# CK-12 Precalculus Concepts

**At Grade**Created by: CK-12

- 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.

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