# Pre-Calculus

I. Sequence and Series

- What is the difference between sequences and series and what are the different types?
- What are the different types of sequences and series?
- What is an arithmetic sequence/series?
- How do we find the sum of a finite arithmetic sequence/series?
- What is a geometric sequence/series?
- How do we find the sum of a finite geometric sequence/series?
- How do we find the sum of an infinite geometric series?

II. Algebraic Skills

- Review long division and introduce the remainder theorem.
- What is the factor theorem?
- What is synthetic division and how can it be used as a tool?
- What are the zeros or roots of a polynomial function?
- How can we find the rational zeros of a polynomial function?
- How do we find the irrational zeros of a polynomial function?
- How can upper and lower bounds be used to determine the roots of a polynomial equation?
- How can we apply polynomial equations to real-life situations?
- What is Decartes Rule of Signs?
- How can we determine the nature of the roots of a polynomial equation?
- What is the relationship between roots and coefficients?
- How do we solve equations have complex roots?
- How do we find the polynomial functions whose zeros are complex numbers?
- What is the fundamental theorem of Algebra?

III. Review of the Graphing Calculator

- How do we store and retrieve numbers and expressions?
- How do we graph a function?
- How can the zeros of a function be calculated?
- How can we evaluate and deselect a function?
- How can a z-box and zoom in-out be used in tracing a function and locating the zeros?

IV. Functions

- How can the domain and range of a function be found?
- How can square root functions and Dirichelet functions be evaluated?
- How can the circle and absolute value functions be drawn and evaluated?
- How do graphs of functions change when functions change?
- What is rational function and greatest integer function?
- What is function notation?
- How can functions be used as mathematical models?
- What are quadratic functions?
- What are the extreme values of quadratics?
- What are increasing, decreasing, inverse and composite functions?

VI. Trigonometry

- What are the different trigonometric ratios and what is the Unit Circle?
- How do we solve linear trigonometric equations?
- How do we solve quadratic trigonometric equations?
- Review the graphs of trigonometric functions.

VII. Complex numbers, Cartesian (Rectangular) and Polar Forms

- How can operations of complex numbers be performed?
- What is the geometric representation of a complex number?
- What is the polar form of a complex number?
- How can we switch from Cartesian to rectangular and rectangular to Cartesian?
- How can we multiply and divide complex numbers in polar form?

What is DeMoivie’s Theorem? - How can DeMoivie’s Theorem be used to find the roots of a complex number in polar form?

VIII. Matrices

- What are matrices?
- How can matrices be added and subtracted?
- How can we multiply one matrix by another matrix?
- What is the multiplicative identity and inverses of a two-by-two matrix?
- How can we solve a system of equations using A-1B and Cramer’s Rule?
- How can the minors, cofactors, determinants, adjoints and multiplicative inverse of a t matrix be found?
- How can we solve a system of equations with three variables?
- What are partial fractions?