What to say in front of the blackboard?

Most students become strangely quiet when they need to go to the blackboard and solve an exercise. So here are a few tips, prepared by our students themselves, on what to say in front of the blackboard!

Choose a folder of your interest and then click on the formula to see the tutorial.

Co powiedzieć pod tablicą?

Studenci często cichną, gdy muszą iść do tablicy i omówić po angielsku etapy rozwiązywanego zadania. Tu znajdziesz kilka wskazówek, przygotowanych przez naszych wspaniałych Studentów, dotyczących poprawnego formułowania zdań w języku angielskim przy rozwiązywaniu zadań przy tablicy!

Wybierz katalog, który Cię interesuje, a następnie kliknij na wzór, żeby zobaczyć opis.

 

I year EPM student, Małgorzata Chlechowicz:

$y = |\log_3(-x)-1|,\quad y = ||3^{x+2}-1|-1| \quad $  

$y = |\frac{1}{2}\sin (2x-\frac{\pi }{2})-1|,\quad y = ||\tan |x|-1|-1| \quad $

I year EPM student, Sandra Arias Lopez:

$y=||2^{x-3}-3|-1|,\quad y=|\log_2(x+3)|+1\quad $ 

$y=||-\cot (x+\frac{\pi }{4})|-1|,\quad y=||2\sin (|x-\frac{\pi }{4}|)-1|-1|\quad $

I year EPM student, Natalia Hałas:

$y=|2^{x-2}|+1,\quad y=|-\log_2(|x|)|-3\quad $

I year EPM student, Damian Głowienka:

$y=||\log_2(x-2)|-1|+1,\quad y=||2^{x-3}-1|-1|\quad $ 

$y=||\cot |x|+1|-1,\quad y=||\sin |x|-\frac{1}{2}|-\frac{1}{2}|\quad $

I year EPM student, Martyna Orzeszek:

$y=|3^{x-1}-3|-1\quad $ 

$y=|\log_{0,5}(|x-2|)|\quad $

I year EPM student, Paulina Nowak:

$y=|\log_2(x-1)-1|+1\quad $

I year EPM student, Marta Kisielowska:

$y=||\log_3(x+2)|-1|,\quad \quad y=|3^{-|x|}-1|\quad $

I year EPM student, Marietta Kamińska:

$y=|\log_2(|x-1|)|,\quad y=|2^{|x|}-2|\quad $

I year EPM student, Ewa Cichosz:

$y=|\log_2|x+1||,\quad y=2^{-(x+3)}-2\quad $

I year EPM student, Natalia Korcz:

$y=||-\cot (x+\frac{\pi }{4})|-1|,\quad y=\frac{1}{2}(\sin (x-\frac{\pi }{4})-1)\quad $

I year EPM student, Kornelia Korf:

$y=|-\cos (|x+\frac{\pi }{2}|)|-\frac{1}{2},\quad y=|\tan \dfrac{x+\frac{\pi }{2}}{2}-1|\quad $

 

I year EPM student, Marta Kisielowska:

$|x-1|+|x-2|>7x \quad $

I year EPM student, Agnieszka Kalinowska:

$|x-7|+|x+7|+|8-x|=x-8 \quad $

I year EPM student, Małgorzata Chlechowicz:

$|2x+6|+|x-3|=2x \quad $

I year EPM student, Natalia Hałas:

$|x-3|-|2x-4|<x \quad $

I year EPM student, Aleksandra Bejnarowicz:

$|7-x|-|8-x|+|x|=10 \quad $

I year EPM student, Paweł Biernacki:

$|x-3|+|x+2|>5 \quad $

I year EPM student, Aleksandra Gostkowska-Krawczyk:

$|x-1|+|2x-4|+|x-3|>10 \quad $

I year EPM student, Ewa Cichosz:

$|2-x|-|3-x|=4+x \quad $

I year EPM student, Natalia Korcz:

$|x|-|x+1|=2x+4 \quad $

 

I year EPM student, Maciej Kowalski:

$(4^x\cdot \log_4x)' \quad $ 

$(\sin ^3x+\sin ^2x+\sin x)' \quad $ 

$((x^2+12x+7)\cdot \ln (x^2+12x+7))'\quad $ 

$((x^2+12x+7)^x)'\quad $

I year BT student, Małgorzata Sobota:

$(x^2\sin x+x\sin^2x+\sin ^3x)',\quad \left(\dfrac{\sin x+\cos x}{\tan x}\right)',\quad \left(\dfrac{1}{\tan ^2x+\cot^2 x}\right)'\quad $ 

$(7^{17x+12\ln x})'\quad $

I year EPM student, Marta Niedźwiecka:

$(\sin (\cos (\sin (\cos x))))',\quad (\arctan (1+x^2))'\quad $

I year EPM student, Małgorzata Wojciechowska:

