An AI calculus tutor for high school: limits, derivatives and integrals

Q: What level of calculus does it cover?

High school calculus, including courses such as AP Calculus AB and A level Maths. It isn't designed for university courses.

Q: Can it help with word problems like optimisation?

Yes. It spends time on setting up the equation from the words, which is where most students get stuck.

Q: Can it check my handwritten working?

Yes. Write your steps on the whiteboard and it finds the first mistake, and whether it was calculus or algebra.

Q: How much does it cost?

There's a 3-day free trial with no card needed, then $15 a month for every subject.

TutorAura · Updated 22 October 2026

Calculus is the maths of change: how fast something is changing (derivatives) and how much has built up (integrals). It's also where gaps in algebra start to really hurt. TutorAura's AI calculus tutor explains each idea from the meaning up, checks your working line by line on a whiteboard, and spots when a mistake is really an algebra problem in disguise.

It's designed for high school calculus (grades 11 and 12), including the calculus in courses such as AP Calculus AB and A level Maths. It isn't a university-level tutor.

Key takeaways

Explains what derivatives and integrals mean before the rules.
Works through differentiation rules, rates of change and optimisation step by step.
Checks your working and separates calculus mistakes from algebra slips.
Built for high school calculus, not university courses.

Example: what a derivative means

A ball's height is $h(t) = 20t - 5t^2$ metres after $t$ seconds. How fast is it rising at $t = 1$ ?

Meaning first. The derivative $h'(t)$ is the rate of change of height: the velocity.
Differentiate term by term with the power rule: $h'(t) = 20 - 10t$ .
Substitute: $h'(1) = 10$ , so the ball is rising at 10 m/s.
Interpret: when is $h'(t) = 0$ ? At $t = 2$ , the top of the flight.

The tutor asks you what each step means physically, not just how to do it.

Example: an optimisation problem

A farmer has 40 m of fencing to make a rectangular pen against a wall (the wall forms one side). What dimensions give the largest area?

Let the sides from the wall be $x$ , so the side parallel to the wall is $40 - 2x$ .
Area: $A = x(40 - 2x) = 40x - 2x^2$ .
Differentiate: $A'(x) = 40 - 4x$ . Set to zero: $x = 10$ .
Check it's a maximum: $A''(x) = -4 < 0$ .
The pen is 10 m by 20 m, with area 200 m².

Most students find step 1, setting up the equation from words, the hardest part. The tutor spends time there.

What it covers

Area	Topics
Limits	Intuitive limits, continuity, limits at infinity
Differentiation	Power, product, quotient and chain rules; derivatives of exponential, logarithmic and trig functions
Applications	Tangents and normals, rates of change, related rates, stationary points, optimisation
Integration	Antiderivatives, definite integrals, area under a curve, substitution
Foundations	The algebra and functions calculus relies on

Tell the tutor which course you're taking; we don't claim full coverage of any syllabus.

When the problem is really algebra

Many calculus mistakes happen in the algebra: simplifying fractions, working with negative exponents, or factorising before solving $f'(x) = 0$ . When the tutor checks your working, it tells you whether the slip was in the calculus step or the algebra, and offers quick practice on the algebra skill if that's the gap. See our AI algebra tutor.

Using the whiteboard

Calculus involves a lot of notation, which is easier to write by hand. Write your working on the whiteboard with a stylus or mouse and ask the tutor to check it. Sketching curves helps too: you can draw a function and its derivative and talk through how the slope of one relates to the height of the other.

Limits

Calculus answers can go wrong in subtle ways, and like any AI the tutor can make mistakes. Check important answers by another method (for example, differentiate your integral to see if you get back to the original function) and follow your teacher's notation and conventions.

Frequently asked questions

What level of calculus does it cover?

High school calculus, including courses such as AP Calculus AB and A level Maths. It isn't designed for university courses.

Can it help with word problems like optimisation?

Yes. It spends time on setting up the equation from the words, which is where most students get stuck.

Can it check my handwritten working?

Yes. Write your steps on the whiteboard and it finds the first mistake, and whether it was calculus or algebra.

How much does it cost?

There's a 3-day free trial with no card needed, then $15 a month for every subject.

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