Egzamin Maturalny (Matura Poland) · Mathematics

Algebra, Functions, Geometry and Probability

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

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All 36 questions

Solve the equation $2 x + 5 = 17$ .
What is the value of $lo g_{2} 32$ ?
What is the slope of the line $y = - 3 x + 7$ ?
What is the sum of the interior angles of a hexagon?
An arithmetic sequence has $a_{1} = 3$ and common difference $r = 4$ . What is $a_{10}$ ?
What are the roots of $x^{2} - 5 x + 6 = 0$ ?
A right triangle has legs of length 5 and 12. How long is the hypotenuse?
What is $sin 3 0^{\circ}$ ?
What is the discriminant of $x^{2} - 4 x + 1$ ?
What is the vertex of the parabola $f (x) = x^{2} - 6 x + 5$ ?
What is the sum of the first five terms of the geometric sequence $2, 6, 18, \dots$ ?
Two fair dice are rolled. What is the probability that the sum is 7?
What is the median of the data set $2, 8, 3, 9, 4, 6$ ?
What is the distance between $A = (1, 2)$ and $B = (4, 6)$ ?
What is the midpoint of the segment with endpoints $(- 2, 4)$ and $(6, 10)$ ?
Which set of $x$ values satisfies $∣ x - 3∣ < 2$ ?
A circle has radius 5. What is its circumference?
In how many ways can a committee of 3 be chosen from 6 people when the order does not matter?
What is the domain of $f (x) = \frac{x + 3}{x - 1}$ ?
What is the derivative of $f (x) = x^{3} - 4 x$ ?
What is the value of $lo g 4 + lo g 25$ (base 10)?
What is the sum of the infinite geometric series $6 + 2 + \frac{2}{3} + \dots$ ?
What is the equation of the line through $(0, 1)$ and $(2, 5)$ ?
Which values of $x$ satisfy $x^{2} - x - 6 < 0$ ?
For an acute angle $α$ with $sin α = \frac{3}{5}$ , what is $cos α$ ?
A cone has base radius 3 and height 4. What is its volume?
A sequence is given by $a_{n} = 5 n - 2$ . What is the sum of its first 20 terms?
For which values of $m$ does $x^{2} - m x + 9 = 0$ have exactly one solution?
An urn holds 4 red and 6 blue balls. Two are drawn without replacement. What is the probability that both are the same colour?
What is the equation of the tangent line to $f (x) = x^{2}$ at $x = 3$ ?
What is the greatest value of $f (x) = - x^{2} + 4 x + 5$ on the interval $[3, 5]$ ?
In a geometric sequence $a_{2} = 6$ and $a_{5} = 162$ . What is $a_{1}$ ?
A triangle has two sides of length 7 and 8 with an angle of $6 0^{\circ}$ between them. How long is the third side?
The circle $x^{2} + y^{2} - 6 x + 4 y - 12 = 0$ has which centre and radius?
How many 3-digit numbers with all digits different are even?
What is the local minimum value of $f (x) = x^{3} - 3 x^{2}$ ?

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