Welcome to AP PreCalculus.  What does the course title mean? AP stands for Advanced Placement, which means that this is college level course. This course represents one semester of college credit for Pre Calculus, that can be earned if you score well enough, 3 or more, on the AP exam.

AP Exam Date: May 12th, 2026

Exam Decision Deadline: November 6, 2025

To avoid potential late fees, students must enroll online and 

confirm they are taking exams before the decision deadline.

This year-long course is designed to develop a strong understanding of functions and their properties, including polynomial, rational, exponential, logarithmic, and trigonometric functions. It focuses on modeling dynamic phenomena, enhancing problem-solving skills, and preparing students for calculus and other advanced mathematics courses. The course also emphasizes procedural and symbolic fluency, multiple representations, and effective communication and reasoning skills.  Therefore, it is very important that you do not get behind. Homeworks, on-line assignments, class assignments, quizzes and tests, will be designed to continually reinforce and challenge your ability to explain and apply the learned  concepts. 

Students should be able to:

• Develop Functional Understanding: Deepen the understanding of various function types (linear, polynomial, rational, exponential, logarithmic, and trigonometric) and their characteristics. 

• Master Modeling and Covariation: Analyze how quantities change together and apply this understanding to model real-world scenarios. 

• Enhance Representational Fluency: Translate mathematical information between graphical, numerical, analytical, and verbal representations. 

• Strengthen Problem-Solving: Improve the ability to solve problems involving equations, inequalities, and systems of equations. 

• Prepare for AP Calculus: Build a solid foundation for calculus by exploring concepts and skills related to functions, trigonometry, and conic sections. 

• Promote Procedural and Symbolic Fluency: Gain proficiency in manipulating functions, equations, and expressions. 

• Foster Communication and Reasoning: Develop the ability to clearly explain mathematical concepts and justify solutions. 

• Unit 1.  Rate of Change

In this unit, students will apply their knowledge of slope for both linear and quadratic functions. They will explore the average rate of change for both functions over any given interval. This unit will prepare students for AP Calculus AB/BC topics such as concavity of a function at an interval where rates of change can either be increasing or decreasing.

• Unit 2.  Polynomial Functions

In this unit, students will be able to describe the behavior of the polynomial function’s graph. Students will identify parts such as local and absolute extrema (maximum/minimum value), points of inflection, and concavity. Simplifying a rational function by using long division on two polynomial functions or by factoring the polynomial functions provide information about its asymptotes, zeros, and holes. This unit provides a foundation to 6 topics in AP Calculus AB/BC.

• Unit 3. Rational Functions

In this unit, students will explore different end behaviors of rational functions based on the quotient of the leading terms of the polynomial in the numerator with the polynomial in the denominator. Students will also be able to check for vertical asymptotes and holes within the graph of a rational function which will help students for limits and continuity topics in AP Calculus AB/BC.

• Unit 4. Function Models and Sequences.

In this unit, students will identify and construct a function model that will be useful and appropriate for modeling scenarios. This function model may come from linear, quadratic, polynomial, piecewise functions, or it could be a transformed function or a regression model. This model will be used to draw conclusions or predict values to answer questions related to the scenario.

• Unit 5. Exponential Functions.

In this unit, students will explore the different properties of exponential functions to rewrite equivalent expressions. Students will also transform exponential functions to model contextual scenarios or data sets. Understanding exponential models will be beneficial in answering free response questions in AP Calculus AB/BC that involve exponential models with differential equations. 

• Unit 6. Composition and Inverse

In this unit, students will rewrite and evaluate the composition of two functions. Students will also determine the inverse of a function by switching the x and y variables and solving for y. The composition of a function and its inverse will yield its identity function. This unit will prepare students on differentiating inverse functions in AP Calculus AB/BC.

• Unit 7. Logarithmic Functions

In this unit, students will learn that the inverse of an exponential function is the logarithmic function. Students will apply the properties of logarithmic and exponential functions to rewrite and solve equivalent expressions. Learning the properties of logarithmic and exponential functions will help students in finding the derivative of a more complex logarithmic and exponential form in AP Calculus AB/BC.

• Unit 8, Sine and Cosine Functions

In this unit, students will focus on the two basic trigonometric functions, sine and cosine.  Students will transform a sinusoidal function and determine how the transformation affects the graph’s amplitude, period, vertical and horizontal shift.  

