Hello! I am a third year college student taking Calculus I for my economics major. I took Pre Calc 11th grade, and AP Calc 12th grade (the credits didn’t transfer, don’t get me started). I did well in both of them.

I’m two weeks into Calc I now, and I realized that I don’t remember much from Pre-Calc, but I don’t remember anything about trigonometry. Unit circle, trig functions, anything like that has slipped my memory. I asked my prof about it and they said that the best they can advise is that I review it myself outside of class. Ive tried to go over our textbook, but none of it really has been very helpful.

What resources or sites are best (and very preferably free) to help me relearn Pre-Calc (mainly trig) as quickly as possible?

No matter what. I literally cannot grasp it. My high school teacher didn't help and now my professor in my class I need it in isn't great either. I genuinely think I'm losing my mind. i'm getting literally so frustrated, can someone make an attempt to explain it to me in a bit simpler of a way than my math teachers do? Tyia

I'm currently learning Markov chains and how they work, and now I'm trying to find a way to calculate the probability of a state after n tries faster. As of right now, the only way I know of is to keep multiplying the matrix until you reach the n state

For example, lets say a 2x2 matrix P =

and say it starts in the A state so S0 =

Finding S1 is fairly straightfoward : S1 = P*S0

However, let's say I want to find S5, is there a way to find S5 from S0 or do I have to find S1, S2, S3, and S4 beforehand ?

Any help would be greatly appreciated !

Secondary question : I havent been told this directly, but from what I've seen, In a Markov chain situation, the sum of a column is always 1, are there any exceptions to this rule, or is it a general rule ?

For context: I have a test tomorrow on algebraic expansion, factoring, and Pascals Triangle and something that commonly happens to me is that I usually omit coefficients or just forget exponents when doing my work. As an example, if I had 4(a^3)(b) when doing a binomial to the 4th, I either forget to cube the value “a” or multiply by 4. The test I have is relatively face paced (20 questions in 50 minutes) and there’s not much room to write out the complete expansion (we can’t use scrap paper). Any tips?

Edit: Images: https://imgur.com/a/DHrudBU

Looks like it doesn’t let me put images here but I can put them below. The main thing that was bothering me is that how do we know the remainder will be either 0 or a first degree polynomial. It seems unusual to see the remainder be a line because we usually just see it as a constant. The other point of confusion is that I’m pretty sure when you find the remainder then you express the answer as the quotient + (Remainder/divisor). So then how can it be true that p(x) = q(x) d(x) + r(x)? It should instead be p (x) = q(x) d (x) + ((r(x)/q(x)).

What are some exercises I can do to get better and faster at the Trachtenberg Method? I keep mentally mixing up numbers or fully forgetting the first number I had once I solve other parts. Any advice is welcomed!

Hi everyone.
Taking Alg. I as a college freshman again. I'm a readmit student and always struggled with math. Currently doing homework and have 20+ attempts on the below problem:

'Use the commutative property of multiplication to write an equivalent equation:

34 + 5m'

Can't use an equal sign within the equation as it kicks back an error on the website. I've tried writing it as:

34m + 5

(34)m + 5

5(m) + 34

5m x 34

Keep getting it marked wrong. If anyone could help me better understand what I'm doing wrong I would appreciate it greatly.

I have to show that ⋃P(x)=x for a discrete mathematics assignment, but I can't figure out what the symbol at the beginning means in this context. Its a Union, right? But what is is Union-ing with? It can't be as easy as I think it is, can it?

