A | math4u.vsb.cz

2010011701

Level:

How many natural numbers belong to the solution set of the inequality

| 3 x - 7 | < 5

3

4

2

1

2010011407

Level:

Find the area of the region bounded by the curves

y = x + 1

and

y = - x^{2} + 3

\frac{9}{2}

2

6

\frac{21}{2}

2010011406

Level:

Find the area of the region bounded by the graph of

f (x) = \sin x - 1

[\frac{π}{2}; π]

and lines

y = 0

and

x = π

\frac{π}{2} - 1

\frac{π}{2}

1

\frac{3 π}{2} - 1

2010011405

Level:

Find the area of the region bounded by

x

-axis, graph of

f (x) = x^{2} + 5

and lines

x = - 1

and

x = 2

18

24

13

\frac{52}{3}

2010011404

Level:

Find the area of the triangle

A B C

highlighted in yellow (see the picture).

16

12

8

20

2010011403

Level:

Find the area of the yellow region indicated in the picture.

2 \sqrt{2}

2 \sqrt{3}

\sqrt{2}

4 \sqrt{2}

2010011402

Level:

Find the area of the yellow triangle

A B C

indicated in the picture. Read all the needed values from the picture.

10.5

36.75

10

15.75

2010011401

Level:

Calculate the area of a plane region bounded by the graphs of the functions

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

and

g (x) = 14 - x^{2}

\frac{125}{3}

\frac{19}{3}

\frac{93}{3}

75

2010011205

Level:

A diagonal of a rectangle has length of

26 cm

and the perimeter of the rectangle is

68 cm

. Find the difference of the length and the width of the rectangle in centimeters.

14

20

24

28

2010011105

Level:

Evaluate the following limit. (Apply L'Hospital's rule repeatedly.)

lim_{x \to 0} \frac{x^{4} + 2 x^{3}}{x - \sin x}

12

0

- 12

6

- 6

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