Everything Lemmas does
Lemmas is a free competition math practice site with 6,507 past problems from the AMC 8, AMC 10, AMC 12, AIME, HMMT, ARML, SMT and PUMaC.
Practice
Open Practice, choose the AMC 10 and start a Sweet spot set. A quick right answer sends the next problem a little higher and a miss sends it back down, so by the tenth problem you are working at the level you actually hold. If one problem has you stuck, the first hint shows the formula cards that fit it and the second shows the solution.
The problems worth your time sit just above what you can already solve, and that spot shifts after every answer you give.
- Speed15 to 35
- Sweet spot35 to 60
- Stretch60 to 100
- Sweet spot
- Problems you can mostly solve. Each right answer moves the next one up a little, more if it was quick, and a miss moves it down.
- Speed
- Easier problems, done fast. Only quick right answers move it up. A slow one brings it down a step, and so does a miss.
- Stretch
- Problems from the top of the difficulty scale. Any right answer moves the next one up, and misses are expected.
- Custom
- A fixed set built from your own filters, such as a contest, a subject or a keyword, in a size of 5, 10, 25 or 50 problems.
- Find my starting level
- 10 problems in a subject you pick place you. It is optional, and you can restore the recommended settings later with one button.
- Hints
- The first hint shows the formula cards that fit the problem. The second shows the solution. A hint stops a correct answer from repairing an earlier miss.
- Sketch
- Scratch space beside every problem: plain Notes, or a Sketch tab with 16 geometry tools.
Pace and stats
A 2:30 countdown runs on every question, and once it passes zero it counts how far over you are. Afterward your profile splits the time per correct answer by subject over the last seven days, which is where a slow subject shows up.
AMC 10 and AMC 12 give 75 minutes for 25 questions, about three minutes each. Timing every attempt to the second shows which subjects eat that budget.
Time left1:48
Over time+0:12
Target 2:30. The clock never affects your score.
- Time left
- A countdown from 2:30 on every question, then the minutes and seconds you are over by. You can pause it, and it never changes your score.
- Average time per answer
- On your profile beside problems solved, study time and your best streak.
- Time per correct answer
- A seven-day chart that splits your average time by subject.
- Completed
- Every problem you have solved, with how many tries it took and your best time on it.
- Skill shape
- Your strength in each subject and your speed on one chart, with a score for each week.
- Activity
- A calendar of the days you practiced, with your current streak and your best one.
- Download your data
- Everything you have done, as a file you keep.
Mistakes
When an answer is wrong, Lemmas asks what happened and offers seven causes, from misreading the question to running out of time. The miss goes on a shelf in your mistake notebook and returns later, as How it works shows, and the notebook keeps a running tally of your causes so you can see which one keeps costing you points.
Getting a problem right once proves little. Solving it again a few days later shows whether it stuck.
- What happened?
- After a miss you pick the cause from seven and can add a note, while the problem is still fresh.
- Mistake notebook
- Three shelves: Ready to re-solve, Resting and Transfer checks.
- Ready to re-solve
- Misses whose rest is over, waiting for you to solve them again from blank paper.
- Transfer checks
- A new problem on the same idea, set after you have repaired a miss.
- Why you missed them
- The notebook tallies your causes, so you can see what keeps costing you points.
Compete
A real past paper in Arena runs on its contest's own clock. The breakdown afterward splits your pace by subject, and each miss can be worked again. For a shorter test, a duel puts you head to head with a friend on five AMC-style problems in twelve minutes.
Arena scores a paper the way the contest does and shows nothing until time is up.
- Arena
- Sit a real past paper on the contest's own clock with AMC scoring. Your answers stay sealed until time is up, then you get a breakdown by subject and pace and can work each miss again.
- The Final 7
- Seven problems at the level of an AMC's #19 to #25, hardest last, for the AMC 10 or the AMC 12. Real AMC problems, mixed with problems from other contests that passed a blind check against them.
- Presets
- Ready-made papers for the AMC 12, the AIME, HMMT and SMT, plus an AIME bridge between the AMC and the AIME. Or build a custom session.
- Duel
- Challenge a friend to a duel. AMC style is five problems in twelve minutes. AIME style is three problems in fifteen.
- Leaderboard
- Rank among your friends or everyone, for this week or all time.
- Solutions from other students
- Read how someone else solved a problem and vote up the ones that helped.
- Badges
- 27 badges, such as Seven days for a week-long streak or Clean paper for getting every problem right in an Arena session of ten or more. XP also moves you through 100 levels in 6 tiers, Bronze to Master.
Learn
Open Formulas and Review hands you each of the 516 cards shortly before you would forget it, while Match and Test drill the same cards in other shapes. The Library holds every card, and a hint during Practice links to the one that fits the problem in front of you. When you want a hard problem with nothing riding on it, the Laboratory has unranked HMMT problems.
- Formulas
- Spaced review, plus Learn, Match, Test and a Library of every card.
- Laboratory
- Unranked HMMT problems that sit outside your practice sets, for when you want a hard one with nothing riding on it.
- Reading shelf
- Books for each subject and stage, with a link to find each one.
Plan and progress
Start with Plan settings: a target contest, a date and how hard you want the weeks to feel. After that the Today page keeps one task on top, and Today's quests add four goals for extra XP. If the AMC is your target, Guessing on the AMC works out when a guess beats a blank worth 1.5 points.
Choosing a contest fills in its date for the season, and the plan counts down the days to it.
- Plan settings
- Pick a target contest and date, then a weekly rhythm and a focus subject. Intensity is Balanced, Sprint or Deep work.
- Today
- The top card of your Today page holds one small task, chosen from the problems due back, the formulas to review and a new problem near your level.
- Today's quests
- Four goals a day that pay extra XP.
- Competition guides
- One row for each contest, with a link to practice it and a link to its official site, plus a table of what every team round asks of you.
- Guessing on the AMC
- A wrong answer scores 0 and a blank scores 1.5, so the guide works out when a guess is worth it.
Compared with a problem archive
What a plain problem archive leaves to you, and what Lemmas does about it.
| A typical problem archive | Lemmas |
|---|---|
| A list of problems and solutions, in the order the contest printed them. | Sweet spot, Speed and Stretch sets that pick the next problem after every answer, from whether you were right and how fast you were. |
| No clock, and no record of how long anything took. | Every attempt timed to the second, a Time left countdown on each question, and your average time by subject on your profile. |
| Problems you missed are yours to remember. | A mistake notebook that asks what happened, schedules the re-solve, and sets a new problem on the same idea once you have repaired it. |
Make an account and try your first problem.
Username, email and password. No card.