Bacalaureat Moldova · Bacalaureat Mathematics (English)

Algebra, Calculus, Geometry and Probability

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

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All 95 questions

Solve the linear equation $3 x - 7 = 11$ .
What are the roots of $x^{2} - 5 x + 6 = 0$ ?
What is the sum of the roots of $2 x^{2} - 3 x - 2 = 0$ ?
Solve the inequality $x^{2} - 4 x + 3 < 0$ .
What is the value of $lo g_{2} 8 + lo g_{3} 9$ ?
Solve $x + 6 = x$ in the real numbers.
In an arithmetic progression $a_{1} = 5$ and the common difference is $d = 3$ . What is $a_{10}$ ?
A geometric progression has $b_{1} = 2$ and ratio $q = 3$ . What is the sum of its first five terms?
What is the domain of $f (x) = \frac{x - 2}{x - 5}$ ?
Find the equation of the line through the points $A (1, 2)$ and $B (3, 8)$ .
Find the derivative of $f (x) = x^{5} - 3 x^{2} + 7$ .
Differentiate $f (x) = x^{2} e^{x}$ .
What is the local minimum value of $f (x) = x^{3} - 3 x^{2}$ ?
Evaluate $\int_{0}^{2} (2 x + 3) d x$ .
What is the area of the region under $y = x^{2}$ above the $x$ -axis between $x = 0$ and $x = 3$ ?
What is the value of $sin 3 0^{\circ} + cos 6 0^{\circ}$ ?
Solve $sin x = \frac{1}{2}$ for $x \in [0, 2 π)$ .
If $x$ is an acute angle and $sin x = \frac{3}{5}$ , what is $tan x$ ?
A right triangle has legs $6$ and $8$ . What is the length of the hypotenuse?
A triangle has sides $13$ , $14$ and $15$ . What is its area?
Find the centre and radius of the circle $x^{2} + y^{2} - 6 x + 4 y - 12 = 0$ .
A cone has base radius $3$ and height $4$ . What is its volume?
Two fair dice are rolled. What is the probability that the sum is $7$ ?
In how many ways can a committee of $2$ students be chosen from $6$ students?
A bag has $4$ red and $6$ blue balls. Two balls are drawn without replacement. What is the probability that both are red?
In an arithmetic progression $a_{3} = 7$ and $a_{8} = 22$ . What is the sum of the first ten terms?
What is the sum of the infinite geometric series $6 + 2 + \frac{2}{3} + \frac{2}{9} + \dots$ ?
For which values of $m$ does $x^{2} + m x + 9 = 0$ have exactly one real root (a double root)?
Find the equation of the tangent line to the graph of $f (x) = x^{2}$ at the point where $x = 3$ .
Compute $(2 + 3 i) (1 - i)$ , where $i^{2} = - 1$ .
What is the greatest value of $f (x) = - x^{2} + 4 x + 1$ ?
In triangle $A B C$ , $A B = 8$ , $A C = 5$ and $∠ A = 6 0^{\circ}$ . What is the length of $B C$ ?
A farmer has $40$ m of fencing for a rectangular pen. What is the greatest area the pen can have?
Solve the equation $2^{x + 1} = 16$ .
Solve $lo g_{3} (x - 1) = 2$ .
Evaluate $x \to \infty lim \frac{3 x ^{2} + x}{2 x ^{2} - 5}$ .
How many different arrangements of all the letters of the word MOLDOVA are there (the two O's are identical)?
What is the determinant of the matrix $(2134)$ ?
The function $f (x) = x^{3} - 12 x$ is defined on $[- 1, 4]$ . What is its greatest value on this interval?
In algebra, what are the real solutions to the quadratic equation $x^{2} - 9 x + 20 = 0$ ?
In algebra, what is the solution set of the logarithmic equation $lo g_{3} (x - 2) = 2$ ?
In algebra, what is the value of the finite arithmetic sum $S_{20} = \sum_{k = 1}^{20} (3 k + 1)$ ?
In algebra, what is the common ratio $q$ of a geometric progression where $b_{2} = 6$ and $b_{5} = 48$ ?
In algebra, what are all real values of $x$ satisfying the absolute value equation $∣2 x - 5∣ = 7$ ?
In algebra, what is the solution interval to the rational inequality $\frac{x - 3}{x + 2} \leq 0$ ?
In algebra, what is the value of the determinant $34 - 2 5$ ?
In algebra, what is the coefficient of $x^{3}$ in the binomial expansion of $(x + 2)^{5}$ ?
In algebra, what is the remainder when the polynomial $P (x) = 2 x^{3} - 5 x^{2} + 3 x - 7$ is divided by $x - 2$ ?
In algebra, what is the real solution to the exponential equation $4^{x + 1} - 2^{2 x} = 48$ ?
In calculus, what is the derivative of the rational function $f (x) = \frac{2 x - 1}{x + 3}$ with respect to $x$ ?
In calculus, what is the equation of the tangent line to the curve $f (x) = x^{3} - 2 x + 1$ at the point where $x = 1$ ?
