AP Pre-Calc: Most Important Topics You Need to Know

Trying to cram for the AP Pre-Calc exam? Don’t know what to study? In this article, I will break down the most important topics for the AP Pre-calc exam to score a 5!

AP Pre-Calc is a very new AP test that Collegeboard just released in 2024. This will be the second year it’s running.

In terms of numbers, over 150 thousand students took the AP Pre-Calc exam in 2024. That may seem a lot, but compared to its sequel, Calculus AB, which has over 1 million test takers every year, it pales in comparison.

This is mostly due to Precalculus not being a college-level course, meaning that most universities will NOT accept it for credit, even if you score a 4 or 5.

So, most students will just use it as a GPA booster, or an indicator of academic rigor, though other AP exams will do the same for you.

AP Pre-Calc Exam Overview

In the picture below, we can see the official weighting for the AP Pre-Calc MCQ portion of the exam. Read more on the AP Precalculus curriculum here.

I will say, the AP exam weighting makes AP-Precalc look like an absolute joke. Seriously.

I mean, almost 70% of the exam is testing you on FUNCTIONS. Yes, functions. Pretty much every single function you’ve learned in Algebra: linear, quadratic, exponential, polynomial, etc, is on this exam. That is what the majority of the test is on. 

So yes, it’s Algebra 1 and 2, but made into an AP exam. If you think that sounds easy, that’s because it is. If you came into PreCalc with a strong algebra foundation, you’re bound to get a 5 already. 

For AP Pre-calc, you only need around a 65-70% to get a 5. Consequently, if you solidify your function knowledge, you’re good to go.

Polynomial and Rational Functions

This is stuff you learn from Algebra 2. I will give a quick overview of what to expect in each subtopic.

End Behavior and Degree of Polynomials

The end behavior of a graph is knowing what happens at the graph’s bounds. This is normally denoted with the symbol.

Essentially, a question will give you a graph and ask you to analyze it. The answer choices will read: “as the graph approaches -, f(x) is + / -”

The degree of a polynomial is the exponent value of the leading coefficient term. For example, if the term was 4x^4, then your degree would be 4.

Finding Zeros of Polynomials

These questions will come in all shapes and forms. Some will give you a graph or provide a function. You will have to factor, so make sure you touch up on that.

Additionally, some may require the use of the Rational Root Theorem, Factor Theorem, or Remainder Theorem. Know these well in case they pop up in the MCQ!

Long Division and Synthetic Division

You need to know BOTH these division tactics for the AP Pre-Calc exam. The latter is actually used in the rational root theorem, so it’s definitely a lot more applicable than regular long division.

Long division is a lot more tedious than synthetic division. However, synthetic division can only be used when dividing by a binomial. Long division can be used in almost any case, as long as the divisor has fewer terms than the dividend.

Graphs of Polynomials

Yet another extremely important part of the AP Pre-Calc exam, you need to be able to analyze graphs. Know how to interpret intercepts, multiplicity, as well as turning points. Also know the definition of concavity as well as increasing/decreasing intervals.

Function notation is also a big portion of this exam, so make sure you’re familiar with that, and are able to differentiate between brackets and parentheses.

Discontinuities

You’ll learn more about continuity in calculus, but the AP Pre-Calc exam is a nice introduction to the topic. You are introduced to two major discontinuities: holes and asymptotes.

A hole is created when you have a cancellation between the numerator and denominator, denoted by a hollow circle. 

An asymptote is created when the function is undefined at a specific point.

Solving Rational Equations

This section is mainly on finding common denominators. Think of adding fractions in elementary school, but more complex. The concepts remain the same, however.

This also reviews a core concept known as cross-multiplying, which will be used to solve for the unknown value.

Exponential and Logarithmic Functions

Once again, this is review from Algebra 2.

Exponent and Log Rules

There are a few rules to memorize when it comes to solving these problems effectively. Some you may have learned already, while some may be new. The only way to memorize these is through consistent practice.

