0
votes
0answers
37 views

What is $(k+1)^2[(k+1)+1]^2$ in factored form?

What is $(k+1)^2[(k+1)+1]^2$ in factored form? I'm a bit confused as to what the term "factored form" means in this context. Thank you.
1
vote
0answers
25 views

Arithmetic and Algebra exercises on latex source code.

I´m currently writing a little book for two student that I teach. The book covers school arithmetics and algebra, and it include theory and examples. Since I don´t have time to prepare a good sets of ...
1
vote
3answers
79 views

$2 \cos^2 x − 2 \cos x− 1 = 0$ Find the solutions if $0^\circ \le x < 360^\circ$

Find the solutions of $$2 \cos^2 x − 2 \cos x− 1 = 0$$ for all $0^\circ ≤ x < 360^\circ$. For $0^\circ \le x < 360^\circ$, I'm getting $x=111.5^\circ$ and $x=248.5^\circ$. Is this ...
0
votes
5answers
172 views

How to teach newbie multiply of complex number

I want to teach a newbie the arithmetic law of complex numbers. the law of add is acceptable psychological. but multiply is not. for example, assume $$z = a+bi, w = c+di$$ He (She) may ask me: why ...
0
votes
1answer
71 views

Parabola problem. How far from the vertex is the focus?

A spotlight has a parabolic cross section that is 8 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? I'm getting 8/5 ft. Is this correct? Appreciated!
3
votes
2answers
243 views

best books for learning algebra

My name is Aniket and I have started 11th class recently. I have studied only my school textbooks(NCERT Books) and I am not happy with them. I want to learn Algebra,i.e, all the topics covered in ...
0
votes
2answers
83 views

Find Vector and Parametric Equation

I'm having some trouble finding answers to these problems. When i try to find help online, all i find are (x,y,z) problems and I'm simply looking for a PreCalculus (x,y) problem solving technique: ...
1
vote
1answer
23 views

function inversion and the horizontal shift

I am currently doing inverse functions and graphing radical equations of the form $y=a\sqrt{x-h}+k$ with my algebra class and one of my students asked me the following question. "Why is it that we ...
3
votes
3answers
250 views

How would you prove that the graph of a linear equation is a straight line, and vice versa, at a “high school” level? [duplicate]

This is something I've been wondering about. Namely, I've always accepted "on intuition" that the equation $$ax + by = c$$ is, when graphed, a line. You can plot the points $(x, y)$ satisfying the ...
0
votes
1answer
82 views

Should i continue trying or am i just not good enough [closed]

You've probably seen many of these, and i'm sorry to create another one but i'm at loss. I want to be a programmer at some point in my life (just finishing highschool) I want to go to university ...
2
votes
2answers
109 views

Explaining how to simplify a quotient with negative exponents?

I work as an after school tutor at my high school. I've had kids come up to me asking how to do these types of problems: $\left(\displaystyle \frac{5xy^{-2}}{3z^{-1}} \right)^{-2}$ My approach is ...
6
votes
1answer
148 views

How to combat memorization

As a student in high school, I never bothered to memorize equations or methods of solving, rather I would try to identify the logic behind the operations and apply them. However, now that I've begun ...
7
votes
6answers
621 views

What we're never taught explicitly

I would like to make a complaint really. School math(s) can be the most boring way to learn: sitting down and rote learning binomial expansion or the volume of a cylinder is just not interesting. It ...
213
votes
32answers
31k views

Pedagogy: How to cure students of the “law of universal linearity”?

One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”: $$ \frac{1}{a+b} ...
4
votes
2answers
197 views

What is a good example to show high school students why a proof for induction is a reasonable kind of proof?

I teach average-level high school students who have not had much beyond Algebra 1. I want to show them why induction makes sense. I want the sort of problem where it is intuitive that a statement is ...
0
votes
2answers
90 views

How to calculate profit share for this example [closed]

How can we calculate a profit share for Rs. 100,000 that remained in an account for 5 days only. See this question illustration below I was confused about which tags were more appropriate for ...
0
votes
2answers
31 views

on visualising arithmetic with roots ansd radicals

Is there a visual way to simplify $4\sqrt{12}+4\sqrt{27}$? I know the answer is $20\sqrt{3}$, but I want to geometrically explain it to a 14 year old. Is there also a way to geometricaly interpret ...
0
votes
1answer
147 views

teaching inverse functions using ideas of codomain and onto functions

I am looking for some resources (books, Web sites, etc.) for teaching calculus students about inverse functions, using the ideas of codomain and onto functions (as well as one-to-one functions, of ...
3
votes
5answers
272 views

General misconception about $\sqrt x$

I noticed a large portion of general public (who knows what square root is) has a different concept regarding the surd of a positive number, $\sqrt\cdot$, or the principal square root function. It ...
3
votes
1answer
66 views

Is a sandwich appropriate here?

