Državna Matura (Croatia) · Mathematics

Mathematics: Algebra, Functions, Geometry, Calculus and Probability

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

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All 36 questions

A sum of $1000$ euros earns compound interest of $10%$ per year. What is the amount after $2$ years?
A price of $100$ euros is reduced by $20%$ and the new price is then increased by $20%$ . What is the final price?
The function $f (x) = x^{3} - 3 x$ has a local minimum at which value of $x$ ?
What is the sum of the interior angles of a hexagon?
The tangent to the parabola $y = x^{2}$ at the point where $x = 3$ meets the $x$ -axis. At what $x$ -value?
What is the area of the region enclosed by the graphs of $y = x^{2}$ and $y = x$ ?
What are the coordinates of the vertex of the parabola $y = x^{2} - 4 x + 7$ ?
For which values of $k$ does $x^{2} + k x + 9 = 0$ have exactly one real solution?
Solve $∣2 x - 1∣ = 5$ .
Solve $lo g_{2} x + lo g_{2} (x - 2) = 3$ .
Two fair dice are thrown. What is the probability that the sum is $7$ ?
What is the volume of a cone with base radius $3$ and height $4$ ?
What is the area of a circle with radius $5$ ?
What is $lo g_{10} 1000$ ?
If $sin x = \frac{3}{5}$ and $x$ is an acute angle, what is $cos x$ ?
What is $2^{3} \cdot 2^{4}$ ?
Solve the equation $3 x - 7 = 11$ .
A bag holds $3$ red and $5$ blue balls. Two balls are drawn without replacement. What is the probability that they have different colours?
Which line passes through $(2, 1)$ and is parallel to $y = 3 x + 1$ ?
What is $15 0^{\circ}$ in radians?
What is the distance between the points $(1, 2)$ and $(4, 6)$ ?
Solve $2^{x + 1} = 16$ .
A sphere is inscribed in a cube of edge $6$ . What volume of the cube lies outside the sphere?
An arithmetic sequence has $a_{1} = 5$ and $a_{4} = 14$ . What is $a_{10}$ ?
Solve the inequality $3 - 2 x > 7$ .
Solve $x^{2} - 5 x + 6 = 0$ .
What is the exact value of $sin 3 0^{\circ}$ ?
An infinite geometric series has first term $12$ and sum $18$ . What is the common ratio?
Evaluate $\int_{0}^{2} 3 x^{2} d x$ .
What is $20%$ of $250$ ?
Solve the system $x + y = 10$ and $x - y = 4$ .
An open box is made from a square sheet of side $12$ cm by cutting a square of side $x$ from each corner and folding up the sides. For which $x$ is the volume largest, and what is it?
A right triangle has legs of length $6$ and $8$ . What is the length of the hypotenuse?
If $tan x = 2$ , what is $sin 2 x$ ?
In how many ways can a committee of $3$ be chosen from $8$ people?
What is the sum of the first $5$ terms of the geometric sequence $3, 6, 12, \dots$ ?

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