## All Tasks

#### The far bottom-left diagonal

In the spirale of numbers, what would be the 10th number on the bottom-left diagonal, completing 1, 9, 25, 49, 81, ...

# Operations with natural numbers

Reasoning

5

#### Order pizza

You and your friends want to order pizza. Your pizza is 3 Euros more expensive than Tim's. Justin's pizza is 4 euros cheaper than yours and Marcel's pizza is 1 euro more expensive than yours. In total you pay 44€.
How much do your pizzas cost each?

# Linear equations

Modeling

9

#### cube tower 2

Set up a term for the tower that can be used to determine the number of visible side faces as a function of the number of cubes.

# Terms with variables

Modeling

7

#### Which unknown is longer?

The total length of each track you see in the image is 30m.
Which of the variables x or y is longer? Fill in the blanks with the words longer or shorter and your calculated values.

# Linear functions

Reasoning

9

#### Chain rule arcsin

Let $f$ be a continuous function on $\mathbb{R}$ and $g$ the function $g(x)=\pi-\arcsin(3+2x)$. Knowing that $f\left(\pi\right)=0$ and $f'\left(\pi\right)=-1$, find the value of the derivative $\left(f\left(g\left(-\frac{3}{2}\right)\right)\right)'$.

# Functions of one variable

Training

13

#### Chain rule arcsin

Let $y=y(x)=\arcsin(2-3x)$ and $x=x(t)=e^{3t^2}$.
Use the chain rule formula to express the derivative $\left.\frac{dy}{dt}\right|_{t=0}$.

# Functions of one variable

Training

13