Nowadays, more students have access to a college-level education than ever before. On the one hand, this is an incredibly beneficial thing. Many young people can get a worthwhile education no matter their socioeconomic conditions.
On the other hand, more students going to college also means more competition, especially if there is a school or university program you’re eager to enter. So, how can you single yourself out from the competition?
There are many ways, but the one we will focus on today is AP classes, specifically AP Precalculus.
“AP’ stands for Advanced Placement, and AP Precalculus is a high-school-level course designed to teach students how to use mathematical functions and concepts to solve real-world problems. It will also prepare them for calculus-level courses once they enter college.
If you are interested in STEM classes, it is almost guaranteed that you will need a background in calculus/precalculus since those are considered launchpads for STEM careers in science, technology, engineering, and mathematics. We’ll have more for you on this later. But first, let’s dive into AP courses and how they can benefit you.
A Breakdown of AP Courses and Exams
Advanced Placement classes allow students to get a taste of college-level courses, and if they do well on the standardized exam, they can also obtain college credits while still in high school. Furthermore, students learn to think more critically, see a problem from different points of view, and create well-grounded arguments.
Taking and passing AP courses and exams shows college admission officers that you sought out the most challenging curriculum your school had to offer and succeeded. Research shows that scoring a 3 or higher on any of the 39 AP subjects is an excellent predictor for completing college compared to non-AP students.
Taking AP classes would benefit you because most US colleges and universities will grant advanced placement, credits, or both to students who successfully pass their AP exams.
These exams are developed by AP teachers and college faculty members who are experts in their fields. All AP exams themselves consist of two main parts: multiple-choice and free-response. A computer grades the multiple-choice section while the teachers and faculty members score the free-response answers.
The scores from these two sections are then weighed, combined, and converted into an AP exam score on a 1-5 scale, which is as follows:
5: Extremely well-qualified A
4: Well-qualified A-, B+, B
3: Qualified B-, C+, C
2: Possibly qualified n/a
1: No recommendation n/a
Now that we’ve covered what AP courses and exams are all about let’s focus more on the AP Precalculus course.
What is AP Precalculus?
Calculus (and also precalculus) is about the study of functions. A function in mathematics is a rule that defines a relationship between two variables: the dependent variable and the independent variable.
To validate certain functions, students will be given different representations, conditions, data sets, and scenarios to understand the behavior and nature of different function types. Students will also learn about symbols and how they can be manipulated. A mathematical object can have different representations based on its function type and the symbols used.
This all probably sounds confusing (because it is), but please keep in mind that calculus is all about communicating with very precise language and using reason and rationale to reach certain conclusions. It is used every day by professionals to solve real-world problems. It is necessary for careers in physics, economics, statistics, engineering, and even finance. So if any of these fields are of interest to you, you might want to consider taking this course.
Why was AP Precalculus created?
The story of AP Precalculus is an interesting one. According to collegeboard.org, this is a brand new AP exam that will be administered for the first time in May 2024.
Why was it necessary? Well, a study was conducted that found that thousands of students had been graduating from high school but were ill-prepared for college-level mathematics courses. One-third of incoming freshmen at four-year public universities ended up having to take remedial math courses, and 40% of those students failed to even complete the remedial courses!
As stated before, a foundational understanding of calculus is a prerequisite for gaining a career in many STEM fields, such as in mathematics, data science, physics, biology, and health science.
The chasm between high school and college-level mathematics has become too large for most students to bridge. That’s why, if you’re interested in a STEM career, most universities are looking for students who have taken calculus and precalculus courses before they begin their college careers.
What grade is it typically taken in?
AP Precalculus is for students in their junior year of high school who have already completed Geometry, Algebra 2, Integrated Math 3, or any similar advanced algebra course. This will ensure that they have learned the content necessary for this course. You can also take it in your senior year, but if you’re serious about a career in STEM, you should be aiming to take an AP Calculus class your senior year. (More on that next week!)
It bears repeating that if you want a career in any of the fields listed above, it should be your prerogative to make yourself prepared for college-level math courses.
What is covered in an AP Precalculus class?
We will now go over what is covered in the class itself. A typical AP Precalculus class consists of four units:
Unit 1: Polynomial and Rational Functions
In this unit, students expand their understanding of rational and polynomial functions through modeling and rates of change. Topics discussed include the behavior of these functions and how they change with respect to each other. You will also identify the assumptions and limitations of these function models. Unit 1 will take up 30-40% of the multiple-choice section.
Unit 2: Exponential and Logarithmic Functions
Next, you will learn more about inverses and explore the relationship between logarithmic and exponential functions. This unit covers how to compose these functions and find inverses. Students will model scenarios with logarithmic functions and validate them using a residual plot. Finally, you will model data sets with exponential functions and learn how to relate them to geometric sequences. Unit 2 represents 27-40% of the multiple-choice section.
