The post Best 3D Graphing Calculator With Multiple Functions appeared first on .
]]>Math is such a daunting subject for many because it can be so abstract.
One way to ground the concepts of math is to graph the functions you study. In beginning math courses, these are typically very basic functions with one variable, like straight lines and parabolas.
As your math courses become more advanced, the functions you study also become more advanced. Eventually, math students study functions with multiple variables. These kinds of functions are extremely insightful and can emulate critical parts of the natural world. However, in order to study them, new tools and technologies must be learned.
While graphing formulas by hand is a possibility, understanding the skill requires that the formulas be graphed, to begin with. This is where graphing calculators come in handy. The scaffolding they provide allows them to be ideal tools in the world of learning math.
In this article, we will discuss an effective tool for studying functions of multiple variables – a 3D graphing calculator. In particular, we will discuss the TI-Nspire CX graphing calculator made by Texas Instruments. This popular brand behind this graphing calculator is unsurprisingly one of the best on the market. With every Texas instrument, you can look forward to a quality calculator that will deliver in all the aspects that you want it to.
After giving a brief overview of this device and emphasizing its benefits and drawbacks, we compare this 3D graphing calculator to similar products, noting why we think the TI-Nspire CX is superior. Finally, we give our thoughts on the future of 3D graphing calculators. This in-depth review will allow you to determine whether or not this is the tool that you need in your math class or profession.
When we were on the hunt to determining what the best 3D graphing calculator was, there were a couple of things that we considered. Among these factors were the durability, functionality, and usability of the graphing calculator.
This graphing calculator can be found on a variety of retailers including Amazon. When you purchase this 3D graphing calculator, you will find that it comes with a rechargeable battery that lasts for up to two weeks, as well as a backlit color screen. It also uses a touchpad to facilitate navigation and has a small keyboard at the bottom.
Furthermore, this 3D graphing calculator weighs about 7 ounces and is considered one of the lightest and thinnest 3D graphing calculators available.
This product also comes with the TI-Nspire CX Student Software, which allows you to essentially turn a computer into your 3D graphing calculator. This connectivity also allows you to transfer data from your computer to your calculator, allowing you to overlay graphs and equations on digital images.
Unlike some other graphing calculators in Texas Instrument’s lineup, the TI-Nspire CX functions very much like a computer, allowing you to create documents and save work on the calculator.
This calculator has also been approved for many college-entrance exams like the SAT and ACT. Since this is a 3D graphing calculator, it allows students to input functions with 3 variables and get an output of a color graph.
There are also a number of integrated math templates on this 3D graphing calculator that allow students from disciplines like chemistry to enter formulas in proper form.
The major distinguishing characteristic of this 3D graphing calculator is its 3D graphing capability. This is an incredible feature that turns your calculator into a powerful learning tool.
In order to access this feature, all you need to do is input an equation of 3 variables into the calculator and graph it. You can then manually rotate the graph in order to observe it from many angles. Additionally, you can press a letter on the keyboard to have the graph rotated continuously.
What’s great about this rotation feature is that students can view the graph from every possible angle, including underneath it or from a bird’s eye view. This can help with visualizing certain functions, which can be difficult for students just starting to study multi-variable functions.
Without graphing these functions on a calculator, many students are forced to graph them by hand in order to get a sense of their shape and properties. While this can be an effective action, it also usually results in a messy graph that is not conducive to building knowledge and memories.
The TI-Nspire CX graphing calculator, however, will produce a cleaner, fuller, more organized picture of a function, providing the aesthetically perfect material for building knowledge and memories. This is important since forming a solid conceptual base will aid you in later math classes.
This 3D graphing feature would be welcome even if it were in black and white. It’s merely the cherry on top that the TI-Nspire CX features a color display, as this is a newer addition to Texas Instrument’s arsenal. This not only enhances the 3D graphing feature, but also makes the calculator easier on your eyes when using for a long period of time.
Colorless calculators can be uninspiring at best and soporific at worst. Furthermore, they can be difficult to use at night in low-light settings. The TI-Nspire CX avoids these consequences by featuring a vibrant, backlit display that is ideal for day or night usage. This makes it a dynamic calculator that can be relied upon at all times.
The software that accompanies this product also makes it very versatile, as many of the calculator’s features can be duplicated on a computer screen. A video of what this looks like can be found here.
This is an attractive feature that makes this calculator ideal for students or teachers.
Many proponents of this software laud it for being able to help students in a more interactive, familiar way. While the TI-Nspire CX’s screen is effective, it’s still only about 3-inches diagonally, making it difficult to use for a long period of time.
A computer screen, however, is usually at least 11 inches diagonally, and often larger. Furthermore, they usually display images in higher resolution. This makes computer screens a better teaching tool for some students, making the associated software an invaluable resource.
The TI-Nspire CX software is also perfect for teachers. This software allows teachers to transfer files from their calculator to their computer, perhaps if they want to continue working on some lesson at home. Many teachers use a 3D graphing calculator to create practice problems for students, but they might need to work on this away from school due to some other commitment. This is only possible on the TI-Nspire CX due to this software.
Additionally, many teachers like to pick up where the class left off, and sometimes this means diving right back into analyzing a graph from the previous class.
Some teachers will spend much of the class just re-drawing a previously studied graph on the board. This is an inefficient use of class time. Teachers with the TI-Nspire CX software can avoid messy hand drawings and instantly represent a graph of a function on a larger screen for the class to study. Then, the teacher can save this image at the end of the class and reproduce it the next day. This makes life a lot easier for the teacher and also prevents inconsistencies between classes.
Even further, the TI-Nspire CX software also allows you to write notes, which would be perfect for a teacher that was designing a lesson plan. Many math teachers plan their lessons around using a 3D graphing calculator, as this technological integration captures the attention of the students and makes learning feel more interactive. Math teachers are able to use the TI-Nspire CX software to plan these lessons ahead of time so that they are prepared to teach.
The main drawback is that the operating system used on the TI-Nspire CX 3D graphing calculator is different than the one used on other Texas Instrument graphing calculators, like the classic TI-83 Plus and TI-84 Plus.
While this newer operating system does have many amazing features, it also has a much higher learning curve. This means that it will take most students several weeks of constant usage before they can use it efficiently. Even then, many students claim it took them several months to fully master.
Even though this 3D graphing calculator looks more like a phone than a traditional calculator, it lacks the former’s instant usability. When you open up a new phone, besides maybe learning several new features, you’re usually able to hit the ground running. This means you can benefit from the device’s features almost immediately.
The TI-Nspire CX 3D graphing calculator, however, will require a bit more patience. This could be detrimental for a student that is relying on a 3D graphing calculator calculator to study for or perform on some exam. These students hardly have enough time to study, let alone learn a new calculator interface.
Even if students do manage to learn the interface quickly, this could still lead to inaccuracies come test time. Students taking a time-sensitive exam should be especially careful if they purchase the TI-Nspire CX. Sticking with your older calculator can be more effective temporarily if you are faster using it.
The other main drawback of this product is the price. Many students claim that $119.99 is not affordable when it comes to a 3D graphing calculator since free online 3D graphing calculators exist.
Yet, these online calculators are not as portable and lack many features of the TI-Nspire CX. If students want to avoid these drawbacks, they might have to take the hit and make the investment.
Despite its price and newer operating system, the TI-Nspire CX 3D graphing calculator is still superior to other 3D graphing calculators on the market.
Texas Instruments also offers the TI-Nspire CX CAS 3D graphing calculator for $144.51. Yet, this calculator is not only more expensive but is also not allowed on the ACT, making it not optimal for high school students.
The TI-Nspire CX CAS can also compute symbolically, making it more advanced than the TI-Nspire CX. This means that you can manipulate matrices with both numbers and various symbols. Ultimately, this makes the TI-Nspire CX CAS ideal for advanced math students or multi-disciplinary students studying science, technology, engineering, and math.
Many online 3D graphing calculators can be found, like the one offered by WolframAlpha.
Many of these online calculators offer some features for free and other functions for an additional cost. For example, WolframAlpha allows you to graph a multi-variable function for free but requires a Pro Plan in order to enlarge the graph and rotate it. This Pro Plan costs $5.49 a month.
Thus, if you are planning on using a 3D graphing calculator for several years, then the initial investment of the TI-Nspire CX might be worthwhile.
If you are only planning on using a 3D graphing calculator for a semester, then you might consider purchasing an online version temporarily. This will allow you to cancel your plan when your course is done and you no longer need a 3D graphing calculator. This could result in saved money.
At the end of the day, we think the TI-Nspire CX is the best 3D graphing calculator available because it’s so portable. Even though it’s expensive, it’s still cheaper than some other 3D graphing calculators on the market.
If you wanted to save money, you could use a free online calculator or even purchase a cheap online plan. However, these options are risky since you don’t know how long you will need the 3D graphing capability. Some students anticipate only taking one math class and end up majoring in it.
If you have even an iota of interest in math, then we recommend purchasing the TI-Nspire CX 3D graphing calculator. The market for used calculators is huge, so it shouldn’t be hard to sell this device if you end up not needing it beyond one math class. If you do need a 3D graphing calculator in later math classes, then you’ll be glad you purchased the TI-Nspire CX 3D, as using a paid online calculator for a long period of time can be costly and inconvenient.
Regardless, we don’t think you should be too attached to the interfaces of these calculators. We think they will be changing considerably in the near future as our technology evolves.
We can envision a future in which graphs are no longer observed from afar as strangers but instead interacted with as friends. We think virtual reality headsets in the future will allow us to study graphs in radical ways, perhaps by climbing on their curves and expanding them to life-size proportions.
While this might seem unrealistic, we think this future is just around the corner.
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]]>The post Increase Your Assets with the Best Accounting Calculator appeared first on .
]]>Debits, credits, assets, expenses: the accounting world could make Einstein’s head spin. Why not bring order to the chaos with the best accounting calculator money can buy?
We’ve all used these convenient products as our mathematical lifesavers at some time. Whether you’re a struggling student or a professional accounting rock star, accounting calculators abound to fit your needs.
How does one choose the best accounting calculator? You'll want to consider several factors, including dependable standbys like price and function. Let’s take a closer look so you can calculate your perfect solution.
Calculators have become a fixture in math. With so many choices (graphing calculators, scientific calculators, oh my!), how can we figure out what calculator type suits our accounting needs?
Perhaps we can bring some much-needed clarity.
Image by Steve Buissinne from Pixabay
All the most precise calculations require a dependable bedrock of data. Choosing the best accounting calculator is no different. We looked to the experts to gain insight on what specs and features help make a truly quality accounting calculator.
We compared prices and features on various brands. Some common benefits emerged amongst the most frequently cited brands and models.
We also took note of product differences. Plentiful customer reviews and ratings added important context and dimension to our analysis. Individuals sounded off on what they loved and loathed about each product.