In calculus, what is the value of the limit $lim_{x \to 0} \frac{s i n ( 5 x )}{2 x}$ ?
In calculus, what is the definite integral $\int_{0}^{2} (3 x^{2} - 4 x + 1) d x$ ?
In calculus, what are the coordinates of the local minimum point of $f (x) = 2 x^{3} - 3 x^{2} - 12 x + 5$ ?
In calculus, what is the area of the region bounded by $y = x^{2}$ and $y = 4$ ?
In calculus, what is the derivative of $g (x) = e^{x^{2} - 3 x}$ with respect to $x$ ?
In calculus, what is the value of the improper integral $\int_{1}^{\infty} \frac{1}{x ^{3}} d x$ ?
In calculus, what is the antiderivative $\int x cos (x) d x$ ?
In trigonometry, what is the exact value of $sin (\frac{7 π}{6})$ ?
In trigonometry, what are all solutions to the trigonometric equation $2 cos (x) - 1 = 0$ in $[0, 2 π)$ ?
In trigonometry, what is the simplified form of the identity $\frac{s i n ( 2 x )}{1 + c o s ( 2 x )}$ for all valid $x$ ?
In trigonometry, if $sin (α) = \frac{3}{5}$ with $α \in (\frac{π}{2}, π)$ , what is $cos (α)$ ?
In geometry, what is the length of the vector $v = (6, - 8)$ in the Cartesian plane?
In geometry, what is the dot product of the two vectors $a = (3, - 4)$ and $b = (5, 2)$ ?
In geometry, for which real value of parameter $m$ are the vectors $u = (m, 4)$ and $w = (2, - 6)$ orthogonal?
In geometry, what is the center and radius of the circle given by $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
In geometry, what is the distance from the point $P (2, 3)$ to the line $3 x + 4 y - 8 = 0$ ?
In geometry, in triangle $A B C$ , side $a = 5$ , side $b = 7$ , and angle $C = 6 0^{\circ}$ . What is side $c$ ?
In combinatorics, in how many distinct ways can a committee of 3 members be selected from 8 candidates?
In combinatorics, how many distinct 4-digit numbers can be formed using the digits ${1, 2, 3, 4, 5}$ without repetition?
In probability theory, what is the probability of rolling a sum of 8 when rolling two fair standard six-sided dice?
In probability theory, if events $A$ and $B$ are independent with $P (A) = 0.4$ and $P (B) = 0.5$ , what is $P (A \cup B)$ ?
In algebra, what is the modulus of the complex number $z = 3 - 4 i$ ?
In algebra, what is the value of $(1 + i)^{4}$ ?
In trigonometry, what is the fundamental period of the function $f (x) = cos (4 x)$ ?
In algebra, what is the domain of the function $f (x) = 16 - x^{2}$ in the real numbers?
In calculus, what is the limit $lim_{x \to \infty} \frac{4 x ^{3} - 2 x + 7}{2 x ^{3} + 5 x ^{2} - 1}$ ?
In calculus, what is the second derivative $f^{''} (x)$ of the function $f (x) = ln (x)$ for $x > 0$ ?
In geometry, what is the slope of the line perpendicular to $2 x - 5 y + 10 = 0$ ?
In algebra, what is the inverse function $f^{- 1} (x)$ of $f (x) = 3 x - 7$ ?
In trigonometry, what is the exact value of $cos (1 5^{\circ})$ ?
In calculus, what is the inflection point of the cubic polynomial $f (x) = x^{3} - 6 x^{2} + 9 x + 2$ ?
In geometry, what is the area of a circle whose circumference is $12 π$ ?
In calculus, what is the integral $\int \frac{2 x}{x ^{2} + 4} d x$ ?
In algebra, what is the sum of the solutions to the equation $x^{2} - 14 x + 45 = 0$ ?
In geometry, what is the volume of a right circular cone with base radius $3$ and height $5$ ?
In probability theory, what is the probability of obtaining at least one head in 3 consecutive fair coin flips?
In calculus, what is the value of the limit $lim_{x \to 0} \frac{e ^{3 x} - 1}{x}$ ?
In geometry, what is the angle between the vectors $u = (1, 1)$ and $v = (0, 2)$ ?
In algebra, what is the solution to the system of equations $2 x + 3 y = 12$ and $x - y = 1$ ?
In calculus, what is the derivative of $f (x) = arctan (3 x)$ with respect to $x$ ?
In geometry, what is the area of a triangle with side lengths $13$ , $14$ , and $15$ ?
In combinatorics, how many subsets does a set containing 6 distinct elements possess?
In algebra, what is the sum of all integers that satisfy $- 3 \leq 2 x - 1 < 7$ ?
In calculus, what is the maximum value of $f (x) = - x^{2} + 6 x - 4$ on the interval $[0, 5]$ ?

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