Pre-Calculus

Functions
1. Continuity
2. Extrema, intervals of increase and decrease
3. Power functions
4. Average rates of change
5. Transformations of graphs
6. Piecewise functions
7. Operations
8. Inverses
Power, Polynomial, and Rational Functions
1. Graphs, real zeros, and end behavior of polynomial functions
2. Dividing polynomial functions
3. The Remainder Theorem and bounds of real zeros
4. Writing polynomial functions and conjugate roots
5. Complex zeros and The Fundamental Theorem of Algebra
6. Graphs of rational functions
7. Rational equations
8. Polynomial inequalities
9. Rational inequalities
Exponential and Logarithmic Expressions
1. Graphing exponential functions
2. Exponential equations not requiring logarithms
3. Exponents and logarithms
4. Evaluating lograithms
5. Logarithms and exponents as inverses
6. Properties of logarithms
7. Writing logs in terms of others
8. Exponential equations requiring logarithms
9. Logarithmic equations, simple
10. Logarithmic equations, hard
11. Graphing logarithmic functions
12. Compound interest
Trigonometry
1. Angles and angle measure
2. Radians and degrees
3. Right triangle trig: Finding ratios
4. Right triangle trig: Finding angles and sides
5. Trig functions of any angle
6. Graphing trig functions
7. Simple trig equations
8. Inverse trig functions
9. Fundamental identities
10. Equations with factoring and fundamental identities
11. Sum and Difference Identities
12. Multiple-Angle Identities
13. Product-to-Sum Identities
14. Equations and Multiple-Angle Identities
15. The Law of Sines
16. The Law of Cosines
17. Area and Laws of Sines and Cosines
Parametric Equations
1. Parametric equations
2. Projectile motion
Polar Coordinates
1. Polar coordinates
2. Graphs of polar equations
3. Polar and rectangular forms of equations
4. Polar forms of conic section
5. Complex numbers in polar form
Vectors
1. Basics
2. Diagrams
3. Operations
4. Dot products
Three-Dimensional Vectors
1. Points in three dimensions
2. Basics
3. Operations
4. Cross products
Matrices and Systems
1. Operations
2. Determinants
3. Inverses
4. Cramer’s Rule
5. Equations
6. Multivariable linear systems and row operations
7. Partial fraction decomposition
Conic Sections
1. Parabolas, graphing & properties
2. Parabolas, writing equations
3. Circles, graphing & properties
4. Circles, writing equations
5. Ellipses, graphing & properties
6. Elilipses, writing equations
7. Hyperbolas, graphing & properties
8. Hyperbolas, writing equations
9. Rotations of conic sections
Discrete Mathematics
1. Sample spaces and The Fundamental Counting Principle
2. Permutations
3. Combinations
4. Permutations vs combinations
5. The Binomial Theorem
6. Mathematical induction
Probability
1. Independent and dependent events, word problems
2. Independent and dependent events
3. Mutually exclusive events, word problems
4. Mutually exclusive events
5. With permutations and combinations
Sequences and Series
1. General sequences
2. Arithmetic sequences
3. Geometric sequences
4. Arithmetic and geometric mean
5. General series
6. Arithmetic series
7. Geometric series
8. Power series
Introduction to Calculus
1. Limits by direct evaluation
2. Limits at kinks and jumps
3. Limits at removable discontinuities
4. Limits at essential discontinuities
5. Limits at infinity
6. Definition of the derivative
7. Instantaneous rates of change
8. Power rule for differentiation
9. Motion along a line
10. Approximating area under a curve
11. Area under a curve by limit of sums
12. Indefinite integrals