All Tasks

Cube tower 1

For each given tower, calculate the number of side faces visible side faces.
 
# Unassigned

Modeling
7

term triangle 2

The depicted sequence of matchstick figures is continued. Give the term that can be used to determine the number of matches needed at the step n.
 
# Unassigned

Modeling
7

term triangle 1

The depicted sequence of matchstick figures is continued. Indicate how many matchsticks are needed for step 4.
 
# Unassigned

Modeling
7

term square 2

The depicted sequence of matchstick figures is continued. Cross all terms that can be used to determine the number of matches needed at the step n can be determined.
 
# Terms with variables

Reasoning
7

Equations using arccotan

The solution of the equation $2\text{arccot}(x+1)=\dfrac{\pi}{2}$ is:
 
# Functions of one variable

Training
13

Chain rule arccotan

Let $f$, $g$, and $h$ be 3 real functions of real variable. If $f$ is defined by $f(x)=g(h(x))$, $g$ is defined by $g(x)=arccot(x)$, and $h$ is a function where the values that $h$ and $h^{\prime}$ take for $x=1$ and $x=2$ are defined in the table, then f'(1) is equal to
 
# Functions of one variable

Reasoning
13