MATH 1330 - Precalculus - University of Houston
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MATH 1330 - Precalculus

Section number: This information applies to ALL face-to-face sections

Delivery format: Hyflex/Online/face-to-face

Prerequisites: MATH 1310 or a satisfactory score on a placement examination.

Course DescriptionThis course concentrates on the various subjects that are important to the study of MATH 1431 Calculus I and MATH 1432 Calculus II, including a review of functions (polynomial, rational, exponential, logarithmic functions), trigonometry, conic sections, vectors in plane, and polar coordinates. *Note: Students with prior credit in MATH 1432 may not receive credit for MATH 1330. TCCNS Equivalent: MATH 2312.

Core Category: Mathematics (20) and Math/Reasoning (90)

Textbook: Available in electronic form (PDF) through CASA for all enrolled students via an Access Code. For more information regarding access to the book, please view your instructor's syllabus.

*Note: The information contained in this class outline is an abbreviated description of the course. Additional important information is contained in the Departmental Course Policies statement and at your instructor’s personal webpage. You are responsible for knowing all of this information.


Course Objectives for Precalculus:

When you successfully complete this course, you will be able to:

1. Recall and apply basic algebra skills without requiring a review.

2. Recognize various kinds of functions (including polynomial, rational, radical, exponential, and logarithmic functions), analyze their behavior, and use the properties of these functions to solve equations and application problems.

3. Define trigonometric functions; understand the right triangle trigonometry and unit circle.

4. Know and apply identities involving the trigonometric functions.

5. Recognize the conic sections and their geometric properties.

6. Exploit graphical and analytical techniques in solving problems.

7. Analyze and explain the important elements of the mathematical solution of equations.

8. Recognize and use the vocabulary of vectors (vector, scalar, magnitude, direction) to perform arithmetic on vectors and to solve application problems.

9. Recognize polar coordinates and use them to draw graphs and plot points.

10. Be self-disciplined and dependable through daily consistent work. 



A student in this class is expected to complete the following assignments:

1. Course Policy Quiz – online on your CASA account – you must make 100% on the course policy quiz in order to have access to the other online assignments in the course. The answers to the quiz may be found in the “Math 13xx Course Policies” document on your instructor’s website.

2. Four Regular Exams

3. Final Exam

4. Online Quizzes

5. Homework

6. Poppers – in-class quizzes given daily starting the 3rd week of classes. 


Components and Weights of Semester Assignments:

5%       Test 1

15%     Test 2

15%     Test 3

15%     Test 4

20%     Final Exam  

8%       Homework

10%     Poppers 

12%     Online Quizzes 

            Total:    100%

Note: The percentage grade on the final exam (without extra credit) can be used to replace your lowest test score if it is better than your lowest test grade. 


Grading Scale:

University of Houston standard grading scale will be used to determine your letter grade in this course.

A x > 93
B- 80 ≤ x < 83 D+ 67 ≤ x < 70
A- 90 ≤ x < 93 C+ 77 ≤ x < 80 D 63 ≤ x < 67
B+ 87 ≤ x < 90 C 73 ≤ x < 77 D- 60 ≤ x < 63
B 83 ≤ x < 87 C- 70 ≤ x < 73 F below 60



Exam Information:

There will be 4 tests along with a mandatory final exam. Test 1 is an online test over the pre-requisite material (algebra). You can find it under online assignments tab at CASA. You have 2 attempts; we take your best score. It is recommended to take practice test 1 first to see what to expect on Test 1. You can review basic algebra topics to prepare for this test.

IMPORTANT: If you score low on Test 1 (below 60 without extra credit); you may consider dropping this course and taking the prerequisite course to prepare yourself for this course. If you decide not to drop, it is strongly recommended that you sign up for an SEP workshop designed for Math 1330 students; you can add a workshop in your PS account before the last day to add.

The remaining tests (Tests 2, 3, 4 and final) are taken at CASA testing center, with reservation. Use “proctored exams” tab at your CASA account to reserve a seat for it. 

To see the exam dates and topics covered, please visit course website. You must make a reservation to take a test prior to the first testing day. You should print out the web page showing your reservation time for your records and proof of your reservation. Reservation generally begins 2 weeks prior to an exam; reserve a seat as soon as the scheduler opens up.

Tests are 50 minutes long. Push the “submit” button when you’re completely ready to leave the Testing Center, AFTER you’ve finished ALL the questions and checked your work.

If you miss a test, you receive a zero for it. When you take the final, the grade on the final will replace that zero. If you miss more than one test, only the first one will be replaced. There are no retakes or makeups in this class. You can NOT use calculators during any of the exams; study accordingly. 

