precalculus

[alpine bluff]

you can think about like

h(1.9), h(1.99) etc

if u can gain an intution on that itll make limits so much easier

[brazen robin]

reall

hi friend

[grim rock]

hello child

[carmine orbit]

wsg brotato

[floral dome]

wdym

ap pre calc, i learn the limits and stuff, idk how the slant asymptotes and number 14

[alpine bluff]

this ?

[west ledge]

i love this

[floral dome]

yes

[alpine bluff]

so in english what is question 14 asking about the function

[floral dome]

wait not as in that question 14

this one

mb i thought u meant slant asymptotes

[alpine bluff]

ah

do you know what 1st,2nd, and 3rd differences are?

[floral dome]

no 😭

i’ve heard of them

[alpine bluff]

actually i dont think u use them here

what i would do is

plot out the points

and see if it looks linear, quadratic or cubic

[floral dome]

okk

[floral dome]

but honestly i was more stuck on b and c, idk what a regression model is and idk what a residual is

[alpine bluff]

regression is when u find a line of best fit

have u done that?

usually you'd put (x,y) points in a calculator and it'll tell you what m and b are

[civic river]

HI

No graphing/scientific calcs. and they expect you to solve in a minute or two.

IDK if I should send it to Calculus

[plush hearth]

You don’t need any calculus for this, you can do it just using graph transformations. Graph y=x^4+x^3, then y=x^4+x^3-1, then finally y=f(x)

[radiant pilot]

whos acc graphing the entire thing tho

[plush hearth]

You can also get away without drawing the absolute value graph since y=|g(x)| and y=g(x) have the same zeros

It really isn’t that bad to graph, it’s fairly quick too

[copper ledge]

But if you don't know the graph of x^4+x^3, you have to use calculus for knowing the gradient which isn't too bad either

[civic river]

yay

[plush hearth]

I’m assuming that graphing polynomials that can be expressed as a product of linear factors is a skill most people encounter before calculus. Of course you need calculus if you want to know the maxima/minima of the function but that isn’t needed for this question

[radiant pilot]

I did it such that i found all 3 mins/maxs to be negative so then that means theres 2 real roots

[native snow]

how wld u factor that polynomial

[plush hearth]

x^4+x^3=x^3(x+1)

[frosty folio]

Hey I need some help with a couple problems if anyones down

[grim rock]

i can try

can someone explain how to like find out arctans. for example arctan(1/root3) is pi/6 but how do i get that

[echo ferry]

it's b for sure (nvm)

[copper ledge]

You can send it here

[native snow]

yeah i get that but i couldnt intuit the answer

i js know it has to be at least 2

[plush hearth]

If you graph x^3(x+1), then translate this down by one unit, the resulting graph intersects with the x-axis exactly twice

[native snow]

true i get that

but idk how i wld graph that without a calc

[rough leaf]

it’s like

tan(x)=1/root 3

you tryna figure out the x

that’s what the arctan function does

so since arctan (1/root3) =pi/6

then tan(pi/6)=1/root3

if that makes any sense

[somber forum]

Trigonometry is not allowed here

[rough leaf]

it’s part of precalc

so it is

it should be

[lofty siren]

guys just saying i just thought about learning some simple calc cus why not
what exactly is a limit?

[grim rock]

it’s like the value x approaches as the input gets closer to a specific number

idk if that makes sense

imagine you’re walking toward a door. the limit is like saying, “no matter how tiny the step I take, I can get as close as I want to the door.” u don’t have to actually touch the door you just get arbitrarily near.

in some cases u can just plug in your x

but as you probably know if the result is 0 over zero, then you have to use the conjugate

[valid topaz]

so basically the destination value of a function when it gets infinitesimally close to that point

[rough leaf]

there’s also other ways

[grim rock]

yea

[valid topaz]

or u could waste ur time learning delta epsilon

[grim rock]

or just use conjugates or even the l’hôpital rule

[rough leaf]

sometimes factoring works too

[valid topaz]

or series expansions for those truly ugly limits

[grim rock]

like difference of squares

[rough leaf]

or the sophie germain identity (the difference of two quadratics to get a quartic binomial i believe)

[valid topaz]

haiya ur gonna break his brain guys

[grim rock]

😭

[rough leaf]

the sophie germain identity isn’t that bad

[grim rock]

if you’re just starting i’d recommend conjugate method

[valid topaz]

just the name

it looks easy enough tho

[rough leaf]

he could lwk js go on khan

[valid topaz]

or desmos

[rough leaf]

cuz i’m oretty sure there a lesson that teaches all the easy ways

for limits

[grim rock]

i don’t like khan academy

[rough leaf]

i love khan

[grim rock]

i use chat it’s taught me lit everything i know

[valid topaz]

why not

khan academy is fun

[valid topaz]

hmmm

[grim rock]

and just remember u can change the equation in anyway as long as the result is the same

[valid topaz]

ai can make mistakes

[grim rock]

i suppose

[valid topaz]

it literally once told me the sinx/x limit was 0 😭

[rough leaf]

isn’t it 1?

i don’t really know i js used lhop for it rn

[valid topaz]

but that's circular reasoning

so i use series expansions

[rough leaf]

i don’t know the expansions

[rough leaf]

wait like taylor series?

