Download Pre-Calculus Standarized Class Syllabus

Wo o d l a k e H i g h S c h o o l
400 West Whitney, Woodlake, Ca 93286, Phone: 559-564-3307
Course Title : Pre Calculus, A & B.
Grade Level: 11th
Elective/Required: Required for College Prep.
Length/Credits: 2 terms/5.0 credits per term.
Prerequisites: Completion of Algebra II with a C or better.
Course Number: Pre Calculus A course #0761
Pre Calculus B #0762
Teacher: Antonio Lopez
Conference Period: I am available before school or after school. If you have any questions or concerns please
contact me by phone at 564-3307(ext. 190) or email at [email protected]
Course Description:
This course is set up to meet college entrance requirements. Students will review and build on concepts from
Algebra 2 and then progress to concepts in Trigonometry, Analysis, Probability, and Statistics. The skills and
concepts that students will experience in this course are necessary for success in subsequent courses such as
calculus, physics or other sciences, and engineering. As skills and concepts are developed, they will be used in
a variety of problem-solving situations.
Instructional Materials:
The textbook that will be used is Pre-Calculus with Limits by Houghton Mifflin. A scientific/graphing calculator (Ti 83 plus) is required and may check out from the library. Students must provide batteries. Additional
material from a variety of sources will be used to supplement the skills and concepts in each chapter, enrichment, extra credit, and class projects.
Course Outline:
Pre Calculus A
In this course, students will expand on the concepts from Algebra 2, examine different types of functions and
their graphs, perform operations on functions, apply functions to real-life situations, examine methods of solving systems of equations and inequalities, and perform operations with matrices.
Standards: Algebra 2 Standards: 1.0, 5.0 - 14.0, 24.0; Math Analysis: 2.0, 4.0, 6.0;
Linear Algebra: 1.0 – 5.6, 9.0 - 11.0
Pre Calculus B
In this course, students will work with exponential & logarithmic functions, trigonometric functions & identities, the laws of sines & cosines, and real life applications of trigonometry. Students will be introduced to
sigma notation, sums of series & sequences, the binomial theorem, and conic sections.
Standards: Algebra 2: 18.0 - 23.0; Trigonometry: 1.0 - 9.0, 12.0, 13.0, 14.0, 19.0;
Probability & Statistics: 1.0 - 3.0; Math Analysis: 5.0
Instructional Methods:
Explicit Direct Instruction (EDI) is employed to foster a dynamic and equitable learning environment where
individual and group participation by a student is the expectation.
Carmita Pena
Dean of Students
Ricardo Rodriguez
Assistant Principal
Lisa Castillo
Principal
Classroom Policies and Procedures:
1.
2.
3.
4.
5.
Respect each other and staff.
Come to class prepared, on time, and ready to learn.
No eating, bottled water is allowed
All electronic devices must be turned off and out of sight.
The bell does not dismiss you, the teacher does.
Homework– Students are responsible to maintain a daily assignment calendar and will be checked once a
week for homework credit. Homework is generally due the following day. No credit will be given
for homework turned in after 2 days from the due date. Not being prepared for class with required
materials, homework, or lack of participation may result in a parent conference and/or lunchtime
detention.
Tests & Quizzes– Only one test and quiz maybe allowed to be retaken. However, students must 1) retake the
chapter test or quiz within two weeks of the first attempt. The test or quiz may be an alternate version of the original. 2) do retesting before school or after school, absolutely no class time will be
used for the retaking of tests or quizzes.
Absences – If you are absent from school, it is your responsibility to obtain and make-up the missed work,
test, or quiz. Students have 2 days for each day absent to make up the class assignment, quiz, or
test.
Assessments and Evaluation:
Parents are encouraged to view student’s class progress on PowerSchool. Students final class grade will be
comprised of weighted percentages on homework assignments, quizzes, chapter tests, benchmark assessments, and the end of the semester class final.
Class Grade Components
Letter Grades
Tests
Class work/Homework
Quizzes & Benchmarks
Class Final
25%
30%
25%
20%
90 - 100 A
80 - 89 B
70 - 79 C
60 - 69 D
59 and below F
Teacher-Student-Parent Compact
As a teacher, I pledge to
 provide motivating, challenging, and relevant learning experiences.
 provide assignments designed to practice, reinforce, and master the math curriculum.
 communicate with students and parents about progress in the classroom..
