Course Syllabus
PreAP/PIP Pre-Calculus
Damon McDaniel email: 832-484-4858 or 832-484-5000 ext. 44858
Amy Sheehan email: 832-484-4865 or 832-484-5000 ext. 44865
I. Description of course: This course will emphasize the study of polynomial, radical, exponential, logarithmic, and trigonometric functions. Functions, equations, and limits will be used as useful tools for expressing generalizations and as a means for analyzing and understanding a broad variety of mathematical relationships. Functions, as well as symbolic reasoning, will be used to represent and connect ideas in geometry, probability, statistics, trigonometry, and calculus and to model physical situations. In addition to the topics studies in Pre-Calculus, other topics will include polar and parametric equations and sequences and series. This course is designed for the math-oriented student and will require independent and guided research. The level of instruction/curriculum will focus on preparing the student for advanced placement or I.B. courses.
II. Objectives:
(a)General requirements. The provisions of this section shall be implemented beginning September 1, 1998, and at that time shall supersede §75.63(bb) of this title (relating to Mathematics). Students can be awarded one-half to one credit for successful completion of this course. Recommended prerequisites: Algebra II, Geometry.
(b)Introduction.
(1)In Precalculus, students continue to build on the K-8, Algebra I, Algebra II, and Geometry foundations as they expand their understanding through other mathematical experiences. Students use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study mathematical concepts and the relationships among them. Students use functions, equations, and limits as useful tools for expressing generalizations and as means for analyzing and understanding a broad variety of mathematical relationships. Students also use functions as well as symbolic reasoning to represent and connect ideas in geometry, probability, statistics, trigonometry, and calculus and to model physical situations. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model functions and equations and solve real-life problems.
(2)As students do mathematics, they continually use problem-solving, language and communication, connections within and outside mathematics, and reasoning (justification and proof). Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.
(c)Knowledge and skills.
(1)The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise-defined functions. The student is expected to:
(A)describe parent functions symbolically and graphically, including f(x) = xn, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = ex, f(x) = |x|, f(x) = ax, f(x) = sin x, f(x) = arcsin x, etc.;
(B)determine the domain and range of functions using graphs, tables, and symbols;
(C)describe symmetry of graphs of even and odd functions;
(D)recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function; and
(E)investigate the concepts of continuity, end behavior, asymptotes, and limits and connect these characteristics to functions represented graphically and numerically.
(2)The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems. The student is expected to:
(A)apply basic transformations, including a • f(x), f(x) + d, f(x - c), f(b • x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;
(B)perform operations including composition on functions, find inverses, and describe these procedures and results verbally, numerically, symbolically, and graphically; and
(C)investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.
(3)The student uses functions and their properties, tools and technology, to model and solve meaningful problems. The student is expected to:
(A)investigate properties of trigonometric and polynomial functions;
(B)use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;
(C)use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation coefficient);
(D)use properties of functions to analyze and solve problems and make predictions; and
(E)solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.
(4)The student uses sequences and series as well as tools and technology to represent, analyze, and solve real-life problems. The student is expected to:
(A)represent patterns using arithmetic and geometric sequences and series;
(B)use arithmetic, geometric, and other sequences and series to solve real-life problems;
(C)describe limits of sequences and apply their properties to investigate convergent and divergent series; and
(D)apply sequences and series to solve problems including sums and binomial expansion.
(5)The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations. The student is expected to:
(A)use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;
(B)use properties of conic sections to describe physical phenomena such as the reflective properties of light and sound;
(C)convert between parametric and rectangular forms of functions and equations to graph them; and
(D)use parametric functions to simulate problems involving motion.
(6)The student uses vectors to model physical situations. The student is expected to:
(A)use the concept of vectors to model situations defined by magnitude and direction; and
(B)analyze and solve vector problems generated by real-life situations.
