Prepare for PreCalculus

PreCalculus starts with some basic math review, but QUICKLY moves through all previous math and maintains a very high pace through some of the most advanced and complicated math up to, and including some introduction to, Calculus.  Having a solid foundation going in can make all the difference in successfully achieving your goals.  This five-day intensive will cover:

Day 1:  Linear Equations 
- Forms of Linear Equations 
   - Standard, slope-intercept, point-slope 
   - Advantages/Disadvantages/Uses of each 
   - Manipulating between forms 
   - Deriving based on available information 
- Equations of parallel lines 
- Equations of perpendicular lines 
- Solving systems of linear equations 
- Application of systems of linear equations (word problems) 

Day 2:  Parabolas/Quadratic Functions 
- Forms of quadratic equations 
   - Standard, factored, vertex 
- Differentiating between quadratic functions, quadratic equations, quadratic expressions, and the quadratic formula 
- Differentiate between roots (aka, zeros) of a quadratic function and x-intercepts 
- Factoring quadratic expressions 
   - Leading coefficient of one 
   - Leading coefficients other than one 
   - Special case 
   - By grouping 
- Completing the square technique 
- Deriving the quadratic formula 
- Complex numbers and interpreting imaginary roots 
 
Day 3:  Parent Functions and Transformations 
- Review of parent functions 
   - Linear 
   - Square 
   - Cubic 
   - Square root 
   - Cube root 
   - Inverse 
   - Exponential 
   - Logarithmic 
- Transformation of Functions 
   - Vertical stretch/compression/reflection
   - Horizontal stretch/compression/reflection
   - Horizontal shift
   - Vertical shift
 
Day 4:  Polynomials and Rational Functions 
- Definition of a Polynomial 
- Characteristics of Polynomial 
- Fundamental theorem of algebra – roots of a Polynomial 
- Roots of a Polynomial – rational Vs irrational Vs imaginary 
- Rational root theorem 
- Long Division and Synthetic Division of Polynomials 
- Graphing Polynomials 
   - Y-intercept 
   - End behavior 
   - Roots/x-intercepts 
- Introduction to Rational Functions 

Day 5:  Trigonometric Functions 
- Definitions of basic trigonometric functions 
- Special triangles and familiarization with angle conversion formulas 
   - Double angle 
   - Half angle 
   - Angle addition 
   - Angle subtraction 
- Unit circle and quadrant ambiguity with inverse trigonometric functions 
- Basic trigonometric identities 
- Graphing trigonometric functions 
- Transformation of trigonometric functions