"Let $x$ and $y$ be integers such that ..."

"If $y$ is a positive integer, what is ... ?"

If you've taken the ACT or an ACT practice test, these types of math questions might look familiar to you. You've likely come across several questions on the ACT that mention the word "integer." And if you don't know what this term means, these problems will be difficult to solve.

Questions involving integers are common on ACT Math, so it's important to have a solid grasp of them as you prepare for the test. What are integers and how do they fit into the larger ACT Math picture?

This article will be your guide to basic integers for the ACT, going over what they are, how they change, and how you'll see them used on the test. For the more advanced integer concepts, including absolute values, exponents, roots, and more, refer to our advanced guide to ACT integers.

Beyond helping someone get an initial hire, recommendation letters can also go a long way toward assisting someone with an internal promotion. If the promotion involves moving into a position of leadership, then a great rec letter from a supervisor or colleague can be useful in showing that the candidate's ready to move up.

In this sample reference, a supervisor recommends that a Customer Experience Advisor at a glasses company move into the position of Team Lead. Read on to see how the supervisor frames her letter.

In our brave new world of ubiquitous internet, some employees work on a remote basis, communicating with teams via email and video chat. Whether they contribute as programmers, writers, or in another field, they might work from anywhere with a wifi connection.

This letter represents this remote relationship with a clothing company manager writing for a freelance web designer. Even though the manager hasn't worked with the candidate on a day-to-day basis, he can still attest to the quality of her work, as well as touch on some of the personal characteristics that he has gotten to know.

Read on to see how the remote manager weaves a strong reference for a web designer.

If you're a college professor, you'll probably write a bunch of recommendation letters for graduate programs and even jobs. In the following sample, an English professor provides a reference letter for a former student applying to teach English in South Korea.

While this professor hasn't seen his student in a teaching role, he can attest to his English language skills and passion for immersing himself in new cultures. Read on for the sample reference letter and an analysis of what it does well.

You don't have to be somebody's boss to write her a recommendation letter. You might have a coworker ask you to write one when she applies for an internal promotion or a position outside the company.

The sample letter in this article is written by a colleague for someone applying to a leadership position at another company. As a coworker and friend to the candidate, the writer can speak both to her professional skills and to her personal interests. Read on to see how the writer supports his colleague's job application.

Have you done some volunteer work or community service and want to get a letter that shows how many hours you've completed and what jobs you did? Or maybe you need a community service letter to apply for a scholarship, job, or to a particular college? Do you know who you should ask to write the letter and what it should include?

Read on to learn what a community service letter is, why it's useful, and how you can get a great one written for you.

Did you know there are over 1.5 million internships in the U.S. each year? If you work in supervisory role in a company, chances are you might find yourself writing a letter of recommendation for an intern. While you may have gotten to know an intern on a part-time, temporary basis, you can still write a personal and detailed letter of recommendation to help her through the job search.

The following sample letter of recommendation is written by an editor at a publishing company for a recent intern. Read on for the reference letter and an analysis of what it does well.

According to the Connecticut State Department of Education, there were up to 29 applicants per teaching position in Connecticut last year! Teaching's a competitive field, so a stand-out letter of recommendation can go a long way.

In the sample letter below, a principal recommends an art teacher applying to another school due to budget cuts. Check out what the principal has to say about this teacher, and then read on for an analysis of what this letter does well.

Not all of the candidates asking for a recommendation letter are full-time or long-term employees. Even if you're writing for a part-time or temporary worker, you can still give great insight into his work performance and strengths.

In the sample letter below, a restaurant manager recommends a server who worked during summers off from college. The candidate's looking to move into his first full-time job after graduation. Read on to learn what this restaurant manager has to say.

Maybe you spent the last year interning in a business and know your supervisor could write a stellar letter about your work ethic and passion for economics. Or you have a long term music teacher who can speak to your lifelong dedication to playing the piano. Or maybe you attend a school with thousands of students and feel like you've barely said ten words to your counselor or classroom teachers all year long.

If any of these scenarios hits home, then you might be considering sending a supplemental recommendation letter along with your college application. Before sending any extra materials, though, you should think hard about whether it's the right course of action. This guide will discuss when it's appropriate to send supplemental recommendations and when you'd be better off holding back.

To start, what are some reasons students think they should send an additional rec letter?

Are you tasked with writing a recommendation letter for someone and not sure where to start? While all letters should be uniquely customized to the candidate, most share a certain fixed structure.

This guide will go over this structure piece by piece to help you through the job recommendation writing process. Read on for a recommendation letter template that you can use to shape your recommendation letter. To begin, let's review the purpose of reference letters for job seekers.

Want to test yourself against the most difficult SAT math questions? Want to know what makes these questions so difficult and how best to solve them? If you're ready to really sink your teeth into the SAT math section and have your sights set on that perfect score, then this is the guide for you.

We've put together what we believe to be the 15 most difficult questions for the current Digital SAT, with strategies and answer explanations for each. These are all hard SAT Math questions from College Board SAT practice tests, which means understanding them is one of the best ways to study for those of you aiming for perfection.

Online classes can provide a convenient and cost-efficient alternative to traditional, face-to-face classes for people who want to further their education. But how do online classes work, exactly?

Most people are aware that online classes are probably different from in-person courses, but many aren't sure what the process of taking an online course is like. To help you develop a working knowledge of how online classes work and what to expect from online courses before you decide to enroll, we're going to cover the following:

• Explain what online classes are and where you can take them
• Answer the question, "How do online college classes work?" by explaining how to enroll and attend online classes
• Discuss what a typical class session is like in an online class as well as go over how online assignments work
• Provide a 5 question quiz to help you determine if online classes are a good fit for you
• Give you 5 tips for succeeding in online classes

So, how do online classes work, and how do you do online classes? Let's find out!

When I applied to college, I was accepted into every school I applied to, including Harvard, Princeton, Stanford, MIT, the Ivy League, UC Berkeley, UCLA, and more. While I had a strong overall application, the two teacher letters of recommendation were critical in getting me admitted.

Why? Both teachers said I was one of the top students they had ever taught. Both enthusiastically advocated for my personality, leadership skills, and energy.

How can you earn recommendation letters that will get you into your top choice colleges? I'll show you how in this article.

For the first time, I'm sharing my full, unedited letters of recommendation as examples for you. These are the exact letters submitted when I applied to college. Even better, you'll see exactly what my Harvard admissions officer underlined—what really stood out as important and noteworthy.

Which science classes are you required to take in high school, and what will you learn in them? Which science subjects will colleges expect you to have studied, and how can you impress them by exceeding these expectations?

Read this guide to learn about the standard science curriculum, what kinds of AP and IB science courses there are, college expectations, and how you can exceed colleges' expectations and use your high school science classes to ultimately strengthen your transcript.