# Questions tagged [precalculus]

Courses designed to prepare students for subsequent calculus courses

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### Advice and Remedial Algebra Resources for Students Committed to Calculus

I've got a student in my introductory calculus course. They're failing because they lack algebra skills. They understand the concepts just fine, and can articulate their understanding fine, but get ...
1k views

### Intuition for order of operations in compound transformations

This is a close cousin of the previous question asked here about transformations inside and outside a function and how they switch things around. I think some of the perspectives there will help here, ...
346 views

### Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?

Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
72 views

### Examples of Financial Institutions that Compute Interest Atypically?

Are there examples of financial institutions that compound their interest more frequently than once-a-month? Are there examples of financial institutions that consider continually compounded interest ...
1 vote
122 views

### Chinese and Japanese most important high school textbooks

I would like to know the best high school math books from Japan and China. Can you suggest some books or free resources? I would like to compare the different approach betweeen China and Japan and ...
14k views

### Requirements to learn calculus

I always was non math background student and programming is my hobby. I was attempting to program code instruction given here. Since I don't know calculus I'm stuck. I would like to know what are the ...
378 views

### Sources on inequity in precalculus sequence

I'm trying to put together some thoughts on the importance of a strong college precalculus sequence (mainly I'm thinking College Algebra, where much of my experience is) for addressing socioeconomic ...
543 views

### Why is isolating for $x$ taught before factoring?

I'm currently working on some precalculus packages for students who need review. For inspiration, I'm looking at some prealgebra books and I'm wondering why isolating for $x$ is taught before ...
4k views

### Why do we teach linear algebra in precalculus classes?

When I took precalculus, we learned about polynomials and how to factor them, we learned about trigonometry and lots of great and useful identities there, and we learned about matrices. They didn't ...
272 views

### Differentiation in integer solutions

What would you suggest as examples to demonstrate as applications of differentiation in finding integer solutions of an equation for advanced level students? Here you have one example which I have ...
3k views

### What are some examples of great functions that are not too elementary (easy)?

I am teaching precalculus/basic calculus to my class (high schoolers of around 18 years of age), and I'm always searching for nice functions to plot and study (finding the domain, the function's sign, ...
3k views

### f(x+h) in the difference quotient

When teaching students how to compute the difference quotient in a precalculus or calculus class, we need them to evaluate the expression $$\frac{f(x+h) - f(x)}{h}$$ for various simple functions, like ...
3k views

### Are there examples of central symmetry, without axial symmetry, in nature?

Examples of axial symmetry abound, but I could not find an example of pure central symmetry (that is, without axial symmetry)! Do you know of any? A butterfly shows axial symmetry, what shows point/...
1 vote
125 views

### Math curricula\programs or any experience using "The Road to Reality" as the\a primary textbook

Primarily a reference request, collaborator search-tips requests, and question-improvement request (including improveent by deletion and re-posting to more appropriate stack, meta, wiki, etc). Rank ...
1k views

### Write $y=\sqrt{3+x}$ as the composite of two functions

For the question "Write $y=\sqrt{3+x}$ as the composite of two functions", what if a student gives the answer $f(x)=\sqrt{3+x}$ and $g(x)=x$? This answer would be technically correct but it ...
123 views

### Do properties of exponents apply only to positive real numbers? [closed]

A common rule given in textbooks is: If $a$, $b$, and $x \in \mathbb{R}$, then $(x^a)^b=x^{ab}$. Suppose I write: $(-9)^{1/2}=(-9)^{2/4}=((-9)^2)^{1/4}=(81)^{1/4}=3$. But this contradicts the fact ...
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### Matriculation exams like in Europe

I just looked at matriculation exams from Finland. They have both basic and advanced level exams. Most US high school seniors could not pass the basic exam. If each US state were to create its own ...
1 vote
437 views

### Honors Precalculus: what topics to cut?

We’re precalculus honors teachers. In this year of Covid and reduced instructional time, what topics can we cut (Demana textbook) that would not hurt our kids in either calc AB or BC?
1 vote
634 views

### When are students taught implicit and parametric representations of curves?

Do students learn implicit equations (such as $x^2+y^2-r^2 = 0$) and parametric equations (e.g., $x=a t^2,\;y= 2 a t$) in a first course in algebra, which in the US would be early high school, maybe ...
2k views

### How are the basic trigonometric functions introduced to students?

The fundamental trigonometric functions $\sin(x)$ and $\cos(x)$ are used throughout the sciences, but I believe students are often introduced to a very limited initial understanding where it is ...
90 views

### Appropriate context for teaching derivative (undergraduate/graduate)

(Repost from MO, where the question will eventually be closed.) This question is related to lectures I have to make concerning differential calculus in one variable, but the students are quite ...
3k views

### How do you explain concavity of a polynomial without any calculus?

How do you explain the concavity of a polynomial without any calculus? As the title suggests, I am struggling to explain when given a graph of a polynomial, how we determine when it is concave up or ...
191 views

### How can I deal with the time pressure of teaching a short course?

I am an undergraduate applied math student. In about a month, I will be teaching two nine-hour math courses (one precalculus, one calculus) to a small group of motivated high school students. My broad ...
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### Good (natural) motivational examples for quadratic equations

I am looking for good motivational examples of how quadratic equations can naturally arise in real life for someone starting high school. The high school book my child is using just jumps into ...
1 vote
501 views

### How can I make "complex" graphs that combine multiple functions with a software?

Til today I've been using geogebra to sketch functions for my students quizzes or homework. Sometimes I use the ones that I found searching in google, but this takes a lot of time specially because I ...
1 vote
70 views

### How to introduce trigonometric ratios (HS) through a cognitive model?

I'm teaching a precalculus course and also taking a class on how to teach mathematics constructing a specific cognitive model for different topics. So, I have this assignment to build a cognitive ...
1k views

### Functions, Domains, and Ranges in Precalculus

Possibly related, though of a different flavour. Background In most of the precalculus texts with which I am familiar, readers/students are given a crash course in set theory, handed the definition ...