Online AP Calculus Help | K-12 Math Curriculum

AP Calculus Is Where Every Gap From the Past Four Years Shows Up

A student who reaches AP Calculus with solid algebra, trigonometry and pre-calculus foundations will find the course demanding but followable. A student who arrives with gaps in any of those areas will find calculus difficult in a way that's hard to explain, because the gaps are often invisible until calculus exposes them.

Limits require a strong understanding of functions. Differentiation requires fluency in algebraic manipulation. Integration requires both. The further into calculus a student gets, the more those earlier foundations are tested.

This is why AP Calculus is one of the subjects where working through a structured, comprehensive curriculum makes the most difference. Understanding each concept properly before moving to the next one is not just good practice at this level. It's the only approach that works.

AP Calculus Is Part of Our Full K-12 Math Curriculum

AP Calculus is covered within our full K-12 math curriculum as part of the personalized plan built around each student.

When your child joins, the Math Doctor assessment maps their math understanding across the full curriculum. If the gaps are in calculus content specifically, the weekly plan targets those. If the difficulty traces back to pre-calculus, algebra or trigonometry foundations, the plan addresses those first. A student who has worked through the full curriculum from pre-calculus onwards arrives at AP Calculus content with the foundations already in place.

One important thing to be clear about: we're a curriculum service, not a test prep service. Our AP Calculus curriculum covers the full course content in depth. A student who genuinely understands that content is well placed for any assessment that tests it, including the AP exam, but building deep understanding is the goal, not exam strategy.

What We Cover in AP Calculus

Our AP Calculus curriculum is fully aligned to Common Core Standards and covers every major topic in the course, from the foundational concept of a limit through to advanced applications of integration.

Functions and Limits

Where AP Calculus begins, and where a strong pre-calculus foundation pays off.

Limits and continuity
Vertical asymptotes and points of discontinuity
End behavior and horizontal asymptotes
Oblique and other asymptotes
Slope of a line and rate of change
Rate of change of non-linear functions
Relating gradient function to original function
Average and instantaneous rate of change

Differential Calculus

The core of AP Calculus AB and a large portion of BC.

Derivative from first principles
Differentiating polynomials
Negative values of n
Differentiating roots of x
The product rule
The quotient rule
The chain rule
Differentiation of exponential functions
Differentiation of logarithmic functions
Derivative of sin x and cos x
Derivative of tan x
Derivatives of inverse trigonometric functions

Applications of Differentiation

Where the calculus connects to real situations and graph analysis.

Decreasing and increasing functions
Stationary points
Maxima and minima
The second derivative and second derivative applied to extrema
Concavity
Curve sketching
Tangents and normals
Slope fields
Maxima and minima in everyday life
Related rates of change
Instantaneous velocity
Velocity and acceleration

Integral Calculus

The second major branch of AP Calculus, building directly on differentiation.

Antidifferentiation
Definite integrals
Integration by recognition
Integration of exponential functions
Integration of sin x and cos x
Integration by inverse trigonometric functions
Integration by substitution
Numerical integration using trapezoids
Numerical integration using midpoints

Applications of Integration

Where integration connects to motion, area and volume.

Position and velocity
Velocity-time graphs
Acceleration
Area under a curve and between curves
Area when curves cross the x-axis
Volumes of solids of revolution

How Our Tutoring Works

Step 1: Math Doctor Assessment

Every student starts with the Math Doctor assessment. At AP Calculus level this is particularly important because gaps in pre-calculus, trigonometry or algebra often only become apparent once calculus begins. The assessment identifies exactly where the foundations are solid and where they are not, so the plan starts in the right place.

Step 2: A Weekly Lesson Plan Built Around Your Child

Every Monday the plan is updated with lessons targeting the areas that need work. Your child works through each lesson at their own pace, with step-by-step solutions built in for every question.

Step 3: Self-Paced Learning

Calculus concepts build on each other tightly. Moving on before a concept is properly understood creates compounding difficulty. Working at their own pace means your child can spend as long as needed on limits before moving to derivatives, and as long as needed on derivatives before moving to integration. Concepts can be revisited as many times as necessary.