III. Course Outline:
First Six Weeks:
Unit 1: Sections 1.1-1.5
Functions and Their Graphs part 1
TEKS: P.2.A; P.1.A; P.1.B; P.1.C; P.1.D; P.3.A
Unit 2: Sections 1.6-1.10
Functions and Their Graphs part 2
TEKS: P.1.A; P.1.B; P.1.C; P.1.D; P.2.A; P.2.B; P.3.B; P.3.C; P.3.D
Unit 3: Sections Appendix A-5; 2.1
Absolute Value, Quadratic, Radical, and Polynomial Equations and Models
TEKS: P.1.A; P.1.D; P.3.A; P.3.B; P.3.D
Second Six Weeks:
Unit 4: Sections 2.2-2.5
Polynomial and Rational Functions
TEKS: P.1.A; P.1.B; P.1.D; P.1.E; P.3.A; P.3.B; P.3.D
Unit 5: Sections Appendix A-4; Appendix A-5; Appendix A-6; 2.6-2.7
Rational Expressions and Functions, Linear and Nonlinear Inequalities
TEKS: P.1.A; P.1.B; P.1.D; P.1.E; P.3.B; P.3.D
Unit 6: Sections Appendix A-2; 3.1-3.2
Exponential and Logarithmic Expressions, Functions, and Graphs
TEKS: P.1.A; P.1.B; P.1.E; P.2.C; P.3.B; P.3.D
Third Six Weeks:
Unit 7: Sections 3.3-3.5
Exponential and Logarithmic Equations and Models
TEKS: P.2.C; P.3.B; P.3.D
Unit 8: Sections 4.1, 4.2, 4.4
Trig Functions
TEKS: P.1.A; P.1.C; P.2.A; P.3.A; P.3.B; P.3.D; P.3.E
Unit 9: Sections 4.5-4.6
Graphing Trig Function
TEKS: P.1.A; P.1.B; P.1.C; P.1.D; P.1.E; P.3.A; P.3.B; P.3.D; P.3.E
Fourth Six Weeks:
Unit 10: Sections 4.3, 4.7, 4.8
Right Triangle Trig, Inverses, Applications and Models
TEKS: P.1.A; P.1.B; P.1.E; P.2.C; P.3.A; P.3.B; P.3.D; P.3.E
Unit 11: Sections 5.1-5.3
Using and Verifying Trig Identities and Solving Trig Equations
TEKS: P.2.C; P.3.E
Unit 12: Sections 5.4-5.5
Trig Formulas
TEKS: P.2.C; P.3.E
Fifth Six Weeks:
Unit 13: Sections 6.1-6.2
Law of Sines and Law of Cosines
TEKS: P.3.E
Unit 14: Sections 6.3-6.4
Vectors
TEKS: P.3.E; P.6.A; P.6.B
Unit 15: Sections 7.4-7.5
Partial Fractions and Systems of Inequalities
TEKS: P.1.D; P.3.C
Unit 16: Sections 9.1-9.3, 9.5
Sequences and Series, Binomial Theorem
TEKS: P.4.A; P.4.B; P.4.D
Sixth Six Weeks:
Unit 17: Sections 10.2-10.4, 10.6
Conics, Parametric Equations
TEKS: P.5.A; P.5.B; P.5.C; P.5.D
Unit 18: Sections 12.1-12.4
Limits
TEKS: P.1.E; P.4.C
Unit 19: Sections 6.5, 10.7-10.8
Trig Form of Complex Numbers, Polars
TEKS: P.1.D; P.2.C; P.3.A; P.3.B; P.3.D; P.3.E
Resources:
college.cengage.com/mathematics/larson/precalculus_limits/1e/resources.html
The solutions manual can be accessed at the following site:
www.calcchat.com/book/Precalculus-With-Limits/
IV. Grading procedures:
Major Grades:
Tests, Projects: 70%
A. Re-teaching of material will take place in class, tutoring before school, after school, or in Panther Den. Students may also listen to the teacher recorded lessons posted on Blackboard. There is no grade repair.
B. A student who earns a grade of lower than 80 on a test (unless a student is in violation of the Honor Code and excluding semester exams) will be afforded the opportunity to earn up to a maximum grade of 80 on that test if the student has turned in completed test corrections. The retake test must be taken within 5 days or in the Panther Den. Students are allowed one retake per test.
Minor Grades:
Quiz/Daily: 20%
Homework: 10%
Extra Credit: Extra credit is not used.
Late Assignments (Major, Minor, and Homework): All late assignments will have a point deduction of 5% per day, up to four days. If the assignment is completed in the Homework Academy, they student will have a 20% grade deduction late penalty. If the assignment is not completed in the Homework Academy, the student will receive a zero.
Make-up assignments: If a student misses an assignment due to excused absence(s), the student will have same number of days they were absent to turn in the assignment for full credit. If a student is absent due to a school function, the student should communicate this to the teacher and is encouraged to make arrangements to stay current with their school work so as to not fall behind.
EOC information: Not applicable for this course.
V. Tutoring schedule:
Monday / Tuesday / Wednesday / Thursday / FridayMr. McDaniel Rm. 281
/ 6:45 AM - 7:15AM / 6:45 AM - 7:15AM
2:30 PM - 3:30PM / 6:45 AM - 7:15AM / 6:45 AM - 7:15AM / 6:45 AM - 7:15AM
Ms. Sheehan Rm. 286 / 6:45 AM - 7:15AM / 6:45 AM - 7:15AM
2:30 PM - 3:20PM / 6:45 AM - 7:15AM / 6:45 AM - 7:15AM
2:30 PM - 3:20PM / By appointment only
The times listed above are subject to change depending upon school obligations and/or personal conflicts. Monday/Wednesday afternoon are reserved for mandatory teacher meetings.
VI. Test days:
Math test days are Tuesday and Thursday.
Test makeup days are Tuesdays from 6:25-7:15 am (you must arrive by 6:45am to be admitted) and Thursdays from 2:35-3:25 pm (you must arrive by 2:50pm to be admitted) in ROOM 289. Student must communicate with their teacher that they are planning on making up the test in the make-up room so their test can be placed there for them.
VII. Required and suggested supplies:
Tablets are used daily, so please bring your tablet, stylus, and charger every day. Pen, pencil and paper are also used.