Državna Matura (Montenegro) · Mathematics (State Matura Montenegro)

Algebra, Functions, Geometry and Probability

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

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All 35 questions

Solve the equation $3 x - 7 = 11$ .
What is the value of $2^{3} \cdot 2^{4}$ written as a single power of 2?
What is the slope of the line $y = - 2 x + 5$ ?
Solve $x^{2} - 5 x + 6 = 0$ .
An arithmetic sequence has $a_{1} = 3$ and common difference $d = 2$ . What is the sum of its first 10 terms?
The first three terms of a geometric sequence are $2, 6, 18$ . What is the fifth term?
Evaluate $lo g_{2} 32 + lo g_{3} 9$ .
A right triangle has legs of length 9 and 12. What is its perimeter?
What is the value of $sin 3 0^{\circ} + cos 6 0^{\circ}$ ?
Find the derivative of $f (x) = x^{3} - 3 x$ .
What is the distance between the points $A (1, 2)$ and $B (4, 6)$ ?
Two fair dice are thrown. What is the probability that the sum is 7?
Solve the inequality $2 x - 3 > 7$ .
What is the volume of a cylinder with radius 3 and height 5?
What is the median of the data set $3, 5, 7, 9, 16$ ?
In how many ways can a committee of 2 people be chosen from 6 people?
Solve $∣ x - 3∣ = 4$ .
What is the sum of the interior angles of a hexagon?
Calculate $(2 + 3 i) (1 - i)$ , where $i^{2} = - 1$ .
Find the equation of the line through the points $(0, 1)$ and $(2, 5)$ .
A price of 80 euros is increased by 25 percent and the new price is then decreased by 20 percent. What is the final price?
Solve the system $x + y = 10$ and $x - y = 2$ .
What is the domain of the function $f (x) = x - 4$ ?
How many diagonals does a convex octagon have?
Evaluate $\int_{0}^{2} 3 x^{2} d x$ .
What are the coordinates of the vertex of the parabola $y = x^{2} - 4 x + 1$ ?
Solve the inequality $(x - 1) (x + 3) < 0$ .
The roots of $x^{2} - 5 x + 3 = 0$ are $x_{1}$ and $x_{2}$ . What is $x_{1}^{2} + x_{2}^{2}$ ?
In an arithmetic sequence $a_{3} = 7$ and $a_{8} = 22$ . What is the sum of the first 10 terms?
A rectangle has perimeter 40. What is the largest area it can have?
In a triangle two sides are 7 and 8 and the angle between them is $6 0^{\circ}$ . What is the length of the third side?
What is the area of the region between the graphs of $y = x$ and $y = x^{2}$ for $0 \leq x \leq 1$ ?
An urn holds 4 red and 6 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
Solve $lo g_{2} x + lo g_{2} (x - 2) = 3$ .
What is the equation of the tangent line to $y = x^{2}$ at the point where $x = 3$ ?

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