[grim rock]

yea that’s why i always double check but for explaining methods and giving practice problems its good

[valid topaz]

ah i see 👍

[grim rock]

yes yes it’s quite useful

[rough leaf]

i’m planning to learn taylor series after i get good with double derivatives and polar coordinates and stuff

[valid topaz]

snap, crackle, and pop

[rough leaf]

what😭✌️

[valid topaz]

4th, 5th, and 6th derivatives of position

[grim rock]

how old are you? have u taken algebra

[rough leaf]

oh

why do we just know this

[valid topaz]

it's unofficial

[valid topaz]

bc i wanted to

[grim rock]

🥹

[rough leaf]

bro why do i have so much fricking homework

i hate french

worst language out there

[valid topaz]

oui oui 🥖

hon hon hon

[rough leaf]

js two more assignment then i can go bsck to math✌️

[grim rock]

non non 🙂‍↔️

bonjour ✌️

[dapper pebble]

Hi
im an 8th grader going into this completely blind

Is this answer correct?
if not then what did i do wrong

-# (i just want to see some advice or smth i guess)

[leaden light]

I believe it's correct

[valid topaz]

correct! but maybe move to #calculus

[tranquil crypt]

mdr

[grim rock]

looks right 👍🏻

[sweet dove]

Is there any higher math channels for pre university

[raw hill]

Just the four - your "higher math" would just fall under uni

iirc, the education roles explicitly mention being about the level you're at rather than age

so

yeah

[sweet dove]

Ahh thank you

[raw hill]

yes some content like calculus is typical for high school in many places

but they chose to be a little more generous

I think the idea was to model it against an average American high schooler

so it's not like they'd be racing through

[sweet dove]

Yea I was looking for calc 2-3 stuff

[raw hill]

they spend quite a lot of time on basic algebra for example

[raw hill]

yeah just go #calculus / #multivariable-calculus

[sweet dove]

Thank you

[raw hill]

[fluid olive]

Iam signing up for a precalculus class in my school, many students in my school also sign up and they usually have a test, any idea what will be in the test suggesting that its a precalclus class?

[sweet dove]

Testing you on pre calculus assuming you have never learned about it?

[grim rock]

id learn at least to limits and get a solid understanding on concepts in trig

like arctan etc

[dapper pebble]

I wish my school did that 🥹

[lofty siren]

Just asking, limits is basically just regular derivatives but just stating whats the limit, right?

[hot badger]

Crazy

[raw hill]

No idea what you’re asking here, but the limit definition of the derivative is a thing.
$$f(x)=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}=\lim_{x \to a} \frac{f(x)-f(a)}{x-a}.$$

[hot badger]

2x2?.?

[lofty siren]

yes that basically

[obsidian monolith]

Civil Service Pigeon

[lofty siren]

actually not that

just asking

wtf is a limit

[hot badger]

Chat someone help

[lofty siren]

factor numerator and denominator

cancel commons

[hot badger]

Bet one sec

[twilit basalt]

is the restrictions included with the answer

[grim rock]

are those x,s?

[grim rock]

bottom is difference of squares top is quadratic

use ac method to factor

actually i don’t think u can do ac

use -b +- square root of delta/2a

[twin forge]

Very good question

Can anybody explain what is a limit?

[muted moth]

I appreciate your trying to help, but please do not advertise on this discord.

[dry verge]

So you know how in an equation like 1/(x-3), the professor tells you that x cannot equal 3, and the closer you get to 3, the closer it gets to infinity?

That's an example of a limit.

It's one of the cornerstones of calculus alongside derivatives and integrals.

[full saddle]

can somebody help me with these?

[grim rock]

that’s a good way to explain it

[fluid olive]

nope never

[raw hill]

Did you try googling it?

Ex: https://math.stackexchange.com/questions/4318588/inverse-of-a-composite-function

[sly oyster]

I see that Madzie already gave an example. But here is my favorite way of describing it.

Take an equation like f(x) = (x^2 - 4) / (x -2). This works just fine but what if x = 2? The answer is 0/0 which doesn't work. But what happens if you put 2.1 in for x then the answer is 4.1 and if you get closer to 2 such as with 2.01 you will see the answer is 4.01 so you can conclude that the limit is 4 for 2 even though you can't directly put 2 into the equation.

This is more of a practical explanation for how a lot of the math works.

[twin forge]

When am I gonna learn limits?

[twin forge]

That’s too much for me to process

[lofty siren]

depends on ur country tbf

mostly starting of a levels if u chose it

[round geyser]

Sure

The denominator is perfect of squares

[round geyser]

Have u did long division

[hot badger]

We did it end of term 4 but our teacher didn’t go in depth so

Js scrammed through it

[lofty siren]

so did u factor it

[hot badger]

Is this correct?

[round geyser]

Yes

[ancient inlet]

good job

[round geyser]

You can do AC method

I think it’s
n^2-19n-42
(n-2)(n-21)
divide by 3 to get
(3n-2)(n-7)

[hot badger]

Ohhhh true true

Thx

[sly oyster]

This is how I teach it to younger students but there are multiple ways to factor. Knowing how to factor complex trinomials like this is extremely important for later calculus. I would recommend getting really comfortable now with them which will make the change that much easier.

[hot badger]

Thank you 🙏 I’m gonna grind algebra

[sly oyster]

Good luck!

[zenith scarab]

@everyone how yall doin?

[sweet dove]

That is crazy. I’ll send you some send in here later.

I’ll give you up to unit 7 I think

[silk scarab]

Questions

?

[warped shuttle]

how can i prove the nested sqrts are 0 ?

[fluid olive]

tysm <3

[celest fiber]

it's just -1, +1, -1, +1 in that order

so let whole thing be x

then √-1+√1+x = x

x² = -1 + √1+x

(x²+1)² = x+1

x⁴+2x²-x=0

x(x³+2x-1) = 0

So either x = 0

or x some imaginary value

[timid pulsar]

nice, think you swapped the sign on the 2x though

[celest fiber]

Yea sorry it's 1 am my brain is low battery

[sweet dove]

I thought this too, but it is not necessarily are proper proof, but works kinda.

