Explore Precalculus with Mr. Ahmed
Read a lesson preview and worked example without an account. Chapter 1 is our full sample chapter.
- 1.1 Real Numbers
- 1.2 Exponents and Radicals
- 1.3 Algebraic Expressions
- 1.4 Rational Expressions
- 1.5 Equations
- 1.6 Complex Numbers
- 1.7 Modeling with Equations
- 1.8 Inequalities
- 1.9 The Coordinate Plane; Graphs of Equations; Circles
- 1.10 Lines
- 1.11 Solving Equations and Inequalities Graphically
- 1.12 Modeling Variation
- 2.1 Functions
- 2.2 Graphs of Functions
- 2.3 Getting Information from the Graph of a Function
- 2.4 Average Rate of Change of a Function
- 2.5 Linear Functions and Models
- 2.6 Transformations of Functions
- 2.7 Combining Functions
- 2.8 One-to-One Functions and Their Inverses
- 2.M Focus on Modeling (Chapter Supplement)
- 3.1 Quadratic Functions and Models
- 3.2 Polynomial Functions and Their Graphs
- 3.3 Dividing Polynomials
- 3.4 Real Zeros of Polynomials
- 3.5 Complex Zeros and the Fundamental Theorem of Algebra
- 3.6 Rational Functions
- 3.7 Polynomial and Rational Inequalities
- 3.M Focus on Modeling (Chapter Supplement)
- 4.1 Exponential Functions
- 4.2 The Natural Exponential Function
- 4.3 Logarithmic Functions
- 4.4 Laws of Logarithms
- 4.5 Exponential and Logarithmic Equations
- 4.6 Modeling with Exponential Functions
- 4.7 Logarithmic Scales
- 4.M Focus on Modeling (Chapter Supplement)
- 5.1 The Unit Circle
- 5.2 Trigonometric Functions of Real Numbers
- 5.3 Trigonometric Graphs
- 5.4 More Trigonometric Graphs
- 5.5 Inverse Trigonometric Functions and Their Graphs
- 5.6 Modeling Harmonic Motion
- 5.M Focus on Modeling (Chapter Supplement)
- 6.1 Angle Measure
- 6.2 Trigonometry of Right Triangles
- 6.3 Trigonometric Functions of Angles
- 6.4 Inverse Trigonometric Functions and Right Triangles
- 6.5 The Law of Sines
- 6.6 The Law of Cosines
- 7.1 Trigonometric Identities
- 7.2 Addition and Subtraction Formulas
- 7.3 Double-Angle, Half-Angle, and Product-Sum Formulas
- 7.4 Basic Trigonometric Equations
- 7.5 More Trigonometric Equations
- 8.1 Polar Coordinates
- 8.2 Graphs of Polar Equations
- 8.3 Polar Form of Complex Numbers; De Moivre’s Theorem
- 8.4 Plane Curves and Parametric Equations
- 9.1 Vectors in Two Dimensions
- 9.2 The Dot Product
- 9.3 Three-Dimensional Coordinate Geometry
- 9.4 Vectors in Three Dimensions
- 9.5 The Cross Product
- 9.6 Equations of Lines and Planes
- 10.1 Systems of Linear Equations in Two Variables
- 10.2 Systems of Linear Equations in Several Variables
- 10.3 Matrices and Systems of Linear Equations
- 10.4 The Algebra of Matrices
- 10.5 Inverses of Matrices and Matrix Equations
- 10.6 Determinants and Cramer’s Rule
- 10.7 Partial Fractions
- 10.8 Systems of Nonlinear Equations
- 10.9 Systems of Inequalities
- 11.1 Parabolas
- 11.2 Ellipses
- 11.3 Hyperbolas
- 11.4 Shifted Conics
- 11.5 Rotation of Axes
- 11.6 Polar Equations of Conics
- 12.1 Sequences and Summation Notation
- 12.2 Arithmetic Sequences
- 12.3 Geometric Sequences
- 12.4 Mathematics of Finance
- 12.5 Mathematical Induction
- 12.6 The Binomial Theorem
- 13.1 Finding Limits Numerically and Graphically
- 13.2 Finding Limits Algebraically
- 13.3 Tangent Lines and Derivatives
- 13.4 Limits at Infinity; Limits of Sequences
- 13.5 Areas