Step 4: Tutor Support When They Need It

Calculus is a subject where written solutions often follow the steps but the underlying reasoning is still unclear. When that happens, talking through it with a real person is the fastest way to resolve it. Your child can call our tutor line, up to 10 hours per week. A tutor works through the specific concept using screen sharing and an interactive whiteboard. No extra charge.

Why Curriculum Foundations Matter for AP Calculus

Most students who struggle in AP Calculus are not struggling because calculus itself is beyond them. They're struggling because something earlier was not fully understood, and calculus has exposed it.

Students who work through our full high school math curriculum, moving from Algebra through Geometry, Algebra 2 and Pre-Calculus into AP Calculus, arrive at each new topic with the prior knowledge that topic requires. That continuity is what makes the difference between following along in a calculus class and genuinely understanding what is happening.

A student who understands AP Calculus properly is also building skills that carry well beyond high school. Calculus underpins university study in mathematics, physics, engineering, economics, computer science and many other fields. The students who find those subjects manageable at university are almost always the ones who built genuine understanding in high school rather than memorized procedures.

A Note on the AP Calculus Exam

AP Calculus is one of the few high school math topics with a specific external exam attached to it. A score of 3 or above on the AP exam can earn college credit at many universities, which makes it a genuinely high-stakes assessment for many families.

We want to be straightforward about what we offer. We cover the AP Calculus course content in full, and a student who works through that content thoroughly will have the understanding the exam tests. What we don't offer is exam strategy, practice papers or score prediction. If your child needs that kind of support alongside curriculum work, that's something to discuss with their school or a dedicated test prep provider.

A student who genuinely understands the calculus curriculum is in the strongest position possible for any assessment that tests it.

Pricing

Math tutoring starts from $24 per week, covering the full K-12 curriculum, the Math Doctor assessment, a personalized weekly lesson plan, access to the tutor helpline and weekly progress reports. New students get their first two weeks free.

$24 / week

Full K-12 math curriculum (AP Calculus included)
Math Doctor diagnostic
Personalized weekly lesson plan
Tutor helpline up to 10 hrs/week
Weekly progress reports

Start Your 2 Weeks Free

Frequently Asked Questions

What AP Calculus content does the curriculum cover?

Our AP Calculus curriculum covers limits and continuity, differential calculus including all major differentiation rules, applications of differentiation, integral calculus including substitution and numerical methods, and applications of integration including area and volume.

My child is taking AP Calculus at school and struggling. Can the curriculum help alongside their class?

Yes. Many students use it to reinforce and fill gaps in what is being taught in their AP Calculus class. Your child can work through the specific topics causing difficulty, revisit worked solutions as many times as needed and call the tutor line when something still isn't clear.

Do you help with the AP Calculus exam?

We cover the AP Calculus course content in full, and genuine understanding of that content is what the exam tests. We don't offer exam strategy, timed practice papers or score predictions. If your child needs dedicated exam preparation alongside curriculum work, their school or a test prep provider would be better placed to help.

My child's school teaches AP Calculus AB. Do you cover both AB and BC?

Our AP Calculus curriculum covers the core calculus content that forms the foundation of both AB and BC courses: limits, differentiation, applications of differentiation, integration and applications of integration. The personalized plan works through that content based on where your child's gaps are, regardless of which variant their school teaches.

What comes before AP Calculus in the curriculum?

AP Calculus follows Pre-Calculus and Trigonometry. Students who have worked through the pre-calculus content will have covered limits, basic differentiation and integration at a foundational level before reaching the full AP Calculus curriculum.

Does the AP Calculus curriculum work for students with ADHD or learning differences?

AP Calculus requires sustained concentration and the ability to hold multi-step reasoning in mind, both of which can be harder for students with ADHD. The advantage of working through our curriculum at home, at their own pace, is that your child controls the environment completely. No classroom distractions, no time pressure, no keeping up with peers. A concept like the chain rule or integration by substitution can be revisited as many times as needed, with a full worked solution available every time. For students who process information differently and have found classroom-based math instruction difficult throughout high school, reaching AP Calculus with the right support in place is absolutely achievable.

Online AP Calculus Help: Limits, Differentiation and Integration