## All Tasks

#### Derivatives using arccotan

The derivative of the function $f(x)=2^{\text{arccot}\left(\ln\left(\sqrt{x-1}\right)-\sqrt{3}\right)}$ at the value of $x$ that is solution of the equation $\text{arccot}(x-3)=\dfrac{3\pi}{4}$ is:

# Functions of one variable

Training

13

#### Construction of a pipeline

Two construction companies participate in the construction of a natural gas pipeline. The construction section of the second company was 60 km shorter than the construction section of the first company. How many kilometers of pipeline were laid by each company?

# Unassigned

Modeling

9

#### How expensive are the clothes?

Julian buys a pair of jeans and a sweatshirt. The jeans are 5 times more expensive than the sweatshirt. In total he pays 63 €. How much € does each item cost?

# Linear equations

Training

9

#### Translate and solve 2

Translate the text into a linear equation that depends on x. Then solve this equation and enter the calculated x value into the free field.
"Multiply a number by 5, add 8, subtract twice the number. You get the sum of 10 and 7."

# Unassigned

Training

9

#### Translate and solve 1

Translate the text into a linear equation that depends on x. Then solve this equation and enter the calculated x value into the free field.
"Multiply a number by 6, subtract 15 from it, add four times the number, you get the sum of 25 and 13."

# Unassigned

Training

9

#### Mathematical translation

Which of the equations fit the text? Mark with a cross.
"If you subtract the sum of 13 and 7 from 28, you get twice an unknown number."

# Unassigned

Reasoning

9