Free math prep for ALEKS placement and the TEAS
Type each step. Lemma shows exactly where it went wrong — and won’t hand you the answer.
Every number on this page is real and live.
Live demo · Two-step equations
Type the next line of work, or just the answer. A right line gets a check mark. A wrong line gets crossed out, and Lemma tells you what went wrong. You get three lines.
The answer looks like x = a single value.
Two identical notebooks and a $18 binder cost $30. What is the price of one notebook?
Every verdict comes from the same math checker the app uses — a computer algebra system, not an AI model. Nothing you type here is saved.
Real mistakes
Six problems from the course, ALEKS and TEAS, each with a wrong line people really write. The message under each one is word for word what Lemma says about that line.
Add and reduce completely.
Named error · Added unlike denominators directly
The pieces have different sizes, so neither numerators nor denominators can be combined yet.How it works
Each card shows one rule at work on a real line of algebra.
Every topic opens on one problem, with no lesson. Solve it on your own and you skip the lesson.
Ask for a hint and that problem is marked as solved with help. It still teaches you; it just doesn’t count as yours alone.
A topic passes on four fresh problems solved without help. Nothing else moves you along.
A wrong line isn’t just marked wrong. When Lemma can tell which move broke it, it says so, and that mistake comes back later as its own practice.
The AI tutor
Ask about the problem you’re on by typing, by talking out loud, or by writing on the page and letting it read your handwriting. It explains; the math checker alone decides what’s right. It’s an AI model, so it can be wrong — the checker can’t be talked out of a verdict.
Free every day: 10 questions, 3 voice sessions, and 40 handwriting reads.
What it covers
Every area below is read from the course itself, in the order you meet it, with its topics named.
One problem, the way Lemma checks it
Every line is checked against the one above it, and both answers against the original: (0, −3) and (3, 0) sit on both graphs.
7 topics
Integers · Order of ops · Fraction sums · Fraction products · Percents · Proportions · Units
6 topics
Simplify · Distribute · Like terms · Exponent rules · Negative powers · Scientific notation
7 topics
One-step equations · Two-step equations · Both sides · Literal equations · Absolute value · Inequalities · Compound inequalities
6 topics
Coordinates · Slope · Line equations · Linear graphs · Substitution · Elimination
5 topics
Evaluate functions · Domain & range · Transformations · Composition · Inverses
9 topics
Polynomial sums · Polynomial products · Factor GCF · Special products · Factor trinomials · Difference of squares · Solve by factoring · Complete square · Quadratic formula
3 topics
Simplify radicals · Radical arithmetic · Radical equations
3 topics
Rational simplify · Rational operations · Rational equations
3 topics
Complex numbers · Polynomial division · Polynomial zeros
5 topics
Exponential equations · Growth & decay · Evaluate logs · Log properties · Log equations
3 topics
Polynomial behavior · Rational functions · Sequences
4 topics
Right triangles · Degrees ↔ radians · Unit circle · Trig identities
4 topics
Trig graphs · Trig equations · Oblique triangles · Trig formulas
1 topic
Conic sections
3 topics
Direct limits · Algebraic limits · Continuity
7 topics
Derivative definition · Power rule · Product rule · Quotient rule · Chain rule · Trig derivatives · Exp & log derivatives
4 topics
Implicit derivatives · Tangent lines · Related rates · Optimization
4 topics
Antiderivatives · Definite integrals · FTC · u-substitution
7 topics
Integers · Order of ops · Fraction sums · Fraction products · Percents · Proportions · Units
3 topics
Simplify · Distribute · Like terms
5 topics
One-step equations · Two-step equations · Both sides · Literal equations · Inequalities
5 topics
Geometry measures · Statistics · Charts · Perimeter & circles · Data shapes
3 topics
Percent change · Doses & rates · Mixed numbers
The ALEKS road
The three stones are ALEKS placement scores — 46, 61, 76 — the cutoffs at the college Lemma was built for; yours may differ. Each topic opens on one problem: solve it and you skip that lesson, which is the blue arc. After placement come 18 optional Calculus I topics.
Taking the TEAS instead? Its math track is its own list of 23 topics, with the 15 science lessons beside it.
Why this exists
I’m preparing for ALEKS placement so I can qualify for Calculus I. I needed a way to see which steps I understood and which ones still depended on help.
Every tool I tried let me fake it. The hint was one tap away before I had written anything. The answer key said I was right without asking how I got there — and on the day, how you got there is the only thing that shows up.
So I built one that refuses. A computer algebra system checks each line against the line above. It won’t help until you’ve tried. And it keeps what you did with help apart from what you did alone, because the test only sees the second kind.
The first learner on it is me: relearning algebra from zero, working toward a 76 or better on ALEKS placement. It’s open now in case it helps you too.
What’s here today
Math for ALEKS placement: 66 topics with unlimited fresh problems, plus 18 optional Calculus I topics. TEAS: a math track plus 15 interactive science lessons and drills; Reading passages are next.
Pricing
Every lesson, problem and review is free. The AI tutor is free up to a daily limit; a paid pass for more tutor time is planned.
Pick your test
No sign-up. A cookie keeps your place in this browser; Account inside the app gives you a link to open the same record on another device.
Questions
Lemma is a free web app for ALEKS placement and TEAS math practice. You type each step of a solution; a computer algebra system checks every line, shows exactly where it went wrong, and names the mistake when it can tell which move broke it. Help unlocks only after you try, and it won’t hand you the answer. No account, no email.
Yes. Lemma covers 66 ALEKS placement topics with unlimited fresh problems, in the order they build, with checkpoints at 46+ Intermediate Algebra, 61+ College Algebra, 76+ Precalculus, plus 18 optional Calculus I topics. Every line you type is checked by a computer algebra system, not an AI model, and a topic passes only on four fresh problems solved without help.
Yes. The TEAS side has its own math track of 23 topics (ratios, percentages, unit conversion, algebra and more), checked step by step the same way, plus 15 interactive science lessons and drills. Reading passages are next.
Every lesson, problem and review is free. The AI tutor is free up to a daily limit: 10 questions, 3 voice sessions and 40 handwriting reads a day. A paid pass for more tutor time is planned.
A chatbot’s verdict on your step is a language model’s guess, and it will usually just give you the answer. In Lemma the verdict on every line comes from a computer algebra system. The AI tutor explains and hints but never grades, any help marks that problem as assisted, and only problems you solve on your own move you forward.
No. Pick ALEKS or TEAS and your first problem opens in about a minute. A cookie keeps your place in this browser, and Account inside the app gives you a link to open the same record on another device. A phone works; a tablet with a pencil is the best seat.
No. Lemma is independent practice. ALEKS is a registered trademark of McGraw Hill, and TEAS is a registered trademark of Assessment Technologies Institute (ATI).
Optional
Leave an email address and it is used for one thing: telling you when full access opens. Studying here still needs no account and no email.
