Free · Year 1 of high school · 50 minutes · 15 questions · no penalty

Practice maths class test — Year 1: monomials, polynomials and special products.

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.

Test prepared by Gaetano Livornese · Aerospace engineer, Politecnico di Milano · maths and physics tutor · updated 13 October 2026

Programme covered by the test

Monomials: operations, degree and like monomials
Polynomials: sum, product and degree
Special products (square and cube of a binomial, sum times difference)
Division of polynomials and Ruffini’s rule
Expressions in algebra

Two worked examples from the test

Question 1 · Monomi, polinomi e prodotti notevoli · Monomi e polinomi

Calcola il prodotto dei due monomi:

$(- 3 a^{2} b) \cdot (4 a b^{3})$

A $12 a^{3} b^{4}$
B $- 12 a^{3} b^{4}$ correct answer
C $- 12 a^{2} b^{3}$
D $a^{3} b^{4}$

Solution

Moltiplica i coefficienti: $(- 3) \cdot 4 = - 12$ .
Somma gli esponenti di $a$ : $2 + 1 = 3$ .
Somma gli esponenti di $b$ : $1 + 3 = 4$ .
Risultato: $- 12 a^{3} b^{4}$ .

Question 2 · Monomi, polinomi e prodotti notevoli · Monomi e polinomi

Sviluppa il prodotto:

$(2 x - 3) (x^{2} + 4 x - 1)$

A $2 x^{3} + 5 x^{2} - 14 x + 3$ correct answer
B $2 x^{3} + 11 x^{2} - 14 x + 3$
C $2 x^{3} + 5 x^{2} - 14 x - 3$
D $2 x^{3} + 5 x^{2} - 10 x + 3$

Solution

Moltiplica $2 x$ per ogni termine: $2 x^{3} + 8 x^{2} - 2 x$ .
Moltiplica $- 3$ per ogni termine: $- 3 x^{2} - 12 x + 3$ .
Riduci i simili: $8 x^{2} - 3 x^{2} = 5 x^{2}$ .
E ancora: $- 2 x - 12 x = - 14 x$ .
Risultato: $2 x^{3} + 5 x^{2} - 14 x + 3$ .

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 PDF

What a maths test on monomials and special products looks like

An expression with monomials and polynomials to reduce, the special products used both forwards and backwards, and a division of polynomials with Ruffini’s rule or long division. The question usually also asks for the degree of the result.

The mistake that costs the grade

Expanding (a − b)² as a² − b², losing the double product and its sign. It works the other way round too: faced with a trinomial you do not spot the square and you lose the part that would have been free.

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 prepare for a maths test in Year 1 — or we look at your results together: the diagnostic is free.

Book the free diagnostic call The other Year 1 tests