Free · Year 2 of high school · 50 minutes · 15 questions · no penalty

Practice mixed test — Year 2: the whole first term.

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

Radicals and rationalising
Linear systems (substitution, elimination, Cramer)
Quadratic equations, including with a parameter
Quadratic inequalities and inequalities with fractions
The line in the coordinate plane: gradient, parallel and perpendicular lines
The parabola: vertex, axis, intersections
Line and parabola: relative positions

Two worked examples from the test

Question 1 · Verifica mista — 2ª superiore · Radicali

Per quali valori di $x$ esiste il radicale $2 x - 6$ ?

A $x > 3$
B $x \leq 3$
C $x \geq 3$ correct answer
D $x \geq 6$

Solution

Indice pari: il radicando deve essere $\geq 0$ .
Risolvo $2 x - 6 \geq 0$ : $2 x \geq 6$ , quindi $x \geq 3$ .
Il valore $x = 3$ è ammesso, perché $0 = 0$ .
Errore tipico: dimenticare di dividere per $2$ oppure rendere la disuguaglianza stretta.

Question 2 · Verifica mista — 2ª superiore · Sistemi lineari

Risolvi con la regola di Cramer il sistema:

${3 x + 2 y = 7 x - 4 y = 7$

A $(3; 1)$
B $(- 3; 1)$
C $(3; - 1)$ correct answer
D $(- 1; 3)$

Solution

Determinante dei coefficienti: $D = 31 2 - 4 = 3 \cdot (- 4) - 2 \cdot 1 = - 14 .$
$D_{x} = 77 2 - 4 = 7 \cdot (- 4) - 2 \cdot 7 = - 42,$ quindi $x = \frac{D _{x}}{D} = \frac{- 42}{- 14} = 3 .$
$D_{y} = 3177 = 3 \cdot 7 - 7 \cdot 1 = 14,$ quindi $y = \frac{D _{y}}{D} = \frac{14}{- 14} = - 1 .$
Verifica: $3 \cdot 3 + 2 \cdot (- 1) = 7$ e $3 - 4 \cdot (- 1) = 7$ .
Errore tipico: sbagliare il segno di $D_{y}$ (colonna dei termini noti al posto di quella dei coefficienti di $y$ ).

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 · 80 KB, ready to print). You receive the solutions by email after taking it online.

Download the PDF

What a maths test on mixed test looks like

The Year 2 end-of-term test: radicals, a system, a quadratic equation including with a parameter, an inequality with fractions and a part of coordinate geometry on the line and the parabola, often with their relative positions.

The mistake that costs the grade

Treating the line and the parabola as two separate chapters: the question that nearly always closes the test is their relative position, and it is solved by setting them up as a system and looking at the discriminant. Anyone who does not connect the two leaves blank the exercise worth the most.

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 handle test anxiety — or we look at your results together: the diagnostic is free.

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