The accounting calculators that appeared mostly a hit with critics and consumers alike comprise our comprehensive list of the best accounting calculators.
Image by Lucia Grzeskiewicz from Pixabay
Cost is a major consideration for many when purchasing any product. Why put your hard-earned money into a purchase that’s ultimately giving nothing but headaches? Just as with any product, accounting calculators come in a spectrum of prices.
The "bargain price" varieties will likely be more akin to a traditional calculator and will have lower storage capacities. For basic accounting functions, a quality low-priced model could do the trick.
Pricier versions will come with larger memories, more functions, and possibly in a bigger size. These versions might also feature add-ons like built-in printers. Does a higher price mean higher quality? That’s a question to be determined.
Several considerations will factor into choosing your best accounting calculator.
If your accounting calculator will serve as your faithful companion for frequent travels, you might want to consider a tougher, more durable build. For greater portability, the size will likely become a greater issue.
Ease of use will prove important as well. If your eyesight needs assistance, opting for a big screen and bigger keypads might help you out immensely. Printing options could be a great asset if you need hard evidence of all that accounting wizardry.
Perhaps most important is your level of comfort with the product. If you’re a beginner, the more advanced models might have overly complicated instructions or capabilities you may never really use.
For the whizzes out there, you’ll probably want a model that packs a maximum punch: large memory, a buffet of functions, and calculation speed that would make NASA envious. HP exert Horowitz reiterates that the time value of money is an essential calculation to master on any financial calculator.
So, let’s take a tour of some of the best accounting calculators on the market, in no particular order.
This nice device could be an ideal complement for amateur accounting.
Convenience is the name of the game. The company proudly touts easy-to-use features designed for maximum comforts, such as large non-stick buttons.
This model also gives you an enhanced display screen with pigmentation that improves the clarity of numbers. Each mathematical function is likewise on prominent display.
The dual firepower of solar and battery offers an additional asset for longer-lasting day or night viewing.
Although some Amazon reviewers had reservations about the key layout, customers generally raved about the easily readable displays and the large, raised buttons. The tabletop-ready design also won with customers.
This calculator rests comfortably in the bargain price range. For the price, reviewers found this model a solid accounting partner.
Compared to other brands, the focus on consumer comfort sets this brand apart, as does the reduced price.
This unique addition to the Sharp line is the “mini-cash register” of our Best Accounting Calculator group. The larger desktop model definitely won’t easily fit in your travel bag like other models, but the enhanced design might make up for the lack of portability.
A sizeable 12-dight display black screen is raised above the keypad, giving you readability that won’t strain your eyes. An additional smaller screen on top offers the versatility of a printing calculator without the paperwork.
This useful all-digital print display is capable of showing 500 lines of results. Up to 300 recorded entries can also survive within this model.
In addition, a full keyboard with touch-typing capabilities gives this offering a leg-up on many competitors. The company highlights a One Touch Change Calculation function. Amazon reviewers came up with descriptive terms like “efficient,” and “innovative."
The added features also add to the price tag, placing this calculator at the high end of our price range.
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With the 80,000-plus product portfolio and 90-year legacy mentioned by Top Products, TI definitely has the respectability and the street cred.
While this “patriarch” of the financial/accounting calculator family is marketed for wide-scale finance endeavors, accounting majors and professionals are a key target audience.
The model proudly touts specialized keys, including cash flow, amortization, and the crucial time value of money. Problems these specialty keys tackle can run the gamut from lump sums to annuities. Profitability calculations and uneven cash flow also merit frequent mentions, as does built-in functionality for statistics calculations with four regression options.
Students and professional reviewers found the product incredibly helpful, after spending time getting acquainted with the calculator’s many functions. Some had difficulty working through concepts like cash flow, and a few found the worksheet mode TI offers a challenge.
Another frequent grievance cited the poor design of the keys, which some reviewers claimed resulted in input errors.
A majority of reviewers who routinely perform advanced accounting discovered a dependable, worthwhile investment in this mid-price-ranged TI offering.
HP’s renowned contribution to the financial calculator game arrives in a stylish compact design. Billed as a CFP Certification Exam-approved calculator, the HP 10bII+ promises an impressive 400-step memory capable of implementing over 100 basic and complex business functions.
According to Dr. Jesswein, lump sums annuities, uneven cash flows, interest rates, loan payment, and much more should be less difficult to tally with this financial jack-of-all-trades.
One Amazon reviewer summed this purchase up as a “good, simple financial calculator” and raved about benefits like “unlimited frequency of cash flow and statistical calculations” and “breakeven quantity calculation.”
Other reviewers backed up the plethora of advanced functions such as trigonometric calculations and the rapid processing speed.
Scattered complaints talked of confusing setting options that could impact accuracy and of cheaply made key buttons.
For its mid-price range and its manufacturers’ solid credentials, this calculator distinguishes itself as one of the best accounting calculators.
Even if accounting jargon is more likely to elicit a “huh?” than a “hmm,” the Casio FC-200V Financial Calculator best accounting calculator choice rocks the typical, easily navigated calculator design. Be warned, though, that some customers did find the instructions confusing and somewhat vague.
On the upside, the Casio comes equipped with solar power and a slide-on case that should help it survive any ill-timed tumble.
It affords the user a respectable host of both simple and compound functions, as detailed by the Top Products website. If you’re into cost-sell margins, interest rates, investment appraisals, depreciation, amortization, and the like, Casio is practically calling your name.
Consumers on Amazon recommended the Casio Financial Calculator for personal finance and accounting classes. Hit features included the four-line display screen and the programmed-in commonly used formulas.
A few users bemoaned the lack of commas and the learning curve required for the product.
Most agreed that the learning investment was worth the payoff.
This printing model “big” title delivers with a big 12-digit screen, bigger keys, and a big paper printing capability. Victor guarantees a printing paper rollout 50 times larger than competitors’ offerings.
The relative heftiness of this model might hamper any travel plans you may have for the device. In contrast to most other calculators, you’ll need a plug-in for this one.
Victor does promise a good selection of nifty financial functions: cost/sell/margin, independent tax keys, item counts and time/date features, and more. One disabled customer on Amazon deemed this printing calculator “a miracle” for its “big, bold, and clear" numbers.
”The same consumer praises the thermal printing capability that makes ink cartridges a relic of the past. Others, including a CPA, also gave high marks to the print readouts. The added expense of needed paper purchases was cited as a concern, however.
The Victor sits at the top of our price range. With over 100 Amazon reviews, this calculator may not have been the most popular accounting calculator on record.
So, what’s the ultimate verdict on our best accounting calculators? As with most any product, it depends on the customer and his or her unique personality and needs.
For the bargain hunters and layman accountants out there, the OFFIDIX might very well reign as king.
Those with a hankering for more intricate, advanced work will find comfort in the standard-bearers of calculator excellence: HP, TI, and Casio. The bountiful memories, diversified functions, and quick, processing of complex data help put these representatives a notch above the competition.
If uniqueness and a little something extra is your speed, try out a printing calculator…if you don’t mind the slightly higher price tag attached.
Whatever your inclination and skill level, the best accounting calculator is waiting for you.
Sound off on your preference for the best accounting calculator in our comments below.
Featured Image: Image by Steve Buissinne from Pixabay
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]]>The post The Best Calculator for SAT Success: Picking Your Graphing Calculator appeared first on .
]]>Choosing the best calculator for SAT testing could have an immeasurable impact on your life. Where you go to college (and if you choose to go at all) could determine pretty much every career choice you make throughout your life.
Of course, the college admission process doesn't start when you fill out your application. The major you pick, the friends you make, and the school you attend all ride on the back of your SAT score.
With that in mind, why risk letting something as seemingly minor as the calculator you use affect you? The college admission process is hard enough, as are your last two years of high school classes.
Between studying for the SAT, performing well in class, and participating in extracurriculars, you don't have time to worry if you have the best calculator for SAT testing.
But don't worry. We've narrowed down the best calculator for SAT use so that you can spend your time focusing on your education instead.
For any college hopeful, taking the SAT is one of the most critical moments of their high school career.
While there are four main sections to the SAT, only one actually requires the use of a calculator. And within this one main section, students are only allowed to use their calculator on one part: the "Math Test — Calculator" subsection.
Still, picking the right calculator to take with you can determine how well you do on a significant portion of the test. However, it's not as simple as going to your local store and buying the first graphing calculator you find. And you definitely can't use your cell phone!
To know which model is the best calculator for SAT use, you first need to know a bit about what kind of calculators are allowed for the SAT.
If you plan to take your trusty calculator into your SAT testing session, it needs to meet a few requirements.
The first is that your calculator must be battery-operated. I don't know about you, but I've never seen a calculator with a power cord. So whatever calculator you choose, it probably won't fail this requirement.
Calculators with characters larger than one inch are permitted, as are raised displays. However, the test administrator may move you so other test takers can't see your screen.
Also, your calculator must be handheld, and you can't use it if it has a stylus.
Something to consider is whether or not you want a graphing calculator. Graphing calculators obviously help you visualize the graph aspects of math problems on the SAT. But scientific calculators give you all of the functions you need to succeed, are often more affordable, and are subject to fewer test restrictions.
If all of this information has you feeling overwhelmed, we recommend following CollegeBoard's suggestions when picking a calculator.
Although you can take any scientific calculator into your SAT session, as long as it meets the above criteria, the same isn't true for graphing calculators. If you plan to use a graphing calculator for your SAT, make sure it shows up on CollegeBoard's approved calculator list.
Ultimately, it's up to you to find the best calculator for SAT testing that meets these requirements and your needs.
Narrowing down the best calculator for SAT use from CollegeBoard's extensive list might seem like a challenge. After all, this list includes both a large number of graphing calculators and countless scientific calculators currently on the market.
So where do you start?
Fortunately, plenty of people want to help students pick the best calculator for SAT testing. That means you have numerous resources at your disposal.
To help narrow down the choices for the best calculator for SAT use, we referenced sources like The Balance Small Business' calculator guide.
Of course, one of the most important factors is how real students feel about the graphing and scientific calculators currently available for the SAT. There's no other way to truly determine the best calculator for SAT use.
Ready to learn which calculators actually made our list? Well, your wait is finally over.
Some of them are old classics. Others are new favorites. Regardless, each model has a rating of at least 4.0 out of 5 stars from Amazon customers.
As you go through our list, keep in mind that these models are in alphabetical order. Depending on your needs and personal preferences, any of these products could be the best calculator for SAT use for you.
Here are our top picks for the best calculator for SAT test takers looking to nail their math section:
The Casio fx-9750GII Graphing Calculator is a fairly streamlined graphing calculator. But it has just about everything you'll need to tackle graphing questions on the SAT.
