Practice maths class test — Year 1: numbers, fractions and powers.
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
- Fractions, proportions and percentages
- Powers and the rules for exponents, including negative ones
- HCF, LCM and prime factorisation
- Scientific notation and orders of magnitude
- Sets and basic logic
The first maths test of Year 1 comes in October, when the class is still halfway through the chapter on numbers: the teacher uses it to see what is left of middle school before moving on to algebra. The test is almost always the same shape — two expressions with fractions and powers to simplify, an exercise on HCF and LCM, a part on scientific notation — and the marks are lost on three precise habits, not on theory.
The first: the minus sign in front of a power is not raised to the power unless it is inside brackets. −3² is −9, (−3)² is 9, and they are two different numbers from one exercise to the next in the same test. The second is about percentages: a 20% discount followed by a 20% increase does not give you back the starting price, because the second 20% is calculated on a base that is already smaller — on €100, −20% gives €80, and +20% of €80 gives €96, not €100. The third is about the LCM: you break each number into prime factors and, for each factor, take the highest exponent of the two — not the sum. LCM(12, 18) comes from 12 = 2²·3 and 18 = 2·3²: the result is 2²·3² = 36, not 2³·3³.
To prepare, do not revise the theory of powers in the abstract: do ten real expressions from your textbook, with the signs in front of the powers and not only inside them, and recheck every conversion into scientific notation by moving the decimal point by hand, digit by digit, before trusting the calculator.
Two worked examples from the test
Calcola la somma:
Solution
- Le frazioni si sommano solo se hanno lo stesso denominatore: cerco il mcm di e .
- e , quindi
- Riscrivo: e
- Sommo solo i numeratori:
- Attenzione: è l'errore più diffuso — numeratori e denominatori non si sommano fra loro.
Calcola il quoziente:
Solution
- Dividere per una frazione equivale a moltiplicare per la sua reciproca: si rovescia la seconda.
- Moltiplico:
- Semplifico dividendo per :
- Se si moltiplica direttamente si ottiene ; se si rovescia la prima frazione si ottiene .
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 · 77 KB, ready to print). You receive the solutions by email after taking it online.
Download the PDFWhat a maths test on fractions and powers looks like
Almost always two long expressions with fractions and powers to simplify down to a result, an exercise on HCF and LCM, and a short part on scientific notation and orders of magnitude. It is the first test of the year and it helps the teacher see what is left of middle school.
The mistake that costs the grade
Applying the rules of powers to a sum: 2³ + 2⁴ is not 2⁷, because the rules only hold for products, quotients and a power of a power. Right after that comes the negative exponent treated as a minus sign in front of the result.
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 the first maths test in Year 1 — or we look at your results together: the diagnostic is free.