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#pre-calc

I’m a first year grad student. This is a weird time in education for everyone.

I was watching a lecture my topology professor put together for us to watch and for the first time, it hit me that for the remainder of the semester, nothing will be the same.

I won’t sit in topology again, next to my friend and discuss silly things like the books we are reading or how Hausdorff sounds like a name of a mythical creature. 

I won’t have a meeting in person with the other pre-calc instructors again.

I won’t have a grading party with those same instructors again as we listen to random spotify stations and hear the most bizarre music and play “who sings this”.

I won’t sit around after advanced calc with my class mates and bemoan the fact that our professor randomly calls us out and that we can’t read his writing.

I won’t be able to walk down the hall from my office and say hello to my research assistant friend.

I won’t sit in TA seminar after a long week and debate how to effectively teach very different classes with the same group of people again.

I won’t be able to go into my office on April 1st and flip my math calendar to the next month.

I won’t be able tease my pre-calc students when they ask me what a number over the same number simplifies to again.

Sure, many of these things I will do again next year. But the situations will be different. I’ll be in different classes with different professors. I’ll be teaching a new group of students. Many of my friends will have graduated because they are master’s students. This thought of these things ending so abruptly made me nearly start crying. So to you seniors who this is the end, my heart breaks for you. Feel free to cry over the lost semester. 

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some pre-calc notes alongside a lovely candle i got for christmas & the sequel to rf kuang’s poppy war. i read it in two days and man!! im not a fan of certain aspects of it but it was an overall very captivating book (。•̀ᴗ-)✧

hope y'all have wonderful new year’s and that the next decade really sees you blossom!!! 💕💕💞💖

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wHEN I TELL YOU I HATE THIS FUCKING PRE CALC TEACHER I FUCKING HATE HER!!!


this fucking bitch. is like “oMg PaY aTtEnTiOn To ThE cLaSs” like fuck off. im taking notes. literally fuck off you dumb bitch.

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I talk about ✨constants✨

Why don’t any of you guys know what a constant is??? I’m so scared for y’all omg

So basically! (From my understanding anyway)

A constant is a variable (x,y,a, etc.) that’s well, constant. Lol.

It’s a variable that’s value does NOT CHANGE once assigned a value!!! So say a=5, a will ALWAYS EQUAL 5!

If it’s asking for something like

Ax+2=3x+2; A is a constant, find A to make the equations equivalent

A would equal 3! No need for fancy systems of equations (bleh) just remember, the constant is essentially, just a hidden number! Hope this helps!!!

Plz reblog to help ur fellow SAT/PSAT takers!

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No, this is not the real chapter four; I’m not going to break away from my “five stages of grief” format I’ve got going for me. You’ve got to wait probably a minimum of 12 hours for the chapter to post. However, tomorrow’s chapter is gonna involve a little bit of math. How I, the author, arrived at the solution will be irrelevant to the story and thus not included in the chapter. However, as someone who enjoys simple math problems like this one, I would like to share the way I found the solution. (I will be linking to this post when I post to tumblr and AO3 as an author’s note. Sorry, FFN people, I can’t do links while using that particular posting platform.)

Without further ado, let’s start.

(x^2 – 2x – 24)/(2x^4 – 5x^3 + 3x^2) ≥ 0

So this is our starting equation. A quadratic trinomial is being divided by a quartic trinomial, and this entire fraction must be greater than or equal to zero.

The trinomial in the numerator is very easily factored by the x-method. Please note that it has been years since I first learned how to factor, and I learned the method so that B is on top and A*C is on the bottom, so this may look a little wonky depending on how one was taught Algebra I.

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[Image description: An “X” is drawn in red, with numbers in the four spaces created by the lines. The numbers written in the vertical compartments are red, and the numbers written in the horizontal compartments are blue. In the upper compartment is negative two, and in the lower compartment is negative twenty-four. In the left compartment is negative six, and in the right compartment is positive four.]

In the meantime, we can easily factor out an x squared from the denominator, giving us this equation:

((x - 6)(x + 4))/(x^2(2x^2 – 5x + 3)) ≥ 0

Once again, we’re going to use the x-method.

image

[Image description: Another “X”, with the same formatting as the previous one. In the upper compartment is negative five, and in the lower compartment is positive six. In the left compartment is negative two, and in the right compartment is negative three.]

However, we can’t just split (2x^2 – 5x + 3) into neat and simple factors of (x - 2) and (x - 3). Instead, we need to split our B term into

2x^2 – 5x + 3

2x^2 – 2x - 3x + 3

2x(x - 1) - 3(x - 1)

(2x - 3)(x - 1)

We can insert our factored expression back into the semi-factored equation that we got (2x^2 – 5x + 3) from.

((x - 6)(x + 4))/(x^2(2x - 3)(x - 1) ) ≥ 0

Do any terms cancel out? No, they don’t. Bummer. However, now that this equation has been completely factored, we know some key aspects.

x must be greater than or equal to positive six and negative four, but we can’t stop at the numerator. x must also never equal zero, positive three halves, and positive one.

Because this is an Algebra II/Pre-Calculus problem, I’m not going to solve for every single case manually. Instead, I will be using a scientific calculator. I’d use Excel, but I can’t copy and paste a graph. The results are as follows:

x < -4 ; positive

x = -4 ; zero

-4 < x < 0 ; negative

x = 0 ; undefined

0 < x < 1 ; negative

x = 1 ; undefined

1 < x < 3/2 ; positive

x = 3/2 ; undefined

x > 3/2 ; positive

Hence, x can be less than or equal to negative four, greater than positive one, and not equal to three halves. Or, to write the answer in a more elegant way,

x ≤ -4 U 1 ≤ x ≤ 3/2 U x ≥ 3/2

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I was sitting beside these 2 girls in pre calculus and this is their conversation:

Girl 1: why are you so sad?

Girl 2: just am

Girl 1: I don’t get it, why are you sad and not me?

Girl 2:

Girl 1: I mean, you should be happy and I should be sad because of everything

Girl 2:

Girl 1: like I should be the one sad here, not you

Girl 2:

Me: what the fuck

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(canadian anon)- thank you so much. google was also confused when i looked this up and idk why but it was bothering me. i saw it in pjo and i just assumed rick made it up but then ms spears did it? turned my world around. yes canada has math but we call it just math in grade 9, functions for 10 and 11, then data, calculus and vectors, and more functions in grade 12. the last time i heard math called algebra was grade 6. thanks for actually answering my question!

Oh yeah no problem! I’ve never heard of functions or vectors as names for math classes before but I think we probably just call them something different here

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