3
votes
6answers
579 views

How should I self-study calculus?

So I already took Pre-Calc, and ended up with a B both semesters. I am an incoming senior in high school. My special-ed case manager won't let me take it because she doesn't want to see me panic ...
3
votes
3answers
91 views

How to prove that $\frac{a+b}{2} \geq \sqrt{ab}$ for $a,b>0$?

I am reading a chapter about mathematical proofs. As an example there is: Prove that: $$(1) \space\space\space\space\space\space\space\space\space\space\space \frac{a+b}{2} \geq \sqrt{ab}$$ for ...
2
votes
3answers
37 views

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$?

Why $ (1- \sin \alpha + \cos \alpha)^2 = 2 (1 - \sin \alpha)(1+ \cos \alpha)$? I am learning trigonometric identities one identity I have to proof is the next: $ (1- \sin \alpha + \cos \alpha)^2 = ...
1
vote
5answers
65 views

Prove $\frac{\sin A}{\sec A+\tan A-1}+ \frac{\cos A}{\csc A+\cot A-1}=1$

$$\frac{\sin A}{\sec A+\tan A-1}+ \frac{\cos A}{\csc A+\cot A-1}=1$$ Prove that L.H.S.$=$R.H.S. This type of questions always creates problem when in right hand side some trigonometry function is ...
0
votes
1answer
73 views

Starting Calculus with a weak foundation in Pre-Calculus

I am struggling in Pre-Calc mathematics, and I want to know is it ok if I start Calculus I with a weak foundation in Pre-calculus mathematics? I understand the general gist of limits, function ...
0
votes
4answers
42 views

Why do you add +- to only one side when you remove square root from both sides?

As the title says, why when you take a square root of both sides of the equation do you add $\pm$ only to the side which is a number, as opposed to an unknown? For example: $$x^2 = 9 \implies x = ...
0
votes
2answers
31 views

Need help with this absolute value equation

I need to solve the following equation involving absolute value: $$|x-1| = 1-x$$ Looking at the term $x-1$, I thought I'd divide the interval into parts: $x < 1$ and $x \geq 1$. Now, when ...
3
votes
5answers
128 views

How do I show that $\sqrt{5+\sqrt{24}} = \sqrt{3}+\sqrt{2}$

According to wolfram alpha this is true: $\sqrt{5+\sqrt{24}} = \sqrt{3}+\sqrt{2}$ But how do you show this? I know of no rules that works with addition inside square roots. I noticed I could do ...
0
votes
1answer
103 views

Sequence of learning mathematics from basic algebra to calculus.

What would be a step by step sequence of learning mathematics from basic algebra to basic calculus? I pose this question because I am in the process of self-learning mathematics as a preparation for a ...
0
votes
1answer
84 views

Cubic root formula derivation

I'm trying to understand the derivation for the cubic root formula. The text I am studying from describes the following steps: $$x^3 + ax^2 + bx + c = 0$$ Reduce this to a depressed form by ...
1
vote
2answers
23 views

Question about method in an algebra precalculus exercise

($a$ real number) So if $\frac{1}{4}<a<\frac{1}{3}$ prove that $\frac{10}9<R(a)<\frac{11}{6}$ where R(x)=$(2x-1)(x+1)(x-3)=2x^3-5x^2-4x+3$ So my idea was to do the same operations in ...
4
votes
0answers
75 views

Transitioning to Higher Level Mathematics

I am just finishing grade 12 pre-calculus at my school and have strong interest in math. The problem is, it seems some important elements of higher level math are not in my schools curriculum that are ...
2
votes
1answer
132 views

Elementary/Intermediate Algebra book with proofs

I am looking for an elementary or Intermediate Algebra book which has proofs. I would like book to present proofs for statements like If $P(x)$ is a polynomial of degree n then will have exactly ...
2
votes
3answers
189 views

Algebra Textbook

Perhaps this questions was asked already, but I browsed through other threads and couldn't find exactly what I am looking for. I am looking for an Algebra Textbook (high-school/undergrad level) that ...
1
vote
1answer
231 views

Finding domain of a rational function

Find the domain and graph: $$f(t)=\frac{-t}{|t|}$$ My book says to define it piecewise. My questions: $\mathbf{1)}$ Do all rational functions have to be defined piecewise, or just this ...
3
votes
3answers
645 views

Improving basic maths & algebraic manipulation skills

I am currently doing a-levels in the UK (received an A in AS) so doing calculus (differential equations/trig integrals)/linear algebra/mechanics/statistics etc. However I feel that a lot of my basic ...
5
votes
4answers
786 views

Self-teaching myself math from pre-calc and beyond.

