Bacalaureat Național (Romania) · Mathematics

Mathematics for the Bacalaureat

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 determinant of the matrix $A = (2134)$ ?
What is the modulus of the complex number $z = 3 + 4 i$ ?
What is $i^{2026}$ , where $i^{2} = - 1$ ?
What is the derivative of $f (x) = x^{3} e^{x}$ ?
How many ways can $4$ different books be arranged in a row on a shelf?
What is the sum of the roots of $x^{2} - 7 x + 10 = 0$ ?
What is the value of $\int_{0}^{1} (2 x + 1) d x$ ?
What is $lo g_{3} 81$ ?
What is the sum of the first $10$ terms of the arithmetic sequence $2, 5, 8, \dots$ ?
The function $f (x) = x^{3} - 12 x$ has a local minimum at which point?
Solve $x + 6 = x$ in the real numbers.
Which is the inverse of the matrix $A = (1325)$ ?
What is the sum of all roots of $z^{2} + 2 z + 5 = 0$ in the complex numbers, and what are the roots?
The probability that a student passes physics is $0.8$ and that another student passes it is $0.7$ , independently. What is the probability that both pass?
What is the equation of the tangent to $f (x) = x^{2} + 1$ at the point with abscissa $x = 1$ ?
What is the limit $lim_{x \to \infty} \frac{3 x ^{2} + x}{x ^{2} - 5}$ ?
How many diagonals does a convex polygon with $8$ sides have?
What is the value of $sin 15 0^{\circ} + cos 12 0^{\circ}$ ?
A function $f (x) = \frac{x - 1}{x + 2}$ is defined on its domain. What is its vertical asymptote and horizontal asymptote?
A composition is given by $f (x) = 2 x + 1$ and $g (x) = x^{2}$ . What is $(f \circ g) (3)$ ?
What is the area of the triangle with vertices $A (0, 0)$ , $B (4, 0)$ and $C (1, 3)$ ?
How many solutions does $cos x = \frac{1}{2}$ have in the interval $[0, 2 π)$ ?
On $R$ the operation $x * y = x y - 3 x - 3 y + 12$ is defined. What is $2 * 5$ ?
What is $lim_{n \to \infty} (1 + \frac{1}{n})^{n}$ ?
The first term of a geometric progression is $2$ and its third term is $18$ with positive ratio. What is the ratio?
Two vectors are $a = (1, 2)$ and $b = (3, - 1)$ . What is their dot product?
What is the domain of $f (x) = ln (x^{2} - 4)$ ?
How many three-digit numbers can be formed with the digits $1, 2, 3, 4, 5$ if no digit repeats?
For which real value of $m$ does the equation $x^{2} - m x + m + 3 = 0$ have a double root, with $m > 0$ ?
Let $f (x) = x^{3} - 3 x + 2$ . How many distinct real roots does $f$ have?
Compute $\int_{0}^{1} x e^{x} d x$ .
Matrix $A = (1011)$ . What is $A^{10}$ ?
The function $f (x) = \frac{x ^{2}}{x - 1}$ has an oblique asymptote. What is its equation?
On $R$ , $x * y = x y - 3 x - 3 y + 12$ . Which real number $e$ satisfies $x * e = x$ for all $x$ ?
In a class, $60$ students: $35$ study French, $30$ study German and $10$ study both. How many study neither?
A box has $5$ red and $3$ blue balls. Two are drawn without replacement. What is the probability that both are red?

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