All Tasks
Cube tower 1
For each given tower, calculate the
number of side faces visible
side faces.
# Numerical expressions
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.
# Terms
Modeling
7
term triangle 1
The depicted sequence of matchstick figures is continued. Indicate how many matchsticks are needed for step 4.
# Terms
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