It might not have the storage or depth that a Texas Instruments (TI) model offers. However, it will get the job done at a much lower price than you'd typically pay for a TI calculator.
So what can the Casio fx-9750GII do?
First off, it runs for over 200 hours on one set of batteries. That's more than enough to handle the SAT and could actually last well into your college career.
As for graphing, this calculator has a wide span of functions, especially for such a compact model.
It can graph X-equals relations, conic sections, and solve for intercepts and intersections. It will help you calculate dependent and independent values and has an interactive equation solver. If you have trouble with variables, this is probably the best calculator for the SAT math section for the price.
If grey or black calculators aren't your style, this model offers a few different color options. The Casio fx-9750GII has a rating of 4.3 out of 5 stars from Amazon customers. You can purchase this simple graphing calculator on Amazon.
If you want something a bit heftier than the Casio model above, we recommend reaching for the Casio fx-9860GII Graphing Calculator.
With a few more features at your disposal, this graphing calculator can stand up against heavyweights like TI.
Despite its beefed up features, this calculator is available within a pretty comfortable price range. That makes it the best calculator for SAT testees who are studying on a budget.
The biggest difference between this model and the Casio fx-9750GII is the display. With a large, high-resolution "textbook" screen, you'll be able to see all of your figures without getting flagged by the test administrator. It even comes with a backlight to improve visibility.
Plus, the display doesn't drain your batteries, so you can still use this calculator for over 200 hours.
Another key feature that sets this model apart is its spreadsheet function. It gives the fx-9860GII an additional level of utility both in and outside of the SAT.
The Casio fx-9860GII Graphing Calculator has a rating of 4.6 out of 5 stars from Amazon customers. You can find this graphing calculator for sale at Amazon.
The Casio PRIZM fx-CG50 gets its name from the large, colorful display. This powerful calculator is not only attractive but also gives you all the information you need to answer a variety of math problems.
The PRIZM fx-CG50 has every feature offered by the other two Casio calculators above and more:
Want to graph in 3D like the TI-89 Titanium? You got it.
But can it work in color? Definitely.
Whatever you want the fx-CG50 to do, it can handle it.
And if you think this calculator must cost an arm and a leg, you're wrong. It falls about midrange in pricing, even with its color display and 3D charting capabilities.
However, if you're planning to cruise through the math section of your SAT and never touch the subject again, this calculator might be more of an investment than you need to make.
If you decide on the Casio PRIZM fx-CG50, you can rest assured it's the best calculator for SAT testing and all of your other math-related subjects! This graphing calculator has a rating of 4.7 out of 5 stars from Amazon customers. You can pick one up online from Amazon.
Many people consider the TI-84 Plus to be the best calculator for SAT testing available in the past 15 years. This calculator can graph over 20 functions, store matrices, run statistical analysis, and handle all sorts of plots.
While we don't have the time to list everything the TI-84 Plus can do, we know you won't be disappointed by its capabilities.
This calculator can perform any function you would find in a statistics or calculus class. Plus, you can save dozens of charts, features, and plots with ease.
It also displays values with 14 digits of accuracy and completely replaces the need for a scientific calculator. In the right hands, it could easily tackle any problem the SAT throws its way.
Despite its age, it's hard to beat the Texas Instruments TI-84 Plus and its features. It's surprisingly easy to learn, as long as you take the time to do so.
This beast of a graphing calculator has a rating of 4.3 out of 5 stars from Amazon customers. You can purchase this model on Amazon or from Best Buy.
Texas Instruments' TI-84 Plus CE Graphing Calculator is one of the leading powerhouses in the graphing calculator world.
If you're taking a standardized test in high school, chances are you've used one of Texas Instruments' calculators before. So why not get one of your own for the big test?
The TI-84 Plus CE takes a few pages out of the smartphone's book. It has a backlit color screen, rather than the more standard black-and-white option. It also has a rechargeable battery, so you don't need to worry about replacing them unexpectedly.
Its color screen isn't just an attractive bonus, though. It makes the screen easier to read and lets you discern different graphs and plots more quickly than the more standard black-and-white display.
On a timed test like the SAT, every second you save is a second well-spent!
This model includes a variety of preloaded applications. Plus, with its range of different color options, it's surprisingly stylish for a graphing calculator.
The TI-84 Plus CE has a rating of 4.6 out of 5 stars from Amazon customers. You can purchase it in eight different colors on Amazon.
The Texas Instruments TI-89 Titanium Graphing Calculator may not be able to render in color, but it does have a significant advantage over the others.
That advantage? 3D rendering. Now you can see your graphs laid out on a 3D plane rather than a 2D one.
The TI-89 Titanium's display is large enough to accommodate a split-screen view, letting you tackle multiple calculations at a time. For example, you can see a chart and the equation used to reach that point.
If equations aren't your strong suit, don't worry.
This calculator displays complicated expressions and equations in full and proper notation. You can quickly solve equations symbolically, factor and expand equations, find anti-derivatives, and more using the built-in Computer Algebra System.
Of course, it doesn't do all the work for you. But it has more under the hood than just about any other graphing calculator on the market.
Sixteen preloaded graphing calculator apps will power through anything the SAT can throw at you, but you might find this calculator is a bit of overkill for the test. If math is your strong suit or you refuse to risk failure, though, the Titanium is a tank of a computing device.
The TI-89 Titanium Graphing Calculator has a rating of 4.1 out of 5 stars from Amazon customers. You can purchase this calculator on Amazon.
Since even a relatively simple scientific calculator would work for this test, the best calculator for SAT questions is largely up to your personal preference.
If you're looking for a budget option that you can still rely on, the simple Casio fx-9750GII will see you through to the other side. It has everything you need, and very little that you don't. If math is just another subject to you, this is probably the best calculator for SAT use.
For more serious math students, the classic TI-84 Plus is a great option. It's reasonably priced, can do just about anything, and has 15 years of experience to back up its reputation.
But the Casio fx-CG50 has a lot going for it as well. With full color, 3D graphing software, and a pretty decent price as well, this is a great alternative to a TI model. Still, these heftier calculators are probably best for students who have math obligations outside of the SAT.
Ultimately, though, any of the calculators on our list will serve you well on the big test day!
So what calculator did you or your student use for the SAT? Did your chosen calculator meet your needs or fail to perform? Leave us a comment and let us know!
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]]>The post How To Use a Graphing Calculator appeared first on .
]]>Like it or not, learning how to use a graphing calculator is a vital part of your education. Even if you know for a fact that math is not an essential aspect of your future career, learning a wide variety of subjects will help develop you into a critical thinker.
You may be surprised by how many fields of study rely on mathematics for their framework. For example, what would sociology be without statistics? It would probably just be philosophy.
Even creative skills, such as art effectively utilize graphs. In any case, knowing how to use a graphing calculator actually makes math easier.
Graphing calculators seem intimidating at a glance but are quite simple in reality. It will just take you a little time to get used to the interface.
You're probably familiar with a standard calculator; the kind that comes with numbers zero to nine, and buttons for basic addition, subtraction, multiplication, and division. There are a few other options, but that's about it for an ordinary calculator.
In contrast, a graphing calculator contains extra buttons for accessing menus and using various functions. Many of the buttons do two or even three things. If this were not the case, then your calculator would be enormous.
All graphing calculators possess the ability to store information for later use, allowing for more complicated processes. Other calculators don't have this.
If you typed 27 * 39 on a standard calculator and hit equals, it would give you the answer 972. But if you then started entering a different number, it would completely forget that 972 existed.
Of course, the most significant feature of a graphing calculator is the ability to create graphs. Once you know where and how to enter the information, your calculator can take functions or data points and turn them into visuals. These can be line graphs, bar graphs, scatter plots, and more.
You may be wondering, "why do I need to know how to use a graphing calculator when I can do all of this in excel or other programs?"
Well first of all, if you're that proficient with spreadsheets then hats off to you. However, graphing calculators are generally better for quick personal reference as they take less setting up. In any case, spreadsheets won't be an option on your SATs or other exams.
When it comes to completing functions and equations without graphing, you may be able to get by with an ordinary calculator. But knowing how to use a graphing calculator will make you much faster because you can just enter the information and let it do the work for you.
That's not to say that going through all the steps on your own isn't good practice. For the sake of saving your precious time, though, why make it harder on yourself?
Now that we've established that they do indeed have a purpose grab your TI-83, TI-84 or another graphing calculator, and get ready to learn.
The first step is, of course, to turn it on. To do this, simply hit the ON button in the bottom-left corner. Notice that OFF is written above the button in orange or blue text. In order to turn the calculator off, press the orange or blue 2ND button near the top-left and then press ON.
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It's possible that you will attempt to turn the calculator on and nothing will happen. Before changing the batteries, try increasing the brightness.
To do this, hold the 2ND key and simultaneously press the up arrow towards the right side calculator. If you'd like to decrease the brightness, press the down arrow instead.
As you learn how to use a graphing calculator, you'll find that there are certain buttons you utilize often, and others that you rarely use if ever.
It's unlikely that you'll need these without someone explaining to you how to use them, so don't worry about it. We'll be going over the most commonly exploited features in detail.
You already recognize some of the buttons from your standard calculator. However, you'll notice that CLEAR replaces the C and CE buttons for erasing things. It will delete everything, while the DEL key will backspace.
The topmost buttons along the bottom of the screen are used to access menus. Use the arrow keys to navigate menus and equations.
To access the orange (or blue) and green features of a button, use the 2ND and ALPHA keys respectively. For example, press 2ND and then MODE to QUIT out of whatever menu you're in.
Using ALPHA allows you to access every letter in the alphabet by pressing it and then pressing the button where the letter is in green.
Contrary to popular belief, these letters are not for passing notes in class! They are for variables in equations, which we'll get to later.
If you want to square a number, first put it into the calculator, then press the X2 button and hit enter. You can do the same to find the square root key, but press 2ND before hitting X2.
The ^ key can also be used to square a number, or for any exponent. For example, find 17 to the power of 3 by entering 17^3 and pressing ENTER.
If you're taking trigonometry, you'll be using SIN, COS, and TAN a lot. The inverse of those functions can be accessed by first pressing 2ND. So, providing a decimal and hitting 2ND and then SIN would give you sin-1, which is one way to find an angle on a triangle.
The last button we'll discuss here is the (-). Use this to make a number negative by pressing it before entering the number.
There are, of course, many more features besides these, but this should give you a general idea of how to use a graphing calculator.
Consider the equation 3(4-12^3) + 7^4 - 3(5). With no understanding of the order of operations, you might try to solve it from left to right. Even then you'd probably have a hard time coming up with an answer.
Chances are you've heard of PEMDAS, and you know that you should resolve the exponent first. On a standard calculator, you'd have to sit there and type out 12 * 12 * 12, get the answer 1724, erase it, and type 4 - 1724.
