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9000020408

Level:

Which of the given equations have at least one root the same?

\begin{aligned} x^{2} + 8 x + 15 & = 0 & (1) \\ x^{2} - 8 x + 15 & = 0 & (2) \\ x^{2} + x - 12 & = 0 & (3) \\ x^{2} - 2 x - 8 & = 0 & (4) \end{aligned}

equations (2) and (3)

equations (1) and (3)

equations (2) and (4)

Such a pair does not exist.

9000019801

Level:

Assuming

x \in N

, find the solution set of the following equation.

x^{3} - 6 x^{2} + 9 x = 0

{3}

\emptyset

{0; 3}

{- 3; 3}

9000019802

Level:

Assuming

x \in N

, find the solution set of the following equation.

2 x^{3} - 3 x^{2} = 0

\emptyset

{0}

{2}

{0; \frac{3}{2}}

9000014807

Level:

Find the

x

-intercepts of the function

f (x) = 3 x^{2} + 6 x - 9

[- 3; 0]

and

[1; 0]

[0; 9]

and

[1; 0]

[- 3; 2]

and

[- 3; - 2]

The function

f

does not have

x

-intercepts.

9000014808

Level:

Find the intervals of monotonicity of the quadratic function

f (x) = 2 x^{2} + 3

The function is increasing on

[0; \infty)

and decreasing on

(- \infty; 0]

The function is increasing on

(3; \infty)

and decreasing on

(- \infty; 3)

The function is increasing on

[- \frac{3}{2}; \infty)

and decreasing on

(- \infty; - \frac{3}{2}]

The function is increasing on its domain.

9000014809

Level:

Find the

y

-intercept of the following function:

f (x) = 10 x^{2} - 18 x - 6.3

[0; - 6.3]

[10; 0]

[0.3; 0]

There is no

y

-intercept.

9000019903

Level:

Identify a true statement related to the following matrix

A

A = (\begin{matrix} - 2 & 3 & 10 & 5 & - 5 \\ 6 & 11 & - 7 & 2 & - 3 \\ - 7 & 15 & - 6 & 2 & 4 \\ - 8 & 1 & 13 & - 5 & 0 \end{matrix})

A

is a

4 \times 5

matrix and

a_{(3, 2)} = 15

A

is a

4 \times 5

matrix and

a_{(2, 3)} = 15

A

is a

5 \times 4

matrix and

a_{(3, 2)} = - 7

A

is a

5 \times 4

matrix and

a_{(3, 2)} = 15

9000019807

Level:

Assuming

x \in R

, find the solution set of the following equation.

(3 x + 2) (x \sqrt{2} + 1) (x^{2} + 1) = 0

{- \frac{\sqrt{2}}{2}; - \frac{2}{3}}

{- \frac{2}{3}; \frac{1}{\sqrt{2}}}

{\frac{2}{3}; \frac{1}{\sqrt{2}}}

{- 1; - \frac{\sqrt{2}}{2}; - \frac{2}{3}}

9000014802

Level:

Let

f (x) = - x^{2} + 11 x - 2

. Which of the following statements is true?

f (- 2) = - 28

f (0) = 2

f (3.5) = 12.25

f (\frac{1}{2}) = \frac{15}{4}

9000014801

Level:

Identify a point which is on the graph of the function

f (x) = 3 x^{2} + 3 x - 2

B = [2; 16]

A = [0; 3]

C = [- 1; 0]

D = [5; - 8]

A

9000020408

9000019801

9000019802

9000014807

9000014808

9000014809

9000019903

9000019807

9000014802

9000014801

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