Muhammad University of Islam
Mathematics Department
Pre-Calculus Syllabus
Instructor: Bro Shahid Muhammad
Course : Pre-Calculus
Credit Hours: Three hours
Prerequisites: Grade of B or better in Geometry
Catalog Description: Review of functions and slope relationships including
Inverse functions, rational, exponential and logarithmic
functions. Trigonometric functions, identities and graphs.
Sequences and series. Matrices, Probability and Analytic
geometry. Introduction to limits and derivatives.
Contact Hours: Five lecture hours per week based on 12 weeks.
Course Objectives: At the completion of this course, the student will be able to
solve and interpret problems and present information
symbolically, visually, numerically, verbally, in writing and
incorporate the use of technology on the following topics:
A. Algebraic Concepts & Linear Functions
***Continue to master finding the slope of a line
***Continue to master writing and sketching linear equations given points on
lines and their slopes.
***Decide whether relations between two variables represent a function.
***Use function notation
***Evaluate and find the domains and ranges of functions
***Use functions to model and solve real-life problems
***Use the vertical line test
***Determine intervals on which functions are increasing, decreasing, or
***Determine relative maximum and relative minimum values of functions
***Identify and graph piecewise-defined functions
***Identify even and odd functions
***Recognize graphs of common functions
***Use vertical and horizontal shifts, reflections, and non-rigid transformations
to graph functions
***Add, subtract, multiply and divide functions
***Calculate the composition of one function with another function
***Use compositions of functions to model and solve real-life problems
B. Rational, Exponential and Logarithmic Functions
*** Analyze graphs of quadratic functions
***Write quadratic functions in standard form and use the results to sketch
graphs of functions.
***Find minimum and maximum values of functions in real-life applications
***Use transformations to sketch graphs of polynomial functions
***Use the leading coefficient test
***Find and use zeros of polynomial functions as sketching aids
***Use the intermediate value theorem
***Use long division to divide polynomials by other polynomials
***Use synthetic division to divide polynomials by binomials of the form (x-k)
***Use the Remainder and Factor Theorem
***Use the Rational Zero Test
***Use Descartes Rule of Signs
***Add, subtract and multiply complex numbers
***Use complex conjugates to write the quotient of two complex numbers in
standard form
***Plot complex numbers in the complex plane
***Use the fundamental theorem of Algebra to determine the number of zeros
of a polynomial function
C. Trigonometry
***Describe angles
***Convert between radian and degree measure
***Evaluate trigonometric functions using the unit circle
***Use domain and period to evaluate sine and cosine functions
***Evaluate trigonometric functions of any angle
***Use the fundamental trigonometric identities
***Use a calculator to evaluate trigonometric functions
***Use reference angles to evaluate trigonometric functions
***Evaluate trigonometric functions of real numbers
***Sketch graphs of basic sine and cosine functions
***Sketch translations of graphs of sine and cosine functions
***Solve real-life problems involving right triangles
***Recognize and write the fundamental trigonometric identities
***Use the fundamental trigonometric identities to evaluate trigonometric
functions, simplify trigonometric expressions, and rewrite trigonometric
***Use standard algebraic techniques to solve trigonometric equations
D. Sequences, Series & Probability
***Write the terms of sequences using sequence notation
***Use factorial and summation notation
***Find sums of infinite series
***Recognize, write and find the nth terms of arithmetic and geometric
***Find the nth partial sums of arithmetic and geometric sequences
***Find sums of infinite geometric series
***Use mathematical induction to prove statements involving a positive integer
***Find the sums of powers of integers
***Find finite differences of sequences
***Use Binomial theorem
***Use Pascal’s triangle
***Use the fundamental Counting Principle
***Use permutations and combinations to solve counting problems
***Find probabilities of events
***Find probabilities of mutually exclusive events
***Find probabilities of independent events
E. Analytic Geometry
***Recognize a conic as the intersection of a plane and a double-napped cone
***Write equations of parabolas, ellipses, and hyperbolas in standard form
***Find eccentricities of ellipses
***Find asymptotes of hyperbolas
***Classify conics from their general equations
***Use properties of conics to solve real-life problems
***Vocabulary: Conic, locus, parabola, directrix, focus, vertex, axis, focal chord,
latus, rectum, ellipse, foci, major axis, minor axis, eccentricity, hyperbola,
transverse axis, center, conjugate axis, asymptote
***Use the discriminant to classify conics
***Solve systems of quadratic equations
***Evaluate sets of parametric equations for given values of the parameter
***Graph curves that are represented by sets of parametric equations
***Plot points in the polar coordinate system
***Convert points and equations from rectangular to polar form and visa versa
F. Limits & Derivatives
*** Discover the meaning of a limit
*** Evaluate limits for given functions
*** Translate limits into derivatives
G. Matrices and Determinants
*** Understand, interpret and define matrices
*** Perform basic operations on matrices
*** Relate matrices to systems of equations
*** Use matrices to solve systems of equations
*** Determine the determinant and inverse of a matrix
***Matrix applications
Classroom Rules & Policies:
Pencils, calculators, and demo kits will be supplied to each
student at the beginning of class and must be returned at the end of class in
the receptacles.
A god is on time with time. Quick thinking and fast moving right
down to the modern times. Excessive lateness to class will be investigated and
a possible parent conference may be called.
A god makes sure they are in class to master the material
presented to them. It is incumbent upon every student to strive for perfect
attendance so as to optimize your success in math class. Each student should
determine two study buddies and get their contact information.
Order and Discipline:
In order for the classroom to run smoothly and to provide the
best learning environment excessive silliness, disrespect, disorder, horseplay,
unnecessary noise and disruptions will not be tolerated. Any student receiving
excessive warnings on misbehavior and disruptive activity will be sent to the
dean for a parent conference. Please maintain order at all times and make
sure you request permission to comment, do not interrupt the teacher or a
fellow student and do not get out of your seat to do anything without
Homework is due the next day unless otherwise specified. Homework
is late if it is not turned in within 48 hours of the date it was assigned. Students
will receive 5% deduction of their grade for every day late after 48 hours.
Homework will be done via the internet unless otherwise specified by
the instructor. Students must have access to website in order to
do their work. Students will go to then sign in under Illinois,
subject is mathematics and click student. After that go to student workbook
and do the assigned work. There will be days when other projects or activities
will be assigned for homework.
Exams: Exams will be taken in class. If a student is absent for an exam
they must bring in a note from parents explaining the reason for absence and
request a make up exam. If students fail to request a make up exam they will
eventually receive a no grade for that exam and it may bring down their
overall average.
Grading Criteria:
Your grade is determined by the following:
*** Classroom Participation:
*** Unit Tests & Quizzes
*** Projects
*** Vocabulary Book
*** Homework/Classwork
Classwork/Homework -------- 30%
Vocabulary Book -------------- 10%
Projects ------------------------- 20%
Tests & Quizzes-------------- 40%
Grading Scale:
A ------ 95% or higher
B ------ 85% to 94%
C ----- 75% to 84%
D ------ 70% to 74%
F ----- 73% and below