Download Renaissance Academy High School Ms. Belinda Dolino

Renaissance Academy High School
Ms. Belinda Dolino - Room 308
Pre-Calculus
Course Syllabus AY 2013 – 2014
A. COURSE DESCRIPTION
The purpose of this course is to bridge abstract thinking skills, the function concept, and the algebraic solution
of problems in various content areas presented in Algebra 2 and develop them further to prepare students for
calculus. In addition to the math analysis content taught, the graphing, solving, and applications of
trigonometry are taught in preparation of their use in calculus as well as other advanced science and math
courses.
I.
II.
III.
IV.
V.
VI.
VII.
Polynomial
Functions
Power Functions
Rational
Functions
Exponential/Log
Functions
General Periodic
Functions
Introducing
Trigonometric
Functions
Combining
Functions
VIII.
IX.
X.
XI.
XII.
XIII.
XIV.
XV.
XVI.
Trigonometric
Identities
Composition
Inverses
Inverse
Trigonometric
Functions
Triangle
Trigonometry
Modeling Data
Optimization
Parametric
Modeling
Related Rates
XVII.
XVIII.
XIX.
XX.
XXI.
XXII.
XXIII.
More About
Sequences and
Series
Vectors
Modeling with
Conic Sections
Polar
Coordinates
Representing
Conics
Graphing Conics
Arithmetic and
Geometric
Sequences and
Series
B. INSTRUCTIONAL Materials Needed in this Class
 2 Composition Notebooks: 1 for Homework AND 1 for note-taking. You should also have at least 100 pages
of loose leafs. There will be different handouts that should be inserted into a binder. The binder will be used
for class activities. The Homework notebook will be checked every Friday.
 All tests and quizzes may be kept in a folder provided to you and should be left in the room. Questions for
the tests and quizzes will come from dittos, other tests and quizzes. All questions about a test or a quiz will
only be entertained during coach class or consultation periods.
 Loose-leaf is required for collected class assignments.
 USE PENCILS IN ALL WORK. No assignments, tests or quizzes will be accepted if written in any other color
ink.
 Graphing papers will be used for graphing. You should have at least 20 pieces in your binder.
 Scientific Calculator (TI 83/84) will be provided in the class but you are encouraged to have your own
calculator for practice at home and all other assignments. (Calculus class should have their own TI
calculator). Please do not take any of my calculators outside the classroom! Serious consequences will be
given!
 A positive attitude
C. COURSE STANDARDS
The Common Core State Standards for
Mathematics (CCSSM) at the high school level
specify the mathematics that all students should
study in order to be college and career ready.
8 Standards of Mathematical Practices
1) Make sense of problems and persevere in solving them.
2) Reason abstractly and quantitatively.
3) Construct viable arguments and critique the reasoning of
others.
4) Model with mathematics.
5) Use appropriate tools strategically.
6) Attend to precision.
7) Look for and make use of structure.
8) Look for and express regularity in repeated reasoning.
Curriculum Map (Aligned to the Common Core)
F.IF.7 Graph function expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more
complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions
c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
d. Graph rational functions, identify zeros and asymptotes when suitable factorizations are available, and showing end behavior.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline,
and amplitude.
N.CN.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
N.CN.4 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular
and polar forms of a given complex number represent the same number.
N.CN.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane: use properties of this
representation for computation.
N.CN.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the
numbers at its endpoints.
F.BF.1 Write a function that describes a relationship between two quantities.
c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of
time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
F.BF.4 Find inverse functions.
b. Verify by composition that one function is the inverse of another.
c. read values of an inverse function from a graph or a table, given that the function has an inverse.
d. Produce an invertible function from a non-invertible function by restricting the domain.
F.BF.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
F.TF.3 Use special triangles to determine geometrically that values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the value of sine,
cosines, and tangent for π –x, π+x, and 2π-x in terms of their values for x, where x is any real number.
F.TF.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
F.TF.6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
F.TF.7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms
of the context.
F.TF.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
N.VM.1 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols
for vectors and their magnitudes.
N.VM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
N.VM.3 Solve problems involving velocity and other quantities that can be represented by vectors.
N.VM.4 Add and subtract vectors.
a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of sum of two vectors is typically not the sum of the
magnitudes.
b. Given two vectors in magnitude and direction form, determination the magnitude and direction of their sum.
c. Understand vector subtraction v - w as v + (-w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction.
Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component –wise.
N.VM.5 Multiply a vector by a scalar.
a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise.
b. Compute the magnitude of a scalar multiple cv using
. Compute the direction of cv knowing that when
, the direction of cv is either along
v (for c < 0) or against v (for c < 0).
N.VM.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
N.VM.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
N.VM.8 Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a communicative operation, but still satisfies the
associative and distributive properties.
N.VM.10 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The
determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
N.VM.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as
transformation of vectors.
N.VM.12 Work with 2 x 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
A.REI.8 Represent a system of linear equations as a single matrix equation in a vector variable.
A.REI.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 x 3 or greater).
G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying
problems, resultant forces).
G.GPE.3 Derive the equations of ellipses and hyperbolas given foci, using the fact that the sum or difference of distances from the foci is constant.
G.GMD.2 Give an informal argument using Cavalier’s principle for the formulas for the volume of a sphere and other solid figures.
S.MD.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability
distribution using the same graphical displays as for data distributions.
S.MD.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
S.MD.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected
value.
