Maturitná skúška (Slovakia) · Mathematics (Maturita)

Mathematics for the Slovak Maturita

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

Practise Mathematics for the Slovak Maturita now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 81 questions

What is the volume of a cylinder with radius 3 cm and height 5 cm?
Solve the inequality $2 x - 5 > 3$ .
Evaluate $lo g_{2} 40 - lo g_{2} 5$ .
The terms of the arithmetic sequence $4, 7, 10, \dots$ are added. How many terms give the sum 175?
What are the solutions of $x^{2} - 7 x + 10 = 0$ ?
1000 euros are invested at 5 percent compound interest per year. What is the amount after 2 years?
A line passes through $(0, - 2)$ and $(4, 6)$ . What is its equation?
In an arithmetic sequence $a_{3} = 7$ and $a_{7} = 19$ . What is $a_{10}$ ?
Find the intersection points of the line $y = x + 1$ and the circle $x^{2} + y^{2} = 13$ .
What is the domain of $f (x) = \frac{1}{x ^{2} - 9}$ ?
What is the midpoint of the segment with end points $A (- 2, 3)$ and $B (6, - 1)$ ?
Two fair dice are rolled. What is the probability that the sum is 7?
Simplify $(a^{2} b^{3}) (a^{4} b)$ .
Solve the equation $5 (x - 2) = 3 x + 4$ .
What is the sum of the interior angles of a pentagon?
Which line passes through $(2, 1)$ and is parallel to $y = 3 x - 1$ ?
A geometric sequence has $a_{1} = 2$ and common ratio $q = 3$ . What is $a_{5}$ ?
What are the coordinates of the vertex of $y = - x^{2} + 4 x - 1$ ?
In how many ways can the six different letters of the word SLOVAK be arranged in a row?
A triangle has sides 6 cm and 8 cm and the angle between them is $3 0^{\circ}$ . What is its area?
Solve the equation $x + 6 = x$ in the real numbers.
A circle has circumference $10 π$ cm. What is its area?
Solve the system $x + 2 y = 8$ , $3 x - y = 3$ .
What is the value of $8^{1/3}$ ?
A sphere is inscribed in a cube of edge 6 cm so that it touches all faces. What is the ratio of the sphere's volume to the cube's volume?
What is the distance between $A (1, 2)$ and $B (4, 6)$ ?
In a geometric sequence $a_{2} = 6$ and $a_{5} = 48$ . What is $a_{8}$ ?
In a triangle two sides are 3 cm and 5 cm and the angle between them is $12 0^{\circ}$ . How long is the third side?
How many different arrangements of the letters of the word BANANA are there?
What is the slope of the tangent to $f (x) = x^{2} + 4 x$ at $x = 1$ ?
A price of 120 euros is reduced by 25 percent, and the new price is then raised by 20 percent. What is the final price?
Solve $2 sin x = 1$ for $0^{\circ} \leq x < 36 0^{\circ}$ .
An urn holds 4 white and 6 black balls. Two balls are drawn without replacement. What is the probability that both are black?
A 5 m ladder stands 3 m from a wall. How high on the wall does it reach?
A committee of 3 people is chosen from 8 candidates. How many different committees are possible?
What is the median of the data 2, 3, 3, 5, 7, 8?
Six workers finish a job in 10 days. How long do 4 workers need if they work at the same rate?
What is the arithmetic mean of 2, 4, 6 and 8?
What is the domain of the function $f (x) = lo g_{3} (4 - x^{2})$ in the set of real numbers?
Solve the exponential equation $2^{2 x} - 5 \cdot 2^{x} + 4 = 0$ for $x \in R$ .
What is the sum of the infinite geometric series $6 + 3 + \frac{3}{2} + \frac{3}{4} + \dots$ ?
Determine the distance between the point $P (1, 4)$ and the line $4 x + 3 y - 1 = 0$ in the coordinate plane.
Evaluate the limit $lim_{x \to 0} \frac{s i n ( 5 x )}{2 x}$ .
A box contains 4 red balls and 6 green balls. Two balls are drawn simultaneously at random. What is the probability that both are red?
