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CK-12 Precalculus Concepts

Difficulty Level: At Grade Created by: CK-12
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Table of Contents

  • 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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Difficulty Level:
At Grade
Authors:
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Grades:
Date Created:
Nov 21, 2012
Last Modified:
Jun 09, 2016
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