Going to be starting grade 12 (pre-calculus) shortly and looking to get ahead. I would like to try some more rigorous stuff on my own and have a couple questions. Ideally I would like to be prepared ...
11
votes
2answers
1k views

Relearning from the basics to Calculus and beyond.

Assume someone has very limited knowledge of math. (low level high school, 5-6 years ago) How would they learn from the basics of algebra, geometry and trigonometry to a solid foundation for calculus ...
3
votes
1answer
355 views

Concrete Mathematics Prerequisite Question

I've been very interested in the book Concrete Mathematics (Graham,Knuth,Patashnik) and I've been reading it for the past few weeks. I'm at the chapter about Sums (Chapter 2), specificaly, the lesson ...
7
votes
4answers
460 views

Arithmetic mean is less than geometric mean (Spivak Calculus 3rd Chapter 2 Problem 22)

If $a_1, \ldots, a_n \ge 0$, the arithmetic mean $$A_n={a_1 + \cdots + a_n \over n}$$ and the geometric mean $$G_n = \sqrt[n]{a_1 \cdots a_n}$$ satisfy $G_n \le A_n$. As a first step to prove this ...
9
votes
3answers
354 views

Being ready to study calculus

Some background: I have a degree in computer science, but the math was limited and this was 10 years ago. High school was way before that. A year ago I relearnt algebra (factoring, solving linear ...
8
votes
8answers
9k views

Calculus book recommendations (for complete beginner)

Well I have not started calculus yet but I am really keen to. I would love if you suggest some books. Points to be noted: I really don't like the way textbooks are written so please no "textbooks" ...
6
votes
2answers
324 views

Filling the gap in knowledge of algebra

Recently, I realize that my inability to solve problems, sometimes, is because I have gaps in my knowldge of algebra. For example, I recently posted a question that asked why $\sqrt{(9x^2)}$ was not ...
0
votes
2answers
115 views

simplify by multiplying by -1 ( Solving equations in terms of a variable)

I am trying to learn Algebra. I'm using Khan Academy, and I just "solved" this problem. I understand all the steps, except #4. Could someone please tell me why I would multiply by -1 to simplify the ...
3
votes
2answers
493 views

Algebra book(s): Beginner through to advanced

I admit, I am not great at Maths; I'm situated in one off the lowest Maths class for my year, partly due to myself losing focus last year. Though, I like maths, I really do. Especially since I do a ...
3
votes
2answers
1k views

Percent change over time

I have the following data: $$\begin{array}{c|c|c}2010 & 2011 & 2012 \\\hline 50 & 20 & 30 \\\end{array}$$ How would the percent change be calculated? Like this: ...
0
votes
1answer
440 views

Good book to help me relearn Algebra 1…

In 8th grade I took Algebra 1 and did not learn a thing.I am now in Cal AB and making B's. I was hoping to reteach myself Algebra 1 this summer by watching Khan Academy and reading a book on Algebra ...
3
votes
2answers
96 views

Problem based on Composite Functions.

Let $f(x) = \sin^{2}{x} + \sin^{2}\left(x + \frac{\pi}{3}\right) + \cos{x}\cos\left(x + \frac{\pi}{3}\right)$ and $g(x) = \left\{\begin{array}{rcc} 2x,\quad0\le x<1 \\x + \frac{1}{4},\quad 1 \le ...
3
votes
2answers
591 views

What's a good progression/path for self-educating from pre-algebra and beyond?

I never got very far in my math studies; I took zero math in college and had terrible teachers in high school. Fast forward to today and I'm a professional developer who's starting to feel that my ...
3
votes
2answers
483 views

Looking for a good precalculus/algebra reference

I'm working my way through Calculus, 9th ed. by Larson and Edwards in independent study. The problem is that many of the exercises and examples use a lot of algebra tricks that are glossed over and ...
6
votes
2answers
519 views

Does anyone know of any good ways to get good at algebra without as much“grind” as doing hundreds of questions a night

I'm coming to a point in college where I can't avoid my math classes any longer. I need to get better at algebra so I don't flunk out of the class when I take it, however I've never been able to get ...
2
votes
2answers
328 views

Good SAT learning resources?

I'm looking to brush up on SAT math. (That's basic algebra, probability and trigonometry.) I'm interested in books and websites.
6
votes
4answers
709 views

What are some good resources for brushing up on geometry and trigonometry?

I'm brushing up on my calculus, and geometry and trigonometry keep coming up. However, these are probably my weakest areas mathematically. Are there any good sites or free PDFs/ebooks that I can use ...