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What to say...

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!

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