[celest fiber]

How

Not proper

[sweet dove]

Like it is, but the way I was talking to my professor about it is using set theory can make it proper. It is technically a proper proof, but like simplified

[celest fiber]

Hmm

Not quite sure how set theory would do that

[sweet dove]

I’ll create something then send it

[celest fiber]

ok

[grim rock]

can someone confirm

[round geyser]

How would u approach this

[grim rock]

also id ask in #prealg-and-algebra

u could also expand the whole thing but that would take agessss

actually wait it’s an an arithmetic sequence

there are multiple answer i think

here’s what i did

[round geyser]

4 solutions

[valid topaz]

basically how i did it

[round geyser]

That’s how I approached this

[valid topaz]

but i didn't sub first

subbed after diff of squares

[grim rock]

thanks for this this was a nice break from calc

😌

[round geyser]

I’m now doing trig

[valid topaz]

solve this with calc

[round geyser]

Pre-calc skill

Rational root theorem

That’s my first 100 in pre-calc

That’s Unit 4

Unit 4B word problems 100

Unit 6 Quiz 1 and 2 100

Unit 7 quiz 1 100

[grim rock]

how 😭

[round geyser]

And ended with a 92

On Unit 7 Quiz 2

And Unit 5 I got 95

And now I’d moved on to Trig

[valid topaz]

[grim rock]

logarithms: i know this is right and im able to get there but like i made multiple mistakes on the way is there a way to do it easily?

[round geyser]

Total of 6 100’s

[valid topaz]

hmm it should just be d/dx(sqrt(x))/(sqrt(x))

too lazy to check if it's right

wait ye it's correct

[round geyser]

100’s I got

[grim rock]

i love word problems

[round geyser]

I did

[round geyser]

Cutout boxes, perimeter around the garden, perimeter without the river, and graph closest to the coordinate

[grim rock]

yea

my baby ❤️‍🩹

[round geyser]

I used Lwh, L^2,

P=2(L+W)

[grim rock]

perm around the garden, that’s in like every single math comp

i remember one in this years amc8

it was like number 9 i think

[round geyser]

And then 2L+W

And the distance formula

[round geyser]

Guess what

I get to use desmos

[grim rock]

number six

[round geyser]

Cutout boxes (1 equation), perimeter around the garden, perimeter without the river(2 equations), and graph closest to the coordinate (2 equations)

In that lwh the h will assume be x and lw will just be (2x-#)

“# as in length*

[valid topaz]

ooh u do amc 8

🔥

[grim rock]

yessss do u

[valid topaz]

ofc

[grim rock]

i’m doing the 10 next year tho

i completely fricking bombed this year tho

[valid topaz]

what did u get this yr, if u took it

[grim rock]

it doesn’t show for me irs so weird

i log in and i don’t see it

[valid topaz]

hmmm

[grim rock]

what did u get?

[valid topaz]

23

sillied 2

[round geyser]

I did like this

[round geyser]

The square cutouts and using Volume of a prism

[grim rock]

seems very excessive

[round geyser]

And I get to see what’s primary and secondary equations

And using Desmos to help with these

As a result that I got an 100

Short and sweet unit

Unit 5 was about rational function

1/x

Like how to graph them

That I got an 95 bc of the x I wrote was part of the domain restriction

[rough leaf]

guys what a set diagram

[valid topaz]

i like food too

[rough leaf]

😭✌️

[valid topaz]

a set diagram is like a fancy venn diagram, drawn out

it's a visual tool

[round geyser]

Is it that has U like A U B

[valid topaz]

many logical operations can be drawn out, but ye, that's one

[round geyser]

I’ll never gonna touch that since I’m now in trig section

After Pre-Calc

Cuz I’m in a class that is Pre-Calc & Trig

[valid topaz]

ooh cool

[opal sparrow]

why is there mc bot

im in ap precalc

anybody take the test

is it hard

[pliant hatch]

ap precalc exists??

i never knew lol

[grim rock]

same

[hardy crypt]

It's more recent than others, i graduated in 2024 and that was the first year it was offered, I didn't get to take it since i was taking ap calc instead

[silk scarab]

Where are questions

[rugged spruce]

I need help with logs 🫩

How did yall learn logs?

[grim rock]

omg

i hate it

i JUST figured it out

it took me a whole day to figure it out

i can help

[rocky silo]

It’s like exponent

But weirder

Like log base a (b) = c means a^c = b

[grim rock]

yes

[rocky silo]

So just think a to the power of what is b

[grim rock]

i think of it as a rope

like this:

[rocky silo]

Wait what

Now I’m confused

Oh nvm

[grim rock]

yeah

my lil system

😭

[rocky silo]

Is it like a to c to b

[grim rock]

yes!

[rocky silo]

So like a to the c = b

[grim rock]

basically

i always see a rope in my mind looking at it

[sly oyster]

First time seeing this way. If it works it works.

[grim rock]

exactly

uhh is this right? i don’t think so

i found it with one sin and divided by two

OH WAIT

i think i have to times by two

never mind

is it 18

[carmine orbit]

yes

[grim rock]

okay 👍🏻 thanks

[carmine orbit]

why is m like that

[muted moth]

If you're looking for problems to help with you can try the help channels in the "Help (Occupied)" section. But please don't post the same thing over and over again.

[rugged spruce]

Yes help

This is what I’m working with here these are lecture notes. Anyone can help

[grim rock]

what do u need help with?

[rare ferry]

Oh logs

[ancient inlet]

I can help

Later

[rugged spruce]

Basically the properties and how to apply them this whole thing is confusing

I have a quiz Friday

[ancient inlet]

I see

[rugged spruce]

I went to a tutor today but still confused

On it all

[fickle lichen]

how do I change my math level?

[ancient inlet]

Wdym?

[fickle lichen]

nvm

I meant role

[fickle lichen]

try graphing them with desmos

graphing and then understanding each part of the graph helps grasp stuff conceptually

[rugged spruce]

Will that me understand the ones without the graphs tho?

[fickle lichen]

well, yeah

one thing is you wont understand how your calculator computes it for a while

which bothered me

it uses a lot of advanced algorithms to do so

compare uh

10 to the x (exponential) and logx

[rugged spruce]

Where’s the log button?

