Ready for calculus? The algebra is what actually breaks

The 58 concepts this check actually probes

The diagnostic is scoped to one target concept: continuity of polynomial and rational functions, the point in Consiliae's single-variable calculus chapter where limits stop being a definition and start being a tool. Everything upstream of that concept in the prerequisite graph is in scope, which works out at 58 concepts spread across 13 sections of five chapters. Six to ten adaptive questions are usually enough to place you in it, because answering correctly high in the graph is evidence for everything beneath it.

The part you would expect is the limits block: the intuitive definition of a limit, one-sided and two-sided limits, the sum, product and quotient limit laws, and evaluating a limit by direct substitution. That is seven concepts out of the 58. The other 51 are algebra and arithmetic, and that is where the questions concentrate.

Named specifically, the algebra is the definition of a function, ordered pairs and the Cartesian plane, exponent notation and positive integer exponents, the polynomial vocabulary a lecturer uses without defining it (monomial, binomial, trinomial, degree, leading term, standard form), and the definition of a rational expression. Underneath that sits integer arithmetic: the sign rules for multiplication and division, subtracting a negative, and order of operations once negatives are in play.

The two gap profiles this check keeps finding

The first is the returning adult. Limits are unfamiliar because nobody ever taught them, and the algebra is intact once it has been shaken awake. That reads as a low percentage on the first pass and it resolves fast, because the missing concepts sit in one contiguous block at the top of the graph: seven of them, each a lesson rather than a project.

The second is the student coming back after a bad calculus exam, and it is the inverse. The limit vocabulary is fine. The gaps are scattered four and five chapters down, in polynomial manipulation and sign handling. That profile looks worse on a gap map and matters more, because scattered low-level gaps are exactly what makes calculus feel like it needs a talent you were not issued. It does not. It needs the distributive property to be automatic.

So the number to read on your result is not the percentage, it is the depth of the deepest gap. A gap in the limits section means your next lesson is a limits lesson and you are close. A gap in integer sign rules means two evenings there first, and every hour after that is cheaper than it would otherwise have been.

What to do about each gap this check can report

Limits only. Work the block in its own order: intuitive limit, one-sided, two-sided, the three limit laws, then direct substitution. Do not jump ahead to L'Hopital's rule or to the epsilon-delta definition. The entire content of the quotient limit law is its precondition, that the denominator's limit is not zero, and skipping past that is why 0/0 later reads as a paradox instead of as an instruction to factor.

Polynomials or rational expressions. This is usually vocabulary rather than skill. People who factor fluently sometimes cannot say on demand which term is the leading term or what the degree of a product is, and continuity arguments are stated in exactly that vocabulary. It is the cheapest gap on the list to close, often a single sitting, and it makes the textbook readable.

Integer sign rules or order of operations with negatives. This is the expensive one, and the one people are most tempted to wave off because it carries a chapter 1.1 label. Do not. Order of operations with negatives is the most common source of a wrong derivative that the student cannot find by re-reading their own work: the calculus is correct and the minus sign in front of the squared term is not.

Nothing missing. Then start at continuity and keep going. The useful next question is not whether you are ready, it is how fast you can move, and that is answered by doing a lesson rather than by taking another diagnostic.

What this check cannot tell you

It does not test trigonometry. The target concept's prerequisite closure contains none, so a clean result here says nothing about whether you can differentiate sine. In a real calculus course the trigonometric derivatives arrive within weeks, so treat that as a separate question and take the trigonometry check for it.

It does not measure speed, stamina or exam technique, and it does not test whether you can hold a multi-step argument together under pressure. It measures coverage of a prerequisite set. Those are different things, and coverage is the only one a ten-question diagnostic can honestly claim to report.

It also stops at continuity. Differentiation, integration, series and the rest of the chapter sit downstream of the target, so they are out of scope by construction. This tells you whether the door opens, not how long the corridor behind it runs.