## All Tasks

#### Cobblestones

One cobblestone is a cube with the edge 8 cm long. How many of these cobblestones fit to one cubic meter? Give the result as a whole number.

# Cubes & cuboids

Modeling

8

#### A problem of one euro

A 1 euro coin is made of a bimetallic layered composition: cupronickel for the silver part (internal) and brass for the gold part (external).
The euro has a 23.25 mm diameter.
What is the radius of the inner circumference if the distance between the golden (outer) and silver (inner) circumferences is d = 3 nm?

# Circle

Training

5

#### Hexagonal prism

The decorative block around the statue of Prince Pribina has the shape of a hexagonal prism, the base of which is an irregular hexagon. The height of the prism is 21 cm. Calculate the sum of the lengths of all edges of this prism in centimetres. Measurements are in centimetres.

# Prism

Training

7

#### Differential Arctan

Consider the function $f(x)= -2 \arctan\left(2x\right)$ with domain $D_f = \mathbb{R}$.
The differential of the function $y=f(x)$ at the point $x=-\dfrac{1}{2}$ is:

# Complements of differential calculus in real numbers

Training

13

#### Approximate values arctan

Consider the function $f(x)= -2 \arctan\left(2x\right)$ with domain $D_f = \mathbb{R}$.
Using differentials, the approximate value of $\ -2 \arctan\left(0.02\right)$ is:

# Complements of differential calculus in real numbers

Training

13

#### Differential Arctan

Consider $f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ with domain $D_f=\mathbb{R} $.
Knowing that the value of $df(x_0)=4 \ dx$, the value of $x_0$, is:

# Complements of differential calculus in real numbers

Training

13