Mathematics for Management -- Supplementary Electronic Materials

Quiz: Numbers & Inequalities

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1. To which number systems does the number \( 2 + \sqrt{2} \) belong?

\( \mathbb{N}_0 \) \( \mathbb{Z} \) \( \mathbb{Q} \) \( \mathbb{R} \)

2. To which number systems does the number \( \frac{7}{4} \) belong?

\( \mathbb{N}_0 \) \( \mathbb{Z} \) \( \mathbb{Q} \) \( \mathbb{R} \setminus \mathbb{Q} \)

3. Which of the following inequalities is correct?

\( \frac{13}{7} < \frac{9}{3} \) \( \frac{13}{7} > \frac{19}{3} \) \( \frac{5}{2} < \frac{2}{5} \) \( \frac{15}{7} > \frac{9}{3} \)

4. Which of the following numbers has the smallest distance from the number \( 0 \) on the number ray?

\( 0.12 \) \( -5.65 \) \( -9 \) \( 0.2 \)

5. If \(-5 > a\) and \(a > b\), then \(-5\) is

less than \( a \) equal to \( b \) greater than \( a \) less than \( b \)

6. The set of solutions of the equation \(|x| = x\) is

\( (0, \infty) \) \( (-\infty, \infty) \) \( \{ 0 \} \) \( [0, \infty) \)

7. Find all values of \(a\) and \(b\) for which \(0\) is a solution of the equation \(2x-b = ax\).

\( a \in \mathbb{R} \), \( b = 0 \) \( a \neq 2 \), \( b = 0 \) \( a = 0 \), \( b = 0 \) \( a \neq 0 \), \( b = 0 \)

8. Solve \(11x - 9 \leq 15x + 3\).

\( x \geq \frac{6}{13} \) \( x \geq \frac{3}{13} \) \( x \geq -1 \frac{1}{2} \) \( x \geq -3 \)

9. Solve \(x^2 + 5x - 6 = 0\).

\( x = -1 \), \( x = 6 \) \( x = 1 \) \( x = 1 \), \( x = -6 \) \( x = 6 \)

10. When factorizing \(x^2 - 4x + 4 = 20\) what goes in the blank? \( (x-\underline{\phantom{uu}})^2 = 20 \).

\( 4 \) \( 8 \) \( 2 \) \( 20 \)

Your grade is: __ of 10

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Solution: 1d; 2c; 3a; 4a; 5c; 6d; 7a; 8d; 9c; 10c

Here, a, b, c, d indicate the 1st, 2nd, 3rd, and 4th answer choice, respectively, for the numbered questions.