Unit 3: Trigonometric and Polar Functions
In this third unit, you will explore and then model periodic phenomena using trigonometric functions. This includes learning right triangle trigonometry as well as the sine, cosine, and tangent functions. You will graph functions using polar coordinates and describe how radii and angles change with respect to each other. Lastly, students will utilize inverse trigonometric functions to solve trigonometric equations. This unit takes up 30-35% of the multiple-choice section score.
Unit 4: Functions Involving Parameters, Vectors, and Matrices
In this final unit, which is not covered on the exam, students will use vectors to describe the motion of an object and then interpret the impact of a transformation matrix on said object. You will then learn how quantities change with respect to each other in a parametric function.
The AP Precalculus Exam
As of the writing of this article, the AP Precalculus exam has yet to be administered. The first exam will occur in May of 2024. Therefore there is not any data yet on the percentage of students who pass or fail the test.
However, we can break down how each section of the test is scored. We will also give details about whether a calculator will be allowed or not.
Based on the AP Precalculus Course and Exam Description, the exam itself is 3 hours long. There are 40 multiple-choice questions and 4 free-response questions, with each one being weighed equally.
Section 1: Multiple choice
- Part A: No calculator permitted, 28 questions, 80 minutes, 43.75% of total score
- Part B: Graphing calculator required, 12 questions, 40 minutes, 18.75% of total score
Section 2: Free-response
- Part A: Graphing calculator required, 2 questions, 30 minutes, 18.75% of total score
- Part B: No calculator is permitted, 2 questions, 30 minutes, 18.75% of total score
Practice 1: Procedural and Symbolic Fluency
- Solve equations and inequalities, 14-17%
- Express equivalent forms, 9-13%
- Construct new functions, 15-19%
Practice 2: Multiple Representations
- Identify information from representations, 14-17%
- Construct equivalent representations, 6-9%
Practice 3: Communication and Reasoning
- Describe characteristics, 10-14%
- Apply results, 9-13%
- Support conclusions, 13%
How should I study for the test?
Besides maybe the SAT or ACT, an AP test might be the most difficult exam you ever take in your high school career. It should not be approached as a regular test; you need to be prepared with a plan. That’s what the following guide is for.
- Shift into study mode. A good time to start preparing for the exam is about 1 to 3 months ahead of it. Many students will relax during spring break and then start getting focused soon after. This will give you enough time to take some practice tests, review old content, and get used to the types of questions you’ll have.
It might also be a good idea to come up with a schedule. Ask yourself these questions:
- How many days and weeks do I have left to study?<
- How many days a week will I devote to studying?
- What time of the day is best for me to really retain the information?
- Focus on previously covered material and your weakest areas. One of the biggest problems with many public high school classes is students tend to forget the material that was covered and tested at the beginning of the class. However, the AP exam will cover everything that you’ve learned up until the day of the test.
That’s why it’s imperative you take out old homework, quizzes, and tests,
then review them all. Keep in mind that if there is a question type you feel you already have a good handle on, put it on the back burner for now and focus on the parts that you still struggle with. These parts should be taking up most of your study time.
- Know the test inside and out. This one is mostly your responsibility. You might think that it falls on the teacher to get you ready for your specific AP exam, but that’s not quite correct. It’s their job to cover the material that will be on the test. It’s up to YOU to study and prepare for it.
But here’s the good news. Now that you know this, you can create a study regimen that works for you personally, which is something your teacher could not give you. So grab some old AP exams and practice with them. Time yourself. Use the tables above this section to see exactly what will be on the test and how much time you’ll have.
Last, but not least, grab some AP study materials. There are so many out there that they’re impossible to count, but many students swear by the guides made by Barron’s and the Princeton Review. Of course, there are no guides yet for AP Precalculus since it hasn’t been administered yet, but be sure to come back to this article when you’re ready to take it.
If you’re seriously considering a position in a STEM field in the future, consider taking part in AP Precalculus. Remember, a large percentage of high school students are not ready for college-level math. Don’t become part of that statistic. Enrolling in this class to help you get a leg up on your college classes (and save your parents a bit of money on college credits while you’re at it).
If you’re worried that AP Precalculus will be too hard for you, keep in mind that this cirriculum was designed to standardize the teaching of precalculus. If your school already had solid math teachers and a prior precalculus course that prepared students for AP Calculus, chances are they your school hasn’t had to change the material at all. You’ll be taking the same precalculus course that they taught the year before; you’ll just get the benefit of receiving college credit for it!