Maturita (Czech Republic) · Mathematics

Mathematics for the Maturita

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

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All 36 questions

Solve the equation $3 x - 7 = 11$ .
What is the area of a circle with radius $5$ cm?
What is $2^{5} \cdot 2^{3}$ ?
What is the value of $sin 3 0^{\circ}$ ?
An arithmetic sequence has $a_{1} = 2$ and difference $d = 3$ . What is $a_{5}$ ?
What is $15%$ of $80$ ?
How many ways can $4$ different books be arranged in a row on a shelf?
Solve $x^{2} - 5 x + 6 = 0$ .
Solve the inequality $(x - 1) (x + 3) < 0$ .
Solve $∣2 x - 1∣ = 5$ .
Solve $lo g_{2} (x + 1) = 3$ .
A geometric sequence has $a_{1} = 3$ and ratio $q = 2$ . What is $a_{6}$ ?
What is the distance between the points $A (1, 2)$ and $B (4, 6)$ ?
What are the coordinates of the midpoint of $A (2, - 4)$ and $B (6, 8)$ ?
Find the equation of the line through $(0, 3)$ that is perpendicular to $y = 2 x + 1$ .
A committee of $2$ people is chosen from $5$ people. How many different committees are possible?
Two fair dice are rolled. What is the probability that the sum is $7$ ?
A right triangle has legs $6$ and $8$ . What is the sine of the angle opposite the side $6$ ?
What is the volume of a cone with radius $3$ and height $4$ ?
What is the slope of the tangent to $y = x^{2} - 3 x$ at $x = 2$ ?
What is the domain of $f (x) = \frac{x + 2}{x - 1}$ ?
The roots of $x^{2} + p x + 12 = 0$ are $3$ and $4$ . What is $p$ ?
Convert $15 0^{\circ}$ to radians.
What is the sum of the integers from $1$ to $20$ ?
What is the median of $2, 3, 3, 8, 9, 11$ ?
Solve $2^{x + 1} = 32$ .
A bank pays $5%$ interest per year, added once a year. What is the balance after $2$ years if you deposit $1000$ CZK?
Solve the system $x + y = 10$ , $x y = 21$ .
In a triangle $a = 10$ , $α = 3 0^{\circ}$ and $β = 4 5^{\circ}$ . What is the side $b$ ?
How many different arrangements are there of the letters of the word KAJAK?
An infinite geometric series has first term $6$ and sum $9$ . What is the ratio $q$ ?
Solve $lo g_{2} x + lo g_{2} (x - 2) = 3$ .
For which values of $k$ does $x^{2} + k x + 9 = 0$ have exactly one real root?
Solve $2 sin^{2} x = sin x$ for $x \in [0, 2 π)$ .
An urn holds $4$ white and $6$ black balls. Two are drawn without replacement. What is the probability that they have different colours?
The space diagonal of a cube is $12$ cm. What is the length of an edge?

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