Congratulations, you solved one small part of this equation!
Luckily, on a graphing calculator, it's much more manageable. Simply type out the equation as you see it and the calculator knows how to solve it. Not only is this less of a headache, but you're not as likely to make mistakes.
Sometimes you'll have an equation that uses one or more variables, and you'll want to assign a number to them before solving an equation. What if the equation we talked about was actually X(4-12^X) + 7^4 -X(5) where X is equal to 3?
You could just replace every X with 3, but for the sake of consistency, there is another way. First, enter 3 and hit STO->, which stands for store. Then type X by pressing ALPHA then STO-> because that's where you write X in green.
Next, you press ENTER. The number 3 is now stored under the variable X, so anytime you type X in an equation it will act as if you typed 3.
You've come a long way in understanding how to use a graphing calculator. Next, we're going to discuss how to create actual graphs.
There are two ways to make a graph. The first is by using a function, such as Y = 2X + 3.
When creating a graph in this way, the calculator will automatically create the points for when X is equal to 1, 2, 3, and so on. This is useful for very complicated equations where you can't easily solve for Y in your head.
To begin, press the Y= button on the top-left. A menu will open with a list that looks like Y1=, Y2=, Y3=, etc. Scroll through the list using the up and down arrow keys. Notice the blinking box next to the Y you have selected.
With Y1 selected, type 2X + 3. Now hit the top right button that says GRAPH. Voila! You have yourself a graph! Use the arrow keys to select different points on your graph to see what they are.
Usually, you'll only need Y1, but sometimes you may want to have multiple functions graphed simultaneously or simply have more than one function stored.
Press the Y= button again, scroll down to Y2 and enter X^2 + 3. Hit GRAPH to return to your graph. You now have two functions graphed, the second of which is a parabola.
You can turn a function off without deleting it, so it is ready to be activated later. Go back to your functions with the Y= button and scroll to Y2. Then tap the left arrow key once so that the equals sign is selected and press ENTER.
Tap the right arrow key. The equals sign no longer has a box around it like the others because it is deactivated. If you press GRAPH, you will see that only the Y1 function is displayed.
You can turn the Y2 function back on in the same way you turned it off.
Graphs are great for getting a sense of how a function behaves. For example, without looking at any of the numbers, it's easy to observe that our Y1 function has a steady positive slope. In contrast, our Y2 function has Y increasing exponentially with every increment in X.
But when it comes to the actual numbers, tables can be much easier to read because they tell you in a list format that when X equals 3, Y equals 12.
To access a table of your functions, just press 2ND before hitting GRAPH. It's as easy as that. You can turn functions on and off the same way you do for the graphs, and only the activated functions will be displayed.
Use the up and down arrow keys to scroll through your list. You can go as high or as low as you want to. Want to know what Y equals when X is -2782? Go for it.
The other way to create graphs is by plotting data points. Use this when X does not directly influence the value of Y. For example, let's say our first point is 2, 7. So X is 2, and Y is 7.
Our second point is 3, 20. There appears to be no relationship between the two points, and so using a function to express them is impossible. Instead, we will create a plot. You'll use these a lot in statistics.
First, make sure that the functions we previously entered are deleted or deactivated. We don't want them interfering with our plot.
Next, press the STAT button located near ALPHA. This will take you to a list of options. The only one we care about at the moment is Edit. With that selected, hit ENTER.
You now have three lists; L1, L2, and L3. L1 is going to represent our X values, while L2 will be our Y values. You might recognize that we are essentially creating a custom table.
Enter in about five values each under L1 and L2. Use the arrow keys to move around the lists. When you've finished, press 2ND then Y= to go to the Stat Plot screen.
Select On and hit ENTER to turn on the stat plot. You can also change the type of plot from this menu from a scatter plot to something else like a bar graph.
Finally, locate the ZOOM button near Y= and press it. Scroll down to where it says Zoom Stat and press ENTER. Whew! Your plot is now ready to go.
Stat plots are extremely useful for statistics, because although Y might not be a perfect product of X, there may be a positive or negative correlation between the two. For example, when X increases, Y may tend to decrease.
You are well on your way to understanding everything about how to use a graphing calculator. Although it might only seem like the tip of the iceberg, you've conquered the most significant hurdles.
Now when you come across something new, you'll be able to quickly look it up, or even figure it out for yourself.
Do you have question, concerns, or suggestions about other ways to use graphing calculators? We invite you to post your thoughts in the comments below.
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]]>If you've ever taken a chemistry class, you know that it's really more math than anything else. There are so many equations that you need to know in order to understand chemical processes. One of these involves how to calculate Delta S.
Delta S has to do with entropy, which is just a scientific word for disorder. It may seem a little strange that someone can measure or calculate disorder, but they actually can. In order to calculate it, however, they need to know a few other variables.
You may or may not be a science buff, but either way, you'll almost certainly find some value in learning a little bit more about thermodynamics. It does, in fact, apply to your life, including how to calculate Delta S.
According to NASA, thermodynamics is "the study of the effects of work, heat, and energy on a system." In other words, all the stuff that moves around and happens in the world? That's a result of energy being used to make it move around and happen. Thermodynamics is the study of that process.
If you want to learn all about how to calculate Delta S, you can take a thermodynamics course. But most people probably don't have the time, energy, or money to do that. However, if you want to have a better understanding of what Delta S is and how to calculate it, you will need to know a little bit about thermodynamics in general.
There are three laws of thermodynamics, and how to calculate Delta S is a big part of the second one.
Before we tell you about the three laws of thermodynamics, we should mention what they refer to. When scientists refer to these laws, they're talking about a system and its surroundings. The surroundings are basically just everything that isn't part of the system.
The system is separated from the surroundings by some sort of a boundary. This can be the wall of the container, for example, if the system is all of the molecules that are in the container. Closed systems are systems where matter is not able to pass between the system and surroundings (like a sealed jar of peanut butter), while open systems allow for this exchange of matter (like the ocean or the atmosphere).
The first law of thermodynamics is the law of conservation of energy. It states that energy can't be created or destroyed within a system. It can only be transferred or converted from one form of energy to another.
There are two processes that can lead to a system experiencing a change in internal energy. These would be heat and work. The system could do work on the surroundings, or heat could flow into the system from the surroundings.
In either of these cases, energy isn't being created or destroyed. It's just being transferred and transformed between the system and surroundings.
According to the second law of thermodynamics, the entropy of any isolated system is always going to be increasing. It's a spontaneous process. Isolated systems are always going to be heading toward thermal equilibrium, which equals the maximum entropy that a system can have.
According to this law, while energy is being transformed or transferred, the natural tendency is for it to be wasted. Any isolated system will have a natural tendency to degenerate into a more disordered state.
All spontaneous processes actually yield increased entropy. Even when it appears that the amount of order is increasing, the entropy level is actually increasing when you take the entire system into account.
One example is that molecules can assemble themselves into a living organism. This would appear to be an increase in order and thus a decrease in entropy, but this is not the case. When you consider the entire system, including the environment, entropy is actually increasing overall.
In another scientific example, when you evaporate water from a salt solution, crystals can form. This may seem like increased order; in a way, it is, because crystals are more orderly than salt molecules that are moving around in the solution. However, the vaporized water that's now traveling through the air is a lot more disorderly than the liquid water that was initially there.
If you need an example that seems more familiar to you, think about your room. If you aren't making some sort of conscious effort to keep it clean, won't it just get messier and messier over time?
When you clean your room, you appear to be increasing order, but you're putting work into that process. The effort that you're putting into cleaning your room has resulted in a decrease in entropy in your room. But, keep in mind, this is not a spontaneous process.
If you allow only spontaneous processes to dictate the cleanliness of your room, it will naturally get more disorderly over time.
It's the second law of thermodynamics that involves how to calculate Delta S.
According to the third law of thermodynamics, as the temperature of a system approaches absolute zero, the entropy of that system will approach a constant value. Typically, this will be zero. The entropy of a pure crystalline substance, which would be in perfect order, would be zero at the temperature of absolute zero.
We've already told you that the second law of thermodynamics is the one that involves how to calculate Delta S. How, you ask?
In the world of chemistry, S is the symbol for entropy. Also, in case you didn't know this, scientists use the "delta" symbol to denote a change in a quantity. It follows from this that Delta S is the change in the entropy of a given system and surroundings.
As you already know, the second law of thermodynamics says that the entropy of the universe will increase for any spontaneous process. A spontaneous process is a process that takes place without the addition of external energy.
In order for a process to be spontaneous, it doesn't have to take place quickly. For example, carbon spontaneously goes from diamond form to graphite form. It's just that the process is so slow, no human being can observe this taking place during his or her lifetime.
It's also important to remember that spontaneous processes can either be exothermic or endothermic. This means that in order for a process to be spontaneous, it doesn't matter whether it releases heat (exothermic) or absorbs heat (endothermic).
How can you tell whether a process is spontaneous? It may not make much sense right now, but you actually use the second law of thermodynamics.
You know that any spontaneous process will increase the entropy in the universe, meaning that the increase in entropy of the universe is equal to the increase in entropy in the system plus the increasing entropy in the surroundings. And that that increase in entropy is going to be greater than zero.
But you can't really measure the entropy change in the entire universe. Theoretically, it's probably possible, but no one person would really be able to do that. Luckily, they don't have to.
In order to determine whether or not a process is spontaneous and thus has a positive value for Delta S, you actually don't need to know how to calculate Delta S for the entire universe. You just need to be able to calculate Gibbs free energy.
When a process occurs at a constant pressure and temperature, you can calculate Gibbs free energy. In order to do this, you just multiply the entropy by the temperature in Kelvins and then subtract that quantity from the enthalpy (H). Enthalpy is another word for heat, in this case meaning the heat in the system.
The change in Gibbs free energy for any chemical process is actually written as Delta G. Given that the temperature (T) and pressure (P) of the system are constant, you can write the equation for Gibbs free energy as follows:
Delta G = Delta H - (T)(Delta S)
When you calculate Delta G, you can use the sign of your result to figure out whether the reaction is spontaneous or not. Every reaction will be spontaneous in one direction or the other. It's just that some reactions will be spontaneous in the reverse direction.
With any given chemical reaction, on a molecular level, there will be some molecules going back to the reactants form. It's just that if the process is spontaneous in the forward direction, there will be more turning into products than turning back into reactants.
If Delta G is less than zero, meaning negative, the process is exergonic. This means it's going to proceed spontaneously in the forward direction and create something new. However, if Delta G has a positive value, the process is endergonic, meaning that it will proceed spontaneously in the reverse direction and break down something to create more starting materials. If Delta G is zero, the system is in equilibrium, meaning the concentrations of both the products and reactants are going to remain constant.
As you can see from the above equation, in order to calculate Delta G, you just need to know Delta H, Delta S, and the temperature in Kelvins.