S.MD.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
S.MD.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
a. Find the expected payoff for a game of chance.
b. Evaluate and compare strategies on the basis of expected values.
D. COURSE REQUIREMENTS AND GRADING PROCEDURES
1. Grading
Participation/Following Directions
Class Assignments
Home Assignments
Assessments/Quizzes/Tests
Projects
10%
20%
10%
30%
30%
100%
Grading Categories
Participation and Following Directions are very important part of your grade. To ensure your success, and
that of other students in class, all students are expected to volunteer to answer questions, do board work,
ask questions and share ideas. In the process, students are expected to follow the teacher’s directions so as
to maintain order and safety in class, and achieve the joy of learning.
Assignments must be completed on time.
a) Homework: Students are expected to complete their homework on time. Each homework
assignment will be worth 4 points. In order to earn full credit, students must:
 Complete each problem of the homework on-time. Assignments are considered complete
when every problem has been honestly attempted. If you get stuck on a homework
problem, you must write out the question(s) that you have so that you can ask during the
homework processing in class the next day!
 Self-correct the assignment during class with a red pen/pencil
 Re-work any missed problems.
 Turn in the completed, corrected, fixed homework.
b) Late work: In order to take full advantage of all learning opportunities and homework processing
time, it is strongly recommended that homework is completed each night. On the rare occasion
that homework is completed late (beyond the packet due date), it may be turned in for ½ credit.
However, these late assignments must be turned in prior to the next unit test to be considered.
c) Group work and in-class activities: An essential part of Precalculus is actively learning the material
and working as a team at times. Attendance and participation are very important. In-class, group
activities are very difficult, and sometimes impossible, to make-up individually. Group work and
in-class activities are considered to be assignments. Students will be expected to be active learners
and participate on class activities.
d) Class Notes: Students are also expected to take clear and organized Cornell notes, study them
regularly. Students will be taking notes in their Student Activity Notebooks.
Tests and quizzes are a very important part of your grade. Any material or information given in class is
subject to testing.
2. Assessments
Formative/Summative Quizzes
End-of-Unit Assessments
Daily School and Home Assignments
E. Policies and PROCEDURES
1. Daily Routine
 Use of any electronic devices inside the class that may disrupt instruction will not be tolerated
(Cellphones, iPods, Cameras, etc.)
 No using of cellphones as calculators
 Enter the classroom quickly and quietly.
 Go to your assigned seat.
 Listen and follow directions carefully.
 Prepare all the needed materials.
 Copy the objective, home assignment and drill from the designated board. Don’t forget to write the
DATE. Notes will be checked every quarter and it will be counted.
 Begin work on the drill immediately.
 Raise your hand and wait to be called on before speaking.
 Do not stand up and go to the “sharpener” area if the teacher is speaking.
 Do not leave the room during discussion and without permission.
 If you are not in your seat when the bell rings, you are considered LATE and that you need to present a
PASS before entering my class.
 The bell does not dismiss you, the teacher does. So remain seated quietly and wait to be dismissed by the
teacher.
 Know due dates and submit coursework on time. Unexcused late work will be zero.
2. Classroom Norms
To achieve a classroom with a positive learning environment, the following rules are in place and
have to be followed at all times:






Report to class daily and on time with all materials needed.
Demonstrate respect for yourself, others, and school property.
Wear your proper uniform always.
Follow classroom procedures at all times.
Work cooperatively with team members and maintain positive attitudes.
Eating, drinking, and use of obscene/profane language will not be permitted at anytime.
 15-minute rule: No hallway passes will be issued for the first 15 or last 15 minutes of the class
period!
 Adhere to the school’s discipline policy and the Baltimore City School’s Code of Conduct.
3. Positive Behaviors:
Students’ positive work efforts and attitudes as well as successes in the classroom are recognized and
commended by verbal praise, positive notes or phone calls to parents and occasional healthy treats.
4. Consequences for Inappropriate Behavior:
If a student chooses to break a rule, the following hierarchy of consequences will be administered:
1. Verbal Warning
2. Conference with the Student
3. Phone Call Home/ Parent-Teacher
Conference
4. Minor Incident Report Completed
5. Demerits Issued by Administrator with
6.
Consequences
Office Referral
F. Extra Assistance
 Students have several opportunities for extra help. This includes Ms. Dolino’s coach class on Tuesdays
and Wednesdays 2:30 – 3:30.
 If you are absent, it is your responsibility to complete the lesson(s) that you missed, and seek my help to
understand the concepts if you have questions. It is also your responsibility to complete the
assignment(s) you missed. Work/Tests cannot be made up if the absence is unexcused. For an excused
absence, you will have one day for each day absent to make up any missed work.
***Please Complete and Return This Portion to Ms. Dolino***
PLEASE PRINT!!!
Name of Student: _______________________________________________________
Period _________
Name(s) of parents/guardians: (First and Last names)
__________________________________________________________
__________________________________________________________
Mailing Address: __________________________________________________________
__________________________________________________________
Parent’s Home phone: _________________________________________________
Parent’s Work phone: _________________________________________________
Best time to call ________________________________________
I have read the Precalculus course expectations and understand that I must take responsibility for
my academic advancement, as well as my classroom behavior.
X ___________________________________________________
Student Signature
__________________
Date
I have read and discussed with my son/daughter the Course Expectations for Ms. Dolino’s
Precalculus course.
X ___________________________________________________
Parent/Guardian Signature
Parents: Please feel free to add any comments.
__________________
Date