Practice mixed test — Year 3: 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.
Programme covered by the test
- Domain, composite and inverse functions
- Geometric transformations of graphs and functions with absolute value
- The parabola: vertex, tangency, problems with a parameter
- The line in the coordinate plane: point-to-line distance and families
- The circle: centre and radius, chords, tangent lines
Two worked examples from the test
Qual è il dominio della funzione
Solution
Passo 1 — Dove si annulla il denominatore. Una frazione algebrica esiste solo se il denominatore è diverso da zero:
Passo 2 — Risolvo l'equazione associata. è una differenza di quadrati:
Passo 3 — Escludo entrambi i valori.
Attenzione. Chi risponde ha estratto una sola radice quadrata dimenticando il segno meno; chi scrive ha risolto come se fosse .
Qual è il dominio di
Solution
Passo 1 — Condizione di esistenza. Radice di indice pari: il radicando deve essere maggiore o uguale a zero.
Passo 2 — Studio i segni. Numeratore per ; denominatore per (e va comunque escluso perché annulla il denominatore).
Passo 3 — Regola dei segni. La frazione è positiva dove numeratore e denominatore hanno lo stesso segno:
Attenzione. L'intervallo è la zona in cui la frazione è negativa: è la risposta di chi inverte la regola dei segni. Il include per errore il valore che annulla il denominatore.
In the online practice test you will find 13 more questions like these; the correct answer to every question arrives by email.
Prefer paper? Download the test as a PDF (15 questions, 4 pages · 80 KB, ready to print). You receive the solutions by email after taking it online.
Download the PDFWhat a maths test on mixed test looks like
The Year 3 end-of-term test: domain and transformations of graphs, a parabola with tangency or a parameter, point-to-line distance and a family, and a circle with chords or tangents. A lot of analytic geometry, little theory.
The mistake that costs the grade
Treating the parabola and the circle as two patterns to remember separately. Tangency questions are always solved the same way — a system with the line and a zero discriminant — and anyone who sees this saves half the time of the test.
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.
Is the score not enough?
See which topics lost you the most marks, then read how to handle test anxiety — or we look at your results together: the diagnostic is free.