Many people will focus only on calculating Gibbs free energy and not worry about calculating Delta S. In fact, many scientists simply obtain Delta S values from a table of standard values. They can do this, given that they know the value of Delta G in that situation.
However, you can easily learn how to calculate Delta S just by looking at the equation for Gibbs free energy.
Since Delta G = Delta H - (T)(Delta S), all you need to do is rearrange the equation if you're trying to figure out how to calculate Delta S. You just need to isolate Delta S in that equation. Once you do that using basic algebra, you'll see that:
Delta S = (Delta G - Delta H) / -T
The units for Delta S are quite complicated. It's typically kJ/(mol-rxn)*K). In other words, this is kilojoules per mole of reaction times temperature. You don't necessarily need to know exactly what these units mean unless you're in the field of chemistry. The main takeaway is that the higher the Delta S value, the more disordered the system is becoming.
If the process is spontaneous, the Delta S value is always going to be positive. The higher it is, the more entropy the reaction is producing.
Most of the time, even if you're studying thermodynamics, you'll just have to calculate Delta G in order to assess whether or not the reaction is spontaneous. Entropy is kind of a difficult concept to pin down, so a lot of people find it easier to just focus on Delta G.
However, it's still good to know how to calculate Delta S. It's relatively straightforward because all you really need to do is rearrange the equation that chemists use to calculate Delta G. The concept of quantities of entropy may not be very straightforward, but fortunately, the process of calculating it is.
If you want to learn how to calculate Delta S, you can easily do so just by following the above equation. However, it doesn't mean much unless you understand the science behind it. You should know what entropy means, and you should understand the concept of a spontaneous process for the quantity of Delta S to mean anything other than some random number in front of you.
You may not have thought that much before about how to calculate Delta S. You probably don't even think about entropy that much, despite the fact that you experience it every single day. One of the wonders of science is that it governs so much of what we do and experience without us really having to think much about it.
Learning the chemistry and math that is behind so many of the chemical reactions that we experience every day can be quite fascinating. It's so important in our lives on a daily basis. However, so many people are entirely unaware of the mechanisms that underlie all of it.
How to calculate Delta S is just one small part of understanding chemistry and thermodynamics. However, now that you have a better understanding of this concept, hopefully, you have a better appreciation for just how intricate and complex these processes are. After all, the world wouldn't be the same without them. In fact, it wouldn't be at all!
What do you think of everything we've just told you about how to calculate Delta S? Tell us about it in the comments section!
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]]>Most high school students come to math class equipped with the best calculator money can buy. Armed with their trusty calculator, no equation is too large or too complex to solve.
Enlightened by their teachers who say they will use all these math equations into adulthood, they study hard and soak up the information like sponges.
But unless you're a math professor, an engineer, or something equally as math-dependant, you won't need to use your scientific calculator to solve quadratic functions or parabola problems.
The average Joe's real-life scenario mostly require nothing more than your average calculator. But if you're wondering if you need something more, say, to help with your taxes, we've got just the thing.
Product | Image | Website |
---|---|---|
Basic: Canon LS-82Z | ||
Basic: Casio Inc. HS8VA | ||
Accounting: Casio Inc. HR-100TM | ||
Accounting: Sharp EL-334WB | ||
Scientific: Texas Instruments TI-30X | ||
Scientific: Casio FX-115ES | ||
Graphing: Casio FX-9750 | ||
Graphing: Texas Instruments TI-84 | ||
Finance: HP 10bll | ||
Finance: Texas Instruments BA II Plus |
First thing's first: to find the best calculator for you, we need to run down what functions each calculator has. All of them do your essential addition, subtraction, multiplication, and division.
But other calculators have essential functions that could make your life a little bit easier.
The basic or standard calculator is the most commonly-used calculator you'll see in your day-to-day activities. You'll see it on your kitchen counter as parents add up their monthly expenditures or in the hands of your little sister playing grocery store.
The everyday calculator has several functions, including addition, subtraction, multiplication, and division. Some of them also have a simple memory function and may also have a square root or percentage button. It has an on and on button and most are solar-powered, so it's ready to go when you need it.
Fun fact: the first solar-powered calculator debuted in 1976. The Sharp EL-8026 (also known as the Sun Man) needed plenty of direct sunlight to power the calculator.
However, as technology evolved, so did calculator solar panels. Today, the panels are small, inconspicuously designed, and require minimal artificial light to power the calculator for days.
The best calculator choice for anyone dealing with numbers daily is an accounting calculator. Professions include accountants, tax professionals, and mortgage brokers.
They're visibly slightly different from your run-of-the-mill standard calculator. While some do run on a combination of battery and solar power, the larger ones run on electricity. These electric, stationary calculators feature an angled LCD screen, tax buttons, and a printer that usually prints both in black and red.
There are also accounting calculators that offer the same functions as electric ones but are more mobile. These are often slightly smaller, do not provide printing capabilities, and run on a combination of batteries and solar power.
Most high school math classes require a scientific calculator for their curriculum. The best calculator for teens taking these kinds of courses offers a wide range of functions. Scientific calculators are rectangular and usually include a sliding case to protect the buttons while not in use.
But unlike basic or accounting calculators, they offer a whole host of other functions besides the basics. They include degrees, exponents, quadratic function, roots and powers, linear regression, and much, much more. Additionally, they offer equation editing capabilities and plenty of memory space.
Some math courses go beyond the capabilities of a scientific calculator and instead, require a graphing calculator. A graphing calculator solves more complex problems that a scientific calculator cannot work through.
Functions include logic operations, random numbers, graphing and dynamic graphing, statistical calculations, and much more.
Visually, they look similar to scientific calculators save for the screen. Graphing calculators have a more substantial screen (both wider and longer). Plus, the screen displays actual graphs which most scientific calculators cannot do.
The other main difference is their power source: graphic calculators tend to use batteries (mostly AAAs), which provides approximately 2,000 hours worth of life.
Before you purchase, it's essential to know which calculators you can and cannot use for both classes and exams. The ACTs, for example, do not allow specific scientific and graphing calculators during the test.
Check what your courses and exams allow before making a decision because even the best calculators are useless if they aren't allowed.
Financial calculators are suitable for a few different situations. Firstly, students working through an introductory financial management course may find a financial calculator within their "must-have" tools. These courses require nothing more than the most basic of financial calculators.
Secondly, those working in finance (or undergraduate students with a finance major) may also require a higher-caliber financial calculator.
They look very similar to scientific calculators (smaller screen than a graphing calculator and solar powered) but have different functions.
A financial calculator does not offer as many of the complex functions as scientific or graphing calculators. However, they provide finance-related functions such as amortization, compound interest calculations, and time-value-money calculations.
We looked far and wide to bring you the best calculators we could find. We've sifted through the world wide web and selected a handful of the best calculators based on real customer feedback and reviews.
To give you some choices, we've selected two of each of the best calculators described above. This way, buyers can make an educated decision based on budget, usage, and personal preference.
Basic: Canon Ls-82z
If you need a basic handheld calculator that won't let you down, look no further than the Canon LS-82Z. This calculator features a super user-friendly set up that is intuitive even to the most stubborn of Luddites (also known as those who are technology-adverse)!
Over 1,300 customers rated this little 1.6-ounce calculator 4.0 stars out a possible 5.
Its large numbers and upright 8-digit LCD makes it easy for those who have vision problems to quickly punch in their calculations. Powering this handy calculator is a combination of a battery as well as solar power. If you forget to press off, fret not: it has an auto-shut off after seven minutes sans use.
Functions include the typical addition, subtraction, multiplication, and division as well as square root, and percentage capabilities. It also features some memory space, accessible via the M buttons. Find the Canon LS-82Z on Amazon or at your local brick-and-mortar office supplies stores.
Basic: Casio Inc. Hs8va
If you don't like how wide the Canon calculator is, the best calculator for you might be the Casio Inc. HS8VA calculator. Measuring 2.2 inches in width, this 1.92-ounce calculator is significantly less broad than the Canon but has the same capabilities.
At 4.3 out of 5 stars, it's rated slightly higher by customers in comparison to the Canon. If you're worried about budget, the Casio Inc. is also slightly less expensive than the Canon.
Instead of a tilted display, this one lays flat like the rest of the calculator, which is ideal if you're transporting it with you from place to place. It displays a maximum of eight characters and is solar powered. Should the solar panel receive insufficient light, a battery picks up the slack.
In terms of sturdiness, this calculator tends to survive whatever life throws at it. You can drop it, spray it with disinfectant, or have your feline pets walk on it without much damage.
However, like most calculators, it is not entirely indestructible. Submerging it in water, for instance, is undoubtedly a recipe for its demise. But for the most part, the Casio Inc. HS8VA (and many other standard calculators) are rather robust.
Accounting: Casio Inc. Hr-100tm
Considering Casio is a leader in calculator manufacturing, it's no surprise one of our two accounting calculator picks is a Casio. We've selected the Casio Inc. HR-100TM, a calculator that customers rate an average of 4.4 stars out of 5.
The Casio Inc. HR-100TM prints up to 2 lines per second (both red and black), features a 12-digit LCD, and comes with an AC adaptor. Besides its essential functions, it also features tax calculations, cost/sell/margin functions, and a markup/markdown key.
At a glance, it's quite a large piece of equipment. It weighs 1.33 pounds and measures 8.62 by 6.51 by 2.12 inches: quite massive in comparison to some handheld calculators. However, its large presence may be a comfort to those with vision problems or large fingers.
It may very well be the best calculator for accountants who have plenty of room on their desk or for home offices. And in terms of sturdiness, take it from us: this calculator is an absolute tank. Unless your dog sinks its teeth into it and rips up all its insides, expect to have it for at least a decade without any issues.
Accounting: Sharp El-334wb
Our second accounting calculator choice is the Texas Instruments. It's fast, compact, and runs on dual power: a battery as well as solar power. Customers rated it a whopping 4.7 stars out of 5, with 85 percent of customers giving it an excellent 5-star rating.
It's advertised as a business calculator but has all the functionality of an accounting calculator, save for printing capabilities. Unlike the Casio, this one is the best calculator for business people on the go.
It's significantly smaller than the Casio: 6.6 by 4.4 by 1.5 inches, to be exact. While it can't necessarily fit in your pocket, its 5 ounces in weight is much lighter than the Casio.
If you have smaller hands, however, you may find the Sharp a little awkward to hold. Then again, thanks to the fold-up kickstand, you can rest it on the table at a comfortable viewing angle.
Like the Casio, the Sharp EL-334WB features cost/sell/margin buttons as well as tax, a double zero key, and large, user-friendly number keys. It also includes an automatic power down function in case you forget to turn it off.