[fickle lichen]

uhh I just write "log"

[rugged spruce]

Oh I see it on functions

[fickle lichen]

but basically as you go further in the positive x direction, or to the right, its basically asking "to what power do I need to get 10 to this x value" and the power is represented on the y axis, while the number you want to get to is represented on the x axis

(for the red line, or log function)

[rugged spruce]

Ok so b4 we jump into graphs I need to learn the concept of logs first

[fickle lichen]

oh I thought you had that down based off your homework

[rugged spruce]

Like common, natural and properties of logs

[fickle lichen]

ohh ok

[rugged spruce]

No 😭

[fickle lichen]

yeah thats relatable

its easy to get those questions right without knowing

but common log is when they dont write a base so it goes like (log)

that just means base 10

then you're gonna have an x after (log) so (log x) this is asking what exponent gets you to x

from 10

so if you have log 100, your answer would be 2 because you have to raise 10 to the second power to reach 100

[rugged spruce]

Yes

[fickle lichen]

and as im sure you probably heard, its basically the opposite of the exponent

which is also why the log graph mirrors the behavior of the exponential graph

do you know what e is?

[rugged spruce]

No

[fickle lichen]

okay thats really important

so e is equivlant to about 2.718...

do you know derivatives

[rugged spruce]

Not yet

[fickle lichen]

okay makes sense

its fine you dont need that yet

anyways it represents the base rate of growth for an exponential function

im gonna explain it to you in terms of compound interest though

if you have 1+1=$2 at the end of the year

but if you compound this more and more, like daily or hourly, you get a little bit more money

do you know the formula for compounding interest

here

[rugged spruce]

It’s like A=p(1+

Yea

[fickle lichen]

anyways, if you plug in a number approaching infinity

so an extremely high number

you're going to find that compounding it infinetely leads to you getting about 2.71 times the money

anyways you dont need to know e at a high level yet but ln is like log in that the base for log is 10 but the base for ln is e (2.71)

ln is also called the natural log

so its essentially log(base e) to x

are you getting this because im aware my explanation is kind of all over the place

[rugged spruce]

Yea I’m getting there now how do we evaluate them

[fickle lichen]

alright

let me show you the graph for ln(x) first

as you go its basically asking "what do we have to raise 2.71 to in order to get this number (x value)

so at 2.71

you raise it to the first power

because 2.71 to the first power is one

what are you trying to get into

after high school

[rugged spruce]

I’m in college rn studying mechanical engineering

But behind on my math

[fickle lichen]

oh ok yeah you need e badly lol

its fine you know ali alquierez

[rugged spruce]

No

[fickle lichen]

hes a really good youtuber you should watch he explains stuff really well

[rugged spruce]

Ok bet finna look him up rn

[fickle lichen]

oh wait no

its ali the dazzling

his videos are really complicated but thats because they force you to actually understand it

best math & physics youtuber

[rugged spruce]

Finna watch rn

[copper ledge]

<@&268886789983436800>

[fossil kindle]

(2.71)¹ is just 2.71?

[ancient inlet]

yes

[sweet dove]

1. Algebra Foundations
   You must be completely comfortable with:

•    Factoring (including special cases and grouping)
•    Solving quadratic equations (factoring, completing the square, quadratic formula)
•    Polynomial operations and synthetic division
•    Rational expressions (simplifying and identifying restrictions)
•    Exponent rules
•    Logarithm rules
•    Solving systems of equations
•    Working with complex numbers

If algebra skills are weak, precalculus becomes very difficult.
2. Functions
Functions are the central idea of the course. You need to understand:

•    Domain and range
•    Function notation
•    Evaluating and composing functions
•    Inverse functions
•    Graphing different types of functions

Types of functions you should recognize and graph:
• Linear
• Quadratic
• Polynomial
• Rational
• Radical
• Absolute value
• Exponential
• Logarithmic
• Piecewise

You must also understand transformations such as shifts, reflections, and stretches.
3. Polynomial and Rational Functions
Important topics include:

•    Zeros and multiplicity
•    End behavior
•    The Fundamental Theorem of Algebra
•    Real and complex roots
•    Vertical, horizontal, and slant asymptotes

4. Exponential and Logarithmic Functions
   You should understand:

•    Growth and decay
•    The number e
•    Natural logarithms
•    Solving exponential equations using logs
•    Applications such as compound interest

You must know how exponential and logarithmic functions are related.
5. Trigonometry
This is a major part of honors precalculus.

Unit Circle:
• Radian measure
• Special angles
• Exact trig values

Trig Functions:
• Sine, cosine, tangent (and their reciprocals)
• Graphing trig functions
• Amplitude
• Period
• Phase shift

Trig Identities:
• Pythagorean identities
• Reciprocal identities
• Quotient identities
• Double-angle and half-angle formulas
• Proving identities

Law of Sines and Law of Cosines are also required for solving non-right triangles.
6. Conic Sections
You should be able to graph and identify:

•    Circles
•    Parabolas
•    Ellipses
•    Hyperbolas

You must know their standard forms and how equations relate to graphs.
7. Sequences and Series
Topics include:

•    Arithmetic sequences
•    Geometric sequences
•    Recursive and explicit formulas
•    Sigma notation
•    Finite series formulas

8.    Parametric and Polar Equations (in many honors classes)

•    Parametric equations and eliminating parameters
•    Polar coordinates
•    Converting between polar and rectangular form

If you want I can send you worksheets and notes that I have from earlier

My notes are kinda mid because I hardly take any.

[hot grotto]

you need help?

