## All Tasks

#### (I) Domain arctan

The domain ($D_f$) and the range ($D'_f$) of the function
$f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ are, respectively,

# Complements of differential calculus in real numbers

Training

13

#### Sum of powers

What is the final value of the following sum:
$ 2^4+3^0+6^2 $

# Powers

Training

8

#### Flag Colours

The picture shows a German Flag with the length 0,8 m and the height 0,5 m.
How big is the area of the red part of the flag? Put your result in $m^2$.

# Fractions

Modeling

6

#### Decimal Numbers in the Form of Fractions

Consider the number 0.25. Now write it separately like this: 0+0.2+0.05.
Every zero to the left of a given number is equivalent to dividing said number by 10. So for example, 2 divided by 10 equals 0.2 and 5 divided by 10 twice equals 0.05.
See how every time you divide a number by 10, the decimal point moves further to the left. To convert a decimal number to a fraction, each individual number must be written like this:
$0 + \dfrac{\text{first number}}{10} + \dfrac{\text{second number}}{100} + \dfrac{\text{third number}}{1000}$.
Once you have done this with all the numbers, you add them all and convert your decimal number to a fraction.
Give it a try! How do you write 0.625 in the form of a fraction?
(Remember to simplify your answer)

# Fractions

Learning

6

#### Remembering the Divisibility Rules

Let's have a look at a simple set of rules used to know if a certain number can be divided by another one. This will come in handy when simplifying fractions.
First read the rules in the picture.
With these rules in mind, apply each one of them from 2 to 9 to simplify the next fraction:
$\dfrac{362880}{1088640}$

# Fractions

Training

6

#### Simplify the powers

Simplify the powers $\left(-2x\right)^2\left(-2x^2\right)$

# Powers of integer exponent

Training

8