Accelerated Integrated Precalculus

1. Accelerated Integrated Precalculus May 3, 2010 Dr. Brian Wynne, Math Dept. Chair Mrs. Sharon Bean, Math Teacher

2. FUNCTIONS Characteristics of functions—domain, range, symmetry, zeros, asymptotes, boundedness, periodicity, points of discontinuity, intervals over which a function increases/decreases, relative extrema Operations with functions—composing two or more functions, finding a function’s inverse, defining a function parametrically Families of functions—polynomial, rational, exponential, logarithmic, trigonometric FUNCTIONS Characteristics of functions—domain, range, symmetry, zeros, asymptotes, boundedness, periodicity, points of discontinuity, intervals over which a function increases/decreases, relative extrema Operations with functions—composing two or more functions, finding the inverse of rational functions Families of functions—rational, trigonometric H. Precalculus vs. AIP

3. EQUATIONS/INEQUALITIES Solving polynomial equations/inequalities over the field of complex numbers Solving rational equations/inequalities Solving exponential/logarithmic equations/inequalities Solving trigonometric equations EQUATIONS/INEQUALITIES Solving rational equations/inequalities Solving trigonometric equations H. Precalculus vs. AIP

4. TRIGONOMETRY Converting angles between degree measure and radian measure Sketching angles in standard position and identifying co-terminal and reference angles Defining trigonometric functions as circular functions as well as the ratio of the sides of right triangles Evaluates and graphs trigonometric functions as well as inverse trigonometric functions Verifies trigonometric identities Law of Sines/Law of Cosines TRIGONOMETRY Converting angles between degree measure and radian measure Sketching angles in standard position and identifying co-terminal and reference angles Defining trigonometric functions as circular functions as well as the ratio of the sides of right triangles Evaluates and graphs trigonometric functions as well as inverse trigonometric functions Verifies trigonometric identities Law of Sines/Law of Cosines H. Precalculus vs. AIP

5. VECTORS/POLAR COORDINATES Graphing vectors in a plane, performing vector operations, and applying vectors to solve contextual problems Using DeMoivre’s Theorem to re-express complex numbers in polar form and perform operations Converting between polar and rectangular coordinates Graphing and analyzing polar equations VECTORS/POLAR COORDINATES Graphing vectors in a plane, performing vector operations, and applying vectors to solve contextual problems Using DeMoivre’s Theorem to re-express complex numbers in polar form and perform operations Converting between polar and rectangular coordinates Graphing and analyzing polar equations H. Precalculus vs. AIP

6. DATA ANALYSIS/ PROBABILITY Using combinations, permutations, and the Fundamental Principle of Counting to “count” events Applying the Binomial Theorem to expand binomial expressions Defining sample spaces, outcomes, and events Computing the probability of an event—including independent, dependent, and conditional Analyzing data using mean, median, mode, standard deviation, and variance DATA ANALYSIS/ PROBABILITY Applying the Central Limit Theorem to calculate confidence intervals for a population Determining the margin or error for a specified level of confidence Using confidence intervals and margins of error to make inferences from data about a population H. Precalculus vs. AIP

7. SEQUENCES/SERIES Determining terms of arithmetic/geometric sequences Using sigma notation Finding partial sums of arithmetic/geometric series Proving the “truth” of a statement using mathematical induction SEQUENCES/SERIES Determining terms of arithmetic/geometric sequences Using sigma notation Finding partial sums of arithmetic/geometric series Proving the “truth” of a statement using mathematical induction H. Precalculus vs. AIP

8. MATRICES Performing operations with matrices Solving 2 x 2 and 3 x 3 systems of equations using matrices Finding the inverse of a square matrix—if it exists Using matrices to de-compose a rational expression into partial fractions MATRICES Nothing included in AIP Curriculum H. Precalculus vs. AIP

9. CONIC SECTIONS Identifying whether an equation represents a circle, a parabola, an ellipse, or a hyperbola Writing an equation for and graphing standard conic sections CONIC SECTIONS Nothing included in AIP Curriculum H. Precalculus vs. AIP

10. Student Expectations: • Do homework every night – not just before test or at end of semester so you can get credit. • Take notes during class. • Exhibit good work ethic – no slacking off! • Come in for extra help when needed.

11. Teacher Expectations: • Have optional prerequisite skills packet on-line that can be done this summer • Hold before school help sessions 2 days each week (after school sessions will be held when needed) • Post calendar for periods of 1 or 2 weeks on-line • Hold study sessions in preparation for the new GHSGT

12. Assessments: • Higher level thinking questions will be included • Will have one or more assessments during each chapter • Will prepare students to take NEW GHSGT • No more PLATO for recovery of low or failing test grades or averages

13. Placement for 2011-2012 School Year AP Calculus AB or AP Calculus BC and/or AP Statistics or New Discrete Math Placement will be determined by student’s work ethic and grades. If a student does not exhibit a good work ethic along with good grades, he or she will not be recommended for the AP Calculus BC class.

14. Contact Information: Dr. Brian Wynne wynneb@fultonschools.org Sharon Bean BeanS@fultonschools.org