E = mc²
e^iπ + 1 = 0
∇ × B = μ₀J
F = ma
∑ 1/n² = π²/6
∫₀^∞ e^-x² dx
∂f/∂x = 0
det(A) ≠ 0
P(A|B)
lim x→0
σ = F/A
λ = h/p
∇²φ = 0
iħ∂ψ/∂t
dx/dt = v
a²+b²=c²
αβγδ
S = k ln W
AI-Powered Practice

Practice problems
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Lemma generates exam-calibrated math and physics problems, then validates your reasoning step by step. Not just answers. Your actual thinking process.

10+ exam formatsInfinite unique problems3-layer verification
lemma.study/practice
Problem #2,847
AMC 12Difficulty 7

Calculate ∫₀^π sin(x) · arctan(cos x) dx

Correct approach detected
1Let u = cos(x), du = -sin(x) dxSubstitution
2Bounds: x=0 → u=1, x=π → u=-1Transform
3∫ arctan(u) evaluated = π/2Result

Trusted by students preparing for

SAT MathJEE AdvancedJEE MainAMC 8AMC 10AMC 12AIMEIMEITAENEMAP CalculusAP PhysicsUSAMOUSAPHOUKMTA-Levels MathSAT MathJEE AdvancedJEE MainAMC 8AMC 10AMC 12AIMEIMEITAENEMAP CalculusAP PhysicsUSAMOUSAPHOUKMTA-Levels Math
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Exam formats

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Problems generated

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The Problem

Your preparation
has a blind spot

You study for hours, solve hundreds of problems, and still feel uncertain. The reason? You never get feedback on where your thinking actually breaks.

Recycled problem banks

You keep solving the same 200 problems everyone else has memorized. No new challenges, no real growth.

Answer-only checking

You know you got it wrong, but not where your reasoning broke. The most critical feedback is missing.

Unfocused practice

Hours spent on topics you already know. No system tells you where the actual gaps are.

Wrong answer.

But where did your reasoning fail?

Your current tools cannot tell you.

Features

Every wrong answer becomes a lesson

Six systems working together to make you measurably better, every single day.

Step-by-step reasoning validation

The AI traces your logic at every step. When you go wrong, it shows you exactly which step broke and why.

Spaced repetition engine

Problems you struggled with resurface at the optimal moment. Built on the SM-2 algorithm.

Daily AI diagnostic

Every morning, a personalized report tells you exactly what to practice today based on your data.

Visual mastery map

See every topic you need to master. Watch areas light up as your understanding deepens.

Problem of the Day

One problem, same for everyone, every day. Global leaderboard ranked by speed and accuracy.

Exam-calibrated difficulty

Problems generated at the exact difficulty curve of your target exam. SAT and IMO are different muscles.

E = mc²
e^iπ + 1 = 0
∇ × B = μ₀J
F = ma
∑ 1/n² = π²/6
∫₀^∞ e^-x² dx
∂f/∂x = 0
det(A) ≠ 0
P(A|B)
lim x→0

The student who knows where they went wrong is already halfway to the right answer.

Every mistake is data. Lemma turns that data into your fastest path to mastery.

How It Works

Three steps to measurable progress

01

Pick your exam

Choose from SAT, JEE, AMC, IME-ITA, ENEM, or any supported format. The system calibrates to that exact difficulty.

02

Solve real problems

AI generates unique problems at your level. Type your solution. 3-layer verification checks every step.

03

Get smarter daily

Spaced repetition resurfaces weak areas. Daily diagnostics guide your focus. Your mastery map grows.

Exam Coverage

Calibrated for your target

SAT Math

College Board

28 topics Intermediate

JEE Advanced

IIT Entrance

45 topics Advanced

AMC / AIME

Math Olympiad Track

35 topics Advanced

IME-ITA

Military Engineering

42 topics Advanced

ENEM

Brazilian National Exam

30 topics Intermediate

AP Physics

College Board AP

32 topics Intermediate
Student Results

Real students, real improvement

I went from scoring 90 to 126 on the AMC 12 in three months. The step-by-step feedback showed me reasoning patterns I never noticed.
Marcus Chen

Marcus Chen

AMC 12 Student

90 to 126 on AMC 12
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FAQ

Questions we get asked

E = mc²
e^iπ + 1 = 0
∇ × B = μ₀J
F = ma
∑ 1/n² = π²/6
∫₀^∞ e^-x² dx

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Neither should your preparation.

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