Precalculus

Precalculus is a pre-AP honors credit course designed to combine three semester-length courses, Trigonometry, Elementary analysis, and Analytical geometry, into a one year course. Its prerequisites are Algebra I, Geometry, and Algebra I. To view the TEKS for this course click here, then click on Chapter 111.mathematics.

Students will need the following supplies for this course:

• One three-subject spiral.
• One one-subject spiral.
• One one-inch three ring binder or a pocket folder with brads.
• Pencils and/or pens
• Ruler
• TI-83 plus, TI-84 or TI-84 plus graphing calculator (calculators may be purchased through the school after school begins)
  
  Six weeks averages will be determined  as follows: 
  
• Daily 25%
• 50-point quizzes 25%
  
• Tests 50%

Syllabus:

First semester will consist of the study of basic functions:

• Review of linear functions
  1. when are relations functions
  2. basic terminology of functions
  3. inverse functions
     
  4. graphing linear functions
  5. writing linear equations
  6. solving systems of linear functions
     
• Properties and graphing of parent functions
  1. quadratic functions
  2. cubic functions
  3. square root functions
  4. absolute value functions
  5. indirect functions
  6. greatest integer (step) functions
  7. translations on the parent graphs
  8. inverse of the parent functions
     
• Finding the roots, zeros, x-intercepts of functions
  1. using remainder theorem
  2. rational root theorem
  3. fundamental theorem of algebra
  4. Descartes rule of signs
  5. location principle
  6. upper bound theorem
     
• The study of conic sections
  1. study of the circle
  2. study of the ellipse
  3. study of the parabola
  4. study of the hyperbola
  5. systems of conic equations

If time permits first semester, we also cover Logarithmic and exponential functions.  If not, they are covered during the fifth and sixth six weeks.

Second semester will consist of the basics of trigonometry and elementary analysis.

• Circular functions
  1. basic circular functions
  2. sine ratio
     
  3. cosine ratio
     
  4. tangent ratio
  5. reciprocal ratios (cosecant, secant and cotangent)
     
  6. ratios for special right triangles (handy dandy chart)
  7. solving trigonometric equations
     
     
• Real world applications of trigonometry
  1. solving right triangles
  2. right triangle real world problems
  3. law of sines
  4. law of cosines
  5. solving oblique triangles
  6. finding the area of triangles
     1. using geometric formulas
     2. using Herons formula
     3. using SAS
        
        
• Graphing trigonometric equations
  1. basic trigonometric parent graphs
     1. sine
     2. cosine
     3. tangent
     4. cosecant
     5. secant
     6. cotangent
  2. transformations on parent graphs
     1. amplitude
     2. period
     3. phase shift
        
        
• Proving trigonometric identities
  1. reciprocal identities
  2. Pythagorean identities
  3. quotient identities
  4. sum and difference identities
  5. double angle identities
  6. half angle identities
     
• Elementary analysis
  1. arithmetic sequences and series
  2. geometric sequences and series
  3. infinite series
  4. introduction to limits
  5. expansion of polynomials using Pascal's triangle
  6. introduction to sigma
  7. expansion of the polynomials using the Binomial Theorem
     
• Algebraic vectors
  1. introduction
  2. two dimension vectors
     
  3. three dimension vectors
     
  4. adding
  5. multiplying and dot product