$(\arcsin (\arccos (\arctan x)))',\quad $ 

$((1+2x+3x^2+4x^3)\cdot (x+x^2+x^3+x^4))'$ 

I year EPM student, Marek Kowalczuk:

$(\ln (e^{2x}+e^x+e))',\quad (\log_4 (x^4))'$

I year EPM student, Martyna Jasińska:

$(x^2\sin x+x\sin ^2x+\sin ^3 x)',\quad \left(\dfrac{\sin x+\cos x}{\tan x}\right)',\quad \left(\dfrac{1}{\tan ^2x+\cot ^2x}\right)',\quad\left(7^{17x+12\ln x}\right)'\quad$

I year EPM student, Joanna Szymańska:

$(\ln (2\sin c+3\cos x))',\quad (\sin (\arcsin x))',\quad (\cos x\sin  (x^3+x^2+x+1))'\quad $

I year EPM student, Adam Pawłowicz:

$(\log_3(\sin x \tan x))',\quad (\sin x\cos x\ln x)',\quad ({\rm{arccot}} (\cot x))'\quad $

I year EPM student, Milena Lipowska:

$(\sin (\cos x+\tan x))',\quad (x\cdot \ln\ln x)',\quad \left(\dfrac{\sin x +1}{\cos x+1}\right)'\quad $

I year EPM student, Anna Brillowska:

$(x^{21}\cos ^7 (x^3))',\quad (\log_4(\log_3(\log_2 x)))',\quad \left(\dfrac{\sin x}{\arcsin x}\right)',\quad (5^{\arctan 4x})'\quad$

I year EPM student, Kinga Basa:

$(\sin (\cos (4x^3+3)))', (\log_7 (\tan (50x^{49}+7x^{14})))',\quad (\arctan (1+\sin x))',\quad (20^{\sin 3x})'\quad $

I year EPM student, Adam Taratuta:

$(\cos (\arccos x))',\quad (\log_3(3^x))',\quad (\arcsin (\arccos  (\arctan x)))',\quad (x^{2x})',\quad ({\rm{arccot}}(\arctan (\arcsin x)))',\quad (2^{\ln (\cos x)})'\quad $

 

I year EPM student, Karolina K.:

$\begin{cases}x+5y=2\\-3x+6y=15\end{cases}\quad $

 

I year EPM student, Karolina K.:

$P(1,0,-5),\;\pi :3x-12y+4z+8=0 \quad $

 

II year EPM student, Aleksandra Lis:

$\displaystyle\sum\limits_{n=1}^{\infty }(-1)^n\cos \left(\frac{1}{n}\right)\quad $

II year EPM student, Karolina K.:

$\displaystyle\sum\limits_{n=1}^{\infty}(-1)^{n+1}\frac{n+3}{n+5}\quad $

II year EPM student, A.Z.:

$\displaystyle\sum\limits_{n=1}^{\infty }\left(\frac{2+n}{n}\right)^{n^2}\quad $

II year EPM student, Kamila Szczepańska:

$\displaystyle\sum\limits_{n=1}^{\infty }\frac{e^{\sqrt{n}}}{\sqrt{n}}\quad $

II year EPM student, Kamila Stankiewicz:

$\displaystyle\sum\limits_{n=1}^{\infty}\frac{(-1)^n n}{2^n}\quad $

II year EPM student, Kamila Zawadzka:

$\displaystyle\sum\limits_{n=1}^{\infty}\frac{(-1)^n}{\sqrt[3]{n^2}}\quad $

II year EPM student, Joanna Szymańska:

$\displaystyle\sum\limits_{n=1}^{\infty }\frac{(-1)^n n}{2n^2+3}\quad $

II year EPM student, Martyna Tokarska:

$\displaystyle\sum\limits_{n=1}^{\infty }\frac{(-1)^{n+1}}{\sqrt[3]{n^4+1}}\quad $

II year EPM student, Małgorzata Wojciechowska:

$\displaystyle\sum\limits_{n=1}^{\infty }(-1)^n\frac{n+1}{2n-1}\quad $

II year EPM student, Marta Niedźwiecka:

$\displaystyle\sum\limits_{n+1}^{\infty}\frac{(-1)^n}{n\cdot 3^n}\quad $

II year EPM student, Iwona Markiewicz:

$\displaystyle\sum\limits_{n=1}^{\infty }(-1)^n\left(\frac{n-1}{n+1}\right)^{n^2}\quad $

II year EPM student, Marek Kowalczuk:

$\displaystyle\sum\limits_{n=1}^{\infty }\frac{(-100)^n}{n!}\quad $

II year EPM student, Jan Góral:

$\displaystyle\sum\limits_{n=1}^{\infty }(-1)^n\frac{n+1}{2n-1}\quad$

More tutorials coming soon!