[sweet dove]

Nah someone wanted to know what precalc is about

[sweet dove]

This proves it

This shows that since we added a square that there will be a extra answer and that answer isn’t fully true

This isn’t set theory but instead inductions

[celest fiber]

thats what I did too

[sweet dove]

Look at the right side

[celest fiber]

but my claim is that

the other two values are

imaginary

and hence, dont work

[sweet dove]

Yea I’m just saying that would be a more formal proof

[sweet dove]

Yours is correct but I then show then if x is 0 then x+1 is also 0

Then there fore it is always zero

[celest fiber]

can u explain

ur induction argument

[sweet dove]

So I show that in the first set of squares it is 0

Then I go a step further to show further in the squares it is also zero

And since it repeats then therefore it will always be zero

[sweet dove]

The image is how I proved it

[sweet dove]

Here

[round geyser]

ill show u my units

Unit 1: Functions
• 1.1: Function definition
• 1.2: Factoring
• 1.3: Even/Odd Functions & Symmetry
Unit 1 quiz
• 1.4: Translations of Graphs
Unit 1 Assessment

Unit 2: Composition & Inverses
• 2.2: Composition of Functions
• 2.3: Inverse
Unit 2 quiz

Unit 3: Limits
• 3.1: Limits (Graphically)
• 3.2: Limits (Algebraically)
Unit 3 quiz
• 3.5: Boundedness
• 3.6: Boundedness & The Desmos Graphing Calculator
Unit 3 Assessment

Unit 4: Polynomial Functions
• 4.1: Long & Synthetic Division w/Polynomials, Factor & Remainder Theorem
• 4.2: Graphing Factorable Polynomials
Unit 4 Quiz (4.1-4.2)
• 4.3: Polynomial Functions - Rational Root Theorem
• 4.4: Rational Root & The Calculator
• 4.5: Complex Zero Theorem
Unit 4 quiz (4.3-4.5)

Unit 4B: Min/max word problem
• 4B.1: Max/Min Word Problems
• 4B.2: More Max/Min Word Problems
Unit 4B Quiz

Unit 5: Rational Functions
• 5.1: Graphing Va's & HA's and Rational Functions
• 5.2: Slant Asymptotes
• 5.3: Common Factors
Unit 5 Assessment

Unit 6: Exponential and Log Functions
• 6.1: Graphing of Exponential Functions
• 6.2: Evaluating Exponential Expressions
Unit 6 Quiz
• 6.3: Evaluate Log Expressions & Laws of Logs
• 6.4: Special Cases of Logs
Unit 6 Assessment

Unit 7 Solving Log Equations
• 7.1: More logs
• 7.2: Solving Log Eqns & More Solving Log Eqns w/DESMOS
Unit 7 Quiz
• 7.3: Banking Word Problems & Solving Log Eqns.
• 7.4: Exponential Growth & Decay Word Problems
Unit 7 Assessment

[sweet dove]

Yikes your units are different than mine.

[round geyser]

Yea

[sweet dove]

I would recommend just looking up videos

Sorry man

[round geyser]

Yea

[round geyser]

Btw I’m now in trig

Since it’s Pre-calc & Trig

[sly oyster]

This is really good for pre-calc

[round geyser]

Yep

[sly oyster]

Some curriculum doesn't even cover basic limits in pre-calc which I hate.

It's interesting that they do graphing first but I guess whatever makes it easier for someone to understand.

[round geyser]

I think limits were invented from f(x)=y

Or f(input)=output

[sly oyster]

What part of the course are you at right now?

[round geyser]

Unit 8 Trig
• 8.1: Intro to Trig Notes & Examples
• 8.2: Evaluate w/Trig Notes & Examples
• 8.3: Special Right Triangles Notes & Example

[round geyser]

Here

We use XY graph

[sly oyster]

Cool

[round geyser]

sin is y/r, cos is x/r and tan is y/x

I know what I mean

Also the co terminal, quadrants

[pliant hatch]

what class are you taking

[round geyser]

Pre-calc and Trig

First semester we did pre-calc

Now I’m in trig

[pliant hatch]

wait is this for hs?

[round geyser]

Yes

[pliant hatch]

oh, i thought most people took alg 2/trig in hs

[sly oyster]

I generally don't see any pre-calc courses in college.

[pliant hatch]

that makes sense

[sly oyster]

Though I bet one probably exists somewhere.

[pliant hatch]

i think at most community colleges they do

[round geyser]

In normal college

Will there be Calc

[pliant hatch]

most likely

[round geyser]

Like public school in the US

[sly oyster]

general layout I think

HS:
Algebra
Geometry
Algrebra 2
Trig
Pre Calc ( can be mixed with the one above it )

College:
Algebra
Calculus 1
Calculus 2
Calculus 3
something Algebra
I forgot the name of this one, I think there is like a 3 letter acyronim
Real Analysis
...

[pliant hatch]

algebra 1 in 9th grade?

[sly oyster]

Yeah its more in middle school.

[round geyser]

Yes

Middle school is pre-algebra

For 8th grade

[pliant hatch]

oh

[sly oyster]

I just included it because its like the first actually important course past like addition

[round geyser]

Algebra 1 is 9th grade, Geometry is 10th grade,
Algebra 2 is 11th grade
Algebra 3 or Pre-Calc & Trig is 12th grade

Some people doesn’t need to take it

[pliant hatch]

if 8th is prealg then what do people learn for 6 and 7th

[round geyser]

In 12th grade

[pliant hatch]

there's people in precalc at like 9th grade at my school lol

[valid topaz]

u can take precalc in 8th at my school

i'm planning to do that

[pliant hatch]

really?

my school never offered that

it was just geometry in 8th

[valid topaz]

diff schools have diff offers

[pliant hatch]

yeah ik but thats surprising

[round geyser]

Woah

[pliant hatch]

then are you taking alg 2 in school rn?

[round geyser]

It’s interesting

I’m 12th grade and taking pre-calc

[valid topaz]

no

i'm in 7th

so geometry

best class i can take

[sly oyster]

7th grade is 12 years old right?

What school are you in that allows you to take geometry in 7th grade @valid topaz ?

[valid topaz]

13

[pliant hatch]

real, the only courses offered to me in 7th were math 7, math 7+ and 7/8 alg (alg 1)

[valid topaz]

but only turned 13 like a month ago

[sly oyster]

Have you done geometry already?

I mean algebra 1

[valid topaz]

maryland

[round geyser]

I would call it math from 1st grade to 7th grade

I would say

Like PEMDAS , exponents

[sly oyster]

So at your rate at 14 you will then take Algebra 2 @valid topaz ?

[valid topaz]

taking alg ii over summer

[sly oyster]

So then you would be 14 doing pre-calc then?