Scientific: Texas Instruments Ti-30x
Texas Instruments is one of the most famous brands when it comes to calculators, especially scientific calculators. The best calculator for students enrolled in math and science class in high school is a scientific one.
While more expensive than standard calculators, scientific calculators tend to last much longer. Believe it or not, I still have my Texas Instruments scientific calculator almost a decade after I purchased it without a single problem!
Our personal experience and that of customers is the reason why we've chosen the TI- 30X IIS as one of the best calculators in this category.
Seventy-five percent of customers who purchased it thought this was the best calculator, as they gave a 5 out of 5-star rating. Overall, it has a 4.5-star rating, which is above average.
We've chosen the pink calculator, but this model is also available in a rainbow of colors including blue, green, grey, and even orange.
This scientific calculator is visibly longer than your standard calculator because it has so many additional features.
Besides your basic functions, it includes a whole host of other features including trigonometric functions, sine/cosine, tangent, and exponents. Unlike basic calculators, scientific ones contain a two-line display and a ten digit answer line.
Thanks to its hard plastic cover, the keys stay protected if you chuck the calculator nonchalantly into your bookbag. Considering a student's typical backpack contents (drinks, lunch, textbooks, etc.), the plastic is well warranted!
Also in the running for the best calculator in the scientific calculator category is the Casio FX-115ES Plus. Customers rated this calculator a total of 4.6 stars out of 5, which is above average for most calculators.
Also good to note is that this scientific calculator is allowed on several exams including NCEES exams, PSAT/NMSQTs, as well as the SAT and ACTs.
The Casio FX-115ES Plus is ideal for students working through high-school courses including trigonometry, statistics, algebra, calculus, engineering, and physics.
It contains over 280 functions, including complex number calculations, standard deviation, polar-rectangular conversions, and much, much more. Users can also go back to their previous calculations and edit them thanks to Casio's multi-replay function.
The Casio is slightly less expensive than the Texas Instruments scientific calculator. But it's also a little bit heavier: the Casio weighs 7.2 ounces while the Texas Instruments weighs 5.6 ounces.
However, when you're lugging around the weight of your textbooks (and teen problems), your calculator weight probably won't matter much!
Moving on now to the next level: graphing calculators! We've selected another Casio calculator for this category: the Casio FX-9750.
It weighs 7.5 ounces and measures 1 by 4 by 6 inches, which is about the length of your hand from the tip of your middle finger to the base of your palm. Customers rated this battery-operated graphing calculator a solid 4.4 stars out of 5.
At a glance, it looks like a relatively complex piece of machinery necessary for many statistics, biology, chemistry, and geometry classes.
It features a large, high-resolution LCD with enlarged dot-area technology. This tech makes all of your graphs (such as inequality, dynamic, integration, and conic section) look bright and crisp.
The one exciting function that this calculator contains is its USB connectivity. The Casio features a built-in USB port so students can share information with other calculators, display their calculator screen to a Casio projector, and even connect to their computer.
Our second graphing calculator choice is yet another Texas Instruments: the TI-84 Plus CE. Over 80 percent of customers rated this the best calculator for them, bestowing it 5 stars out of 5. Despite the vast price difference, the TI-84 Plus CE has an average rating of 4.5 stars out of 5.
While its priced relatively high, its quality far surpasses other graphing calculators. Just at a glance, you'll note a crisp, light-up screen that mimics a smartphone's brightness and quality.
Another excellent quality is its battery: most Texas Instruments products feature a rechargeable battery which reduces on waste. The battery lasts from one to three days of regular use. Students also can add applications to the calculator (much like a smartphone), which extends the calculator's functionality.
But all those features and functions come at a price — both monetary and in terms of weight. Instead of the usual 7 or 8 ounces, this graphing calculator weighs 15.5. However, this may very well be the best calculator for environmentally-conscious math and science students if you can afford its higher price tag.
Our first finance calculator is the HP (Hewlett-Packard) 10bll, rated 4.3 stars out of a possible 5. While it may look similar to scientific calculators, it offers very different functions.
Users can calculate loan payments, interest rates, percentage, and a whole host of other functions thanks to the HP 10bll. There are over 100 different functions as well to assist financial students and professionals in all their day-to-day problems.
Its a slim calculator (0.6 by 3.2 by 5.7 inches) and weighs a mere 8 ounces — perfectly acceptable for chucking in your briefcase on your way to work.
HP promises a user-friendly, easy-to-learn interface and a quick processor for immediate results. The price is also reasonable: not particularly cheap but not entirely out of the question either. Also included is a slide-on case to protect the calculator en route from place to place.
Texas Instruments BA II Plus Financial Calculator
Our second financial calculator choice (and last calculator) is the equally-as-affordable Texas Instruments BA II Plus. The star rating on Amazon for this calculator is also identical to that of the HP: 4.3 stars out of 5.
Like the HP, the TI BA II Plus offers plenty of functions including amortization keys, time-value-of-money keys, pension calculation capabilities, and much more. Its price is also comparable to the HP. Depending on the retailer, the price could be mere dollars different.
The display is what differentiates the TI from the HP calculator. This one features a light grey background while the HP's features a green-tinted display. The TI BA II Plus also weighs less than the HP: 4.16 ounces less, to be exact!
Both models are very similar in functions and price but different in appearances, button layout, and weight. Figuring out which one works best may boil down to personal preference or brand loyalty.
Choosing just one calculator out of our list of the best calculators is easier said than done. It's dependent on many things, including budget, mobility, and (most importantly) primary use.
However, if you don't work in finance and aren't a student, you merely require something to get you by your day-to-day calculations. In that case, we recommend the Casio Inc. HS8VA. It's small, lightweight, and practically bullet-proof.
What is your top pick for the best calculator? Share your thoughts in the comments below.
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]]>Even in a second-semester calculus class, determining the sum of an infinite series is beyond the scope of what you'll typically be asked to do.
One exception to this, however, is when you're working with an infinite geometric series, and you need to determine whether its sum is finite or infinite.
For example, if you have 1/4 + 1/8 + 1/16 … the sum of this infinite series will ultimately approach – that is, converge upon – 1/2, and that makes its sum finite.
On the other hand, if you have 10 + 20 + 40 + 80 … the sum of the series only continues to become larger, making it infinite.
As with most other calculus equations, you can determine if the sum of a series is finite or infinite as well as the sum of a finite series by hand, and it's not a bad idea to know how to do it this way.
For speed and ease, however, there are several different types of convergence calculators you can use which we'll go over below.
First, there needs to be a distinction made in the way "infinite" is being used.
Both the sample series above are infinite: the first approaches 1/2 without ever reaching it – there will always be more numbers in the series but they will become smaller and smaller – while the second series is infinite as it adds more, larger numbers forever.
The key distinction here, however, is whether the sums of these infinite series are finite (converging on a certain number such as 1/2) or infinite by only becoming larger into infinity.
The basic form of a geometric series is a1 + a1r + a1r2 + a1r3 +... so that a1 is the first term and r is the common ratio.
When the value of r is between −1 and 1, you can calculate the finite sum of an infinite geometric series. If r is greater than 1, however, the sum of the series is infinite and is represented by the ∞ symbol.
Therefore, the finite sum S of a geometric series where −1 < r < 1 is determined by the formula S=a1/1−r.
There are four steps to determine if an infinite geometric series has a finite sum and, if so, what that sum is:
To see an example problem solved, check out this detailed step-by-step solution.
See, that's not complicated at all! Or to put it another way, that's why there are a variety of convergence calculators available to do the heavy lifting for you.
As you'll see below, there are many different online convergence calculators to choose from.
Each one, however, offers slightly different options and levels of accompanying information.
Or, if you're using a TI-83 or TI-84 Plus, you can skip straight to the ticalc.org section to download programs to perform this function on your graphing calculator.
The Symbolab website provides multiple calculators to perform functions using integrals, equations, limits, tangent lines, and more.
Plus, you can use scientific notation and math symbols as opposed to just inputting numbers and text.
On the convergence calculator page, it's simple enough to use the available math symbols to create your geometric series formula.
After that, you'll receive not just the answer but also a step-by-step solution with accompanying explanations along the way. In addition, you can access absolute convergence and power series calculators.
With over sixty million registered users, a free account lets you store up to ten problems as well as do practice problems on a single topic.
A paid account offers additional features such as no ads, a mobile app, unlimited storage, and thousands of practice quizzes.
Wolfram|Alpha's goal is to help people at all skill levels perform dynamic calculations on their own as opposed to hunting endlessly through the Internet for a specific answer.
In addition to its web-based tools, it also has subject-specific and reference mobile apps for the iPhone, iPad, Kindle fire, Android, and Windows.
The convergence calculator is easy enough to use and only requires numbers and text in three fields to produce both the geometric series formula and the sum for a finite series.
Unfortunately, you cannot access the steps by which the equation was performed. You can, however, customize and embed the calculator on your own web page or easily share it with others.
This site also offers students many tools and resources to choose from.
Not only are there dozens of calculators organized by subject – algebra 1 and 2, calculus, linear algebra, statistics, and more – you can also access math games, logic puzzles, and answers to previously submitted math questions.
Have a question of your own? Register for free to submit it.
The series and sum calculator page gives you six options to choose from: geometric, binomial series, power, arithmetic, infinite, and partial sum.
Once again, there are four value fields you'll enter the necessary formula info into, and after that, you'll be provided with the geometric series formula and the answer.
In addition, there are handy instructions at the top of the page which walk you through the steps for each of the different series and sum processes available.
One note of caution: This site is dependent on advertising and if you open too many different pages at it at once, your web browser's performance may begin to bog down.
TutorVista is primarily an online tutoring company, so the information you'll be able to access for free is relatively limited.
If you do sign up for its services, you can receive help for both K-12 and college courses in math, statistics, chemistry, and physics and work with a live, online tutor for seven or fifteen hours a month.
As is, the convergence calculator is very barebones. You'll plug in the necessary information as with the sites above, and you'll receive the geometric series formula and finite sum (if available) as output.
The page does, however, provide an overview of solving this equation by hand as well as sample problems with answers you can work through to see how well you're doing.
Desmos provides educational support for math, primarily for grades 6-12.
It has a proprietary, web-based graphing calculator which can be used by visually impaired students as well as be embedded on external web pages. In addition, teachers can utilize the Activity Builder to create their own lessons and learning exercises.
For calculating the convergence of an infinite geometric series, a split screen is used.
The left side allows students to input the necessary equation values step-by-step while the graphical results are plotted on an x-y axis on the right-hand side of the screen.
While the options available are powerful compared to many of the sites above, it's not very intuitive to use, and you'll need to take a close look at the instructions and tutorials to utilize its features.
There's no one right choice out of the options above.
All of them will perform the basic, necessary calculations while some provide additional bells and whistles you may not need or want to use.
You should look at each one, however, to find the one which will work best for your purposes.
