Practice mixed test — Year 5: the whole first term.

15 questions drawn at random from a bank of 25, on the block of the programme your teacher is finishing: every attempt is a different test. No penalty for wrong answers, so answer even if you are not sure. At the end you receive by email the correct answer to every question and your weak topics — with an account you see them straight away here on the page. The step-by-step solution unlocks with your first lesson.

A class test is the written test an Italian high-school class sits after each block of the programme; this practice version is multiple choice.

Test in ItalianThe questions of this simulator are in Italian, as in the real exam.

Test prepared by Gaetano Livornese · Aerospace engineer, Politecnico di Milano · maths and physics tutor · updated 13 October 2026

The mixed test of Year 5 comes in January, closes the first term and puts limits and derivatives in the same test — it is in effect half a second paper, and the way it is marked reflects that: questions that mix the two topics are worth more than isolated ones.

The first mistake comes from exactly this: when the exercise explicitly asks you to compute a derivative “from the definition”, that is with the limit of the difference quotient, applying the differentiation rules instead gives the same number but zero marks — the required method is a different one, and it is the one that is assessed.

The second concerns oblique asymptotes, which are a limit and not a mechanical rule: the coefficient m is found as the limit at infinity of f(x)/x, and only if this limit exists, is finite and is different from 0 does it make sense to compute n as the limit of f(x) − mx. If the first limit does not exist or is infinite, there is no oblique asymptote, and trying to compute n anyway with a random value is wasted time, not a cautious attempt.

The third concerns monotonicity: f′(x₀) = 0 at an isolated point does not stop the function from being increasing. f(x) = x³ has f′(0) = 0 but stays increasing on all of R, because the sign of f′ does not change around 0. The opposite mistake — declaring every point with a zero derivative a maximum or a minimum without checking the sign around it — is the one that costs the most marks in this kind of test.

To prepare, do an exercise that forces you to go from a limit to a derivative in the same question, not two separate exercises: it is the transition, not the single topic, that is the weak point of this test.

What a maths test on mixed test looks like

The Year 5 end-of-term test: limits and indeterminate forms, continuity and discontinuities, asymptotes, derivatives with all the rules, tangent line, monotonicity and finding maxima and minima. In practice, half a second paper.

The mistake that costs the grade

Studying limits and derivatives as separate chapters. In Year 5 every question mixes at least two — an oblique asymptote is a limit, a corner point is a limit of the difference quotient — and anyone who keeps the two topics in different drawers gets stuck halfway through the exercise.

How to use this practice test

Take it once cold, without revising and with the timer on: it is there to show you where you stand, not to look good. Then look at your weak topics, revise only those — usually two or three, not the whole chapter — and retake it after a few days. The 15 questions are drawn from a bank of 25, so the second attempt is not the same test and the scores are genuinely comparable.