Grade 12 - After break 1st class

What's the name of the mathematician who created a formula for the sum of consecutive integers (arithmetic sequence) when solving a challenge in elementary school?

• Gottfried Wilhelm Leibniz

• Leonhard Euler

• Carl Friedrich Gauss

• Amalie Emmy Noether

What expression describes the general term of the geometric sequence 3, -6, 12, -24, ... ?

•  $u_n=-3\left(2\right)^{n-1}$  

•  $u_n=3\left(-2\right)^n$  

•  $u_n=-6\left(2\right)^n$  

•  $u_n=3\left(-2\right)^{n-1}$  

What's the most famous and prestigious prize a mathematician can get?

• The Abel Prize

• The Nobel Prize in Mathematics

• The Kenneth O. May Medal

• The Fields Medal

In the usual notation for sequences, the sum of the first  $n$  terms of a geometric sequence can be calculated using the formula:

•  $S_n=\frac{u_1\left(1-r^n\right)}{1-r}$  

•  $S_n=\frac{u_1\left(1-r^{n-1}\right)}{1-r}$  

•  $S_n=\frac{u_1\left(r^n-1\right)}{1-u_1}$  

•  $S_n=\frac{u_1\left(r^{n-1}-1\right)}{1-u_1}$  

What are the first terms of the famous Fibonacci Sequence?

• 0, 1, 1, 2, 3, 5, 8, 13, ...

• 1, 2, 3, 5, 8, 13, 22, ...

• 0, 1, 2, 2, 3, 6, 8, 13, ...

• 1, 1, 2, 3, 6, 8, 13, 21, ...

Using sigma notation one can represent long sums in a concise way. Which of the following sums can be represented by the expression  $\sum_{n=1}^7\left(5n-n^2\right)$  ?

•  $4+6+4+2+0+\left(-4\right)+\left(-6\right)$  

•  $4+6+6+4+0+\left(-6\right)+\left(-14\right)$  

•  $4+6+4+6+0+\left(-4\right)+\left(-14\right)$  

•  $4+6+6+4+0+\left(-6\right)+\left(-6\right)$  

What base did the Babylonian number system use?

• Base 10

• Base 60

• Base 6

• Base 12

An infinite geometric series converges when ( $r$  represents the common ratio):

•  $0\le r\le1$  

•  $-1\le r\le0$  

•  $-1\le r\le1$  

•  $-1<r<1$  

What's the name of the famous problem Euler solved that involved crossing bridges?

• Paris Bridge Problem

• Königsberg Bridge Problem

• Basel Bridge Problem

• Venice Bridge Problem

What's the value of the expression  $\frac{8!4!}{10!}$  ?

•  $\frac{8}{5}$  

•  $\frac{4}{5}$  

•  $\frac{4}{15}$  

•  $\frac{8}{15}$