r/mathshelp

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please ignore me not stating the rules btw

How to score good in maths

I always try to practice MATHS but stuck in every second question ❓

Hi everyone,

I need to score at least 1500/1600 on the SAT to get into my dream bachelor's program. Unfortunately, because of financial difficulties and some poor educational choices, I've been away from serious math (and studying in general) for about five years. To be honest, my fundamentals feel terrible right now. I struggle with mental calculations, and sometimes I feel embarrassed by how much I've forgotten. I have four months to dedicate to this goal, and I'm fully committed. I've always been a good student when I put in the work, and I'm willing to study consistently every day.

My biggest problem is that I'm completely overwhelmed by the sheer number of resources online. Every time I search for SAT advice, I find hundreds of books, courses, YouTube channels, and study plans, and I end up not knowing where to begin. I don't want to waste precious time on unnecessary classes or mediocre resources. I want the most efficient roadmap possible to maximize my chances of reaching 1500+.

So, if you were in my position, where would you start? What would your month-by-month (or week-by-week) plan look like? Which resources are truly worth using, and which ones should I avoid?

Any advice from people who started with weak fundamentals and still achieved a high score would mean a lot to me. Thank you!

I already understand the algebraic proofs using the Fundamental Theorem of Linear Algebra, Rank-Nullity Theorem, Gaussian elimination, etc. Those are clear to me.

What I'm looking for is the deep intuition behind why this has to be true.

In other words, why is the dimension of the column space always equal to the dimension of the row space of the same matrix?

Geometrically, the column space and row space live in different vector spaces (R^m vs. R^n), so it isn't obvious to me why they should always have the same number of independent directions. What is the underlying constraint that forces this equality?

I'm not looking for another algebraic derivation. Instead, I'd love explanations that answer questions like:

What is the geometric picture?

Is there an information-theoretic, transformational, or degrees-of-freedom interpretation that makes this equality feel inevitable rather than something we simply prove algebraically?

Are there any visualizations or mental models that make this theorem "click"?

I'm especially interested in explanations that make the result feel almost obvious once you see the right perspective.

---

Edit:

I know most of the popular formal algebraic proofs to prove this, what i am looking for is intuitive perspective

For example, we can intuitively understand why

rank(A) + nullity(A) = n

When we apply the transformation A to vectors, each independent direction has only two possibilities: it either survives (maps to a nonzero independent direction) or it is killed (maps to the zero vector). Since these are the only two outcomes for the n independent input directions, it is intuitive that

rank(A) + nullity(A) = n

I'm looking for a similarly intuitive explanation for this theorem. Rather than an algebraic proof, I want a geometric or conceptual way to understand why it must be true

Same as title. Need yr help thodi si

(Solved, no more help needed 😁)
Not even my old maths teacher understood what I’m on about, hopefully some people here can.

I had a taster session for a sixth form in maths, AQA A-level, and my teacher made us do some basic sequences. She made us all write down a sequence and create our own, where the difference is always the same number. I chose 7 as the first number as 4 as the difference. I got the sequence 7, 11, 15, 19, 23, 27 (it’s wrong in the photo I know, that’s because I rushed to note it at the end). And we formed 2 simultaneous equations from this sequence. For me it was 7x+11y=15 and 19x+23y=27.
When everyone solved their equations, we all got (-1,2)!!!! And she didn’t really explain it, and told us to go research it but I have no clue on how to explain it. She said to research the proof on why it does it. Is anyone able to provide the name of the theory or maybe a website that helps me learn the proof?? I’m not waiting 9 weeks 😔

Thanks if anyone does!!!

Edit: the whole class created their own sequences, everyone got (-1,2).

I’m a bit confused about the way HDFC Bank calculates interest on part prepayments and would appreciate if anyone who has dealt with this can explain.
My situation:

Home Loan with HDFC
Interest rate: 7.95% (floating)
EMI date: 25th of every month

Planned part prepayment: Rs. 5,00,000
I initially wanted to make the part prepayment on 29 June, but the HDFC representative advised me to wait until 3 July.
According to them:
If I prepay on 29 June, I’ll have to pay around Rs. 3,000 as simple interest.
If I prepay on 3 July, I’ll pay only around Rs. 200 as simple interest because of the way they calculate the EMI cycle and prepayment window.

This is where I’m confused.
My understanding was that if I prepay earlier, my principal reduces earlier, so I should save more interest overall. HDFC is saying that waiting until 3 July is actually better.
Has anyone experienced this with HDFC or another bank?
Is this a standard banking practice?

Is this “simple interest” just interest accrued since the last EMI, or is there some internal accounting rule?
Even if the immediate interest component is lower on 3 July, does delaying the prepayment mean I end up paying more total interest over the life of the loan?
Which option would you choose, and why?
If anyone has an amortization example or works in banking, I’d really appreciate your explanation.

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i would like to know what diffrent methods are there to understand it better i hope and if anything similar to what i did can be done .

i am preparing for IOQM- that is a test / competitive exam for slection of representatives for IMO .

my way , i dont know if its right , i feel its wrong but i cant understand how to do it similar to this way .

Hi,

My son is in class IX and follows ICSE Mathematics for class IX Book 1 by

OP Malhotra

SK Gupta

Anuhutai Ganguli

Ayushree Gangal

Please suggest some brilliant books for ICSE Class IX so that I can well prepare him for the ICSE exams.

Thanks

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Hello I need help with this problem. I've established that the sequence is increasing. I want to use the MCT that it is bounded --> this sequence is convergent.

I've tried using induction to show it's bounded above but it has not worked. I know this is related to the harmonic series that is divergent. I tried using a similar proof as in the book that used to establish that the harmonic series is divergent. I have not learned about series so I cannot use series properties here. I recognize that:

y_1 = 1/2 is less than or equal to 1/2

y_2 = 1/3 + 1/4 is less than or equal to 1/2 + 1/2 = 2/2 = 1

y_3 = 1/4 + 1/5 + 1/6 is less than or equal to 3/2 = 1.5

y_4 = 1/4 + 1/5 + 1/6 + 1/7 + 1/8 is less than or equal to 4/2 = 2

So y_n is less than or equal to n/2. . . How do I find a definite upper bound?

Thank you.

I'm currently a rising 9th grader that has decided to skip geometry over the summer. As of right now, I only have about a month to prepare. By the near end of the summer, I have to take an advancement exam which requires a minimum of an 85% to pass. My goal is to get an extreme clear understanding on most to every topic. Are there any suggestions on any resources, (websites, apps, etc,) how to prepare, or any material, topics, or concepts I should really review, revise, or focus on in preparation for the exam?

(the curriculum is based off of is the big ideas math geometry textbook)

2+2x2=

I was one of the suckers who took an sba eidl loan during covid. I enjoyed a year of deferred payments, but not interest.

Something got messed up on their end and my original payments were not being applied to that loan (or any loan)

I believe I've overpaid many thousands in interest, but they deny that claim over and over.

Details:

Loan closed 6/17/2020

Loan amount $149,400

Rate 3.75

1st payment due was $728 on 6/17/21 however, I've made extra payments of $272 ($1000 a month total) starting 6/17/21.

Extra payments went to interest first.

It took until 10/24 to start touching the interest. I've emailed, called, messaged through the website and always told it's correct. Help!