Whether you need to determine the convergence – that is, the finite sum – of one infinite geometric series or will be doing it for a whole semester, these tools will make your life much easier than doing it by hand.
Need a quadratic equation calculator? Check out o available to use. ur guide to the best resources
*Images are screenshots by the author.
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]]>While the first handheld calculators performed basic mathematical functions – adding, subtracting, division – the first graphing calculator wasn't introduced until 1985.
Additional features included executing tasks with variables, plotting graphs, and solving equations simultaneously.
Plus, graphing calculators typically allow users to create programs for scientific or educational applications.
Finally, because of the amount of information needing to be displayed, screens of graphing calculators are bigger than their more traditional counterparts.
In 1993, Texas Instruments released the TI-82, an upgraded version of the TI-81. It was an immediate hit with users and was the de facto standard in classrooms and laboratories across the United States for the next ten years.
Even though it was replaced in 2004 by the TI-83, the TI-82 is a workhorse still easily available on Ebay and commonly used by students in high school and college.
Have a TI-82 you'd like to use? Want to know if its features will work for your purposes? We'll cover all the relevant details below.
The TI-82 comes with a 6 MHz Zilog Z80 processor and 28 kB of RAM.
The monochrome display screen is 96 by 64 pixels and has up to 8 lines of text with 16 characters each.
It's powered by four AAA batteries and an additional lithium battery to preserve stored data when the primary batteries are being changed.
The TI BASIC programming language is also included, and there's an i/o port to connect to other devices.
Almost all buttons have two functions, and some have three. The primary function is printed on the button.
Secondary functions are printed in blue or gray above the button and are accessible after first pressing the 2nd key.
Tertiary functions, if available, are listed in white above and to the right of the button and are accessible after first pressing the ALPHA key.
Depending on exactly which version of the TI-82 you have, there will be some design variations.
After being introduced in 1993, the first redesign took place in 1999 when the original sloped screen was reconfigured, and the body of the calculator was made more contoured.
A second redesign in 2001 produced yet another slightly different case style, improved screen quality, and internal circuit board changes which reduced production costs.
Image CC 1.0 Public Domain by Stefan B via elliniWikimedia Commons
The TI-82 can be a bit daunting at first, especially as multiple functions are tied to one key or button. Here's an overview of the basics you'll need to know to get started.
Once you're familiar with the basics of using your TI-82, you'll be ready to move on to its more specialized features discussed below and which give the calculator its real power.
For the nuts and bolts info on how to perform these operations, however, you should refer to the official TI-82 Graphing Calcula. tor Guidebook
Additional special functions include the ability to change from degree mode to radian measure, graphing functions on an interval, and graphing trigonometry functions.
You can also use the LOGIC features to include operators like "and," "not," and others to create truth tables or even Boolean algebra.
In addition, you can find the terms of sequences, recursion formulas, and the arithmetic of lists.
Of course, beyond being a graphic calculator, another powerful feature of the TI-82 is it comes with the TI BASIC programming language.
This allows users to write programs to perform ongoing tasks and calculations instead of being forced to do each one individually.
First, you'll access the program editor by pressing PRGM. Then, select NEW on the menu and press ENTER. After that, you'll be prompted to name your new program.
From there, you'll go to the program editor where you can key in your program using commands available by pressing the PRGM key.
Once you're done, you can access all your saved programs from the home screen by pressing PRGM, then EDIT, and then selecting the program you want to run.
Check out this t to learn how to create a simple program using most of the commands available in TI BASIC. utorial
The TI-82 is a much-loved calculator, and there is plenty of information available to help you navigate its use.
For example, this over is a good place to start. Another view of its specifications and additional resourcesuseful site is TI-Freakware which is devoted to all things Texas Instruments.
Finally, there are many instructional videos available on YouTube:
Despite being discontinued by Texas Instruments in 2004, the TI-82 is more than just a collector's item. Instead, its power and versatility—and low price on Ebay—make it an excellent starter calculator for math students.
Plus, once you're thoroughly familiar with its operation, you'll be ready to move up to a calculator with even more bells and whistles if the need arises.
Want to learn more about graphing inequalities with a calculator? Check out our guide to the best resources available to do this!
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]]>The post Trapezoidal Rule Calculator: Applications, GeoGebra, And More appeared first on .
]]>Imagine you have an x-y graph with a plotted line running from left to right. In addition to marking these specific data points, you may need to calculate the area of the region under the line. While this is easy enough to do with a straight line, a curving, irregular line is more problematic. This is where the trapezoidal rule comes into play.
The trapezoidal rule creates a series of side-by-side, left-to-right trapezoids under the curve. All the individual trapezoid areas are then added together to calculate the total area under the x-y points making up the curving line. The more trapezoids you use, the more accurate the total area calculated will be.
If you're taking calculus or are an engineer, you likely use the trapezoidal rule on a regular basis. And, while you can solve this by hand, there's no need to because of the free trapezoidal rule calculators and software available to do it for you. We'll go over your best options below.
The first known use of the trapezoidal rule dates to 50 BCE when it was used for integrating Jupiter's velocity on the ecliptic. While other equations such as Simpson's Rule can provide an even more accurate integral – that is, the total area under the graph – the trapezoidal rule is still used for periodic functions and double exponential functions.
In more tangible, real-world applications, the trapezoidal rule is often used in civil engineering:
If you need a free trapezoidal rule calculator, there are websites which will do this for you while providing varying degrees of information. You can also download software to your graphing calculator or computer. Here are your best options.
Wolfram|Alpha's goal is to make systematic knowledge computable and accessible to everyone. This has been made possible over the past thirty years via two means: the Wolfram Language programming code and a New Kind of Science (NKS), the discovery of new algorithms for computation. Designed to be used by students, educators, and researchers, a variety of online and mobile apps are available.
On the trapezoidal rule calculator page, there are four input fields: function, number of trapezoids, lower limit, and upper limit. For example, you could input the following information:
After pressing Submit, you'll get the answer: 0.790821. You will not, however, receive any additional information about how the calculation was performed.
You can share the page via email, Twitter, and Facebook. It's also easy to customize the calculator and embed it on your own webpage, Blogger, or WordPress site. In addition, if you set up an account at Wolfram|Alpha, you can build your own apps through the developer interface.
This site is more basic and less robust in its offerings than Wolfram|Alpha, yet it does provide some additional information of value to students in particular. Once again, to use the trapezoidal rule calculator, you'll be prompted to enter the same four categories of information as above albeit in a slightly different order:
After pressing Submit, you'll get the answer: 1.4753289483117. Unlike Wolfram|Alpha, however, you have the option to see how all the steps were performed in addition to accompanying explanatory information.
Unfortunately, there is no option to embed this calculator on your own site even though you can share it via email or social media. There are also quite a few advertisements which clutter the page's layout.
Based in Russia, PlanetCalc is a collection of more than 550 online calculators. If you need a calculator not on the site, you can submit a detailed request which will be directed to one of its more than 100 volunteer programmers. Any PlanetCalc calculator can also be embedded on your website.
As with the previous online calculators, you'll enter the function, lower and upper limits, and the number of intervals/trapezoids. Unlike them, however, you can adjust the precision of the answer from zero to twenty decimal points. You will also be able to see all the steps performed in the calculation as well as accompanying explanatory notes. Even more helpful, an x-y graph as per your inputted data will be generated so you'll have a visual representation of what you've just calculated.
GeoGebra is another education site with many online apps for everything from geometry to 3D graphing to spreadsheets and more. In addition, many of the apps can be downloaded for iOS, Android, Windows, Mac, Chromebook, and Linux operating systems.
What makes GeoGebra's trapezoidal rule calculator stand out is its interactive, split-screen design. On the left-hand side, you're prompted to enter the necessary information to perform integral calculation. On the right-hand side, there's a live x-y axis which immediately adjusts your graph with the data you've inputted. Plus, it shows you the steps the solve the equation.
This interactive design is also available for other, even more complex online calculators including the Simpson Rule of Numerical Integration as well as a comparison of the trapezoidal rule and Simpson Rule which allows you to toggle back and forth between the two.
NA-Labs is another barebones site which offers five online calculators: the trapezoidal rule, Simpson's Rule, Riemann Right Endpoint Rule, Riemann Left Endpoint Rule, and Riemann Midpoint Rule.
Once again, you'll enter the function, upper and lower limits, and the number of trapezoids to use. The default results are displayed in degrees mode. You are given the option, however, to easily convert to radians for evaluating trigonometric functions.
WanerMath is another stripped-down site which nonetheless provides a number of useful resources for finite mathematics and applied calculus for students. These include online tutorials, review exercises, and true-false quizzes. In addition, the site is available in Spanish.
Instead of offering an online calculator like the options above, the trapezoidal rule webpage provides the step-by-step code to program your TI-83 graphing calculator to do this for you. After all, a webpage is handy enough, but being able to perform multiple trapezoidal rule calculations without needing Internet access is a big plus. You can also immediately use the data you generate for other equations and operations on your calculator.
The coding is relatively simple as there are only 20 lines required to compute left- and right-hand Riemann sums using the trapezoidal rule. While you're there, you can also grab the code to use Simpson's Rule, a 17-line program. You can't beat it: A few lines of code to perform heavy-duty calculations any time you have the need.
One of the oldest, unofficial Texas Instruments support sites, ticalc.org is loaded with useful information. Registered users can upload and download files, read and submit reviews, and rate files based on their quality. You'll also be able to access new games for TI calculators as well as patches and other fixes.
This site is useful because you may not want to manually key in the code on your TI-83 or TI-84 Plus. On ticalc.org's TI-83/84 Plus Basic Math Programs (Calculus) page, you can access almost 300 program files to download to your TI graphing calculator. This includes over 25 different trapezoidal rule calculator programs. In addition to the trapezoidal rule, many of these files contain multiple calculus-related programs you'll find handy too.
There is also a handy legend which indicates which features a file has: file with screenshots, file with animated screenshots, and file with reviews.
Then again, perhaps you want the software for a trapezoidal rule calculator to run on a machine other than a TI calculator. In that case, CodingAlpha is a site you should look at as it provides the code to do this in the C programming language.
In less than 30 lines of C programming code, you'll be able to calculate the trapezoidal rule on your own computer. Not only is the code provided, but there are handy troubleshooting tips too. The code utilized a GNU GGC compiler on a Linux Ubuntu operating system, but it should run on any other operating system too.
Users can also download C programs for other numerical calculations such as Weddle’s Rule Algorithm, Picard’s Method, and Euler’s Method.
Just like engineers don't use slide rules anymore, there's no need to calculate trapezoidal rule integrals by hand. Whether you want to use an online calculator or download code to your own graphing calculator or computer, there are many options available to let you work smart, not hard. That way, you can spend more time on the big picture issues of the problem you are working to solve.
