CK-12-Pre-Calculus Concepts

(Marvins-Underground-K-12) #1

  • 1 Functions and Graphs Contents

    • 1.1 Function Families

    • 1.2 Graphical Transformations

    • 1.3 Point Notation and Function Notation

    • 1.4 Domain and Range

    • 1.5 Maximums and Minimums

    • 1.6 Symmetry

    • 1.7 Increasing and Decreasing

    • 1.8 Zeroes and Intercepts of Functions

    • 1.9 Asymptotes and End Behavior

    • 1.10 Continuity and Discontinuity

    • 1.11 Function Composition

    • 1.12 Inverses of Functions

    • 1.13 References



  • 2 Polynomials and Rational Functions

    • 2.1 Factoring Review

    • 2.2 Advanced Factoring

    • 2.3 Polynomial Expansion and Pascal’s Triangle

    • 2.4 Rational Expressions

    • 2.5 Polynomial Long Division and Synthetic Division

    • 2.6 Solving Rational Equations

    • 2.7 Holes in Rational Functions

    • 2.8 Zeroes of Rational Functions

    • 2.9 Vertical Asymptotes

    • 2.10 Horizontal Asymptotes

    • 2.11 Oblique Asymptotes

    • 2.12 Sign Test for Rational Function Graphs

    • 2.13 Graphs of Rational Functions by Hand

    • 2.14 References



  • 3 Logs and Exponents

    • 3.1 Exponential Functions

    • 3.2 Properties of Exponents

    • 3.3 Scientific Notation

    • 3.4 Properties of Logs

    • 3.5 Change of Base

    • 3.6 Exponential Equations

    • 3.7 Logistic Functions

    • 3.8 References



  • 4 Basic Triangle Trigonometry

    • 4.1 Angles in Radians and Degrees http://www.ck12.org Contents

    • 4.2 Circular Motion and Dimensional Analysis

    • 4.3 Special Right Triangles

    • 4.4 Right Triangle Trigonometry

    • 4.5 Law of Cosines

    • 4.6 Law of Sines

    • 4.7 Area of a Triangle

    • 4.8 Applications of Basic Triangle Trigonometry

    • 4.9 References



  • 5 Trigonometric Functions

    • 5.1 The Unit Circle

    • 5.2 The Sinusoidal Function Family

    • 5.3 Amplitude of Sinusoidal Functions

    • 5.4 Vertical Shift of Sinusoidal Functions

    • 5.5 Frequency and Period of Sinusoidal Functions

    • 5.6 Phase Shift of Sinusoidal Functions

    • 5.7 Graphs of Other Trigonometric Functions

    • 5.8 Graphs of Inverse Trigonometric Functions

    • 5.9 References



  • 6 Analytic Trigonometry

    • 6.1 Basic Trigonometric Identities

    • 6.2 Pythagorean Identities

    • 6.3 Sum and Difference Identities

    • 6.4 Double, Half, and Power Reducing Identities

    • 6.5 Trigonometric Equations

    • 6.6 References



  • 7 Vectors

    • 7.1 Basic Properties of Vectors

    • 7.2 Operations with Vectors

    • 7.3 Resolution of Vectors into Components

    • 7.4 Dot Product and Angle Between Two Vectors

    • 7.5 Vector Projection

    • 7.6 References



  • 8 Systems and Matrices

    • 8.1 Systems of Two Equations and Two Unknowns

    • 8.2 Systems of Three Equations and Three Unknowns

    • 8.3 Matrices to Represent Data

    • 8.4 Matrix Algebra

    • 8.5 Row Operations and Row Echelon Forms

    • 8.6 Augmented Matrices

    • 8.7 Determinant of Matrices

    • 8.8 Cramer’s Rule

    • 8.9 Inverse Matrices

    • 8.10 Partial Fractions

    • 8.11 References



  • 9 Conics

    • 9.1 General Form of a Conic

    • 9.2 Parabolas Contents http://www.ck12.org

    • 9.3 Circles

    • 9.4 Ellipses

    • 9.5 Hyperbolas

    • 9.6 Degenerate Conics

    • 9.7 References



  • 10 Polar and Parametric Equations

    • 10.1 Polar and Rectangular Coordinates

    • 10.2 Polar Equations of Conics

    • 10.3 Parameters and Parameter Elimination

    • 10.4 Parametric Inverses

    • 10.5 Applications of Parametric Equations

    • 10.6 References



  • 11 Complex Numbers

    • 11.1 Fundamental Theorem of Algebra

    • 11.2 Arithmetic with Complex Numbers

    • 11.3 Trigonometric Polar Form of Complex Numbers

    • 11.4 De Moivre’s Theorem and nth Roots

    • 11.5 References



  • 12 Discrete Math

    • 12.1 Recursion

    • 12.2 Arithmetic and Geometric Sequences

    • 12.3 Sigma Notation

    • 12.4 Arithmetic Series

    • 12.5 Geometric Series

    • 12.6 Counting with Permutations and Combinations

    • 12.7 Basic Probability

    • 12.8 Binomial Theorem

    • 12.9 Induction Proofs

    • 12.10 References



  • 13 Finance

    • 13.1 Simple Interest

    • 13.2 Compound Interest per Year

    • 13.3 Compound Interest per Period

    • 13.4 Continuous Interest

    • 13.5 APR and APY (Nominal and Effective Rates)

    • 13.6 Annuities

    • 13.7 Annuities for Loans



  • 14 Concepts of Calculus

    • 14.1 Limit Notation

    • 14.2 Graphs to Find Limits

    • 14.3 Tables to Find Limits

    • 14.4 Substitution to Find Limits

    • 14.5 Rationalization to Find Limits

    • 14.6 One Sided Limits and Continuity

    • 14.7 Intermediate and Extreme Value Theorems

    • 14.8 Instantaneous Rate of Change

    • 14.9 Area Under a Curve http://www.ck12.org Contents

    • 14.10 References



  • 15 Concepts of Statistics

    • 15.1 Mean, Median and Mode

    • 15.2 Expected Value and Payoffs

    • 15.3 Five Number Summary

    • 15.4 Graphic Displays of Data

    • 15.5 Variance

    • 15.6 The Normal Curve

    • 15.7 Linear Correlation

    • 15.8 Modeling with Regression

    • 15.9 References



  • 16 Logic and Set Theory

    • 16.1 And and Or Statements

    • 16.2 If-Then Statements

    • 16.3 Negative Statements

    • 16.4 Inverse, Converse, and Contrapositive

    • 16.5 References



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