Pre Calculus Syllabus
This course is offered exclusively as a one-on-one class and is not available in a small-group format.
Syllabus
Lesson 1 : Graphs
1.1 The Distance and Midpoint Formulas;Introduction to Graphing Equations
1.2 Intercepts;Symmetry
1.3 Solving Equations Using a Graphing Utility
1.4 Lines
1.5 Circles
Lesson 2 : Functions and Their Graphs
2.1 Functions
2.2 The Graph of a Function
2.3 Properties of Functions
2.4 Library of Functions;Piecewise-defined Functions
2.5 Graphing Techniques:Transformations
2.6 Mathematical Models:Building Functions
Lesson 3 : Linear and Quadratic Functions
3.1 Linear Functions and Their Properties
3.2 Linear Models:Building Linear Functions from Data
3.3 Quadratic Functions and Their Properties
3.4 Build Quadratic Models from Verbal Descriptions and from Data
3.5 Inequalities Involving Quadratic Functions
Lesson 4 : Polynomial and Rational Functions 1
4.1 Polynomial Functions and Models
4.2 The Real Zeros of a Polynomial Function
4.3 Complex Zeros;Fundamental Theorem of Algebra
Lesson 5 : Polynomial and Rational Functions 2
4.4 Properties of Rational Functions
4.5 The Graph of a Rational Function
4.6 Polynomial and Rational Inequalities
Lesson 6 : Exponential and Logarithmic Functions 1
5.1 Composite Functions
5.2 One-to-One Functions; Inverse Functions
5.3 Exponential Functions
5.4 Logarithmic Functions
Lesson 7 : Exponential and Logarithmic Functions 2
5.5 Properties of Logarithms
5.6 Logarithmic and Exponential Equations
5.7 Financial Models
5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
5.9 Building Exponential, Logarithmic, and Logistic Models from Data
Lesson 8 : Trigonometric Functions 1
6.1Angles and Their Measure
6.2 Trigonometric Functions: Unit Circle Approach
6.3Properties of the Trigonometric Functions
Lesson 9 : Trigonometric Functions 2
6.4 Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
6.6 Phase Shift; Sinusoidal Curve Fitting
Lesson 10 : Analytic Trigonometry 1
7.1 The Inverse Sine, Cosine, and Tangent Functions
7.2 The Inverse Trigonometric Functions(Continued)
7.3 Trigonometric Equations
7.4 Trigonometric Identities
Lesson 11 : Analytic Trigonometry 2
7.5 Sum and Difference Formulas
7.6 Double-angle and Half-angle Formulas
7.7 Product-to-Sum and Sum-to-Product Formulas
Lesson 12 : Applications of Trigonometric Functions
8.1 Right Triangle Trigonometry;Applications
8.2 The Law of Sines
8.3 The Law of Cosines
8.4 Area of a Triangle
8.5 Simple Harmonic Motion;Damped Motion; Combining Waves
Lesson 13 : Polar Coordinates
9.1Polar Coordinates
9.2 Polar Equations and Graphs
9.3 The Complex Plane; De Moivre's Theorem
Lesson 14 : Vectors
9.4 Vectors
9.5 The Dot Product
9.6 Vectors in Space
9.7 The Cross Product
Lesson 15 : Analytic Geometry 1
10.1 Conics
10.2 The Parabola
10.3 The Ellipse
Lesson 16 : Analytic Geometry 2
10.4 The Hyperbola
10.5 Rotation of Axes;General Form of a Conic
10.6 Polar Equations of Conics
10.7 Plane Curves and Parametric Equations
Lesson 17 : Systems of Equations and Inequalities 1
11.1 Systems of Linear Equations:Substitution and Elimination
11.2 Systems of Linear Equations:Matrices
11.3 Systems of Linear Equations:Determinants
Lesson 18 : Systems of Equations and Inequalities 2
11.4 Matrix Algebra
11.5 Partial Fraction Decomposition
11.6 Systems of Nonlinear Equations
11.7 Systems of Inequalities
11.8 Linear Programming
Lesson 19 : Sequences;Induction;the Binomial Theorem 1
12.1 Sequences
12.2 Arithmetic Sequences
12.3 Geometric Sequences;Geometric Series
Lesson 20 : Sequences;Induction;the Binomial Theorem 2
12.4 Mathematical Induction
12.5 The Binomial Theorem
Lesson 21 : Counting and Probability 1
13.1 Counting
13.2 Permutations and Combinations
Lesson 22 : Counting and Probability 2
13.3 Probability
Lesson 23 : A Preview of Calculus: The Limit, Derivative, and Integral of a Function 1
14.1 Finding Limits Using Tables and Graphs
14.2 Algebra Techniques for Finding Limits
14.3 One-sided Limits; Continuous Functions
Lesson 24 : A Preview of Calculus: The Limit, Derivative, and Integral of a Function 2
14.4 The Tangent Problem; The Derivative
14.5 The Area Problem; The Integral
Introduction
This course is a more in depth look at Advanced Algebra topics from a function perspective and is a pre-requisite for any student taking Calculus in high school.
Course topics include: functions, polynomials, radicals, exponents & logarithms, sequences & series, trigonometry, parametric equations, and probability.
Exploratory labs and calculator investigations will be the foundation for both reviewing concepts from Advanced Algebra and developing deeper connections between topics.
Who Should Take This Class?
This course is suitable for students who have completed Algebra 2