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1003067803

Level:

For

x \in (1; 2)

choose the correct form of the equation

| 2 x^{2} - 5 x - 7 | = | x^{2} - 3 x + 1 |

that does not contain an absolute value.

- 2 x^{2} + 5 x + 7 = - x^{2} + 3 x - 1

2 x^{2} - 5 x - 7 = - x^{2} + 3 x - 1

2 x^{2} + 5 x + 7 = x^{2} - 3 x + 1

- 2 x^{2} + 5 x + 7 = x^{2} - 3 x + 1

1003067802

Level:

For

x \in (- \infty; 3)

choose the correct form of the equation

| x^{2} - 9 x + 20 | = 1

that does not contain an absolute value.

x^{2} - 9 x + 20 = 1

- x^{2} + 9 x - 20 = 1

x^{2} - 9 x + 20 = - 1

x^{2} + 9 x - 20 = 1

1103067801

Level:

Given the graph of the function

f (x) = x^{2} + 2 x - 4

, find the solution set of the following equation.

| x^{2} + 2 x - 4 | = 4

{- 4; - 2; 0; 2}

{- 4; 2}

{- 4; 0; 2}

{- 1 - \sqrt{5}; - 1 + \sqrt{5}}

1003041603

Level:

There are

30

students in a class, of them are

14

girls and the rest are boys. The teacher selects two students for weekly routine help. If selection is done at random, what is the probability that these students are not two girls? Round the result to two decimal places.

\frac{(\binom{16}{2}) + (\binom{16}{1}) \cdot (\binom{14}{1})}{(\binom{30}{2})} ≐ 0.79

\frac{(\binom{16}{2})}{(\binom{30}{2})} ≐ 0.28

\frac{(\binom{14}{2})}{(\binom{30}{2})} ≐ 0.21

\frac{(\binom{16}{1}) \cdot (\binom{14}{1})}{(\binom{30}{2})} ≐ 0.51

1003041602

Level:

A box contains

50

transistors and

4

of them are lower quality. From all transistors

5

are selected at random for inspection. What is the probability that of lower quality is at most one of the selected transistors? Round the result to two decimal places.

\frac{(\binom{46}{5}) + (\binom{46}{4}) \cdot (\binom{4}{1})}{(\binom{50}{5})} ≐ 0.96

\frac{\frac{46!}{41!} + \frac{46!}{42!}}{\frac{50!}{45!}} ≐ 0.66

\frac{(\binom{46}{5}) + (\binom{46}{4})}{(\binom{50}{5})} ≐ 0.72

\frac{\frac{46!}{41!} + \frac{46!}{42!} \cdot \frac{4!}{3!}}{\frac{50!}{45!}} ≐ 0.71

1003049204

Level:

Let

f (x) = | x |

. Identify which of the statements is false.

\forall a, b \in R : f (a + b) = f (a) + f (b)

\forall a, b \in R : f (a \cdot b) = f (a) \cdot f (b)

\forall a \in R, b \in R ∖ {0} : f (\frac{a}{b}) = \frac{f (a)}{f (b)}

\forall a \in R : f (a) = f (- a)

1003049203

Level:

Identify which of the statements is false.

\forall a, b \in R : | a + b | = | a | + | b |

\forall a, b \in R : | a \cdot b | = | a | \cdot | b |

\forall a \in R, b \in R ∖ {0} : | \frac{a}{b} | = \frac{| a |}{| b |}

a \in R : | a | = | - a |

1003049202

Level:

Let

f (x) = | x | - | 3 - 2 | x | |

. Identify which of the following function values is the smallest.

f (- 6.5)

f (- 2)

f (0)

f (0.5)

1003028402

Level:

Let

f (x) = \frac{2 x - 4}{x^{2} - 4}

. Which of the statements about the domain and the range of the function

f

is true?

- 2 \notin D (f) \land - 2 \in H (f)

- 2 \in D (f) \land - 2 \notin H (f)

- 2 \in D (f) \land - 2 \in H (f)

- 2 \notin D (f) \land - 2 \notin H (f)

1003028401

Level:

Let

f (x) = \frac{3 x - 9}{x^{2} - 3}

. Which of the statements about the domain and the range of the function

f

is true?

3 \in D (f) \land 3 \in H (f)

3 \in D (f) \land 3 \notin H (f)

3 \notin D (f) \land 3 \in H (f)

3 \notin D (f) \land 3 \notin H (f)

C

1003067803

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