Solve Exponential and Log Equations

Once you know your rules, get ready to apply them. This will also combine natural logarithms too, so make sure you know those.

One very important topic they stress is the use of the change of base rule. You will need to convert all the bases to base 10 to plug them into your calculator.

Exponential Growth and Decay

While not a difficult topic on its own, students often struggle with its applications. The AP-Precalc exam is no exception, as almost all forms of this concept are present in a word problem.

Know the real-world applications, and try not to get stumped with the wording. The concept and equation remain the same, no matter how bizarre the question is.

Inverse Relationships

Not just for logs but for all functions, they will test your knowledge of this concept. Sometimes, they might have you algebraically evaluate an inverse function, or give you a graph and ask you to analyze it.

It’s important to understand the relationship exponential and log functions have with each other as that is a new relationship you learn in Algebra 2. Make sure to review this, too.

Transformations

As with all types of functions, it’s essential that you know their transformations. Logarithmic functions have a special type of graph, thus, have very unique transformations.

This is especially true for the natural log function, its applications extending far beyond the scope of the AP Pre-calc course.

Trigonometric and Polar Functions

The only new topic that is introduced in AP Pre-Calc, it covers basic trigonometric identities, functions, and applications. While it does go over polar functions, the main focus remains on trigonometry.

Unit Circle and Radians

The foundations for all of trigonometry, memorizing the unit circle is vital to succeeding on the AP test. Additionally, familiarize yourself with radians and prepare to use them often.

On the exam, I would recommend drawing out a unit circle to visualize the coordinates.

Trig Identities

Once again, this is pure memorization. Make sure you are familiar with each type of identity, including the cofunction identities. 

Draw the unit circle to visualize these identities if you need to.

Trig Graphs

This might be difficult to grasp at first, but consistent practice can solve that issue. Know all the key parts of trig graphs like the amplitude, phase shift, etc. 

You will need to know sine, cosine, and tangent graphs, as well as the reciprocal identity graphs of those functions.

Inverse Trig Functions

On the topic of reciprocal identities, it is important that you know how to apply these. Trig solutions can take on multiple different forms, so its imperative that you can recognize them.

The key ones are secant, cosecant, and cotangent. These will be used often when simplifying trig expressions as well too.

Solving Trig Equations

When solving these make sure you convert all the variables into one type of trig function. Additionally, pay attention to what the question asks for. Does it want ALL the solutions, or just within one period (i.e 2)

This also ties back to knowing your identities very well, because most will require algebraic manipulation. If you don’t know the identities, then you won’t be able to isolate the variable.

Polar Coordinates and Graphs

The AP Pre-Calc exam will focus on foundational knowledge. This comes down to understanding what a polar coordinate is, its application, as well as how to visualize them. 

Knowing the various types of polar graphs such as cardiods, limacons, leminscates, etc., will be essential to scoring high. 

Have a strong grasp of the (r,) form as that will be tested often.

Converting Between Polar and Rectangular Coordinates

Yet another great reason to know your trig identities. Because polar coordinates involve radian angles, this is one of trigonometry’s many applications.

This means, more algebraic manipulation, but instead of solving for a variable, you need to convert it between cartesian and polar coordinates.

This means going from a cardioid function to a circle function, or vice versa.

Once again, make sure you have a strong grasp of each type of polar function as well as the (r,) form.

Final Thoughts: Master these AP Pre-Calc Topics!

The AP Pre-Calc exam may seem intimidating at first, but once you break it down, it’s all about mastering the fundamentals.

If you focus on polynomial/rational functions, exponential/logarithmic equations, and trigonometry/polar graphs, you’re already 90% of the way there.

Don’t get caught up in minor topics—follow the weighting, target your weak spots, and prioritize practice. With a solid Algebra 2 foundation and consistent review of graphs, identities, and transformations, scoring a 5 is 100% achievable.

✅ Want more study hacks, guides, and walkthroughs?
Be sure to bookmark this blog, and check out my full breakdowns for each topic — complete with visuals and practice questions coming soon!

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