Centralizētie Eksāmeni (Latvia) · Mathematics

Mathematics for Centralizētie eksāmeni

57 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 57 questions

In algebra, what are the solutions of the quadratic equation $x^{2} - 9 x + 14 = 0$ ?
In algebra, what is the value of the logarithmic expression $lo g_{2} (64)$ ?
In algebra, what is the solution set of the linear inequality $5 - 3 x < 14$ ?
In algebra, what is the 8th term of an arithmetic progression with first term $a_{1} = 4$ and common difference $d = 3$ ?
In algebra, what is the 5th term of a geometric sequence with first term $b_{1} = 5$ and common ratio $q = 2$ ?
In algebra, what is the natural domain of the function $f (x) = 3 x - 12$ ?
In algebra, what is the sum of the solutions of the equation $3 x^{2} - 15 x + 8 = 0$ ?
In algebra, what is the solution of the exponential equation $3^{x + 2} = 81$ ?
In algebra, what is the solution of the logarithmic equation $lo g_{5} (2 x - 1) = 2$ ?
In trigonometry, what is the exact value of $sin (6 0^{\circ}) \cdot cos (3 0^{\circ})$ ?
In trigonometry, which identity represents $sin (2 α)$ ?
In trigonometry, what is the fundamental period of the cosine function $f (x) = cos (x)$ ?
In trigonometry, what are the real solutions to the equation $cos (x) = 1$ ?
In trigonometry, what is the value of $tan (π /4)$ ?
In calculus, what is the derivative of $f (x) = 2 x^{3} - 5 x + 7$ with respect to $x$ ?
In calculus, what is the derivative of the natural logarithm function $f (x) = ln (4 x)$ for $x > 0$ ?
In calculus, what is the slope of the tangent line to $y = x^{3}$ at the point $x = 2$ ?
In calculus, what is the critical point of $f (x) = x^{2} - 8 x + 15$ ?
In calculus, what is the value of the definite integral $\int_{0}^{2} (3 x^{2} + 1) d x$ ?
In calculus, what is the indefinite integral $\int e^{2 x} d x$ ?
In geometry, what is the area of a triangle with base $b = 10$ and corresponding height $h = 7$ ?
In geometry, what is the hypotenuse of a right triangle with legs $8$ and $15$ ?
In geometry, what is the sum of the interior angles of a convex pentagon (5 sides)?
In geometry, what is the area of a square whose diagonal has length $d = 62$ ?
In geometry, what is the area of a circle with radius $r = 6$ ?
In geometry, what is the length of an arc of a circle with radius $r = 9$ subtending a central angle of $6 0^{\circ}$ ?
In geometry, what is the area of a parallelogram with sides $a = 6$ , $b = 8$ , and included angle $3 0^{\circ}$ ?
In geometry, what is the median of a trapezoid with parallel bases of lengths $7$ and $13$ ?
In coordinate geometry, what is the distance between the points $P (2, 3)$ and $Q (5, 7)$ ?
In coordinate geometry, what is the midpoint of the segment connecting $A (- 2, 6)$ and $B (4, - 2)$ ?
In vector algebra, what is the scalar product of $a = (3, 4)$ and $b = (2, - 1)$ ?
In vector algebra, what is the magnitude (length) of the vector $v = (6, - 8)$ ?
In stereometry, what is the volume of a right circular cone with base radius $r = 3$ and height $h = 7$ ?
In stereometry, what is the volume of a sphere with radius $r = 3$ ?
In stereometry, what is the total surface area of a cylinder with radius $r = 2$ and height $h = 5$ ?
In probability theory, what is the probability of obtaining two heads when tossing two fair coins?
In combinatorics, how many ways can 3 students be chosen from a group of 6 for a competition?
In statistics, what is the arithmetic mean of the dataset ${4, 7, 10, 11, 18}$ ?
In algebra, what is the solution of the linear system ${x + y = 10, x - y = 4}$ ?
In algebra, what is the simplified form of $\frac{x ^{2} - 16}{x - 4}$ for $x \neq = 4$ ?
In algebra, what are the vertical asymptotes of the rational function $f (x) = \frac{1}{x ^{2} - 4}$ ?
In algebra, what is the value of $1 6^{3/4}$ ?
In trigonometry, what is the value of $sin^{2} (7 5^{\circ}) + cos^{2} (7 5^{\circ})$ ?
In calculus, what is the derivative of $f (x) = sin (3 x)$ ?
In calculus, what is the local minimum value of $f (x) = x^{2} - 4 x + 9$ ?
In geometry, what is the volume of a cube with total surface area equal to $54$ ?
In coordinate geometry, what is the slope of the line perpendicular to $y = 2 x + 5$ ?
In geometry, what is the radius of the inscribed circle in a right triangle with legs $6$ and $8$ and hypotenuse $10$ ?
In probability theory, what is the probability of rolling a sum of 7 with two fair standard dice?
In algebra, what is the sum of an infinite geometric series with $b_{1} = 6$ and $q = \frac{1}{3}$ ?
In algebra, what is the solution of $∣2 x - 3∣ = 7$ ?
In trigonometry, what is $cos (π)$ ?
In calculus, what is the area bounded by the curve $y = 3 x^{2}$ , the x-axis, and the vertical lines $x = 0$ and $x = 2$ ?
In stereometry, what is the volume of a regular square pyramid with base side $a = 6$ and height $h = 5$ ?
In algebra, what is the inverse function of $f (x) = 2 x - 6$ ?
In combinatorics, how many distinct 3-digit numbers can be formed using digits ${1, 2, 3, 4, 5}$ without repetition?
In geometry, if two similar triangles have a linear scale ratio of $1 : 3$ , what is the ratio of their areas?

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