MATH 2312 - Precalculus - University of Houston
Skip to main content

MATH 2312 - Precalculus

***This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

*this course was previously MATH 1330*

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

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

Prerequisites: MATH 1314 or a satisfactory score on a placement examination.

Course DescriptionThis course concentrates on the various subjects that are important to the study of MATH 2413 Calculus I and MATH 2414 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 2414 may not receive credit for MATH 2312.

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

Textbook & Access Code: 
The textbook,online quizzes, and additional help materials will be made available by logging into CASA Campus Services (CCS) at . Students pay for access to CCS as part of their fee bill via CTAP. If one opts out of the CTAP, they can purchase an access code for this course at UH Bookstore. In this case, if the code is not entered by the deadline specified on CASA, students will lose access to CASA. No make ups will be given for assignments missed during the no-access period.

More information on the Cougar Textbook Access Program (CTAP) & Canvas/CCS:


Course Objectives for Precalculus:

Upon successful completion of this course, students will:

  • Demonstrate and apply knowledge of properties of functions.
  • Recognize and apply algebraic and transcendental functions and solve related equations.
  • Apply graphing techniques to algebraic and transcendental functions.
  • Compute the values of trigonometric functions for key angles in all quadrants of the unit circle measured in both degrees and radians.
  • Prove trigonometric identities.
  • Solve right and oblique triangles

[Additional course curriculum details: In-depth combined study of algebra, trigonometry, and other topics for calculus readiness.] 


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

  • Course Policy Quiz
  • Regular Exams
  • Final Exam
  • Online Quizzes
  • Homework
  • Poppers – in-class quizzes 



 Learning Objectives for Precalculus:


  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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
  • 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.
  • Find all solutions of a trigonometric equation.
    • Solve trigonometric equations quadratic in form.
    • Use identities to solve trigonometric equations.
  • 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.
  • 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
    • Circles
    • Ellipses
    • Parabolas
    • Hyperbolas 


Grading, Exams, Extra Credit, Homework, Quizzes, Poppers Information: Please consult your instructor's syllabus regarding any and all grading guidelines.


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

Justin Dart Jr. Center 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 Justin Dart Jr. Student Accessibility Center website at for more information.


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.