## College Prep. Pre-Calculus Topics

*All topics listed below are presented to the students in a way that is consistent with the vision of the*

*NCTM (National Council of Teachers of Mathematics)*

__Functions and their Graphs__**Lines in a Plane**

**Functions**

**Graphs of Functions**

**Shifting, Reflecting, and Stretching Graphs**

**Combinations of Functions**

**Inverse Functions**

**Linear Models and Scatter Plots**

__Polynomials and Rational Functions__**Quadratic Functions**

Complex Numbers

**Polynomial Functions of Higher Degree****Real Zeros of Polynomial Functions**Complex Numbers

**The Fundamental Theorem of Algebra**

**Rational Functions and Asymptotes**

**Graphs of Rational Functions**

**Quadratic Models**

__Exponential and Logarithmic Functions__**Exponential Functions and their Graphs**

**Logarithmic Functions and their Graphs**

**Properties of Logarithms**

**Solving Exponential and Logarithmic Equations**

**Exponential and Logarithmic Models**

**NonLinear Models**

__Trigonometric Functions__**Radian and Degree Measure**

**Trigonometric Functions and the Unit Circle**

**Right Triangle Trigonometry**

**Trig Functions of Any Angle**

**Graphs of Trig Functions**

**Inverse Trig Functions**

**Applications and Models**

__Analytic Trigonometry__**Using Fundamental Identities**

**Verifying Trig Identities**

**Solving Trig Equations**

**Sum and Difference Formulas**

**Mutiple Angle and Sum-To-Product Formulas**

__Additional Topics in Trigonometry__**Law of Sines**

**Law of Cosines**

**Area Formulas**

**Trig Form of a Complex Number**

**Multiplying, Dividing, Raising to a Power, and taking nth Roots of Complex Numbers in Trig Form**

__Sequences, Series__**Sequences, and Series**

**Arithmetic Sequences and Partial Sums**

**Geometric Sequences and Series**

**The Binomial Theorem**

__Probability and Statistics__

The counting principle

Permutations and Combinations

Probability

Measures of Central Tendency: Mean, Median, Mode, and Standard Deviation

**Normal distribution--- z-scores**