Download Advanced Algebra and Trigonometry

Fullerton Joint Union High School District
COURSE SYLLABUS
Advanced Algebra & Trigonometry
Mrs. Jay
562 266 5250
[email protected]
Course Description
Advanced Algebra & Trigonometry includes material from a number of branches of mathematics,
thereby enabling students to experience connections among them. The course of study would include
functions, solving systems of equations, matrices, polynomials, trigonometric functions, vectors,
conic sections, and exponential and logarithmic functions. The student will further develop their
ability to explore and solve mathematical problems, think critically, work cooperatively with others,
and communicate mathematical ideas clearly
Course Goals for Advanced Algebra & Trigonometry
1. The student will demonstrate an understanding of functions and their properties, including
rational functions, exponential functions, and logarithmic functions and their applications.
2. The student will demonstrate competency in using algebraic principles including graphing,
solving equations/inequalities, rational and radical expressions, polynomials, and applications.
3. The student will exhibit an understanding of solving systems of equations using algebraic,
geometric, and matrix theories, and apply these to real-life situations.
4. The student will have a solid understanding of the geometry of conics and apply this
knowledge to problem-solving situations.
5. The student will demonstrate an understanding of the six trigonometric functions, their
properties, and apply these concepts to real-life applications.
Course Content and Objectives
A. Functions
The student will:
1. determine if a relation is a function and justify the conclusion.
2. determine domain and range from a graph, a set, or an equation.
3. perform the basic four operations on functions.
4. perform and evaluate composition of functions.
5. find the inverse of a function.
6. describe the effect of a rotation, translation and/or reflection on a function in the plane.
7. graph the rotation, translation, and/or reflection of a function.
8. graph a rational function identifying its asymptotes and zeros.
9. demonstrate the laws of exponents in simplifying expressions.
10. graph and interpret exponential and logarithmic functions.
11. describe the relationship between exponents and logarithms.
12. convert an exponential equation to a logarithmic equation and visa versa.
13. use the properties of logs to simplify expressions.
14. solve exponential and log equations.
15. apply knowledge of exponential and logarithmic functions to solve real-life problems of
growth and decay.
B. Algebraic principles & equations
1. solve equations algebraically and graphically over the field of real numbers.
2. solve equations algebraically over the field of complex numbers.
3. graph complex numbers in the complex plane.
4. solve absolute value equations and inequalities.
5. graph solution sets of absolute value equations and inequalities.
6. simplify rational expressions.
7. solve rational equations.
8. simplify radical expressions.
9. rationalize radical expressions.
10. solve radical equations
11. solve quadratic equations by factoring, completing the square or using the quadratic formula.
12. graph quadratic equations.
13. simplify polynomial expressions.
14. given a polynomial of nth degree, determine the number of real and complex roots.
15. apply the Factor Theorem, Remainder Theorem, Descartes' rule of signs, and the Rational
Zeros Theorem to find the real and complex zeros of a polynomial.
16. apply knowledge of equations and inequalities to solve real-life problems.
C. Systems of equations
1. find the solution for a system of equations or inequalities using a variety of methods
(substitution, elimination, graphically, and using matrices).
2. identify the number and type of solutions in linear systems.
3. compute sums, differences, and products of matrices in real-life situations.
4. find the determinant of a matrix.
5. determine the inverse of a matrix.
6. apply knowledge of systems of equations and inequalities to solve real-life problems.
D. Analytic geometry
1. state and use the definitions of each of the four conic sections.
2. identify and graph standard conic sections.
3. rewrite the quadratic equation in standard form to identify the conic section.
4. determine all pertinent parts of each of the four conic sections.
5. use translation formulas to graph a conic section.
6. write an equation in standard form of the conic using a geometric description.
E. Trigonometric functions and applications
1. measure angles in radians and degrees.
2. find the arc length and central angle of a circular sector.
3. convert from degrees to radians and vice versa.
4. define sine and cosine functions as coordinates on the unit circle.
5. use the special angles in locating the coordinates of points on the unit circle.
6. define the six trig functions in terms of the x-coordinate, y-coordinate, and radius.
7. give exact values of the six trigonometric functions of angles in radian measure.
8. derive the basic Pythagorean Identity and complete appropriate proofs for other Pythagorean
Identities.
9. using trig functions solve for all sides and angles of a right triangle.
10. apply knowledge of trig functions to solve real-life problems.
11. graph all six trig functions with transformations.
12. given a trig graph and/or equation identify amplitude, frequency, period, phase shift, and
vertical shift.
13. define and graph the inverse trig functions of sine, cosine, and tangent.
14. compute the inverse trig values at various standard points.
15. apply the law of sines and the law of cosines to solve triangles.
16. determine the number of solutions when given a triangle that is the ambiguous case of the law
of sines.
17. calculate the area of a triangle using appropriate formulas.
18. apply the sum and difference identities.
19. apply the double angle and half angle identities.
20. apply and simplify expressions using appropriate identities. •
21. solve trig equations.
Advanced Algebra and Trigonometry
Mrs. Jay
Class Work
Students will complete a Packet of worksheets for each chapter. Students must show all work to
receive credit. Class work packets are due as soon as completed without prior notice. Notes are due
on the day of the Final Exam
Home Work
 Homework is assigned every day but over the weekend.
 Monday’s homework is to correct Friday’s test/quiz and is worth 10 points.
 Tuesday through Thursday’s homework is out of Precalculus textbook and is worth 5 points.
 Late homework is worth 2 points.
 Any other late work is worth half credit.
 Homework is graded on effort.
 Students must show work in order to receive credit.
 Homework is posted on the school’s website on the day it is assigned.
Test/Quiz
There is a test/quiz every Friday. In case of an absence, students are allowed to be excused from
making up one test/quiz per quarter. Test make-ups are to be arranged with the teacher
Students are allowed to retake one test/quiz per quarter in order to improve their grade.
Absent work
Students are to make up all work missed due to absence. Students are allowed one day to make up
absent work for each day of absence.
Classroom Expectations
 Students are to be in class and ready to work as soon the bell rings. School wide tardy policy
will be applied to students who are tardy.
 Students will be given three hall passes per semester. Students who do not return to class
within 5 minutes will be assigned a detention.
 Students are not allowed to bring food to class. Beverages are allowed in closed bottles only.
Grading Policy/Guidelines
Tests/Quiz category will count as 80% of the grade, Homework/Classwork – 20%.
Advanced Algebra and Trigonometry
Student and Parent Signatures
This verifies that I have read and understood the above information as it was explained in the handout
and discussed in class.
Student Name _________________________________________ Date ____________
(please print)
Student Signature _______________________________________________________
Parent/Guardian Name _________________________________ Date ____________
(please print)
Parent/Guardian Signature ________________________________________________
Telephone Number ________________________ Email ________________________