What is the derivative of the function $f (x) = \frac{x ^{2}}{x + 1}$ for $x \neq = - 1$ ?
In triangle $A B C$ , side $a = 5$ , side $b = 7$ , and the angle between them is $γ = 6 0^{\circ}$ . What is the length of side $c$ ?
Find the equation of the tangent line to the curve $y = x^{2} - 3 x + 1$ at the point where $x = 2$ .
How many distinct permutations can be formed from all letters of the word 'KORUNA'?
What is the modulus $∣ z ∣$ of the complex number $z = 3 - 4 i$ ?
Solve the logarithmic equation $lo g_{2} (x) + lo g_{2} (x - 2) = 3$ in $R$ .
What is the volume of a right circular cone with base radius $r = 6 cm$ and height $h = 10 cm$ ?
For what value of $k$ are the vectors $u = (2, k)$ and $v = (6, - 4)$ perpendicular?
Evaluate the definite integral $\int_{1}^{3} (3 x^{2} - 4 x + 1) d x$ .
What is the range of the function $f (x) = 3 sin (x) - 2$ for $x \in R$ ?
If the roots of the quadratic equation $x^{2} - 7 x + 10 = 0$ are $α$ and $β$ , what is the value of $α^{2} + β^{2}$ ?
How many subsets of all sizes does a set with 5 elements have?
Find the center and radius of the circle given by $x^{2} + y^{2} + 4 x - 8 y - 5 = 0$ .
What is the exact value of $cos (10 5^{\circ})$ using the sum-to-product or angle sum formulas?
Solve the inequality $\frac{x - 3}{x + 2} \geq 0$ in the set of real numbers.
In an arithmetic sequence, the 3rd term is 8 and the 7th term is 20. What is the common difference $d$ ?
Evaluate $\int_{0}^{π} sin (x) d x$ .
What is the maximum value of the quadratic function $f (x) = - 2 x^{2} + 8 x - 3$ ?
A committee of 3 people is chosen from a group of 5 men and 4 women. What is the probability that all 3 are women?
Find the acute angle between the lines $y = 3 x + 2$ and $y = 0$ (the x-axis).
What is the value of $lo g_{10} (25) + lo g_{10} (4)$ ?
If $f (x) = e^{2 x + 1}$ , what is $f^{''} (0)$ , the second derivative at $x = 0$ ?
Find the real solution to the equation $2 x + 7 = x + 2$ .
What is the total surface area of a cube whose volume is $64 cm^{3}$ ?
In how many ways can 4 boys and 3 girls sit in a row if all 3 girls must sit together?
What is the period of the function $f (x) = 5 cos (4 x - 1)$ ?
Determine the value of the parameter $m$ such that the line $y = 2 x + m$ is tangent to the parabola $y = x^{2}$ .
Evaluate the sum $\sum_{k = 1}^{5} (2 k - 1)$ .
What is the scalar projection of vector $a = (3, 4)$ onto vector $b = (1, 0)$ ?
For what real values of $x$ is the function $f (x) = x^{3} - 3 x$ strictly increasing?
What is the remainder when the polynomial $P (x) = x^{3} - 2 x^{2} + 4 x - 5$ is divided by $x - 2$ ?
What is the eccentricity $e$ of a circle?
If $tan θ = \frac{4}{3}$ and $θ$ is in the third quadrant, what is $sin θ$ ?
What is the area of the region enclosed by the parabola $y = 4 - x^{2}$ and the x-axis ( $y = 0$ )?
How many diagonal lines can be drawn in a regular convex hexagon?
Solve the equation $∣ x - 4∣ = ∣2 x + 1∣$ in $R$ .
Find the limit $lim_{x \to \infty} (1 + \frac{3}{x})^{2 x}$ .

Keep practising

More Maturitná skúška (Slovakia) topics

Slovak Language and Literature for the Maturita78 questions
History of Slovakia for the Maturita78 questions
Aritmetika a algebra49 questions
Funkcie a postupnosti6 questions
Planimetria, stereometria a vektory6 questions
Kombinatorika, pravdepodobnosť a štatistika6 questions

All Maturitná skúška (Slovakia) practice →

Ready for the full Maturitná skúška (Slovakia) test?

Take a mock test Maturitná skúška (Slovakia) hub