Need to calculate arc length? Check out our how-to guide to perform this important equation!
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]]>The post SAT Calculator Hacks: Trigonometric Values, Graphing, And More appeared first on .
]]>The SATs (Scholastic Aptitude Tests) are among the more nerve-wracking of high-school experiences, as many colleges use the SATs as a primary factor when determining student admission. Scholarships and more can rest in the balance of an SAT score, leading to crippling test anxiety among even the most dedicated students.
Compounding matters is the fact that the test is timed, which can further increase a student’s anxiety. Even if a student is very well-prepared, knowing that a proctor is sitting with a running stopwatch can place an additional strain on a student’s psyche.
But this article isn’t meant to further stress out an already-anxious student. Once a student is comfortable with a calculator, many of the math problems on the SAT become routine. Read on to learn the very best SAT Calculator Hacks that we could find.
One of the biggest misconceptions regarding the SAT is the idea that the test can be taken without a calculator. While this is technically true, most students are doing themselves a great disservice by not obtaining a calculator and familiarizing themselves with the quick functions on it.
The Balance Small Business compiled a list of the 7 Best Graphing Calculators to Buy in 2018. Here is a rundown of some of the calculators from their list, along with corresponding links and price range for each:
As you can see, the price ranges for graphing calculators vary quite a bit. But all of these calculators are quite sophisticated, and more than capable of doing the job.
Parents and students should investigate the available options at the student’s school. Many schools have graphing calculators that they issue to students taking higher-level math courses, and some schools have a reserve of calculators from which they can lend. Students should take advantage of everything their respective schools have to offer, particularly as it concerns preparing for the SAT.
Once a student has decided on a calculator, becoming comfortable with the calculator is crucial. Even if a student does not purchase the newest or most-expensive calculator on the market, most of the current offerings are light-years ahead of what was available just five to ten years ago. Comfort, not the willingness to spend, is key when making a decision on an SAT Calculator.
Once a student has decided on a Calculator, the next step is learning the most effective hacks and shortcuts the machine has to offer. Read on to learn some of the best SAT Calculator Hacks.
Because the TI-84 and similar TI series calculators tend to be the most popular, they will be covered at length in this article.
The first series of calculator hacks apply to Texas Instruments TI-84 graphing calculators and will work on similar calculators within the TI series.
As noted above, these are considered the best calculators on the market by many people, and rightly so. TI graphing calculators can be found in high schools across the country, and TI models such as the TI-84 continue to rate very highly among professionals.
Before you dig into the TI-84 hacks, understand that there are two Math sections under the current SAT format. Under the current setup, students are allowed to use calculators (and the programs available on the calculator) for one of the two sections. It is highly recommended that students double-check all testing rules before the day of the test, as these rules are constantly influx and changing.
Here are some of the most helpful hacks for the Ti-84 Series:
This function converts decimals into fractions, if it’s mathematically-possible to do so. The FRAC Key can shave precious seconds by saving students the hassle of a long-form conversion. It also removes human error from the equation, assuming the student puts in the proper numbers.
Here is how to use the FRAC Key Function:
Conversely, if the student needs to convert a fraction into a decimal, just hit the DEC key from the same menu.
This easy trick is potentially a major time-saver, allowing students to focus on the equations themselves and not stress over tedious conversions.
Programming your TI-84 calculator is the ultimate series of SAT Calculator Hacks. Below are some of the more frequently-used programs that you might want to consider programming into your calculator:
The quadratic equation is often used in trigonometry, and a student will absolutely be tested on their ability to implement the formula on the SAT. It’s very important for students to memorize the quadratic formula, as certain questions on the SAT’s No Calculator Math section will require its use.
The quadratic formula is “Negative B plus or minus the square root of B squared minus 4AC all over 2A.”
The formula is used to reveal the x-intercepts of a quadratic equation, also called the “roots” or “zeros” of the function (because the x-intercepts occur when y = 0).
So, when a student is seeking to find the x-intercepts of a quadratic on the Calculator Math section of the SAT, a quadratic formula program on your calculator could be invaluable.
The TI calculator website can show you how to install these programs for free. If the student needs help installing the programs onto their calculator, this video explains the process well.
Students can use programs to perform difficult operations, such as FOILing, factoring quadratics, solving quadratic equations using the quadratic formula, and solving systems of equations with two variables.
Solving Systems of Equations with Multiple Variables is a program that most students using a graphing calculator should pick up. This topic is very common on both the SAT and ACT.
In short, some systems have one solution, some have multiple solutions, and some have no solution. Students can use algebra to deduce these solutions, or they can utilize a program on their TI model calculator.
On the TI website, a search for “systems of equations” will generate numerous programs that complete the algebra automatically. This is another arrow in the quiver for a student taking the SAT.
A complete guide to the quadratic equation is available at the TI website referenced above, in addition to many more formulas and programs that students could find useful.
Another way to eliminate busy work is to program Factoring functions into your TI model calculator.
Factor form is a different way to represent an equation, and it can tell you the zeros of the function. Problems like this are peppered throughout the SAT.
It’s important for students to know how to Factor without using a calculator, as Factoring problems will appear on the No Calculator Math section of the current format SAT. However, programming Factoring functions into your calculator can again save some needless busy work, and help a student continue to cruise through the Math section.
Once programmed into a calculator, all a student needs to do is enter the A, B, and C values of a quadratic. The calculator does the rest, again saving precious time.
Here is how to use this program on your TI-84 or similar model calculator:
Something to keep in mind is that Factor form is a bit different from solutions. If your solutions are 4 and -9, Factor form would be (x-4) (x+9).
TO FIND A QUADRATIC EQUATION WITHIN WORD PROBLEMS – AND THEN TO APPLY WITHIN THE CONTEXT OF THE QUESTION – YOU CAN USE YOUR CALCULATOR TO QUICKLY FIND THE ZEROES WHILE YOU’RE FIGURING OUT A PART OF THE QUADRATIC.
Additionally, if you see an x2 term in a word problem, use of a quadratic formula can help the student find and determine the zeros if not in a Factor or vertex form.
Two equations and two unknowns need to be solved for X and Y so that both of these equations are true.
Students will usually see them in some variation of this form:
AX + BY = C
DX + EY = F
ALGDOS is a multi-function program that includes a two-variable equation solver. Students can use this program to quickly find multiple variables when calculating a quadratic.
To use the program, the student will need to input the values of the coefficients. These values will be A, B, C, D, E, and F. After inputting the values, the calculator will then solve for X and Y.
This program is particularly useful for the word problems that are on the easier part of the test. These problems admittedly are not impossible to solve down, but having your calculator do it for you helps avoid careless errors.
Another very useful program is Slope Intercept, which will help students find the slope of a curve on their TI-84 calculator. Here is an overview of the concept.
The Slope Intercept program can take in two points and give you the slope and the intercept of a line.
This process can help a student with problems asking for the slope of the line, or problems asking which graph contains the points given by the test question.
To use the program, the student just needs to enter the points into the program and hit ENTER. The TI-84 will give the student the equation of the line, including the slope.
Graphing can be a bit time-consuming, but it can also be a life-saver if a student is stuck on a particular problem. On the SAT, an approximate graph can be close enough to the correct answer that the student does not need to solve the complete problem.
Students can use graphing to solve systems of equations, quadratics, or graphing problems. If the test presents a given equation and asks which of the graphs represents the equation, the student can then use the calculator to graph it.
Students can graph absolute values, inequalities, absolute value inequalities, parabolas, or ellipses. Graphing can find interception points that cannot be found with the linear equation solver, because some problems won’t be linear.
MANY STUDENTS MAY NOT REALIZE THAT GRAPHING CALCULATORS STORE EACH AND EVERY TRIGONOMETRIC VALUE, INCLUDING ALL COSINES AND TANGENT. THIS CAN BE INCREDIBLY HELPFUL WHEN FIGURING OUT COMPLICATED TRIG PROBLEMS ON THE SAT.
Common Trigonometric Values include angles of 0, 15, 30, 45, 60, and 90 degrees. Each of these can be stored in a TI series graphing calculator for quick reference while taking the test.
Students will also want to refer to this handy TI-84 Cheat Sheet, which condenses the latest TI-84 codes and functions into a single, easy-to-read document. This cheat sheet is specifically meant to be used with the TI-84 Plus, but many of the codes will work on other TI-84 series calculators.
Lastly, students may want to review this video on calculating Trigonometric Values. A better understanding of the principles at play will make for more effortless work when using a calculator during the actual SAT.
This article has covered the TI-84 and TI series calculators at length. While the TI calculators are deservedly popular, they aren’t the only calculators that students will potentially use on the SAT.
As mentioned at the top of the article, Casio makes two highly-rated calculators that deserve consideration: The Casio fx-9860GII, and the Casio fx-CG10 PRIZM.
While some of the Casio models do not have the same graphing functions as most of the TI models, Casio remains a viable alternative for students.
Ultimately, the decision on which calculator to use will come down to availability and a student’s comfort with a particular model, but it should be noted that many experts prefer Casio models due to their simplicity. In the case of a timed-test like the SAT, simplicity is elegance, as it potentially allows to complete problems more quickly and efficiently.
Programs and functions for the PRIZM series can be found at this link on Casio’s official site. Meanwhile, 9860GII users can click here for the complete user’s guide.
Students who are debating between Casio and TI model calculators can check out these links to help decide between the two:
Despite claims to the contrary, the SAT does not measure intelligence or accurately predict the type of grades a student will get in college. Rather, the SAT makes itself “harder” by quizzing students on obscure concepts within mathematics.
After all, complex mathematical formulas often take hours, days, or weeks to complete. The SAT is not measuring a student’s ability to complete these elite-level mathematical formulas, but instead testing students on things that most of their contemporaries probably don’t know.
In addition to the SAT Calculator Hacks presented above, it is recommended to SAT test-takers to brush up on the following Math formulas and topics:
Again, it can be extremely frustrating for a student who has prepared for months to come across a math question that they have no idea how to answer. It is important for parents and teachers to educate students on some of the realities of the SAT, which is that the test will ask a lot of obscure questions largely unrelated to practical situations, as well as present questions that students likely have not seen before.
Parents and teachers should want all students to do as well as possible on the SAT – after all, there’s room for everyone to succeed. Part of being successful on the SAT is understanding that the test will present some off-the-wall questions. Students can better prepare themselves by reading up on a few of these topics, and gain a working-if-not-perfect understanding of them.
The SAT is in many ways a sprint, as students hustle through questions in the interest of completing the test. A shot-in-the-dark guess is better than an unanswered question, so the testing format encourages students to not devote excessive time to any single question.
While students may not use their calculator on the bulk of the Math section, they can enter the test more confidently knowing that they can use a handful of stored programs to help complete it.
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