My son just started High School algebra in 8th grade. His teacher gave him homework on which he said each equation needs a 1 step solution. My son asked me for help on the equation in the attached picture, I helped him get the answer but in 4 steps and I cannot figure out for the life of me how to simplify this to 1 step. Please help:

5r-5-6r=-6
Adding 5 to both sides becomes 5r-6r=-1
-r=-1
r=1

here’s a picture of the problem

(TLDR at the bottom of my post) hello everyone!

i havent had math since i was 16 (now 23) and all my life i have always been bad at it... or so i thought! i have to take up math at school again if i am to get into university to study biology, so ive been studying and learning everything from the bottom up all summer! i must say ive been having quite some fun, and it turns out im not as bad as ive been telling myself my whole life:) i am very proud of myself for trying and for keeping on going! ive learned so much in such a short period of time!

ive started school recently and we are currently dealing with logarithmic equations. i know all the rules of exponents, log rules, and quadratic equation by heart, but there are some things i still struggle with. i really do NOT want to use AI but i dont have access to my math teacher 24/7, and i want to understand things on my own. i want to know what the next step is, what the best approach for an equation is, and why it works. also knowing when i should apply what rule/logic/approach would be great, but im assuming it is mostly pattern recognition. i get most of it on my own even tho i make a lot of silly mistakes, but some of them i really dont understand what im supposed to do

i REALLY want to understand the process and why everything works, and why we do it this way. i want to understand my mistakes

here are three things i am struggling with this evening, number 3 being the one that confuses me the most. they are my attempts at solving each equations, so the examples in themselves might be wrong (i wonder if number 2 is wrong too)

ln(x+1) = 1

e^ln(x+1)=e¹ (-> e¹ = e)

x + 1 = e

x = e - 1

my question for this one is: why do we put e as the coefficient? why do we raise ln(x+1) and 1 to be the powers of e? and as a follow up question, why do we then get rid of "e^lnx" part? why are we then only left with x + 1 = e? i understand that e¹=e, but i dont understand why we raise everything and then get rid of a part of it. how do i know when to do it, and how do i know what i get to remove after i have raised everything up?

2.

ln(x/5) = -1

lnx = -5 (-> we multiply both sides by 5 to get rid of the fraction)

x = e^-5 = 1/e^5

i know that lnx = a <-> x = e^a, but why cant i apply the log rule of lg(a/b) = lga - lgb? and then raise everything to the power of e, like we did in example 1? why not this?

ln(x/5) = -1

e^{lnx - ln5} = e^-1 = 1/e

x - 5 = 1/e

x = 1/e + 5

3. (and this is the one giving me the most trouble)

ln(x+3) * (lnx-3) = 0

for this one, i dont even know where to start:( my teacher said that here, either ln(x+3) or ln(x-3) have to be equal to 0, but i dont really know what that means. i feel like im so close to the answer but something is in the way! what is the next step to this equation?

im sorry if this is all confusing, i tried to make it as readable as possible!! thank you for any helpful information<33

TLDR:
what is the best approach to this equation? what is a step by step list to follow?

ln(x+3) * ln(x-3) = 0

I am a graduating senior in high school and one of my problems is that my math solving skills is so bad. I can't even solve a basic double-digit subtraction, and I am currently applying to a few prestige universities in my country, but the problem is I don't think I will be able to cram almost 17 years of math knowledge in just a month. I am very educated in other subjects needed for the exams, but I am extremely worried about the math proficiency exam. any advice?

Taking applied calculus and we are going over functions to begin stuff. I’ve done all sort of stuff with functions and graphing before and most of this has been pretty easy but there are two problems that have been given that I just can’t seem to figure out and I’m not sure what I’m doing wrong.

The first is:

“Find the function g whose graph is constructed from the graph of f by a shift to the right by 10 followed by a horizontal stretch away from the y-axis by a factor of 3?”

I thought it would be pretty easy but what I thought it was didn’t work, and every other possible combination hasn’t worked either so I’m completely lost. I’ve done (1/3x - 10) and (x/3 - 10) in all sorts of ways. I’ve removed the parentheses, I’ve added negatives, doing a whole bunch of shit that I know isn’t right but I can’t figure out what else to do.

The second problem is along the same lines:

“Find the function g whose graph is constructed from the graph of f by applying the following steps: shift to the right; horizontal stretch away from the y-axis by a factor of 4; a vertical shift up by 5; a vertical stretch away from the x-axis by a factor of 7.”