__________________________
Teacher’s Signature
As a student, I pledge to
 be in class on time with the required materials and supplies for the class.
 follow the classroom rules and participate in class discussions.
 keep track of my progress, turn in assignments when due, study for tests, and always know my grade.
 ask my teacher questions when I have a concern or do not understand.
__________________________
Student ‘s Signature
As a parent, I pledge to
 help my son/daughter meet his/her responsibilities as a WHS student
 monitor my student’s progress in mathematics.
________________________________
encourage good study habits and provide positive reinforcement.
________________________________
 communicate with my student's teacher when there is a concern.
Student’s Signature
Parent’s Signature
__________________________
Parent’s Signature
Pre Calculus A Standards
Algebra 2
1.0 Students solve equations and inequalities involving absolute value.
5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.
6.0 Students add, subtract, multiply, and divide complex numbers.
7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the
denominator.
8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.
9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions;
that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b) 2+
c.
10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
11.0 Students prove simple laws of logarithms.
11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship to solve
problems involving logarithms and exponents.
11.2 Students judge the validity of an argument according to whether the properties of real numbers, exponents, and
logarithms have been applied correctly at each step.
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in
problems involving exponential growth and decay.
13.0 Students use the definition of logarithms to translate between logarithms in any base.
14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to
identify their approximate values.
24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and
performing arithmetic operations on functions.
Math Analysis
2.0 Students are adept at the arithmetic of complex numbers. They can use the trigonometric form of complex numbers and understand that a function of a complex variable can be viewed as a function of two real variables. They
know the proof of DeMoivre’s theorem.
4.0 Students know the statement of, and can apply, the fundamental theorem of algebra.
6.0 Students find the roots and poles of a rational function and can graph the function and locate its asymptotes.
Linear Algebra
1.0 Students solve linear equations in any number of variables by using Gauss-Jordan elimination.
2.0 Students interpret linear systems as coefficient matrices and the Gauss-Jordan method as row operations on the
coefficient matrix.
3.0 Students reduce rectangular matrices to row echelon form.
4.0 Students perform addition on matrices and vectors.
5.0 Students perform matrix multiplication and multiply vectors by matrices and by scalars.
6.0 Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly
one solution, or have infinitely many solutions.
9.0 Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to
solve systems of linear equations.
10.0 Students compute the determinants of 2 × 2 and 3 × 3 matrices and are familiar with their geometric interpretations as the area and volume of the parallelepipeds spanned by the images under the matrices of the standard basis
vectors in two-dimensional and three-dimensional spaces.
11.0 Students know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute
the inverse to 2 × 2 and 3 × 3 matrices using row reduction methods or Cramer’s rule.
Pre Calculus B & H Pre Calculus B State Standards
Algebra 2
18.0 Students use fundamental counting principles to compute combinations and permutations.
19.0 Students use combinations and permutations to compute probabilities.
20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.
21.0 Students apply the method of mathematical induction to prove general statements about the positive integers.
22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.
24.0 Students solve problems involving functional
Trigonometry
1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees
and radians.
2.0 Students know the definition of sine and cosine as y-and x-coordinates of points on the unit circle and are familiar with the
graphs of the sine and cosine functions.
3.0 Students know the identity cos2 (x) + sin2 (x) = 1:
3.1 Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).
3.2 Students prove other trigonometric identities and simplify others by using the identity cos2 (x) + sin2 (x) = 1. For example, students use this identity to prove that sec2 (x) = tan2 (x) + 1.
4.0 Students graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude,
frequency, period, and phase shift.
5.0 Students know the definitions of the tangent and cotangent functions and can graph them.
6.0 Students know the definitions of the secant and cosecant functions and can graph them.
7.0 Students know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.
8.0 Students know the definitions of the inverse trigonometric functions and can graph the functions.
12.0 Students use trigonometry to determine unknown sides or angles in right triangles.
13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems.
14.0 Students determine the area of a triangle, given one angle and the two adjacent sides.
Math Analysis
5.0 Students can take a quadratic equation in two variables; put it in standard form by completing the square and using rotations and
translations, if necessary; determine what type of conic section the equation represents; and determine its geometric components
(foci, asymptotes, and so forth).
Probability and Statistics
1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.
2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.
3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of
outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.