Practice maths class test — Year 1: Euclidean geometry.
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
- Complementary, supplementary and adjacent angles
- Sum of the interior and exterior angles of a triangle
- The three congruence criteria for triangles
- The isosceles triangle and the properties of its base
- The triangle inequality and the relations between sides and angles
- Parallel lines cut by a transversal
- Interior and exterior angles of convex polygons
- Special points: medians, centroid and perpendicular bisector of a segment
Two worked examples from the test
In un triangolo due angoli interni misurano e . Quanto misura il terzo angolo?
Solution
- La somma degli angoli interni di un triangolo vale sempre .
- Somma i due angoli noti: .
- Il terzo angolo è .
- L'errore tipico è fermarsi a , che è la somma dei due angoli dati e non il terzo angolo.
In un triangolo isoscele l'angolo al vertice misura . Quanto misura ciascun angolo alla base?
Solution
- In un triangolo isoscele gli angoli alla base sono congruenti fra loro.
- I due angoli alla base valgono insieme .
- Ciascuno vale quindi .
- L'errore classico è rispondere , dimenticando di dividere per due; il dimezza invece l'angolo al vertice, e il ripete il dato del testo.
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 · 74 KB, ready to print). You receive the solutions by email after taking it online.
Download the PDFWhat a maths test on Euclidean geometry looks like
Two or three proofs with the hypothesis and the conclusion stated, almost always resting on a congruence criterion, plus numerical exercises on the angles of triangles and polygons. What the teacher cares about is the chain of logic, not the drawing.
The mistake that costs the grade
Using as a hypothesis what you have to prove. The second most expensive mistake is invoking the wrong criterion: two sides and any angle are not enough — the angle must be the one between them, and whole proofs are lost on this.
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 study maths without stress — or we look at your results together: the diagnostic is free.