2022 Since Collegeboard announced in mid-May that it would open AP Precaclulus, the discussion on the Internet has exploded.
Among them, the Reddit discussion thread was almost overwhelmingly critical. What exactly is AP Precalculus? How is it different from regular Precalculus? What impact will it have on Asian students?

First, we need to understand the mathematics curriculum under the American academic system. Traditionally, in the fourth grade of high school, Geometry is taken in ninth grade, and Algebra 2 is taken in tenth grade. Those who miss science must take Precalculus in eleventh grade in order to connect to AP Calculus (AB or BC, depending on the school) in grade 12. If you are not into science or engineering, you may choose Precalculus in grade 11, but AP Statistics in grade 12. Excellent 12th grade students who want to major in business will also take Calculus AB in addition to statistics.

However, in recent years, the mathematics level of American students has begun to decline. Many students have not completed Algebra 2 until the 11th grade, which makes it too late to take AP Calculus. Usually after these students enter college, their mathematics level is not up to standard but they need to take calculus. Therefore, many universities have begun to offer so-called College Algebra prerequisite courses so that these students can have the foundation to take calculus. As far as the syllabus is concerned, the contents of College Algebra and Precalculus are pretty much the same: nothing more than the operations and applications of various functions.

We can get a glimpse of this from the course schedule suggested by CollegeBoard:

➤Suggestions from CollegeBoard – Three major directions
1.Algebra 2 -> (AP) Precalculus -> AP Calculus AB/BC/Statistics

This sequence is the traditional path for science and engineering students, the only difference is that now students can choose to take regular or AP Precalculus, the difference will be explained later in this article.

2. Algebra 2 -> AP Statistics -> AP Calculus AB/BC/Precalculus

The disadvantage of this sequence arrangement is that it will be very difficult for students to take Calculus because they do not have a foundation in Precalculus, but the advantage is that they can take AP Statistics, which may be attractive to business students.

3. Algebra 2 -> AP Calculus AB -> AP Calculus BC

This arrangement is not recommended. The gap between jumping from Algebra to Calculus AB is too big, and the difference from jumping from Calculus AB to BC is too small, because 60% of the course content is repeated.

So what is the positioning of AP Precalculus??

AP Precalculus can be regarded as a course that can be deducted from College Algebra. For students who want to study science and engineering, they have to take Precalculus anyway. Now that it has AP in the name, and you can get a multiplier on your GPA, why not? 

➤The devil is in the details
(Disclaimer: The Precalculus syllabus of each school is different. This article refers to the recommended AP Precalculus syllabus released by Collegeboard as a benchmark and does not represent the AP Precalculus course content of each school)

Opening the introduction of AP Precalculus on the official website, we can see that there are four major topics: functions, exponential logarithms, trigonometric functions, and matrices and vectors. The highlight is that matrices and vectors are not tested, only the first three units are tested. This leaves less preparation for students.

The following is a comparison of the syllabus of a traditional and solid Precalculus course and AP Precalculus:

PRACALCULUS	AP PRECALCULUS
A. Polynomial and Rational Functions	A. Polynomial and Rational Functions
B. Exponential and Logarithmic Functions	B. Exponential and Logarithmic Functions
C. Trigonometric and Polar Functions	C. Trigonometric and Polar Functions
D. Applications of Trigonometry
E. Sequences and Series
F. Conic Sections
G. Vectors, Matrices, Parametric Equations	G. Vectors, Matrices, Parametric Equations (not tested)
H.Probability
I. Limits*

You can see that the AP Precalculus syllabus has been deleted and only the skeleton is left. Although the official syllabus recommends four major units, only the first three units were actually tested. Let's take a look at the impact of missing these units:

D. Application of trigonometric functions: Traditionally, this unit is about finding the sides, angles, and area of any triangle, and finding the roots of complex numbers through De Mevere's formula.

Application: Engineering planning and design, measurement, etc. Euler's formula is a necessary knowledge for sophomore engineering mathematics.

E. Sequences and Series: One of the watershed points between AP Calculus AB and BC (BC is tested, AB is not tested). If you have not studied sequence and series, it may be difficult to get started when you encounter Taylor series in AP Calculus BC. After learning infinite series, the concepts of limits and definite integrals are easier to absorb.

