- 1. Functions and Graphs
Explore domain and range, symmetry, intercepts, asymptotes and continuity of functions. Work with inverses of functions and function composition.
- 2. Polynomials and Rational Functions
Divide polynomials, and explore the connections between polynomials and rational expressions. Investigate rational functions and three different types of asymptotes.
- 3. Logs and Exponents
Use properties of exponents and logarithms, and apply exponential, logarithmic, and logistic functions to real world situations.
- 4. 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.
- 5. Trigonometric Functions
Extend the concept of trigonometric ratios to trigonometric functions. Investigate amplitude, frequency, period, and phase shift of trigonometric functions.
- 6. Analytic Trigonometry
Use and prove trigonometric identities, sum and difference identities, Pythagorean identities, and double and half angle identities. Solve trigonometric equations.
- 7. Vectors
Add and subtract vectors, find the product of vectors, find the angle between two vectors, and use vector projection to solve problems.
- 8. Systems and Matrices
Represent data with matrices, find determinants and inverses of matrices, and use matrices to solve systems of equations.
- 9. Conics
Investigate and use parabolas, circles, ellipses, and hyperbolas, as well as degenerate conics.
- 10. Polar and Parametric Equations
Translate between polar and rectangular coordinates and equations. Use parametric equations to represent an object in flight.
- 11. Complex Numbers
Add, subtract, multiply, and divide complex numbers. Find roots and powers of complex numbers using De Moivre's Theorem.
- 12. Discrete Math
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.
- 13. Finance
Calculate simple, compound, and continuous interest. Investigate APR , APY and annuities.
- 14. Concepts of Calculus
Find limits of functions using graphs, tables, substitution, and rationalization. Calculate instantaneous rates of change and areas under curves.
- 15. 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.
- 16. Logic and Set Theory
Compare the use of "and" and "or" in mathematical statements. Find the inverse, converse, and contrapositive of if-then statements.