Practice problems
that think back
Lemma generates exam-calibrated math and physics problems, then validates your reasoning step by step. Not just answers. Your actual thinking process.
Calculate ∫₀^π sin(x) · arctan(cos x) dx
Trusted by students preparing for
Exam formats
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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.
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.
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.
Three steps to measurable progress
Pick your exam
Choose from SAT, JEE, AMC, IME-ITA, ENEM, or any supported format. The system calibrates to that exact difficulty.
Solve real problems
AI generates unique problems at your level. Type your solution. 3-layer verification checks every step.
Get smarter daily
Spaced repetition resurfaces weak areas. Daily diagnostics guide your focus. Your mastery map grows.
Calibrated for your target
SAT Math
College Board
JEE Advanced
IIT Entrance
AMC / AIME
Math Olympiad Track
IME-ITA
Military Engineering
ENEM
Brazilian National Exam
AP Physics
College Board AP
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
AMC 12 Student
Less than a single tutoring session
Free
Start practicing with no commitment. See what real feedback feels like.
- 5 problems per day
- Basic step feedback
- 1 exam format
- Progress tracking
Scholar
Unlimited practice, full analysis, daily AI diagnostics.
- Unlimited problems
- Full reasoning validation
- All exam formats
- Spaced repetition
- Daily AI diagnostic
- Mastery map
- Priority support
Classroom
For teachers managing student preparation at scale.
- Everything in Scholar
- Up to 30 students
- Class analytics
- Assignment creation
- Student tracking
- Bulk generation
- Dedicated support
Questions we get asked
Your exam date is not waiting.
Neither should your preparation.
Start with 5 free problems today. No credit card. No commitment.