1003034305
Level:
B
Let \( A=(-\infty;-4)\cup(2;+\infty) \) and \( B = [ 2;8 ) \). Give the intersection \( A'\cap B \).
\( \{2\} \)
\( \emptyset \)
\( (2;8) \)
\( [2;8) \)
B
1003034304
Level:
B
Given the sets \( A=(-\infty;-5] \), \( B=[-5;0) \) and \( C=(-7;-1) \), find \( A\setminus(B\cap C) \).
\( (-\infty;-5) \)
\( (-\infty;-5] \)
\( [-5;-1) \)
\( (-\infty;0) \)
1003034303
Level:
B
Let \( A=(-\infty;2] \), \( B=[-4;3) \) and \( C=(-\infty;2] \). Determine \( (A\cup B)\setminus C \).
\( (2;3) \)
\( [2;3) \)
\( (-\infty;-4) \)
\( (-\infty;3) \)
1003034302
Level:
B
Given the sets \( A=(-6;2] \), \( B=[-2;8) \) and \( C=(0;3] \), determine \( (A\cap B)\setminus C \).
\( [-2;0] \)
\( [-2;0) \)
\( [-6;8) \)
\( (-6;0)\cup(3;8) \)
1003034301
Level:
B
Given the sets \( A=(-1;+\infty) \) and \( B=[-3;6) \), find the intersection \( A'\cap B \).
\( [-3;-1] \)
\( [-1;6) \)
\( [-3;-1) \)
\( (-3;-1) \)
1003023207
Level:
B
In the past we were taught in a driving school that the steering wheel should be held in the position of „ten to two“. Give the degree measure of the angle between the hour hand and the minute hand which corresponds to this time.
\( 115^{\circ} \)
\( 120^{\circ} \)
\( 90^{\circ} \)
\( 105^{\circ} \)
1003023206
Level:
B
In a driving school we learn to hold the steering wheel in the position of „a quarter to three“. Determine the degree measure of the angle between the hour hand and the minute hand which corresponds to the mentioned time.
\( 172.5^{\circ} \)
\( 180^{\circ} \)
\( 165^{\circ} \)
\( 157.5^{\circ} \)
1003076810
Level:
B
Interior angles of a triangle \( ABC \) are in the ratio \( 2:3:4 \). A circle is inscribed into the triangle \( ABC \). Points of tangency divide the circle into three arcs. What is the ratio of the lengths of these arcs?
\( 5:6:7 \)
\( 4:5:6 \)
\( 2:3:4 \)
\( 3:4:5 \)
1003076808
Level:
B
In a triangle \( ABC \) the measure of \( \measuredangle CAB \) is \( 45^{\circ} \) and the measure of \( \measuredangle CBA \) is \( 60^{\circ} \). The altitude to side \( AB \) is \( 1\,\mathrm{cm} \) long. Calculate the area of the triangle \( ABC \) in \(\mathrm{cm}^2 \).
\( \frac{\sqrt3+1}{2\sqrt3} \)
\( \frac{\sqrt3+1}{\sqrt3} \)
\( \frac{\sqrt3+1}{2} \)
\( \frac{\sqrt3+1}{4} \)
1003027306
Level:
B
Evaluate the following indefinite integral on \( \left(3;\infty \right) \).
\[ \int\frac{x^2-5x+6}{x-3}\,\mathrm{d}x \]
\( \frac{x^2}2-2x+c\text{, }c\in\mathbb{R} \)
\( x-2+c\text{, }c\in\mathbb{R} \)
\( \frac{x^2}2+2x+c\text{, }c\in\mathbb{R} \)
\( \frac{x^2}2-x+c\text{, }c\in\mathbb{R} \)