Questions tagged [precalculus]

Courses designed to prepare students for subsequent calculus courses

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How can you elicit the $\log x = {\log} \cdot x$ error?

You know the error, when you're watching a student work through an algebraic calculation to solve for a variable trapped in the argument of a function, usually $\log$ or a trig function, and you watch ...
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Algebra/trig/precalculus review questions that elicit common student errors

This semester I have decided to give students a simple question or two at the beginning of every calculus class that will trap them into making the most common errors that we all know...e.g. the ...
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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, ...
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Best PreCalculus Textbook

What is your favorite PreCalculus textbook for someone that needs to get their algebra skills up to snuff? Something comprehensive with some tricky problems. Stewart? Sullivan? Blitzer? Something ...
568 views

How to word this exercise about converting "English" into interval notation?

I am writing an exercise for a precalculus homework assignment that deals with the topic of interval notation. The point of the exercise is to convert open, closed, and half open intervals described ...
359 views

Is Trigonometry done differently in the US?

I'm Italian and I've watched some videos from Americans and noticed a weird thing. Let's talk about a linear trigonometric equation like this: $$\sin x+\cos x+\sqrt3=0.$$ I've seen Americans solving ...
392 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 ...
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Is the AC Method of Factoring polynomials more popular and used by teachers than others methods of factoring polynomials?

This is an example of the AC Method: $x^2 + 16x +63$ (1) $x² + 7x$ (2) $9x + 63$ (1) $x(x + 7)$ (2) $9(x + 7)$ so we have: $x(x + 7)+ 9(x + 7)$ (1) with (2) The Result is: $(x+9)(x+7)$ I have more ...
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How should I introduce the concept of a function to a precalculus student?

My brother has not taken a math class in $10-15$ years. He is studying for the GRE so I have been teaching him a chapter or two from my precalculus book. So far, he has learned (and excelled at) basic ...
1k views

Best Way to Learn Trigonometry

What are the best resources to learn trigometry? I recently decided to pursue a BS in mathematics at uni. I used to fail all my math classes with D's or F's until I started teaching myself, and so far ...
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Which textbooks on College Algebra, Trigonometry, Pre-calculus, Calculus, Linear Algebra, ODE are written by world-class mathematicians?

For example, Trigonometry was written by Wolf-Prize winner Israel Gelfand, one of the top mathematicians in the 20th century. I am wondering if other world-class mathematicians have written textbooks ...
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How to help new students accept function notation

I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation. Their main ...
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Is there a pre-calculus introduction to the formal definition of a limit?

To give an example of what I mean, I'll answer a similarly worded question: “is there a pre-calculus introduction to the derivative?” I would say yes, since there already are the ideas of a slopes of ...
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Enlighten younger students about the concept of "procedural justice" in mathematics?

I am tutoring a 16-year-old student from my home country (in Asia) in, roughly speaking, precalculus. I would like to give him a feeling of procedural justice, so to speak, in modern mathematics, ...
563 views

Why "plug in numbers" when solving inequality?

Let me use this example, Solve $x^3-4x>0$ After factorization, we have $$(x+2)x(x-2)>0$$, in order to have product of several numbers positive, even(0,2,4,...) of them have to be negative ...
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Physical devices for exploring calculus or pre-calculus

I saw this partial derivative machine yesterday, and it got me excited about other physical devices for exploring calculus concepts in a "lab" setting (e.g. make a prediction, collect data, etc.) Do ...
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A more rigorous approach to Precalculus

I am a pure mathematics PhD student and graduate teaching assistant at a major state university. During the summers here, teaching assistants are typically appointed to teach an entire course, rather ...
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In the early 1900s Felix Klein lay out his vision for secondary mathematics curriculum. He wanted schools to teach calculus, so that universities would not be burdened by it. And at the core of the ...
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Why are we even studying cyclotomic polynomials?

My students found an exercise about cyclotomic polynomials in the AOPS precalculus text. They asked me why this construction exists in the first place and what it's good for... I am looking to give ...
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Examples (for beginners) of real functions which are not given by elementary formulae

Question: What are good examples of functions $f: \Bbb R \rightarrow \Bbb R$ (or $f: D \rightarrow \Bbb R$ with $D \subseteq \Bbb R$) which are not just given by "a formula" (or finitely many formulae ...
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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
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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
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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 ...
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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 ...
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Should Measurement of Angles Using Degree (and perhaps Common Logarithm as well) be Avoided in Pre-Calculus?

People use degrees and radians to measure angles and though degree measurement is acceptable and is widely used in everyday life, it is not in the International System of Units and mathematically it ...
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Math topics that reward going beyond cookbook methods

Students fresh out of high school are often under the impression that mathematics is a discipline based entirely in recognizing the type of problem and applying an algorithm or cookbook method. These ...
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Deriving Jerk Equations without using Calculus

I am thinking about the links between SUVAT equations (constant acceleration), and equations for motion when higher-order measurements are constant (for example, when jerk is constant, or snap is ...
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Ideas for a 2 weeks project focused in polynomial functions

Right now I’m teaching precalculus in high school and I want to propose a project to my students about polynomial functions. They already know enough about quadratic functions and we study variation ...
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When discussing inverse functions, how can our notation and methods reinforce student understanding?

Yesterday in my precalculus class, I decided to teach students how to find the formula for an inverse function in a new way (to me). In this curriculum, they have already used the notation $f^{-1}(x)$...
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Why do we teach that every line is a linear function?

Teaching my precalculus class today, I noticed something very simple that I hadn't taken into account previously. The definition in our textbook read: "A linear function is a function defined by ...
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The Order in Pre-Calculus Textbooks

Every Pre-Calculus I have examined starts with functions in general, then polynomial and rational functions, followed by exponential and logarithmic functions and Trigonometry, and ending with ...
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How can I improve my problem solving/critical thinking skills and learn higher math?

I'm a rising sophomore in high school. So far, I've taken Algebra One, Two, and Geometry in school. I want to learn higher math such as precalculus/trigonometry, calculus, linear algebra, and more, so ...
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Is there a more intuitive way to solve combined rates of work problems?

I am helping my brother study for the GRE and we have come across some problems like this in my old precalculus textbook: 1) Karen and Betty have been hired to pain a house. Working together, they ...
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Consolidating three descriptions of a parabola in precalculus

I want to present these three descriptions of a parabolic curve to my precalculus class: The graph of a quadratic function $f(x) = ax^2+bx+c$. Given a line called the directrix and a point called the ...
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Explaining the domain of a function to students?

I mostly tutor community college students ranging from beginning algebra to calculus level. There are several ways in which I explain the domain: "The domain of a function is all the values you can ...
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How to explain the range to students?

I mostly tutor students ranging from beginning algebra to calculus level. I think the explaining the range as "the set of all possible outputs" would not really cut it for someone struggling with math ...
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Teaching a Pre-Calculus Course using Basic Mathematics by Serge Lang

I am considering using Basic Mathematics by Serge Lang as the primary text for my High School Pre-Calculus course. My students have all spent a year working through the first six books of Euclid and ...
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For purposes of teaching, should constant functions be considered "linear functions"?

I can see arguments both for and against classifying constant functions as linear functions. Against: "Linear function" means "first-degree polynomial function", and constant functions are not first-...
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Teaching about absolute values not centered at $0$
One of my peers is studying for the GRE and ran into the following problem: When is $|x-4|$ equal to $4-x$? I tried to attempt teaching this by developing the intuition for why |x| = \begin{...