And then I assume you just do a bunch of APs

[pliant hatch]

do most people go directly to ap calc bc after precalc

[valid topaz]

i'm still gonna be 13 during the first half of 8th grade

but ye

[sly oyster]

Most people do precalc when they are like 17, so they don't really spend time doing any APs

I started working on my calc 1 when I was 14, but that was quite an outlier. I am very impressed with the fact that people are still able to get ahead like that.

[pliant hatch]

its cause nowadays everone wants to get ahead in math to look good to admissions officers

according to my math teacher, "back in the days" there were only a couple of students in alg 1 in 8th

[sly oyster]

I never ever wanted to go to a nice college or anything so I guess thats a big difference.

When I was 12/13 I for sure wasn't thinking of admissions officers. I wonder if a large part of the push is from the parents.

[valid topaz]

u also need to realize that it's important

can't rely on ur parents for everything

[sly oyster]

it being important is subjective, depending on what career you want

[valid topaz]

ig, ye

[pliant hatch]

what career are you planning on doing

or even your major ig

[sly oyster]

cyber security

I will most likely never have to use any advanced mathematics that I have learned.

[pliant hatch]

don't you need a lot of cs though

and cs involves quite a bit of math understanding

[sly oyster]

No more then algrebra.

My real analysis isn't going to help me there lol

[valid topaz]

what branch?

[sly oyster]

pentesting

[wheat lily]

will sheaf theory help me with paleontology?

[sly oyster]

maybe, quite possibly?? Probably not

[wheat lily]

"this bracheopod reminds me of cech cohomology, i gotta tell ya"

[sly oyster]

"sir we asked how many items you found why did you send this: (we found one rock at place A and one rock at place B so we can conclude 1+1=2 because of zermelo-fraenkel set theory we can define 0 := ∅ ( empty set )

then we just like define the successor function for set x so S(x) := x U {x}

so since 0 := ∅, and we have our function 1= S(0) := 0 U {0} - {∅}

therefore: 2 = S(1) = 1 U {1}

uhhh lets put like 1 = ∅

2 = {∅} U {{∅}} or 2 = {∅,{∅}} cause no one likes U
so therefore if we then replace it with the 0,1,2 cause we can do whatever we want we get:
3={0,1,2,}

then if 3={0,1,2} then that must mean that n={0,1,2,…,n-1} maybe or it might be like n-n(lower 2 idk how you write that)

therefore then 1=n and the answer 2=n(lower 2 whatever) so 1+1=2)"

[wheat lily]

1+1=2 by definition of addition

[sly oyster]

real

[stoic sleet]

they asked me to do cross products and 3d matrix multiplication in precalc

[sharp geyser]

i failed my logs quiz in precalc because my teacher wasnt thrre for 2 weeks and barely taught us the subject

[ocean obsidian]

Hello!

[rugged spruce]

I have a quiz on logs tomorrow

And on rational functions and exponential functions

[stoic sleet]

💀

[grim rock]

lock in

[ancient inlet]

Need vc?

[rugged spruce]

Not at the moment

Imma see how much I can retain first

[rugged spruce]

Trying to it’s like so much to remember

[fickle lichen]

can somebody explain how you graph functions like sin, cos etc on polar graphs

[sharp geyser]

good luck tho!!

[worldly scarab]

Hello guys, I think I have very weak basis of maths since I can’t answer any questions that people ask on this server. What is the best way to get good basis in maths?

[grim rock]

well how old are you? usually as you learn

[woven surge]

i mean you want like a a break down or what specifically?

[round geyser]

You mean

y/r, x/r, and y/x?

[lucid ledge]

how do i go through precalc while in school?

[round geyser]

Scroll TikTok

[ancient inlet]

are we serious rn

[round geyser]

That’s how I learn stuff

[ancient inlet]

i see

[round geyser]

Yes

[alpine crescent]

Even tho its another guys question i want the same help,im 17 its my last year on school and im struggling with mvt,tangent lines,integrals and bit with derivatives

[rare ferry]

🪵

[grim rock]

riemann sums can someone pls confirm?

[raw hill]

This belongs in #calculus, not #precalculus. The answer is fine, but you're missing a dx on your integral.

[grim rock]

sorry and thanks

[winged bolt]

check out professor Leonard

[fickle lichen]

uh I dont really have an intuitive understanding of the topic, like I understand polar notation but thats about it

[rough leaf]

yo how do you do ts typa questions

im ass at riemann sums

[valid topaz]

do daily limits

or recognize the form

this case it's f(1+5i/n)

[grim rock]

just identify the different components

[rough leaf]

howd you turn it into an integral

[valid topaz]

it was lim n to inf ∑(i=1,n) (1+5i/n)^3 * 5/n. the part containing (1+5i/n) and the 5/n would be of the form ∫ x^3 dx, and then u just have to choose bounds

[rough leaf]

wait howd you determine delta x = 5/2

[grim rock]

i think that was meant to be an n

oops

[round geyser]

How can we imply log

[valid topaz]

||set 9 to 3^2, and so the exponents must be equivalent (4^√2^x)=2. then take ln of both sides (cuz i like ln) to get (√2^x)ln(4)=ln(2). from this we can get √2^x=log 4 2, so √2^x=1/2, and x=-2||

[rough leaf]

i see

[gleaming matrix]

can someone help me with this

[round geyser]

Use this to help you

[rugged spruce]

Guys should I take calc 1 during the summer so I can get caught up or is that not a good idea?

[ancient inlet]

sure

you can

[tulip scaffold]

How are you that far 😭 I’m starting inverse functions next week

[grim rock]

are you learning yourself? that’s pretty good tbh

[tender scroll]

f (t) = {sec^3 (t) - tan^3 (t)} / tan (t)

lim [f(t)]
t->π/2

help-

[tender scroll]

THE SNAIL!

[rough leaf]

you could simplify this down cant you?

