Maturità / Esame di Stato (Italy) · Mathematics

Mathematics for the Esame di Stato

36 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 36 questions

What is the derivative of $f (x) = x^{3} - 6 x^{2} + 5$ with respect to $x$ ?
What are the solutions of $x^{2} - 7 x + 12 = 0$ ?
What is the value of $lo g_{2} 32$ ?
What is $lim_{x \to 0} \frac{s i n x}{x}$ ?
What is the slope of the line through $A (1, 2)$ and $B (4, 11)$ ?
What is the integral $\int 2 x d x$ (with constant $C$ )?
A fair six-sided die is rolled once. What is the probability of an even number greater than $2$ ?
What is the sum of the interior angles of a convex hexagon?
Which of these is the equation of a circle with centre $(2, - 1)$ and radius $3$ ?
What is the derivative of $f (x) = x ln x$ for $x > 0$ ?
For which value of $k$ does $x^{2} + k x + 9 = 0$ have exactly one real solution with $k > 0$ ?
What is the value of $\int_{0}^{1} (3 x^{2} + 2 x) d x$ ?
The function $f (x) = x^{3} - 3 x$ has a local maximum at which $x$ ?
A geometric sequence has first term $3$ and ratio $2$ . What is its fifth term?
What is $sin \frac{π}{6} + cos \frac{π}{3}$ ?
How many ways can $3$ different books be chosen from $6$ different books when the order does not matter?
What is the domain of $f (x) = \frac{x - 1}{x - 4}$ ?
Which line is tangent to $y = x^{2}$ at the point $(2, 4)$ ?
What is the length of the vector $v = (3, - 4)$ ?
A shirt costs $80$ euro after a price rise of $25%$ . What was its price before the rise?
Which statement about the function $f (x) = e^{x}$ is correct?
Solve $2^{x + 1} = 32$ .
What is the area enclosed between $y = x$ and $y = x^{2}$ for $0 \leq x \leq 1$ ?
A rectangular box has sides $3$ , $4$ and $12$ . What is the length of its space diagonal?
Two events $A$ and $B$ are independent with $P (A) = 0.4$ and $P (B) = 0.5$ . What is $P (A \cap B)$ ?
What is the remainder when $x^{3} - 2 x + 5$ is divided by $x - 2$ ?
Which of these functions is even?
What is the distance between the points $(1, 2)$ and $(4, 6)$ ?
The function $f (x) = x^{3} - 3 x^{2} + k$ has a local minimum value of $- 2$ . What is $k$ ?
Evaluate $\int_{0}^{π} x sin x d x$ .
The sum of the first $n$ terms of an arithmetic sequence is $S_{n} = 3 n^{2} + 2 n$ . What is the common difference?
Three fair coins are tossed. Given that at least one shows heads, what is the probability that exactly two show heads?
For which values of $m$ does the line $y = m x + 1$ meet the parabola $y = x^{2}$ in two distinct points?
The function $f (x) = \frac{x ^{2} - 1}{x - 1}$ is extended at $x = 1$ so that it is continuous. What value must be assigned to $f (1)$ ?
A cylinder has volume $54 π$ and height equal to twice its radius. What is its radius?
A function satisfies $f^{'} (x) = 6 x - 4$ and $f (1) = 3$ . What is $f (2)$ ?

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