Free · Year 4 of high school · 50 minutes · 15 questions · no penalty

Practice maths class test — Year 4: exponentials and logarithms.

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

Powers with real exponents and the exponential function
Definition of a logarithm and change of base
The laws of logarithms
Exponential equations
Logarithmic equations and domain restrictions
Exponential and logarithmic inequalities
Graphs of exponentials and logarithms and their transformations

Two worked examples from the test

Question 1 · Esponenziali e logaritmi · Esponenziali: proprietà e grafici

Quanto vale $(2^{3})^{3} ?$

A $2^{23}$
B $8$ correct answer
C $6$
D $9$

Solution

Passo 1 — Potenza di potenza. Elevando una potenza a un altro esponente gli esponenti si moltiplicano, anche se irrazionali:

$(2^{3})^{3} = 2^{3 \cdot 3}$

Passo 2 — Calcolo l'esponente. $3 \cdot 3 = 3$ .

Passo 3 — Concludo.

$2^{3} = 8$

Chi risponde $2^{23}$ ha sommato gli esponenti invece di moltiplicarli; $6$ nasce dal moltiplicare la base per l'esponente.

Question 2 · Esponenziali e logaritmi · Esponenziali: proprietà e grafici

Qual è l'equazione dell'asintoto orizzontale della funzione $y = 3^{x - 1} - 4$ ?

A $y = 0$
B $y = 4$
C $x = 1$
D $y = - 4$ correct answer

Solution

Passo 1 — Grafico di partenza. $y = 3^{x}$ ha asintoto orizzontale $y = 0$ .

Passo 2 — Traslazione orizzontale. $3^{x - 1}$ sposta il grafico di 1 unità verso destra: l'asintoto resta $y = 0$ .

Passo 3 — Traslazione verticale. Il $- 4$ abbassa tutto di 4 unità, quindi l'asintoto diventa

$y = - 4$

Passo 4 — Verifica. Per $x \to - \infty$ si ha $3^{x - 1} \to 0$ e quindi $y \to - 4$ .

Un esponenziale non ha mai asintoti verticali, quindi $x = 1$ è da escludere a priori.

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

Download the PDF

What a maths test on exponentials and logarithms looks like

Laws of logarithms applied backwards to condense an expression, a change of base, exponential equations that reduce to the same base or are solved with logarithms, logarithmic equations with the domain restrictions and at least one inequality.

The mistake that costs the grade

Writing log(a + b) as log a + log b: the logarithm splits a product, not a sum. In inequalities, not reversing the sign when the base is between 0 and 1 — and solving logarithmic equations without the domain, accepting negative arguments.

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 other Year 4 test, on trigonometric functions — or we look at your results together: the diagnostic is free.

Book the free diagnostic call The other Year 4 tests