[rough leaf]

yo chill it was 5 am i was gekked

geeked*

[rough leaf]

i simplified this to something really weird idk

[rough leaf]

yo @tender scroll

i solved it

do you wanna see my work

i js simplified it fown

[valid topaz]

gaijin is here

to suck out ur wallet

[tender scroll]

my wallet is already- yk

im done for

[tender scroll]

yea sure

[warped shuttle]

thanks!

[rough leaf]

wait mb

i was at sci obly

oly*

it’s like

it’s js pure simplification

wait i’ll send you a pic jm afew

in a few*

[true oasis]

hi

[versed garnet]

does anyone know how to graph inverse trig functions

im struggling

[lunar pumice]

inverse is just flipping the graph across y=x

mark some points if you need to

[versed garnet]

i don't understand the domain part

[raw hill]

$$\sin \left(\frac{\pi}{8} (x-8) \right) \neq 0 \implies \frac{\pi}{8}(x-8) \neq n\pi$$ for some integer $n$.

[obsidian monolith]

Civil Service Pigeon

[raw hill]

$$\implies x-8 \neq 8n \implies x \neq 8n+8=8(n+1)$$
but $n+1$ is also an integer, so rebrand it as $k$ for convenience

[obsidian monolith]

Civil Service Pigeon

[versed garnet]

thank you

[raw hill]

[round geyser]

Wait

Let’s convert into degrees

[round geyser]

This

[brazen robin]

pi/8 = pi/4/2

[river otter]

hey can anybody give me a simple explanation for this thing

I actually don’t know if this is precal or not so sorry if advance if it’s not

[willow wraith]

Looks like precalc

I assume you’re somewhat familiar of the concept of a piecewise function?

if not basically

the right function is only performed if the left condition for x is true

and then you see you see

assume d is greater than or equal to zero

and solve for x and y

looks like a systems of equations problem at its core

[spare basin]

Bro you play this roblox game too? What stage r u on, maybe we can grind equations together

just solve the 2nd equation to get x^2-1=y

then 2^x+x^2=17, we can solve for small value and we get x= 3, therfore y=8 and therfore x+y=11

[rough leaf]

is it 11?

[round geyser]

Solve y first

[round geyser]

Plug 0 into the first one

3! =6

Then it’s just 1+y=16

And hence y=15

[rough leaf]

yeah

8?

[round geyser]

y=15

16-1

[rough leaf]

8 works too

[round geyser]

How did you do that

[rough leaf]

it doesn’t fit the second criteria

[round geyser]

15+1=16

Take the sqrt(16)=4

[rough leaf]

but 2^4 is 16

[round geyser]

x=4

And y=15

[rough leaf]

16+15 doesnt equal 16

[round geyser]

2^0 is 1

[rough leaf]

then x has to be 0 not 4

the second criteria domt work

y has to be 8

and x =3

[round geyser]

Where did you get that

we know x >= 0

[rough leaf]

okay so i js plugged random values in the firsy equation for x

[round geyser]

It has to be a negative number

[rough leaf]

i decided to test 3

[round geyser]

or 0

I used 0

[rough leaf]

meaning if x=3

y would have to be

8

[round geyser]

I used 0 to plug the first criteria

[rough leaf]

and it fits rhr second equation

[rough leaf]

yeah so in your case y=15

[round geyser]

Then use that value for the second one

[rough leaf]

but you get sqrt(16)=0

which is weong

[round geyser]

Wait

x is greater than or equal to 0

What if we used 1

[rough leaf]

yes

y=14

doesnt work

for the second equation

[round geyser]

Only 3 works if I’m right

Bc u get 8

[rough leaf]

yes

that’s what i’ve been saying

[round geyser]

x=3 and y=8

Then x+y=11

[rough leaf]

yup

[round geyser]

Other else

Or is that it only x=3 works

[civic river]

Hi 👱‍♀️

😃😁

😀

Hello

????

Is this channel dead

[fossil kindle]

yes

[round geyser]

Hey

I wonder how would u guys approach to this

I only thought of using Pythagorean Theorem

[grim rock]

what are we finding

[valid topaz]

u could use power of a point i think

if u wanted to be fancy

[round geyser]

r

[grim rock]

oh esdius

radius

[round geyser]

The radius

I thought of take 64 and divide by 4 sides

[valid topaz]

so 144=8r

PoAP

[round geyser]

To get 64/4=16

[round geyser]

I wonder where did u get 144

[valid topaz]

wait no

[grim rock]

12^2 =144

[valid topaz]

u can't use power of a point

so that won't work

[round geyser]

What are some theorem we can apply

[valid topaz]

Pythagorean is the only method then i think

[round geyser]

Cord- cord theorem

[valid topaz]

that's when the chords intersect inside a circle

not applicable here

[round geyser]

Let me think

[round geyser]

I see an arc

Is there an theorem with arcs

[valid topaz]

well, if 2 angles intercept the same arc, and one lies on circle center and one lies on circumference, then those angles are in a 2:1 ratio

not useful here tho

[round geyser]

We only know radii is the same

[round geyser]

Ohh

[round geyser]

That’s a tangent

[valid topaz]

arc

relies on arcs

[round geyser]

The length of a tangent is 12

[round geyser]

That’s my previous notes

Does it look similar

[valid topaz]

mhm

that's basically the q

but with diff numbers

[round geyser]

q?

I thought of

First take 64 and divide by 4 to get 16

[valid topaz]

question

[round geyser]

Oh

Okay

16+r is the c

a=12, b=r, and c=16+r

[round geyser]

Like this

[valid topaz]

yes

js solve

[round geyser]

Okay

[round geyser]

It’s r^2+144= 256+32r+r^2

Move the 144 to the 256 and r^2 cancels

112+32r=0

[valid topaz]

um

sqrt(64) is not 16

it's 8

[round geyser]

(r+16)^2=r^2+32r+256

[round geyser]

?

