Study Guide

Calculus Flashcard App

Calculus asks you to hold a lot in your head at once: derivative rules, standard integrals, limit laws, and the theorems that tie them together.

Space Repeat shows them the way your textbook does, with real fractions, integrals and limits, and schedules each card so the rules are still there at exam time.

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Why spaced repetition works here

Calculus exams reward speed on the routine steps. If you have to re-derive the derivative of tan x or hunt for the right integration technique, you lose time you need for the hard part of the problem. Spaced repetition makes the standard derivatives, integrals and theorems instant, and frees your attention for setting the problem up.

Ideas for your flashcards

  • Derivative rules: power, product, quotient and chain rule
  • Derivatives and integrals of the standard functions (trig, exponential, logarithm)
  • Integration techniques and when to reach for each one
  • Key theorems: the Fundamental Theorem of Calculus, the Mean Value Theorem

Start from a ready-made deck

New accounts can add starter decks for calculus in one click, written with real notation. They're ordinary decks, so you can edit them, add your own cards, or import the ones you already have from a CSV file.

  • Calculus: Derivatives15 cards
  • Calculus: Integrals15 cards

Example calculus flashcards

Shown the way Space Repeat shows them, formulas and all: one clear question, one short answer.

Question

Chain rule: ddx f(g(x))\dfrac{d}{dx}\,f(g(x))

Answer

f′(g(x))⋅g′(x)f'(g(x)) \cdot g'(x)

Question

What is ddxtan⁡x\dfrac{d}{dx}\tan x?

Answer

sec⁡2x\sec^2 x

Question

Evaluate ∫1x dx\displaystyle\int \frac{1}{x}\,dx

Answer

ln⁡∣x∣+C\ln|x| + C

Question

The Fundamental Theorem of Calculus (evaluation part)

Answer

∫abf(x) dx=F(b)−F(a)\displaystyle\int_a^b f(x)\,dx = F(b) - F(a), where F′=fF' = f

How to use spaced repetition for calculus

Give every rule its own card, and test the direction you'll need in the exam: the function on the front, its derivative or integral on the back.

Start reviewing in the first week of the course. Derivatives you know cold make integration far easier, because so much of it is running the rules backwards.

How Space Repeat works

Smart scheduling

The algorithm tracks every card and shows it again right before you would forget it. No manual planning required.

Formulas and code

Fractions, integrals, chemical equations and highlighted code look right on every card. Plain text works too.

Free during the beta

Every feature, spaced repetition included, is free to use while Space Repeat is in beta. Early users will be looked after when pricing arrives.

Start studying calculus

Free to start. No credit card required.

Frequently asked questions

Does Space Repeat come with ready-made flashcards for this?

Yes. New accounts can add starter decks for calculus: Calculus: Derivatives, Calculus: Integrals. They're ordinary decks, so you can edit, add or delete cards, and write or import your own alongside them.

Is Space Repeat good for AP Calculus?

Yes. Build a deck for the AB or BC topics, or start from the derivatives and integrals starter decks, which cover the core rules in real notation. Pair your reviews with practice problems and past free-response questions.

How do I write an integral on a flashcard?

Type it in LaTeX between dollar signs, for example $\int_0^1 x^2\,dx$, or use the Math & code toolbar, which inserts integrals, limits, sums and fractions and shows a preview.

Should I learn derivatives before integrals?

Yes. So much of integration is running the derivative rules backwards that knowing derivatives cold makes integrals much easier. Start reviewing derivatives in the first weeks of the course and keep them in rotation.

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