MathCastle

$\forall$ students, Grade 4 to the Putnam

Master math, one castle at a time.

25 book-style courses, 50,000+ problems with step-by-step solutions, 92 real-format contests, a 3D castle to climb and friends to duel. All in one place, all free.

Or explore without an account — take the placement quiz to find your level.

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Problem · Superchallenge

Evaluate exactly:

2\arctan\tfrac13 + \arctan\tfrac17

Your answer…

Correct! Answer:

\tfrac{\pi}{4}

— with a 5-step worked solution.

Scroll to see everything MathCastle offers

Courses, Grade 4 → Putnam

50,000+

Practice problems

Full-length practice contests

100%

With worked solutions

§1Real problems, every level

Typed answers, instant checking, and a step-by-step worked solution behind every problem. Try one now — no account needed.

Try one right now — no account

What is the sum of the interior angles of a hexagon, in degrees?

Easy

Evaluate

\log_2 32

Answer:

5

Medium

Solve

x^2 - 5x + 6 = 0

Answer:

x = 2, 3

Hard

Find

\dfrac{d}{dx}\left(x^3 - 4x\right)

Answer:

3x^2 - 4

Superchallenge

Evaluate exactly:

2\arctan\tfrac13 + \arctan\tfrac17

Answer:

\tfrac{\pi}{4}

Medium

Two fair dice are rolled. Find

P(\text{sum is prime})

Answer:

\tfrac{5}{12}

Hard

Compute

\displaystyle\int_0^1 2x\,dx

Answer:

1

§2Learn, practice, compete

Learn

25 book-style courses from Grade 4 to the Putnam: every formula proved, worked examples and quick checks on every page, quizzes, unit tests and a final.

Browse courses

Practice

50,000+ original problems at five levels, easy to superchallenge, each with a step-by-step solution. Missed problems come back on a spaced-repetition schedule.

Start practicing

Compete

92 practice contests at real length and timing (AMC, MathCounts, AIME, USAMO, Putnam), plus a castle to climb, Countdown duels and Problem Rush.

See the contests

Also built in

LaTeX notebook 2D / 3D grapher Geometry lab Review missed Duel a friend The Courtyard

§325 courses, Grade 4 to Putnam

Each course is a book: lessons with a proof of every formula, worked problems, practice after every section, and a printable booklet.

Grade 4

8 topics

Grade 5

7 topics

Grade 6

11 topics

Pre-Algebra

16 topics

Algebra 1

13 topics

Algebra 2

13 topics

Precalculus

13 topics

Linear Algebra

11 topics

Geometry

12 topics

Trigonometry

14 topics

Calculus

14 topics

Multivariable Calculus

11 topics

Differential Equations

15 topics

Counting & Probability

12 topics

Statistics & Data

11 topics

Number Theory

11 topics

Groups and Fields

17 topics

Graph Theory

11 topics

Proof Writing & Problem Solving

8 topics

USAMO (Olympiad Proofs)

29 topics

AMC 8 / MathCounts

8 topics

AMC 10

10 topics

AMC 12

9 topics

AIME

11 topics

Putnam

23 topics

§4Compete & play

92 numbered practice contests at real length and timing, with official scoring, full solutions at the end, and a printable PDF of every set.

AMC 8

AMC 10

AMC 12

MathCounts

AIME

USAMO

Putnam

Printable PDFs

Climb the MathCastle

Ascend the castle floor by floor — each level raises the difficulty.

Math Countdown Round

Head-to-head, one problem at a time, against the clock.

Problem Rush

Race the clock — solve as many as you can on one life. Starts hard.

§5The Courtyard — made by mathletes like you

Write problems and worksheets with the built-in LaTeX creator, publish them for everyone, and get a feed tuned to the topics you practice. Suggest your best problem as the site's Daily challenge — and download anything as a LaTeX file.

Visit the Courtyard

Start building your streak today.

Create a free account to save your progress — or, not sure where to start? Twelve adaptive questions place you at exactly the right level.