Help & Information

Everything you need to know about Calculus Ninja.

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Rules & Guidelines

No cheating: Using external calculators (like WolframAlpha, Symbolab) or AI tools during ranked matches is strictly prohibited.
Time limits: Rapid uses the time limit you choose, and each incorrect answer removes 5 seconds. In PvP and Multiplayer, you race against others.
Scoring: Correct answers increase your score and earn XP. Rating changes only after competitive matches. Incorrect answers may result in penalties depending on the game mode.
Respect others: Maintain a positive environment in multiplayer modes.

Problem Sources

Calculus Ninja selects reusable problems from a versioned bank. Original templates are checked with exact mathematical methods and rendering tests before publication. Automatic validation does not mean every problem has been reviewed by a person. AI can assist offline authoring; gameplay selection and grading do not call OpenAI. Adapted problems retain their source credits, modification notices, and content license in the answer review and saved replay. These content licenses apply to the identified adaptations. The problems cover a wide range of topics including:

Integration
Differentiation
Limits
Series
Differential Equations
Multivariable Calculus

Difficulty and problem reports

Easy uses fundamental rules; Medium combines standard techniques; Hard requires several steps or careful domain and convergence analysis; Olympiad asks you to discover a concealed identity or transformation. These are template estimates, not measured solve-time rankings. A category may be unavailable while content is under review.

Use the copyable problem ID and revision in an answer review to report an issue. Corrections create a new revision, so previous games and results keep their original questions. A round avoids duplicate problems and limits repeated families; small categories use a bounded relaxation of recent-history and family limits.

Ratings & Ranks

Rating measures competitive results in PvP and Multiplayer. Each opponent is compared separately using both players’ ratings from the start of the match. An upset earns more than an expected win; a tie counts as half a win. Changes are balanced between players and bounded by 32 points per match, regardless of room size. Difficulty rewards XP, not extra rating. Empty and all-wrong games do not transfer rating. PvP ends when both players finish; target-score Multiplayer ends when the target is reached. Timed games use a shared deadline, and other competitive games have a 30-minute limit.

Overall rating is independent of topic ratings. Topic ratings compare only the same questions that both players attempted; unseen questions do not count as mistakes. Equal scores share a position. A player who never answers cannot win over someone who participated. Existing ratings are preserved, start at zero for new players, and can go below zero. Unrated means no qualifying competitive result yet.

Every correct answer earns 10 XP (Easy), 20 XP (Medium), 30 XP (Hard), or 50 XP (Olympiad), in every mode. There are no placement bonuses. Level L requires 100 × L² total XP: level 1 needs 100, level 2 needs 400, and level 3 needs 900. Topic levels follow the same curve.

Unrated

No rated matches

Bronze

Below 500 (rated)

Silver

500 - 999

Gold

1000 - 1499

Platinum

1500 - 1999

Diamond

2000 - 2499

Grandmaster

2500+

History, replay & analysis

Your stored round history has no automatic record limit. History displays 25 rounds per page; use date ranges, mode, topic, difficulty, recorded result, and replay capability to find older rounds. Filters search the full stored history. Unknown dates remain available under All dates.

New rounds capture the exact bank problem revision and choice order, server-confirmed answers and scores, and your browser’s observed interactions. Replay is private to participants; only your own detailed perspective and public opponent scores are shown. Solutions and analysis unlock after the entire match ends, including when you finish your questions first.

Recorded playback follows the original timeline, including countdowns, penalties and captured feedback. You can pause, seek, change speed, and jump between questions or events. Analysis shows solutions separately and labels any later explanation clarifications. Viewing a replay does not submit answers, generate problems, award XP, change ratings, or alter the match result.

Recording means the round is still in progress. Syncing means captured events are waiting to upload. Available means the expected evidence synchronized; Partial means some events or timing could not be recovered. Unavailable means the replay data could not be loaded. Legacy — replay was not recorded for this round. Rounds already in progress when replay launched remain Legacy.

Keep this device’s site data until synchronization finishes. Events are saved incrementally on this device and retried after reconnecting. Closing the browser, clearing site data, denied storage, or a crash can leave a partial replay. Unknown timings are shown as unknown. Reloads use separate clock segments; an unaligned segment is not given an invented time.

History and synchronized replays are not automatically deleted. To bound recording cost, capture allows up to 4,096 client events per player per round, 32 page sessions, and 128 chunks per session, with at most 32 events and 24 KB per chunk. Reaching a recording limit marks the replay partial and does not change gameplay or remove the round from history. Chat and account credentials are not recorded in replay events.

Legacy problems

Legacy identifies a problem from an original bank construction. In Settings → Experimental, you can include reviewed legacy problems in new Test and Rapid rounds, when available. This is off by default. Every eligible revision must pass the same mathematical, explanation and choice-quality review as other problems.

PvP and Multiplayer use a shared pool without legacy problems. Changing the preference keeps current rounds, saved results and replays intact. It cannot bring back withdrawn or unreviewed questions.

Mathematical notation

We use common mathematical conventions, with Wolfram MathWorld as a reference. Where several conventions are accepted, the choices below apply throughout Calculus Ninja.

These conventions apply to questions, answer choices, and worked solutions. Any extra symbols are defined where they are introduced; a solution uses the values in your question.

Logarithms: $\ln x$ is the natural logarithm (base $e$ ). Other bases are written explicitly, such as $\log_{10}x$ or $\log_b x\quad(b>0,\ b\ne1)$ .
Products and special functions: We use $(a)_n=a(a+1)\cdots(a+n-1),\quad(a)_0=1$ for the rising factorial. Less familiar functions and symbols are defined in the problem or solution.
Angles and inverse functions: Angles are in radians unless degrees are stated. We write $\arcsin x,\ \arccos x,\ \arctan x$ for inverse trigonometric functions, and $1/\sin x$ for a reciprocal. Inverse hyperbolic functions use $\operatorname{arcsinh},\ \operatorname{arccosh},\ \operatorname{arctanh}$ .
Derivatives and integrals: $f'(x),\ \frac{\mathrm{d}f}{\mathrm{d}x},\ \frac{\partial f}{\partial x}$ distinguish ordinary and partial derivatives. Differentials use upright $\mathrm{d}x$ . An indefinite integral includes its arbitrary constant $C$ ; logarithmic antiderivatives use absolute values when the stated real domain requires them.
Domains and exact answers: Variables are real unless a problem states otherwise. Square roots are the principal nonnegative real roots on their domain. Any complex branches, convergence conditions, or unusual special functions are specified. Answers are exact unless an approximation is requested: $=$ means equality, $\approx$ approximation, and $\sim$ asymptotic equivalence.
Reading a solution: Prose explains the idea; equations show its application. Summation indices and auxiliary functions are introduced before use. A symbol such as $m$ has no hidden generator meaning. If an explanation is clarified after a round, the original question, submitted answer, and recorded result are retained.

Tips & How to Practice

1. Start with Test Mode

Use the Test mode to practice without time pressure. Review the step-by-step LaTeX explanations after answering to understand the methodology.

2. Build Speed in Rapid Mode

Once you are comfortable with the concepts, use Rapid mode to improve your mental math and pattern recognition speed. Focus on accuracy first, then speed.

3. Memorize Common Derivatives & Integrals

Having common rules (power rule, trig functions, exponential/logarithmic rules) memorized will significantly decrease your solve time in competitive modes.

4. Review Your Mistakes

Don't just guess! If you get a problem wrong, take the time to read the explanation and understand why the correct answer is what it is.