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Hyperbolic Functions to the Rescue – My New Lecture on the Blog

16 August 2024 / Krystian Karczyński

I wrote a new Lecture entirely dedicated to hyperbolic functions and their inverses. In it, I explain what hyperbolic functions are, when - for example - they are useful, and why they sometimes appear in Wolfram results, generally causing panic among students. However, the hyperbolic sine isn't that scary - I invite you to the Lecture.

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Cyclometric Functions (arcus) – New Lecture on the Blog

04 August 2024 / Krystian Karczyński

I've added a new article with a video to the "Lectures" section (on the right sidebar): Cyclometric Functions. It's dedicated to cyclometric functions (arcsinx, arccosx, arctgx, arcctgx) and is divided into two parts. In the first part, I quickly show how to calculate them, and in the second part, I delve deeper into the topic (definitions, graphs).

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A Few Things You Should Learn Well in High School, But No One Told You – Part 4: The Square Root of x Squared

22 July 2024 / Krystian Karczyński

Today, it's going to be short. My quick question for you is: What is the square root of x squared? When I was still giving tutoring sessions, I asked this question to many high school and college students. Do you know how many knew the correct answer? Two.

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A Few Things You Should Learn Well in High School, But No One Told You – Part 3: Quadratic Function

22 July 2024 / Krystian Karczyński

This post is already the third in a row where I want to draw your attention to things that are worth reviewing at the very beginning of your mathematics studies at university. A quick review of them will make your life in university much easier. Today it's the turn of the quadratic function. Quadratic function? The topic of the quadratic function is, of course, very broad, and I don't mean at all that you should take a high school textbook and go through the entire chapter from cover to cover. Let's just focus on a few important details, nuances, and traps.

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A Few Things You Should Have Learned Well in Middle School, But No One Told You – Part 2: Quantifiers

16 July 2024 / Krystian Karczyński

Quantifiers - but they weren't really there... Alright, but who needs this? In most mathematical definitions and theorems, concepts like "every" and "exists" are used. See how to use them correctly.

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High school graduates ask, eTrapez answers. Derivation of the height formula in a right-angled triangle.

09 July 2024 / Krystian Karczyński

This post is dedicated to a piece of a high school exam question sent to me by a high school graduate via email. It's worth taking a look out of curiosity and never repeating again that university math is harder than advanced high school math. Here I show the derivation of the height formula in a right-angled triangle.

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Some Things You Should Have Learned Well in High School But Nobody Told You So – Part 5 Multiplying or dividing inequalities on both sides

18 October 2011 / Krystian Karczyński

In this post, I will continue with topics from high school that you may not have placed much emphasis on, but which will make your life much easier when you go to college. This is part 5 - if you just came here now, you can take a look at the previous 4 posts :) Here I will deal with mutual multiplication and division of inequalities.

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