[valid topaz]

the side length of the square is 8, not 16

[round geyser]

Okay now it’s

[round geyser]

r^2+144=r^2+16r+64

144-64=80

r=80/16=5

r=5

[round geyser]

That’s a 5-12-13 triple

[round geyser]

Wait btw I forgot to mention

The base is 12 cm^2

I have to also use 1/2 bh

[civic river]

why are you guys doing geomtry in precalc

just ask #algebraic-geometry

they know sheet

[valid topaz]

you genuinely don't know what algebraic geo is right?

it's not just basic geo

it's a predominately postgrad class bruh

[civic river]

im jk

just jk

[civic river]

then why does it have geo in it

[valid topaz]

😔

has to be ragebait

[civic river]

no im just asking for math and sience and fax

i really want to get in ISEF real bad

[round geyser]

Is there math on ISEF

[valid topaz]

probably

[civic river]

One time i tried to get to IMO but my country's entrance exam was online and had no supervision so everybody cheated using chatgpt except me bc i wanted to play fair

[round geyser]

Ok

[civic river]

thats not ok

AND I LOST

[valid topaz]

that sounds like a huge overlook

[civic river]

BADLY

[round geyser]

Can we just make it x=1 and y=5 then plug the value

[civic river]

yes

yes we can

[round geyser]

Then it’s 6

[civic river]

now i cant participat in IMO and i got forced to participate in the chemestry version yuck

[valid topaz]

wdym

you can retake

at least in US u can

[civic river]

us

[round geyser]

Is ur user Silver Nitrate

[civic river]

yeah im retaking it this year but my friends suggested that i go to IOI

[civic river]

Yes

I want to go to MIT/Standford real bad

and these Olympiads are the only way to guarantee my success

[civic river]

yk none of thte students good at math in our school got in except for people who are somehow still passing got in

some of them even got the gold medal

i hated math that time

until i found out that the problem was the exam itself

there was a national math competition and i got a full mark out of 7 people from the idk how many students around the country

Got third place in advanced mathematics

and hope i get first this year

if ifocused on math only and skipped the science part i could get a very high mark

[valid topaz]

hmmm

[thick bay]

Anyone help

[civic river]

wtf is this

[valid topaz]

supposed to be in #discrete-math

i don't think there's a graph theory channel

[civic river]

thx for the reminder of studying graph theory i need that real bad

[round geyser]

What about this

I guess Ann is wrong

[chrome elk]

Wrong

[winter comet]

for a second i thought you meant the Ann in this server and then I read the problem 💀

o wait she left the server again 💀

[fossil kindle]

ann is correct

[round geyser]

Do we add 36 and 48

[fossil kindle]

yeah

[round geyser]

Making it 84

Then is it 84/2

42 girls and 42 boys?

[deft rampart]

can anyone help plz

[hasty mica]

#calculus

[rough leaf]

ts a great problem

imma try it later

[round geyser]

How did you approach to it

[idle field]

you have to calculate du/dx

[fossil kindle]

no

[idle field]

try this

[round geyser]

Is this a word problem

[fossil kindle]

i added the two then divided 36 and 48 by 84

[civic river]

i cant read this

[round geyser]

36/84 and 48/84

[fossil kindle]

yes

36/84 is 3/7

48/84 is 4/7

[round geyser]

So their the same

Ann is correct

[idle field]

Is it too dark?

[round geyser]

Have u heard about GCSE exam

[idle field]

Or is it messy?

[civic river]

no the sin kinda looks weird

[round geyser]

This one is easy

[idle field]

I tried getting rid of the sin(2x)

[round geyser]

x^3-x^2+12=0

Rational root theorem

[civic river]

no the way you write the sine

[round geyser]

1,2,3,4,6,12/1

[idle field]

because I was writting sen, which is sin in portuguese

[civic river]

oh

جا is sin in arabic

[round geyser]

Cos?

[civic river]

EXCUSE ME

????

[round geyser]

Cosine

[idle field]

Cosine

[civic river]

oh

[round geyser]

Yea

[civic river]

its جتا

[round geyser]

I meant cosine in Arabic

[civic river]

ظا is tangent

ظتا is cotangent

غا is sec

غتا is cosec

or csc

[round geyser]

ظا= جتا/جا

Guess this formula

[civic river]

yes

why do you have an arabic keyboard??

[round geyser]

Idk

I copy out of your text

I meant to do

tan=sin/cos

[civic river]

ohh

OH-

[round geyser]

Check my work

[idle field]

it's correct

well done

[deft rampart]

took me about 35 mins to answer

i got it correct tho

[round geyser]

One real and 2 imaginary

[idle field]

yes

[round geyser]

When I graphed it

You will see one solution

Which is -2

If I see decimal ans

It has to be a radical ans

[round geyser]

This too

[round geyser]

Also this

What kind of equation is this

[raw hill]

This is just finding the limit of a recursion, albeit without proving that the limit exists in the first place.

[round geyser]

How would the graph look

[raw hill]

You can do this yourself on Wolfram Alpha

[round geyser]

Thanks

[loud salmon]

Where would I go for help with matrices

[raw hill]

The regular help channels would always suffice.

#❓how-to-get-help

[carmine orbit]

linear algebra

[viscid nimbus]

Hey I can help

[tardy birch]

omgg why were yall up at 1:08 am!!!!!!!

[wraith ledge]

discordian discovers timezones

[tardy birch]

ooo...i mean iggg...chat i was busy watching a kdrama! ngl

[wraith ledge]

ok

[tardy birch]

lol yeaa

[round geyser]

Hey

Check this for me

[valid topaz]

yea, but you could've just used definition of log

[round geyser]

What is it

[valid topaz]

if log a b=c, then a^c=b

[round geyser]

I thought if that too

X^15=12

[tardy birch]

tuff 😛

[visual plaza]

guys idk why but im strugglingg with diferentiating this can someone help and explain the chain rule+product rule and how to apply them together here? i get the whole u'v+uv' thing but after getting the derivatives of both parts of the function im stuck. ik you have to common favctor but i just think imn not totally getting how to go about this

[ancient inlet]

let u = smth and let v = smth

differentiate both using chain rule

then combine them together using product rule and factor them out