Matura Shtetërore (Albania) · Mathematics (Matura Shteterore)

Mathematics for the Matura Shtetërore

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

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

All 41 questions

The roots of $x^{2} - 6 x + k = 0$ are such that one root is twice the other. What is $k$ ?
Solve the inequality $(x - 1) (x + 3) < 0$ .
What is the minimum value of $f (x) = x^{2} - 6 x + 11$ ?
Find all real solutions of $2^{2 x} - 5 \cdot 2^{x} + 4 = 0$ .
A right triangle has legs of 6 cm and 8 cm. How long is the hypotenuse?
What is the sum of the interior angles of a convex hexagon?
What is the distance from the point $(1, 2)$ to the line $3 x + 4 y - 5 = 0$ ?
Differentiate $f (x) = x e^{x}$ .
Solve the system $x + y = 7$ , $x - y = 1$ .
What is the slope of the tangent to $y = x^{2} - 3 x$ at $x = 2$ ?
What is the arithmetic mean of the data 4, 8, 6, 10, 12?
What is the inverse function of $f (x) = 3 x - 6$ ?
If $sin α = \frac{3}{5}$ and $α$ is acute, what is $cos 2 α$ ?
A rectangle has perimeter 40 cm. What is the largest area it can have?
What is the value of $sin 3 0^{\circ}$ ?
A triangle has sides 13 cm, 14 cm and 15 cm. What is its area?
Evaluate $\int_{0}^{2} 3 x^{2} d x$ .
Solve the equation $3 x - 7 = 11$ .
Solve $lo g_{2} (x + 1) = 4$ .
In how many ways can 2 students be chosen from a group of 6 (order does not matter)?
A bag holds 2 red and 3 blue balls. Two balls are drawn without replacement. What is the probability that both are red?
What is the maximum value of $f (x) = x^{3} - 12 x$ on the interval $[- 3, 3]$ ?
What are the roots of $x^{2} - 5 x + 6 = 0$ ?
Find the area enclosed between the curves $y = x$ and $y = x^{2}$ .
If $f (x) = 2 x + 1$ and $g (x) = x^{2}$ , what is $f (g (3))$ ?
What is the horizontal asymptote of $f (x) = \frac{2 x + 1}{x - 3}$ ?
What is the discriminant of $2 x^{2} - 4 x + 5 = 0$ , and what does it tell you?
Solve $∣2 x - 3∣ = 7$ .
For which values of $m$ does $x^{2} + m x + 9 = 0$ have exactly one (double) real root?
Find $\int (6 x^{2} + 2) d x$ .
The roots of $2 x^{2} - 7 x + 3 = 0$ are $x_{1}$ and $x_{2}$ . What is $x_{1} + x_{2}$ ?
An arithmetic sequence has first term 5 and common difference 3. What is the 10th term?
What is the volume of a cone with base radius 3 cm and height 4 cm?
A fair six-sided die is rolled once. What is the probability of an even number?
What is the derivative of $f (x) = 4 x^{3} - 2 x$ ?
What is the domain of $f (x) = x - 2$ ?
In a triangle, two sides are 5 cm and 8 cm and the angle between them is $6 0^{\circ}$ . How long is the third side?
What is the sum of the infinite geometric series $8 + 4 + 2 + 1 + \dots$ ?
Solve $sin x = \frac{1}{2}$ for $0 \leq x \leq 2 π$ .
What is the sum of the first 5 terms of the geometric sequence $3, 6, 12, \dots$ ?
What are the centre and radius of the circle $(x - 2)^{2} + (y + 1)^{2} = 25$ ?

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