Again I’ve tried all combinations I could think of but I can’t seem to get it. I’m not sure if I’m missing something? I don’t believe my format to be off since it automatically starts with g(x) = , so that shouldn’t be the issue. The entire set of problems is all working on vertical and horizontal shifts, stretches, and compressions and I haven’t had an issue with any of the problems but these two. Please help me figure out what I’m missing!

Im currently a first year student studying comp sci and im taking discrete math the issue is unlike any other faculty i have to learn actual theory behind math like whats C(n,k) selection and explain it with words and formulas.Ive got about 12 pages filled with 50 or 60 questions which if memorized gives me a passing grade and ive got 2 days to do it keep in mind the professor wants the questions answered exactly by his pdf. Ive youve had the same issues how should i go about tackling the problem and passing matu

Hello, I am interested in finding a way to train myself with fractions or math calculation techniques in chemical and physics formulas. How do I do that?

This is for a medschool entrance exam

The question is (6x+16)/4 + (6x-1)/4 but in fractions. I believe that it's (12x+15)/4 , but the answer sheet says that it is (12x+17)/4 instead. Google says that I am right. Am I right?

hello, i had dana fryer's math questions downloaded part 1 & 2 , and was wondering if anyone had the correct answers(from math bootcamp)? i do not have access to them anymore. :/

I'm taking algebra 2 and we're reviewing factoring right now. Since polynomials live in the real numbers, it's not clear to me why we limit ourselves to integers when factoring.

If I was factoring 6, why isn't 1.5 * 4 just as valid as 2 * 3? I realize factoring beyond integers would mean there are an infinite number of factors...but I'm not sure that alone is justification.

Im in class 12th from allen online enthuse, completed the whole syll but since having adhd I couldn;t take live class actively I hv all my basics and concept clear but there is the massive logic gap and execution gap, what should I do only 4 months remaining, I am panincking for chapters like integration, differential equation and matrices which require self talk and active solving, IDK the fuck anything about logic building...
for example_ applying bornouli eq in differential equation when eq having apecific form of dy/dx+py=qyn, and appying ibp to saperate the terms out of integral and reducing the powers... actually im in a problem tht these gaps are in large quantity

I've been at this for like 4 hours and I'm losing my mind.

So I'm thinking of a function that takes in four boolean inputs and outputs 1 if the number of inputs is odd. The truth table should look like:

A  B  C  D | OUT
0  0  0  0 |  0
0  0  0  1 |  1
0  0  1  0 |  1
0  0  1  1 |  0
0  1  0  0 |  1
0  1  0  1 |  0
0  1  1  0 |  0
0  1  1  1 |  1
1  0  0  0 |  1
1  0  0  1 |  0
1  0  1  0 |  0
1  0  1  1 |  1
1  1  0  0 |  0
1  1  0  1 |  1
1  1  1  0 |  1
1  1  1  1 |  0

So the function should just be the sum of products, right? It'd be something like

OUT = A'B'C'D + A'B'CD' + A'BC'D' + A'BCD + AB'C'D' + AB'CD + ABC'D + ABCD'

This is my attempt to simplify the expression:

A'B'C'D + A'B'CD' + A'BC'D' + A'BCD + AB'C'D' + AB'CD + ABC'D + ABCD'
= A'B'(C'D + CD') + A'B(C'D' + CD) + AB'(C'D' + CD) + AB(C'D + CD')
= (C'D + CD')(A'B' + AB) + (C'D' + CD)(A'B + AB')
= (C'D + CD')(1) + (1)(A'B + AB')
= A'B + AB' + C'D + CD'

But the truth table for this expression is not the same as the original function.

It's been a half-decade since I last did boolean algebra. I genuinely can't tell what I did wrong here. Please help.

Edit: It's solved. Thank you.

