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Using TI-Nspire™ Technology To Creatively Solve ACT® Math Problems

Posted 02/22/2021 by Jeff McCalla, St. Mary’s Episcopal School Math Teacher (@jmccalla1)

One of the keys to doing well on the ACT® math exam is to be open to solving problems in non-traditional ways. The average ACT® score of the students at my school is a 30. Many of my students, who could solve problems the traditional way, choose alternative methods that might be faster or easier to pull off. There are 60 problems on the ACT®, and the problems tend to get more difficult as you get closer to problem #60. Here is an example of a pretty challenging problem, #47.

Problem #47

If a student doesn’t know the formula for a vertical ellipse (which many students don’t have memorized), the traditional method of solving this problem is not possible. Adding to the difficulty of the test question, the form the answers are in is not what students would expect (with the exception of answer choice “E”).

One powerful method of solving ACT® problems is to work backward. In other words, take the answers and use those to solve the problem. If you are using a graphing calculator, you can graph each answer choice until you find the correct answer. Using the TI-Nspire™ CX graphing calculator, you can graph each answer choice without solving the equations for y (this saves a ton of time). How? By using the Relations command on a graphs page.

Problem #47

Another great method is to use the Such That command on TI-Nspire™ technology to substitute numbers into the equations. In this problem, there are two ordered pairs that can be substituted into the equations. If the equation is true for both ordered pairs, you may have found the answer.

Problem #47

There are some calculator commands that are not widely known. Did you know that the TI-Nspire™ CX graphing calculator can convert radians to degree and degree to radians? Oh yes, it can!

Problem #47

To solve this problem using the TI-Nspire™ CX graphing calculator, it depends on what mode your calculator is in. Generally, I recommend using degree mode when taking an ACT® exam. In the top right corner of your screen, you can see if you are in radian or degree mode. If you want to change modes, just click the name of the mode in the top right corner of the screen.

Problem #47

Pretty neat, huh? Get to know your TI-Nspire™ CX graphing calculator — it can pay off in a big way on the ACT® exam. If you are a teacher and are interested in learning more about both the TI-Nspire™ CX graphing calculator and the ACT® exam, check out the offerings in the Professional Development section of education.ti.com.

ACT is a registered trademark of ACT, Inc., which does not endorse TI products. Policies subject to change. Visit www.act.org.

About the author: Jeff McCalla, author of “TI-84 Plus Graphing Calculator for Dummies,” 2nd ed. (Wiley, 2013) and “TI-Nspire for Dummies,” 2nd ed. (Wiley, 2011), teaches math at St. Mary’s Episcopal School in Memphis. McCalla received the Presidential Award of Excellence in Mathematics and Science Teaching in 2009. Follow him on Twitter @jmccalla1.

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