Gauss stairs

The legend says that the young Carl Friedrich Gauss found a way to baffle his teacher by finding a way to sum all the integers between 1 and 100 in a matter of seconds. Do you know the answer?

# Sequences

Reasoning
5

Graphs f(x)=ax²

The graphs of the image correspond to the functions f(x)=-2x², f(x)=$\frac{1}{2}$x², f(x)=$\frac{-1}{3}$x² and 3x². How affects the quadratic coefficient to the graphs?

Training
8

Identifying translations from y=-ax²

From the green graph, corresponding to y=-ax² (a>0), obtain the equation of the blue graph and its vertex. One point of this graph is (1,-3)

Reasoning
8

A spirale of numbers

Look at the spiral of numbers. See how they are increasing, starting from 1, then 2 to its left, 3 above, 4 on its right, and turning around in a clock-wise fashion. What is the number to appear just below the 10?

# Operations with natural numbers

Training
5

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