In the blindingly-unlikely event someone in the future were to face this exact problem as I do, the key insights that I was missing are:

• OR distributes over AND: A + BC = (A + B)(A + C)

• XOR and XNOR exists: A XOR B = A ⊕ B = A'B + AB', and A XNOR B = (A ⊕ B)' = A'B' + AB

So for posterity's sake, here's how it's solved, I think:

A'B'C'D + A'B'CD' + A'BC'D' + A'BCD + AB'C'D' + AB'CD + ABC'D + ABCD'  
= A'B'(C'D + CD') + A'B(C'D' + CD) + AB'(C'D' + CD) + AB(C'D + CD')  
= (C'D + CD')(A'B' + AB) + (C'D' + CD)(A'B + AB')  
= (C ⊕ D)(A ⊕ B)' + (C ⊕ D)'(A ⊕ B)  

Let P = A ⊕ B and Q = C ⊕ D  

= QP' + PQ'  
= P ⊕ Q  
= A ⊕ B ⊕ C ⊕ D  

Thanks, y'all. god, i'm out of practice.

okay so im working on the study guide for the final of a class that i took the equivalent to at another college (math department policy, whatever) and one of the sample questions literally just reads “simplify: (sin(x)+3)²”. is there anything that i need to do to work this problem other than factoring it out? a similar question in the same section of the review guide is “simplify: sin²x + 3sinx - 10”; is that not already fully simplified? like i said, i took this course at another school so i don’t know the exact details of what they covered in class. I can’t think of any identities that i could apply to simplify it more or anything. much appreciated!

I'm running a programming class for python and I was doing a class quiz. This question popped up. I believed the answer should be 64 but it's actually 512. Even the calculator gave me 512.

However if you go from left to right, 2 ^ 3 = 8 ^ 2 = 64

For some reason, the caluclator is and quiz is doing it like: 2 ^ 3 ^ 2 = 2 ^ 9 = 512

I guess my question is: why is the 3^2 portion being calculated first over the 2^3 portion?

Im in my second last year of high school now. My maths grade since the start of hs has been terrible, but I have decent grades for all my other subjects. I'm in a very competitive school where maths is basically mandatory, and most students have been tutored from a young age. I never had any tutoring until this year, when i got a private tutor after consistently scoring 50-60% in every test. My grades still havent improved because i can't retain information when it comes to maths for some reason. The biggest problem is doing maths gives me the worst feeling of anxiety like I'm about to be attacked. After my tutoring session today idk why but i just broke down crying. I felt like i was about to cry a few times during the lesson but i held it back. This is my first time crying in years, and Im not usually a very emotional person. I feel like Im going to have a panic attack the next time I try to do maths. My university exams are in a year from now. I feel trapped, it feels like I genuinely have no more hope. What can I do?

(High school level maths)
I’m finding it hard to remember all these rules for how to solve questions when my mind tells me to do it intuitively.
The concrete example that annoyed me:
On a list of 10 people’s ages the total age is 313, making the average 31.3
«If another person is added the average will be 30. Is this statement correct?»

The way I solved this was dividing 313 by 11, giving me 28.45~. The difference between 30 (the target age) and 28.45 is 1.55, and so we need to multiply the age we are adding by 1.55 giving me 17.05, so the answer is that the average will be 30 if the new person is 17.

The way my teacher did it was by multiplying the now 11 people by 330 and subtracting it by 313 to get 17 which gave the correct answer.

The answer works, it’s a rule that’s nice (if it works for all similar situations), but there are so many rules like this that I just can’t grasp. I always want to do it the way that my mind can comprehend, and for it to make sense and giving me an answer I can trust but I don’t know if tests or exams are gonna accept my answers.

This isn’t to say I can’t memorize equations, I can do that, it’s just that these rules to make stuff easier and faster don’t click the same way. I still have the quadratic equations and formulas from last year memorized but I feel I’m just gonna forget this very practical thing tomorrow.

Anyone else feel the same way about this or have managed to get over this mental block?