous interest. Investigate APR , APY and annuities.
Concepts of Calculus
Find limits of functions using graphs, tables, substitution, and rationalization. Calculate instantaneous rates of change and areas under curves.
Concepts of Statistics
Compare mean, median, and mode and consider different ways to display data. Investigate the normal curve, linear correlation, and modeling with regression.
Logic and Set Theory
Compare the use of "and" and "or" in mathematical statements. Find the inverse, converse, and contrapositive of if-then statements.