*Exceptions may be made per the Student Academic Adjustments/Auxiliary Aids Policy for students with approved CSD accommodations (see the CSD Accommodations section below)


Exam topics: (Any change on the exam topics or dates will be announced on the instructor’s website or on the CASA Calendar)

Test 1

Prerequisite Material


Test 2

Algebra review, 4.1, 4.2, 4.3


Test 3

4.4, Chapter 5, 6.1, 6.2


Test 4

6.3, Chapter 7, Vectors



Comprehensive (covers all chapters)








Final Exam:

Final is comprehensive and mandatory for all students. There is no “exemption” or “opt-out” from the final in Math 1330. No make-ups/no excuses. No early finalsCheck course website for final exam schedule. Final is given at CASA testing center. Reserve a seat for it when reservation begins. Your raw score on the final will be used to replace the lowest test score if it is better. *Exceptions may be made per the Student Academic Adjustments/Auxiliary Aids Policy for students with approved CSD accommodations (see the CSD Accommodations section below).


Extra Credit:

There are practice tests and a practice final on Courseware. If you take the practice test, then 10% of the highest score you earn will be applied to the relevant test as extra credit on the corresponding exam. You can take the practice tests several times (up to 20 times) and we only take your best score. Pay attention to the “end” dates on these. None of the practice tests will ever be re-opened. 


Instructions for Quizzes:

Online quizzes will be given regularly in this course.

  • The quizzes are located in the CASA CourseWare course website under the “Online Assignments” tab.
  • The quizzes will close on the due dates given on CourseWare at 11:59 pm and will not re-open.
  • One of the lowest quizzes will be dropped.
  • You have 20 times to take each quiz.
  • There is a 60 minute time limit for each quiz.
  • There may be 2 or more quizzes due every week; check the due dates carefully.


There will be no makeup quizzes for any reason.  Neither I, nor the Math Department, is responsible for any difficulty that you have in accessing the quizzes.  Please don’t delay taking quizzes – there are times during the week when CourseWare is slow or overloaded. There is no amnesty period for the quizzes; the quizzes will NOT be reopened at the end of the semester. If you miss a quiz, you will not have a chance to make up for it. *Exceptions may be made per the Student Academic Adjustments/Auxiliary Aids Policy for students with approved CSD accommodations (see the CSD Accommodations section below).

Please contact CourseWare tech support directly if you are having problems.  The email link is on the CASA homepage.


Instructions for Poppers:

  • For each lecture starting on the third week of classes you will be asked a series of problems that will have to do with the lecture.
  • The forms are for sale at the BOOK STORE. Please buy the package for Math 1330 with your section number printed on it. You must use the right popper forms for credit; you can’t turn in your answers on any other kind of paper.
  • You are required to fill in your id number, popper number and blacken the correct circles.  Make sure that your id number and popper number are correct before turning in the popper at the end of the lecture.  If these are not filled out correctly or if the darken circles are too light you will not get credit for that day’s lecture even if you attended.
  • The total number of questions for the course will be counted, 85% of the total number of questions will be the 100%.  For example, if there are 5 questions each class for 24 classes, which is 120 questions.  Your grade will be calculated out of 120(.85) = 102 points.
  • There will be no make-up Poppers.

If your popper is not graded even though you turned it in, that means you’ve made a bubbling mistake and there is nothing we can do about it. You will not receive credit for such poppers.

*Exceptions may be made per the Student Academic Adjustments/Auxiliary Aids Policy for students with approved CSD accommodations (see the CSD Accommodations section below).



Instructions for Homework:

  • There are weekly homework assignments starting the third week.
  • The homework problems and due dates will be posted on course website.
  • You will submit your answers using “EMCF” tab at CASA before the due date.
  • Two of the lowest homework assignment scores will be dropped.
  • No late homework; no make ups on the homework.
  • Your score on the homework is the number of correct answers out of the total number of questions.
*Exceptions may be made per the Student Academic Adjustments/Auxiliary Aids Policy for students with approved CSD accommodations (see the CSD Accommodations section below).



Late Assignment and Make-Up Policy:

 This course is a cumulative course.  You as a student need to keep up with the reading, quizzes, homework assignments and exams.  Thus, late work or make-ups will not be accepted for any reason. The instructor reserves the right to make changes on these policies. Any changes will be announced on the course website in a timely manner.



Counseling and Psychological Services (CAPS) can help students who are having difficulties managing stress, adjusting to college, or feeling sad and hopeless. You can reach CAPS ( by calling 713-743-5454 during and after business hours for routine appointments or if you or someone you know is in crisis. No appointment is necessary for the "Let's Talk" program, a drop-in consultation service at convenient locations and hours around campus.   


CSD Accommodations:

Academic Adjustments/Auxiliary Aids: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit The Center for Students with DisABILITIES (CSD) website at for more information.

Accommodation Forms: Students seeking academic adjustments/auxiliary aids must, in a timely manner (usually at the beginning of the semester), provide their instructor with a current Student Accommodation Form (SAF) (paper copy or online version, as appropriate) from the CSD office before an approved accommodation can be implemented.

Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) document under [STEP 4: Student Submission (5.4.1 & 5.4.2), Page 6]. For more information please visit the Center for Students with Disabilities Student Resources page.