• Unit 9. Other Trigonometric Functions

In this unit, students will explore the other trigonometric functions and its reciprocal functions. Students will be able to establish a relationship between the ratio of the change in y and the change in x as a slope between two points, and the ratio of the sine and cosine function as the tangent function.

• Unit 10. Inverse, Identities and Equations

In this unit, students will rewrite trigonometric expressions in equivalent forms using Pythagorean, sine, and cosine identities. Proficiency in solving right triangle trigonometry, simplifying, manipulating, or rearranging trigonometric functions using identities, provide the skill they need on finding the derivatives of the trigonometric functions and its inverse in AP Calculus AB/BC.

• Unit 11. Polar  Functions

In this unit, students will learn how to plot points on a polar grid, as well as converting polar coordinates to rectangular coordinate systems, and vice-versa. Students will use the average rate of change of the radius with respect to the angle given to describe the graph of a polar function. This topic helps students for the AP Calculus (BC only) unit on polar coordinates. 

It is expected that each student take responsibility for his/her own learning. It is expected honesty from each student. Integrity, once lost, cannot be easily regained. The work you submit for credit must be your own work. Students who copy someone else’s work or allow someone else to copy their own work will be given zero credit for that assignment. Group learning and collaboration is encouraged; however, each student is expected to make a genuine personal contribution.

TI-Nspire CX Graphing calculators will be used in this course. You will have assigned a calculator and a textbook (Larson – Hostetler - Edwards: Calculus of a Single Variable 8th Ed) assigned for your personal use. Textbook is also available in electronic format. It is extremely important that you be responsible of the items assigned to you. If one of these items is lost or damaged, the Assistant Principal will determine the responsibility of the student to whom this calculator/textbook was assigned, and the corresponding replacement cost.

All assignments are expected to be completed on time. These are an important part of your grade. Consistent progress in your assignments is imperative to your success in this class. AP Tests are difficult and practicing problems is essential. Following along in class is not the same as doing it yourself. Working with other students is very helpful, but copying will not be accepted.

If by a justified reason you miss a Test, teacher must be notified as soon as possible to program a new extra class test, to get the corresponding grade.

Homeworks are extremely important. Remember, this is a college level class, and at this level, one hour in class demands two or three hours of extra out-of-classroom work (studying and practicing). Your assigned homework is your key to succeed in tests and quizzes. For justified late class work or homework, ask to teacher for a new due date. 

On-line Lectures at AP Classroom will be assigned regularly, and students must have to take them in the assigned days in order to do not struggle with the related classwork and practice. These are important assignments that students have to get used to accomplish; in College, students will be required to do on-line assignments regularly. 

Semester Exams are mandatory, and are an opportunity to improve your final grade. These exams have to include all the subjects covered during the semester, but it could have more emphasis on the last chapters, if these are considered very important. Semester Exams are Mock portions of the AP PreCalculus A request for a make-up Semester exam should be done to teacher and will be programmed extra class. 

The AP Precalculus Exam has two sections. The first section contains 40 multiple-choice questions. The second section contains four free-response questions.  

Section I: Multiple Choice.   40 Questions   |   2 Hours   |   62.5% of Exam Score

• Part A: 28 questions; 80 minutes; 43.75% of exam score (calculator not permitted)

• Part B: 12 questions; 40 minutes; 18.75% of exam score (graphing calculator required)

Section II: Free Response.  4 Questions   |   1 Hour   |   37.5% of Exam Score

• Part A: 2 questions; 30 minutes; 18.75% of exam score (graphing calculator required)

Free-Response Question 1: Function Concepts

Free-Response Question 2: Modeling a Non-Periodic Context

•  Part B: 2 questions; 30 minutes; 18.75% of exam score (calculator not permitted)

Free-Response Question 3: Modeling a Periodic Context

Free-Response Question 4: Symbolic Manipulations 

Tutorials initially will be available Wednesdays from 2:55 to 3:45. Any modification to this schedule will be announced during class. Tutorials in a different day or hour will be available by previous appointment. 

On-line tutorials and on-line lectures are always available for students at AP Classroom.

Remember that this is a College Level class, and in College there is not make-up work or exam corrections, everything has to be accomplished at the given deadlines. In this class, make-up work has to be authorized by the Assistant Principal coordinating the AP classes. In case of authorized make-up work, students will have five (5) school days to complete it and turn it in. works.