Državna Matura (Croatia) · Mathematics

Mathematics: Advanced Functions, Geometry, Calculus and Probability

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

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In algebra, what is the solution set of the linear equation $3 (2 x - 5) + 4 = 5 x - 7$ over real numbers?
In coordinate geometry, what is the distance between the points $A (- 2, 3)$ and $B (4, - 5)$ in the Cartesian plane?
What is the exact value of the logarithmic expression $lo g_{2} (32) - lo g_{3} (81) + ln (e^{4})$ ?
In trigonometry, which value equals $sin (\frac{7 π}{6})$ ?
A geometric sequence has first term $a_{1} = 3$ and common ratio $r = 2$ . What is the sum of its first $6$ terms?
What is the derivative of the polynomial function $f (x) = 4 x^{3} - 5 x^{2} + 7 x - 9$ at $x = 2$ ?
In probability theory, what is the probability of rolling a sum of $7$ when throwing two fair standard six-sided dice?
What is the slope of the line perpendicular to the linear equation $2 x - 5 y + 10 = 0$ ?
Which interval represents the domain of the real-valued function $g (x) = 9 - x^{2}$ ?
What is the value of the definite integral $\int_{1}^{3} (3 x^{2} - 4 x + 1) d x$ ?
In plane geometry, what is the area of a triangle with side lengths $13$ , $14$ , and $15$ ?
What is the center and radius of the circle defined by the equation $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
Solve the exponential equation $4^{x + 1} = 8^{x - 1}$ for $x$ .
What is the scalar product (dot product) of the vectors $u = 3 i - 4 j$ and $v = 5 i + 2 j$ ?
In a right triangle, the hypotenuse is $c = 25$ and one leg is $a = 7$ . What is the sine of angle $α$ opposite to leg $a$ ?
What is the limit $lim_{x \to 0} \frac{s i n ( 4 x )}{3 x}$ ?
Which expression represents the inverse function $f^{- 1} (x)$ for $f (x) = \frac{2 x - 3}{x + 4}$ , where $x \neq = - 4$ ?
What is the complex conjugate of $z = \frac{5 + i}{2 - i}$ in standard rectangular form $a + bi$ ?
How many distinct permutations can be formed using all letters of the word 'ZAGREB'?
What is the solution of the absolute value inequality $∣2 x - 3∣ < 7$ ?
What is the volume of a right circular cone with base radius $r = 6 cm$ and height $h = 10 cm$ ?
What is the fundamental period of the trigonometric function $h (x) = 3 cos (4 x - π)$ ?
In an arithmetic progression, the 4th term is $15$ and the 9th term is $35$ . What is the common difference $d$ ?
At which point does the cubic curve $y = x^{3} - 3 x^{2} + 2$ achieve its local maximum?
What is the probability of obtaining at least one head when flipping $4$ fair coins?
What is the remainder when $P (x) = 2 x^{3} - 5 x^{2} + 3 x - 7$ is divided by $x - 2$ ?
What is the exact value of $cos (7 5^{\circ})$ using angle addition formulas?
What is the equation of the tangent line to the curve $y = x^{2} - 4 x + 5$ at $x = 3$ ?
What is the real solution of the logarithmic equation $lo g_{3} (x) + lo g_{3} (x - 2) = 1$ ?
In a box with $5$ red balls and $7$ green balls, two balls are drawn at random without replacement. What is the probability that both balls are red?
What is the area enclosed between the parabola $y = x^{2}$ and the horizontal line $y = 4$ ?
What is the sum of all interior angles of a convex polygon with $8$ sides (an octagon)?
What is the exact value of $tan (\frac{5 π}{4})$ ?
Which values of $k$ make the quadratic equation $x^{2} - 6 x + k = 0$ have two distinct real roots?
What is the magnitude of the 3D vector $w = 2 i - 3 j + 6 k$ ?
What is the horizontal asymptote of the rational function $f (x) = \frac{4 x ^{2} - 3 x + 1}{2 x ^{2} + 5 x - 7}$ as $x \to \infty$ ?
If the mean of five numbers $4, 8, x, 14, 18$ is $12$ , what is the value of $x$ ?
What is the solution of the trigonometric equation $2 sin (x) - 1 = 0$ on the interval $[0, 2 π)$ ?
What is the total surface area of a cube whose space diagonal measures $63 cm$ ?
What is the value of the binomial coefficient $(3 8)$ ?
What is the solution of the system of linear equations $2 x + 3 y = 13$ and $x - y = - 1$ ?
What is the sum of the infinite geometric series $12 + 6 + 3 + 1.5 + \dots$ ?
What is the second derivative $f^{''} (x)$ of $f (x) = e^{2 x} + sin (x)$ evaluated at $x = 0$ ?
What is the length of an arc subtended by a central angle of $6 0^{\circ}$ in a circle of radius $r = 9 cm$ ?
What is the standard deviation of the population consisting of numbers $2, 4, 4, 4, 5, 5, 7, 9$ ?
In vector algebra, what is the angle between the vectors $a = (1, 1)$ and $b = (0, 2)$ ?
What is the value of $x$ satisfying the exponential equation $3^{2 x - 1} = 27$ ?
What is the focus of the parabola given by $y^{2} = 12 x$ in coordinate geometry?
What is the value of the algebraic fraction $\frac{x ^{3} - 8}{x - 2}$ when evaluated at $x = 5$ ?
What is the acute angle of intersection between the line $y = x + 3$ and the x-axis?
What is the value of the definite integral $\int_{0}^{π /2} cos (x) d x$ ?
What is the coefficient of $x^{3}$ in the binomial expansion of $(x + 2)^{5}$ ?
What is the radius of the incircle of a right triangle with legs $6 cm$ and $8 cm$ ?
Given $lo g_{10} (2) \approx 0.3010$ , what is the approximate value of $lo g_{10} (5)$ ?
What is the maximum value of the quadratic function $f (x) = - 2 x^{2} + 8 x - 3$ ?
What is the derivative of $f (x) = ln (x^{2} + 1)$ with respect to $x$ ?
In how many ways can a committee of $3$ students be chosen from a group of $7$ students?
What is the length of the diagonal of a rectangle with length $12 cm$ and width $5 cm$ ?
What is the value of the limit $lim_{x \to 2} \frac{x ^{2} - 4}{x - 2}$ ?
What is the area of a regular hexagon with side length $s = 4 cm$ ?

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