Additionally, if a student is requesting a (CSD approved) testing accommodation, then the student will also complete a Request for Individualized Testing Accommodations (RITA) paper form to arrange for tests to be administered at the CSD office. CSD suggests that the student meet with their instructor during office hours and/or make an appointment to complete the RITA form to ensure confidentiality.

*Note: RITA forms must be completed at least 48 hours in advance of the original test date. Please consult your counselor ahead of time to ensure that your tests are scheduled in a timely manner. Please keep in mind that if you run over the agreed upon time limit for your exam, you will be penalized in proportion to the amount of extra time taken.


Learning Objectives for Precalculus:


1. Recognize various kinds of functions (including polynomial, rational, radical, exponential, and logarithmic functions), analyze their behavior, and use the properties of these functions to solve equations and application problems. Recognize that exponential and logarithmic functions are inverses, recall the characteristics of these functions, and solve equations and application problems involving exponential and logarithmic functions. Apply the concepts learned about limits at infinity to afore mentioned functions.

2. Recognize and use the vocabulary of angles (including standard position, initial and terminal sides, quadrantal angles, coterminal angles, acute, right, and obtuse angles).
-Use degrees and radians to measure angles.
-Convert angles from degrees to radians and vice versa.
-Compute the length of a circular arc given the radius and the interior angle.
-Apply the concepts of linear and angular speed to solve problems concerning motion on a circular path.

3. Use right triangles to evaluate the six trigonometric functions.
-State the trigonometric function values for 300, 450, 600. Use right triangle trigonometry to solve application problems that can be visualized using right triangles.
4. Compute the six trigonometric functions of any angle and use the unit circle to define the six trigonometric functions for all real numbers.
-Define the trigonometric functions for any angle.
-Identify the signs of the trigonometric functions.
-Find reference angles and use them to evaluate trigonometric functions.
-Identify even and odd trigonometric functions.
5. Know and draw the graphs of the six trigonometric functions and their variations.
- Compute the amplitude, period, phase shift, vertical shift, domain, and range of a sinusoidal functions. Compute the period, domain, range, vertical asymptotes, and x-intercepts of the tangent and cotangent functions.
- Draw the graphs of y = csc x and y = sec x; recognize the relationship between the graph of a cosecant function (respectively, secant) and the graph of a sine (respectively, cosine) function.
6. Understand the definitions of the inverse trigonometric functions.
-Compute the domain and range of the inverse trigonometric functions.
-Evaluate inverse trigonometric functions using a calculator (*optional).
-Find exact values of composite functions with inverse trigonometric functions
7. Know and apply identities involving the trigonometric functions.
-Use trigonometric identities to simplify expressions and to evaluate the trigonometric functions. Use the trigonometric functions to solve triangles.
-Use fundamental trigonometric identities to verify other identities.
-Apply the sum and difference formulas for sine, cosine, and tangent.
-Apply the double-angle and half-angle formulas for sine, cosine, and tangent.
-Apply the Law of Sines and/or the Law of Cosines either to solve triangles.
8. Find all solutions of a trigonometric equation.
-Solve trigonometric equations quadratic in form.
-Use identities to solve trigonometric equations.
9. Recognize conic sections and their geometric properties.
-Differentiate between four conic sections (circle, ellipse, hyperbola, parabola) using the standard and the general form of the equations.
-Describe the terms center, foci, vertices, and directrix.
-Graph the conic sections.
-Solve non-linear systems with two variables using algebra and/or graphing.
10. Recognize and use the vocabulary of vectors (vector, scalar, magnitude, direction) to perform arithmetic on vectors and to solve application problems.
-Draw the components of a vector.
-Construct a visual representation of scalar multiplication, vector addition, and vector subtraction.
-Find the dot product of two vectors; find the angle between two vectors.
-Use the dot product to determine if two vectors are orthogonal, parallel, or neither.


Precalculus Topic List:


Algebra Review: Functions

            -Methods of Combining Functions
            -Inverse Function
            -Polynomial and Rational Functions
            -Exponential Functions
            -Logarithmic Functions

Chapter 4: Trigonometric Functions

            -Special Right Triangles and Trigonometric Ratios
            -Radians, Arc Length and the area of a Sector
            -Unit Circle Trigonometry
            -Trigonometric Expressions and Identities

Chapter 5: Graphing Trigonometric Functions

            -Trigonometric Functions of Real numbers
            -Graphs of the Sine and Cosine Functions
            -Graphs of the other Trigonometric Functions
            -Inverse Trigonometric Functions

Chapter 6: Trigonometric Formulas and Equations

            -Sum and Difference Formulas
            -The Double-Angle and Half-Angle Formulas
            -Solving Trigonometric Equations


Chapter 7:Trigonometric Applications

           -Solving Right Triangles
           -Area of a Triangle
           -The Law of Sines and The Law of Cosines


Chapter 8:Analytic Geometry