Precalculus

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This course is designed to emphasize topics which are fundamental to the study of calculus. The student will analyze functions in depth including transformations, inverses and compositions, while paying particular attention to quadratic, polynomial, rational, exponential and logarithmic functions and their graphs. Other topics include right triangle trigonometry, trigonometric identities and equations, vectors, complex numbers, laws of sines and cosines, the binomial theorem, arithmetic, geometric sequences and series, systems, partial fractions, matrices and determinants, conic sections and probability. The student will solve applications and modeling problems related to the above topics. Upon completion, students will be able to solve practical problems and use appropriate models for analysis.
Prerequisite: Intermediate Algebra with a grade of C or better.

Chapter 1

Functions and their Graphs

Lessons Homework HW Quiz
1.1   Complex Numbers 1.1 1.1
1.2   Linear Functions 1.2 1.2
1.3   Properties of Functions 1.3 1.3
1.4   Combinations of Functions 1.4 1.4
1.5   Graphs of Functions 1.5 1.5
1.6   Transformation of Functions 1.6 1.6
1.7   Inverse Functions 1.7 1.7
Chapter 1 Test   (21 questions)

Chapter 2

Polynomial and Rational Functions

Lessons Homework HW Quiz
2.1   Quadratic Functions 2.1 2.1
2.2   Polynomial Functions 2.2 2.2
2.3   Division of Polynomials 2.3 2.3
2.4   Zeros of Polynomial Functions 2.4 2.4
2.5   More on Zeros of Polynomial Functions 2.5 2.5
2.6   Graphs of Rational Functions 2.6 2.6
Chapter 2 Test   (19 questions)

Chapter 3

Exponential and Logarithmic Functions

Lessons Homework HW Quiz
3.1   Exponential Functions 3.1 3.1
3.2   Logarithmic Functions 3.2 3.2
3.3   Properties of Logarithmic Functions 3.3 3.3
3.4   Exponential and Logarithmic Equations 3.4 3.4
3.5   Applications 3.5 3.5
Chapter 3 Test   (23 questions)

Chapter 4

Trigonometric Functions

Lessons Homework HW Quiz
4.1   The Rectangular Coordinate System 4.1 4.1
4.2   Angles, Degrees and Special Triangles 4.2 4.2
4.3   Trigonometric Functions 4.3 4.3
4.4   Introduction to the Unit Circle 4.4 4.4
4.5   Right Triangle Trigonometry 4.5 4.5
4.6   Other Angles and Trigonometric Functions 4.6 4.6
4.7   Solving Right Triangles 4.7 4.7
4.8   Applications 4.8 4.8
Chapter 4 Test   (26 questions)

Chapter 5

Radian Measure & Trigonometric Identities

Lessons Homework HW Quiz
5.1   Reference Angle 5.1 5.1
5.2   Radians and Degrees 5.2 5.2
5.3   Circular Functions 5.3 5.3
5.4   Proving Identities 5.4 5.4
5.5   Sum and Difference Formula 5.5 5.5
5.6   Double-Angle Formula 5.6 5.6
5.7   Half-Angle Formula 5.7 5.7
Chapter 5 Test   (27 questions)

Chapter 6

Additional Trigonometry Topics

Lessons Homework HW Quiz
6.1   Graphs of Basic Trigonometric Functions 6.1 6.1
6.2   Inverse Trigonometric Functions 6.2 6.2
6.3   Trigonometric Equations 6.3 6.3
6.4   Law of Cosines 6.4 6.4
6.5   Law of Sines 6.5 6.5
6.6   Vectors 6.6 6.6
6.7   Trigonometric Form of a Complex Number 6.7 6.7
Chapter 6 Test   (25 questions)

Chapter 7

Systems of Equations

Lessons Homework HW Quiz
7.1   Linear Systems in Two Variables 7.1 7.1
7.2   Linear Systems in Three Variables 7.2 7.2
7.3   Partial Fractions 7.3 7.3
7.4   Nonlinear Systems in Two Variables 7.4 7.4
Chapter 7 Test   (12 questions)

Chapter 8

Matrices

Lessons Homework HW Quiz
8.1   Introduction to Matrices 8.1 8.1
8.2   Matrix Multiplication 8.2 8.2
8.3   Gauss-Jordan Elimination 8.3 8.3
8.4   Systems without Unique Solutions 8.4 8.4
8.5   Applications of Linear Systems using Matrices 8.5 8.5
8.6   Determinants 8.6 8.6
8.7   Inverse of a Matrix 8.7 8.7
Chapter 8 Test   (17 questions)

Chapter 9

Sequence, Series, Counting and Probability

Lessons Homework HW Quiz
9.1   Sequences and Series 9.1 9.1
9.2   Arithmetic Sequences 9.2 9.2
9.3   Geometric Sequences 9.3 9.3
9.4   Binomial Theorem 9.4 9.4
9.5   Counting 9.5 9.5
9.6   Permutations and Combinations 9.6 9.6
9.7   Finite Basic Probabilities 9.7 9.7
9.8   Basic Laws of Probability 9.8 9.8
Chapter 9 Test   (26 questions)

Chapter 10

Conic Sections

Lessons Homework HW Quiz
10.1   The Circle 10.1 10.1
10.2   The Parabola 10.2 10.2
10.3   The Ellipse 10.3 10.3
10.4   The Hyperbola 10.4 10.4
10.5   Systems of Inequalities 10.5 10.5
Chapter 10 Test   (21 questions)
Final for Precalculus   (59 questions)
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