§1Why I built these as books, not just videos
By 2015 I had a YouTube channel with hundreds of AP Calculus videos. Students could find a video on almost any topic. What they couldn't do was follow a structured, sequential FRQ-prep experience in one place — work through a problem type, see the worked example, watch the explanation, and then try the next problem, all without jumping between tabs and playlists.
The Apple Distinguished Educator Summer Institute in 2015 gave me the push to do it differently. The "One Best Thing" project — the ADE deliverable for that cohort — became The Power of the Flipped Classroom, my first Apple Book. That experience showed me what a multi-touch book could do that a video playlist couldn't: it could hold a student through a complete problem-type arc, not just a single explanation.
The six AP Calculus FRQ Reviewer books came from the same instinct applied to the question types that come up most often on the AP Calc exam. Each book takes one FRQ topic and goes deep — worked problems, reader prompts, and embedded video all in one place. They are free on Apple Books. They have always been free. That's not a promotion; it's just what they are.
Dr. Esperanza is an Apple Distinguished Educator. These books were built using Apple's multi-touch authoring tools and are designed for the Apple Books app on iPad and Mac. They are not available as PDFs — the multi-touch and embedded video features require the Apple Books environment.
§2The six volumes
Each book covers one FRQ topic type in depth. The topics below are the ones that appear most frequently on the AP Calculus AB and BC exams in the free response section. You do not need to read them in order — each is self-contained. Pick the topic where you lose the most points on practice exams and start there.
Accumulation FRQs ask students to interpret and evaluate definite integrals as cumulative change. These problems appear on nearly every AP Calculus AB and BC exam. This book walks through the setup, the common traps, and the exact language the College Board rewards.
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Implicit differentiation FRQs test whether students can differentiate equations where y is not isolated — and then use that derivative to find tangent lines, normal lines, or critical points. This book covers the technique and the follow-through moves the exam rewards.
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Particle-in-motion FRQs connect position, velocity, and acceleration using derivatives and integrals. They are among the most frequently tested AP Calculus scenarios. This book builds the position-velocity-acceleration chain and applies it to every question form the exam uses.
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Area between curves and volumes of revolution are classic AP Calculus FRQ topics. Setting up the integral correctly is where most students lose points — this book focuses on that setup process, with worked problems using both disk/washer and shell methods.
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Differential equation FRQs test slope fields, separation of variables, and solution verification. These problems require both conceptual understanding and procedural precision. This book covers all three question forms — sketch, solve, and interpret — that the AP exam uses.
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Function analysis FRQs ask students to read a function — or its derivative — and make conclusions about increasing/decreasing behavior, concavity, relative extrema, and inflection points. This book treats the analytical reasoning the exam is testing, not just the procedural steps.
Get on Apple Books →Open the Apple Books app on your iPad or Mac. Tap any "Get on Apple Books" link above — it will open directly in the app. Each book downloads in seconds. All six are free and do not require an Apple account to browse, but you will need to sign in to download.
§3How to use these books in your AP Calculus prep
The books are not a replacement for your AP Calculus course. They are an FRQ-specific supplement — the part of exam prep that practice tests alone don't cover well, because practice tests give you the whole exam and these books give you one problem type at a time, worked all the way through, until the pattern is recognizable.
The approach I'd recommend
Take one AP Calculus practice exam — official College Board materials if you have them. Look at your FRQ scores. Find the topic where you lost the most points. Open that volume. Work through the book once, doing the reader exercises before looking at the answers. Then take another practice FRQ on the same topic — a different problem, same type — and see if the pattern holds.
Repeat for the next-weakest topic. Most students need three to four focused sessions with two or three of the books, not all six cover-to-cover. The books are short enough that one session is enough to get through a full volume if you're working steadily.
For AP Calculus teachers
If you're teaching AP Calculus AB or BC, the six books map cleanly to the FRQ clusters that appear most often. You can assign a specific volume as a supplement to a unit — Differential Equations with your Unit 7 or 8 sequence, Particle in Motion with your related rates and applications unit, Accumulation Problems with your Unit 5 or 6 integral applications work.
The embedded video in each book is from the Numberbender YouTube channel. Students can rewatch it outside the book via the NumberbenderEN channel (English-exclusive, global audience) or the main Numberbender channel.
The AP Calculus FRQ scoring guidelines reward complete, justified answers — not just a correct final answer. Each book covers the justification language the College Board rewards: "because f'(x) changes from negative to positive," "by the Fundamental Theorem of Calculus," "the particle changes direction when v(t) = 0 and v changes sign." This is the language the readers look for. The books make it explicit.
§4The first Numberbender book: The Power of the Flipped Classroom
Before the six FRQ Reviewer volumes, there was The Power of the Flipped Classroom — the Apple Book I wrote for the 2015 ADE Summer Institute. It's a different kind of book: it's for teachers, not students. It explains the flipped classroom model, how I built it at Barstow High School starting in 2012, and what the model looks like in practice for a math class.
If you're a teacher who found these FRQ books and you're curious about the pedagogical approach behind the Numberbender videos — why they're short, why they're structured the way they are — the flipped classroom book is where that comes from. It's also free, also on Apple Books.
The canonical link is education.apple.com/resource/250011019. Apple Books link: The Power of the Flipped Classroom on Apple Books. More on the flipped classroom model is at the main flipped classroom guide and the books spoke.
§5FAQ
Are the AP Calculus FRQ reviewer books really free?
Yes — all six volumes are free on Apple Books. They have always been free. You do not pay anything to download them. You need the Apple Books app on iPad or Mac and an Apple ID to download, but there is no charge.
Do I need an iPad to use these books?
The books are optimized for iPad, where the multi-touch features and embedded video work best. They are also readable on Mac via the Apple Books app. They are not available on Android or Windows — the Apple Books environment is required for the multi-touch and video features to work.
Which AP Calculus exam do these books cover — AB or BC?
The six FRQ topic types — Accumulation Problems, Implicit Differentiation, Particle in Motion, Areas and Volumes, Differential Equations, and Function Analysis — appear on both the AP Calculus AB and BC exams. Most of what's covered is AB material that also appears in BC. If you're taking BC and working on topics like series or parametric equations, the FRQ Reviewer series doesn't cover those — those are BC-specific topics not in the current six volumes.
Can I use these books in my AP Calculus class?
Yes — that is exactly what they are designed for. They are free, openly available, and each volume maps to a standard AP Calculus unit. If you're assigning FRQ practice, these books give students the worked examples and embedded video explanations that a practice test doesn't. Point your class at the Apple Books links for whichever topic you're covering.
What order should I read the books in?
There's no required order — each book is self-contained. A practical approach: take a practice FRQ section, find the topic where you lost the most points, and start with that volume. If you're doing general exam prep without a specific weak spot, a reasonable sequence is Function Analysis → Implicit Differentiation → Particle in Motion → Accumulation Problems → Areas and Volumes → Differential Equations.