F. Conic sections: used in the design of bridge steel cable mechanics, satellite orbits, etc.

G. Vectors, matrices, and parametric equations: In physics, mechanics can be completely calculated by vectors, and can also be represented and calculated by parametric equations. In addition, the computing principles of computer science are inseparable from matrices.

8. Probability: The foundation of discrete mathematics will be used in computer science disciplines.

9. Limits: Not every Precalculus course will cover limits. More rigorous courses will cover a part of it first.

As can be seen from the above, what the AP Precalculus course lacks are the foundations needed for advanced engineering science. Although students will learn these subjects later in college, it would be better if they were fully prepared in high school. For science and engineering-oriented students, there is no significant impact in the short term (referring to transcript scores, AP scores, SAT scores), but on the premise of long-term, complete, and good scientific literacy, the AP Precalculus curriculum is seriously insufficient.

➤Impact on Asian students:
The content of AP Precalculus should almost be taught in the school's regular curriculum. Students may find it difficult to apply questions, model questions, and rate of change questions, so courses are still needed to accurately prepare and become familiar with the question types. If you want to major in science and engineering, it is recommended to take the AP exam in May to get an extra five points on your AP score sheet.

If you want to study science, its very likely that you will have to learn all of the topics anyway. Since the test only tests a fraction of what you have to learn anyway, why not take the course/test and score an easy AP on your transcript and a handsome 5 on your AP scores?

➤AP Calculus AB/BC Differences
No matter what subjects you choose in grade 11, if you decide to take AP Calculus in grade 12, whether you choose AB or BC is also a matter of knowledge. In short, AB is the calculus taken in the first semester of college, and BC is the calculus taken in the first and second semesters of college. So going back to what I said before in the article, the reason why it is not recommended to take BC after completing AB is because the repetition is too high.

AP Calculus AB (12th grade) (calculus in the first semester of the first year of college)	AP Calculus BC (12th grade) (calculus in the second semester of first-year college)
1. Limits and Continuity
2. Differentiation and Applications
3. Integration and Applications
4. Differential Equations
	5. Parametric Equations, Polar coordinates, vector valued functions
	6. Sequences and Series

In terms of syllabus, AB is easier. AB dilutes one semester of college courses into one high school year, while BC students have a harder time, so the progress will really be compared to the pace of college. In addition to the vectors and parametric functions in unit 5, and the sequences and series in chapter 6 (these are not tested in AP Precalc), BC will learn more deeply and difficultly in the overlapping chapters 1, 2, 3 and 4. like: Partial integrals, arc length, surface area, cylindrical shell method, Robida's rule, etc., inverse trigonometric function substitution method.

In terms of AP exam score distribution, on average 40% of students in AP Calculus BC will get a five. On average, as long as the correct answer rate reaches 60%, you can get a test score of 5 points.

➤Summary
On average, students have to score easily on AP Calculus BC and have to be proficient in Precalculus functions, exponential logarithms, and trigonometric functions. Trigonometric functions, in particular, are a barrier for many students (also for IB students, especially IB AA HL, which teaches them in depth). Trigonometric functions usually span three chapters (basics, analysis, and applications), and the many formulas in them are not enough to be included. Just remembering it is very difficult, let alone using it easily. A good Precalculus teacher can remind students about the rules of these formulas to make the formulas logical. Memorizing one is equivalent to memorizing three, which makes it easier to master with twice the result.

At the same time, whether it is school progress exams or AP exams, students also need to integrate and review before the exam, and systematically identify weaknesses. The subject of AP Precalculus itself is not difficult, but how to learn it without reciting a lot (experience has proven that memorizing it by force usually only has short-term effects, and students cannot apply it to unseen question types) is a skill. The decisive point of AP Precalculus is how to integrate the concepts with the least amount of effort and be able to draw inferences from one example. At the same time, the difficulty is also that it requires a high degree of self-discipline and precise practice. After all, practicing more is not as good as practicing skillfully.

immediately with AEI Education course consultant contact, to learn more about your goals and the most suitable AP subjects and planning directions!