On an exam we were asked: what is the domain of the following function? $$\large f(x)=\frac{\frac{x}{x-2}}{\frac{2x+7}{x-1}}$$ My solution: This is the same as $$\large ...
7
votes
5answers
947 views

How can I convince my math teacher?

Ok, so I got an answer wrong on my exam because my teacher says that the function $f(x)=\frac{(x+2)x}{x+2}=x$ but I insist that it isn't defined for x=-2. If it was then $\frac{x}{x}=1$ for all reals ...
-4
votes
1answer
83 views

Elementary Algebra question

Ok guys so I've been out of school for eight years, never used algebra again, also I was forcibly removed from school in 9th grade. I need to ask a few questions on Elementary Algebra, what are the () ...
80
votes
11answers
10k views

How to convince a math teacher of this simple and obvious fact?

I have in my presence a mathematics teacher, who asserts that $$ \frac{a}{b} = \frac{c}{d} $$ Implies: $$ a = c, \space b=d $$ She has been shown in multiple ways why this is not true: $$ ...
19
votes
4answers
1k views

How to respond to “solve this equation” in a basic algebra class

If it's acceptable practice on math.se, I'd like to really only ask this question of math educators as opposed to students or mathematical researchers. Some researchers will undoubtedly think the ...
5
votes
2answers
498 views

How can I make sure I never forget.

I am currently refreshing my Elementary Algebra using Schaum's Outlines. I find them useful as they are choc full of exercises (Which I now realize is the only way to master algebra). I am worried ...
45
votes
12answers
3k views

How can I introduce complex numbers to precalculus students?

I teach a precalculus course almost every semester, and over these semesters I've found various things that work quite well. For example, when talking about polynomials and rational functions, in ...
0
votes
1answer
62 views

How is each factor of an expression called? [closed]

$$mc^2.$$ is called an expression. Correct me if I'm wrong. I'd like to see this expression as $$m * c^2.$$ Here, one of the expression's factors is $m$. Is there a general name for the factors of an ...
4
votes
3answers
826 views

why 0=0 is not possible??

Hi one of my friend showed me one proof i.e. $1)$ $2^2 - 2^2 = 10 - 10$ $2)$ $(2+2) (2-2) = 5 (2-2)$ $3)$ dividing both sides by (2-2) $4)$ $(2 + 2) = 5$ I know this is wrong in first line as ...
2
votes
2answers
419 views

How to get better at algebraic manipulations?

I've always been able to manipulate equations found in school homework easily. But when tackling more challenging questions from puzzle books - where I might need three quarters of a page to ...
1
vote
1answer
168 views

Should students be taught that $\int dx/x = \log(|x|)$? [closed]

I think in precalculus students should be taught the following: Euler's identity for $e^{i \theta}$. The principal value of $log(x)$ for $x<0$. Then in Calculus they should be taught that $\int ...
36
votes
25answers
6k views

“Negative” versus “Minus”

As a math educator, do you think it is appropriate to insist that students say "negative $0.8$" and not "minus $0.8$" to denote $-0.8$? The so called "textbook answer" regarding this question reads: ...
3
votes
4answers
385 views

Factoring $ac$ to factor $ax^2+bx+c$

I was watching a first-year high-school-algebra student struggle with factoring quadratics last night. Given a quadratic $ax^2+bx+c$ (I'll give you the exact example in a moment), her method — ...
1
vote
1answer
263 views

When my teacher gives me a question involving summation notation, do they expect us to calculate it by hand?

Assuming we don't have a calculator that can do summation notation. My class is not up to summation yet, but I'm asking a question involving this concept because I'm not all that experienced using it. ...
2
votes
1answer
167 views

Depth of the winding river… Not satisfied with answer…

I'm currently studying for the SAT. I'm taking a practice quiz and came across this problem: Now, using simple logic (and a bit of cheating by trial and error) we can easily determine the answer ...
4
votes
2answers
560 views

How should I teach a high school student about inverse functions?

Today I tried to teach a high school student about inverse functions. I gave him this problem and defined the parts that he didn't understand: Let $f: \mathbb{R} \to \mathbb{R}$, $x \mapsto ...
12
votes
4answers
280 views

Should the domain of a function be inferred?

It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collection ...
14
votes
6answers
2k views

No radical in the denominator — why?

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to ...
1
vote
3answers
452 views

Free introductory resources for learning algebra?

I have a non-mathematician friend who is interested in re-learning algebra. I am more than happy to help, but I am in no position to judge what is a good introductory text --- only to identify when a ...