Državna Matura (North Macedonia) · Mathematics

Mathematics for State Matura

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.

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In algebra, what are the real solutions to the quadratic equation $x^{2} - 7 x + 12 = 0$ ?
In algebra, what is the product of the roots of the quadratic equation $3 x^{2} - 11 x + 6 = 0$ ?
In algebra, what is the sum of the roots of the equation $2 x^{2} - 10 x + 7 = 0$ ?
In algebra, what is the discriminant of the quadratic equation $2 x^{2} - 4 x + 5 = 0$ ?
In algebra, for what value of $k$ does the equation $x^{2} - 6 x + k = 0$ have exactly one real root?
In algebra, what is the solution set of the linear inequality $4 - 2 x \geq 10$ ?
In algebra, what is the solution set of the absolute value inequality $∣2 x - 3∣ \leq 7$ ?
In algebra, what is the simplified form of $\frac{x ^{2} - 16}{x ^{2} - 4 x}$ for $x \neq = 0, 4$ ?
In algebra, what is the value of $x$ satisfying the exponential equation $3^{2 x - 1} = 27$ ?
In algebra, what is the value of $lo g_{3} (81)$ ?
In algebra, what is the value of $lo g_{5} (\frac{1}{125})$ ?
In algebra, what is the solution to $lo g_{2} (x - 2) = 4$ ?
In algebra, what is the simplified value of $lo g_{10} (25) + lo g_{10} (4)$ ?
In algebra, what is the 10th term of an arithmetic progression with first term $a_{1} = 3$ and common difference $d = 4$ ?
In algebra, what is the sum of the first 12 terms of an arithmetic sequence with $a_{1} = 2$ and common difference $d = 3$ ?
In algebra, what is the 6th term of a geometric sequence with first term $b_{1} = 3$ and common ratio $q = 2$ ?
In algebra, what is the sum of an infinite geometric series with first term $a_{1} = 8$ and common ratio $q = \frac{1}{2}$ ?
In analytic geometry, what is the distance between the points $A (1, 2)$ and $B (4, 6)$ ?
In analytic geometry, what are the coordinates of the midpoint of segment connecting $P (- 2, 5)$ and $Q (4, - 1)$ ?
In analytic geometry, what is the slope of the line passing through $(2, 3)$ and $(6, 11)$ ?
In analytic geometry, what is the slope of a line perpendicular to the line $y = - \frac{1}{3} x + 4$ ?
In analytic geometry, what is the equation of the line passing through $(0, 4)$ with slope $m = - 2$ ?
In analytic geometry, what is the center and radius of the circle given by $(x - 3)^{2} + (y + 2)^{2} = 25$ ?
In mathematics, what is the domain of the real-valued function $f (x) = 2 x - 6$ ?
In mathematics, what is the domain of the function $g (x) = \frac{1}{x ^{2} - 9}$ ?
In mathematics, what are the coordinates of the vertex of the parabola $y = x^{2} - 4 x + 7$ ?
In trigonometry, what is the exact value of $sin (3 0^{\circ}) + cos (6 0^{\circ})$ ?
In trigonometry, what is the exact value of $tan (4 5^{\circ}) + cos (0^{\circ})$ ?
In trigonometry, if $sin (α) = \frac{3}{5}$ and $α$ is acute, what is $cos (α)$ ?
In trigonometry, what is the simplified value of $sin^{2} (7 5^{\circ}) + cos^{2} (7 5^{\circ})$ ?
In trigonometry, what is the double-angle identity for $sin (2 α)$ ?
In trigonometry, what is the period of the function $f (x) = sin (3 x)$ ?
In calculus, what is the first derivative of $f (x) = 4 x^{3} - 5 x^{2} + 7 x - 9$ ?
In calculus, what is the derivative of $g (x) = sin (2 x)$ ?
In calculus, what is the slope of the tangent line to the curve $y = x^{2} - 3 x + 2$ at $x = 4$ ?
In calculus, at what value of $x$ does the function $f (x) = x^{3} - 3 x$ have a local minimum?
In calculus, what is the definite integral $\int_{0}^{3} (2 x + 1) d x$ ?
In calculus, what is the definite integral $\int_{1}^{2} 3 x^{2} d x$ ?
In probability, what is the probability of rolling a sum of 7 with two fair standard six-sided dice?
In combinatorics, how many different 3-person committees can be selected from a group of 8 people?
In combinatorics, what is the value of $\frac{6 !}{4 ! \cdot 2 !}$ ?
In combinatorics, how many distinct arrangements can be made using all letters of the word 'MAMA'?
In geometry, what is the area of a right-angled triangle with legs of length $6 cm$ and $8 cm$ ?
In geometry, what is the length of the hypotenuse of a right-angled triangle with legs 5 and 12?
In geometry, what is the sum of the interior angles of a regular hexagon?
In geometry, what is the measure of each interior angle of a regular octagon?
In geometry, what is the volume of a sphere with radius $r = 3 cm$ ?
In geometry, what is the total surface area of a cube with edge length $a = 4 cm$ ?
In geometry, what is the volume of a right circular cylinder with radius $r = 3$ and height $h = 5$ ?
In geometry, if the perimeter of an equilateral triangle is $18 cm$ , what is its area?
In vector algebra, what is the magnitude of the vector $v = (3, - 4)$ ?
In vector algebra, what is the dot product of $u = (2, 5)$ and $v = (- 3, 4)$ ?
In vector algebra, what condition must two nonzero vectors satisfy to be mutually perpendicular?
In algebra, what is the determinant of the $2 \times 2$ matrix $(4325)$ ?
In algebra, what is the solution for $x$ in $x + 5 = 4$ ?
In algebra, what is the value of $(2 + 3 i) (2 - 3 i)$ where $i = - 1$ ?
In algebra, what is the real part of the complex number $z = \frac{1}{1 + i}$ ?

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