Practice maths class test — Year 5: probability and geometry in space.
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.
Want to see the reasoning before you try? Look atthe interactive probability tree.
Test in ItalianThe questions of this simulator are in Italian, as in the real exam.
Programme covered by the test
- Discrete random variables and expected value
- Bernoulli trials and the binomial distribution
- Mean and variance of a binomial distribution
- Conditional probability, independence and Bayes
- Coordinates in space: distance and midpoint
- Equation of a sphere
- A plane in space: normal vector and point-to-plane distance
- Median, mean and standard deviation
Two worked examples from the test
Si lancia un dado equo a sei facce. Quanto vale il valore atteso del punteggio?
Solution
- Il valore atteso è la somma dei valori pesati per le rispettive probabilità, tutte pari a .
- Il risultato non è uno dei valori possibili, e non è un errore: il valore atteso è una media, non un esito.
- L'opzione lo arrotonda per difetto, come se dovesse essere un esito possibile; è la probabilità di ciascuna faccia, non il valore atteso.
Una variabile aleatoria assume i valori , e con probabilità rispettivamente , e . Quanto vale ?
Solution
- Le probabilità non sono uguali, quindi la media va pesata.
- Controllo preliminare utile: la somma delle probabilità deve fare , e infatti .
- L'opzione è la media aritmetica semplice dei tre valori: ignora che lo è di gran lunga il più probabile.
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 · 78 KB, ready to print). You receive the solutions by email after taking it online.
Download the PDFWhat a maths test on probability and space looks like
A discrete random variable with expected value and variance, a Bernoulli scheme with the binomial distribution, an exercise on conditional probability or Bayes, and on the geometry side a sphere, a plane in space and the point-to-plane distance.
The mistake that costs the grade
Applying the binomial to trials that are not independent or that do not have a constant probability of success. In geometry in space, mistaking the coefficients of the plane for a point: (a, b, c) is the normal vector, not a point of the plane.
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.