Algebra test with a map of knowledge gaps

An online tool for testing your algebra knowledge from grade 5 to grade 11. The adaptive test picks tasks to match your answers, builds a map of every curriculum topic, finds gaps in what you’ve covered, names typical mistakes, and shows what to study first.

How to take the test

Choose your grade and format

Your grade decides which topics the test covers; the full diagnostic maps every topic, the quick check gives your level and weak areas.

Solve the problems on scratch paper

Enter your answer as a number — a fraction can be written as 3/4, roots separated by “;”. If you don’t know it, click “I don’t know.”

Study your knowledge map

See your level, mastered topics, gaps, typical mistakes, and the “what to study first” list.

Retake it after some time

The tasks are new every time — compare scores on the same scale and track your progress.

Check every school algebra topic in one diagnostic

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How the test works, and how accurate it is

Every task is generated fresh with new numbers, so a retake never turns into memorizing answers. Tasks are chosen adaptively: an item response theory (IRT) model updates your level across all of algebra, each section, and each topic after every answer, and picks the next task wherever a topic’s status is still unclear.

The curriculum has more topics than the test has tasks, so for untested topics the test gives a forecast based on nearby topics and your overall level, and honestly labels it “forecast.” Topics still ahead in the curriculum are never called gaps.

We checked accuracy by simulation: “students” with known knowledge took the test through the same engine, with task difficulty in the model deliberately distorted — the way it is when task calibration is imprecise. The full diagnostic correctly judged whether a topic was mastered in 80–84% of cases; gross errors (calling a mastered topic unmastered, or the reverse) happened in 2–4%; real gaps were found in 84–97% of cases. The difficulty of each task type is refined weekly from real students’ answers.

Topics and grade levels follow the Russian federal school curriculum (algebra for grades 7–9, algebra and calculus for grades 10–11, foundations from grades 5–6). Schools in other countries teach the same algebra, sometimes in a different year — so a topic marked ‘ahead’ may already be familiar to you, and vice versa. The test was built by the Tembrica team; it is a self-assessment, not an official exam.

What the test can do

A map of every topic — from fractions to derivatives

Numbers and computation, expressions, equations, inequalities, functions, progressions, word problems, probability, trigonometry, logarithms and calculus basics: every topic gets its own status.

Tasks match your answers

After every answer, the IRT model updates your level for the topic and section and asks where the status is still unclear — so 15–33 tasks are enough.

Names the mistake, not just “wrong”

If your answer matches the result of a typical mistake — "(a + b)² = a² + b²," a lost root, a not-flipped inequality sign — the test names it and gives the rule.

What to study first

The plan follows a graph of prerequisites: gaps from earlier grades that block new material come first. The PDF breakdown adds a step-by-step solution for every mistake, a week-by-week plan, and a workbook on your topics.

New tasks on every attempt

Every task is generated with fresh numbers, so a retake measures knowledge, not memory, and scores on one scale show your progress.

Teacher mode

One link for the whole class: students take the test without registering, and the teacher sees the class topic map, common mistakes, and an exportable table.

Frequently asked questions

How does the test find gaps if there are fewer tasks than topics?

Knowledge of neighboring topics is connected: someone who confidently solves quadratic equations can almost certainly expand brackets. The model estimates your overall level, each section’s level, and each topic’s level; tasks are asked where a topic’s status is unclear, and other topics get a forecast labeled “forecast.” Gaps are only named for topics already covered in the curriculum.

Why did I get tasks that aren’t from my grade?

The test also checks fundamentals from earlier years — fractions, negative numbers, percentages: gaps there are usually what blocks new topics. Topics from your current grade aren’t counted as gaps until spring — you may simply not have covered them yet.

What should I do if I don’t know the answer — guess?

Better to click “I don’t know.” A guessed answer throws off the model: a topic might wrongly get the status “mastered.” “I don’t know” honestly shows the gap, and the plan comes out more accurate.

How do I enter an answer?

As a number: a whole number, a decimal with a point (2.5), or a fraction with a slash (3/4). For multiple roots, separate them with a semicolon (-2; 3); if there are no roots, use the “∅” button. Inequality and factoring tasks offer four options to choose from.

How can a teacher check a whole class?

Click “Check a class,” create a class, and send students the link. Students take the test without registering, entering only their name. The teacher gets a results table, a class topic map, the most common typical mistakes, and a CSV export.

What’s in the PDF breakdown?

A step-by-step solution for every task you got wrong or skipped with “I don’t know” — with the name of the typical mistake and the rule; a knowledge map for every topic; a week-by-week study plan from fundamentals to advanced material; a workbook with problems on your topics, answers, and solutions. If the test was completed fully at a normal pace, the first page is a certificate with a code you can verify on the site.

Can I use the test to prepare for exams?

Yes, as a diagnostic: it shows which topics of school algebra are still shaky and in what order to review them. Geometry, problems with parameters and olympiad-style puzzles are not covered — the report says so.

How do I show the result to a parent or tutor?

On the result screen, tap “Link to result” and send it. The link opens this result with the topic map, gaps and answers — view only: it cannot be used to continue the test. If you are signed in, your previous attempts are also visible on your other devices.

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Published 24 Sep 2026 Updated 25 Sep 2026 Author: The Supreme