Practice maths class test — Year 2: Pythagoras, Euclid and probability.
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
- Pythagoras’ theorem and Pythagorean triples
- Euclid’s first and second theorems
- Similarity criteria for triangles
- Ratio of similarity between perimeters and between areas
- Thales’ theorem and parallel lines
- Diagonals of a square, rectangle and rhombus
- Classical probability: favourable cases over possible cases
- Incompatible and complementary events, and the union of events
Two worked examples from the test
In un triangolo rettangolo i cateti misurano cm e cm. Quanto misura l'ipotenusa?
Solution
- Teorema di Pitagora: l'ipotenusa è la radice della somma dei quadrati dei cateti.
- L'opzione cm è la somma dei cateti: i cateti si sommano dopo essere stati elevati al quadrato, non prima.
- Controllo di plausibilità: l'ipotenusa deve essere maggiore di ogni cateto ma minore della loro somma.
L'ipotenusa di un triangolo rettangolo misura cm e un cateto cm. Quanto misura l'altro cateto?
Solution
- Per trovare un cateto si sottrae, non si somma:
- L'opzione nasce dall'aver sommato invece di sottrarre.
- L'opzione è la differenza : come nel caso precedente, la sottrazione va fatta fra i quadrati.
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 · 76 KB, ready to print). You receive the solutions by email after taking it online.
Download the PDFWhat a maths test on Pythagoras and similarity looks like
Numerical applications of Pythagoras and the two Euclid theorems on a right-angled triangle, a similarity to recognise and use, the ratio between the areas of similar figures and a part on classical probability with compound events.
The mistake that costs the grade
In the ratio between similar figures, using the same number for perimeters and areas: if lengths are in the ratio k, areas are in the ratio k². In probability, adding the probabilities of events that can happen together without subtracting the intersection.
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 the guide to probability and combinatorics — or we look at your results together: the diagnostic is free.