The next scheduled __ACT® Test__ is October 26, 2024 (with a __registration__ deadline date of September 20) run on February 6, 2021. The math portion of the ACT® is a standardized assessment designed to test mathematical skills that a typical student should have acquired by the end of their junior year, and is designed for students in grades 10, 11 or 12. For many colleges, the ACT is an acceptable college entrance exam for all four-year universitites, either by itself or in conjunction with the SAT®.

The mathematics test is a multiple-choice assessment with 60 questions to be completed in 60 minutes - i.e. not a lot of time to 'ponder' questions. While you are allowed to use a calculator on all parts of the math test (__ACT Calculator Policy__), you really don't have the time to use a calculator for every problem, nor should you. You want to be strategic when you take the time to utilize a calculator. This post provides some strategies for deciding when to use, and more importantly how to use, a calculator on the ACT®.

You are allowed to use a four-function, a graphing, or a scientific-calculator, and this post will focus on graphing, using the __fx-9750GIII__ graphing calculator, one of my personal favorites, and an extremely affordable calculator. Casio graphing calculators are an incredibly efficient tool to utilize since you don't ave to remember where certain functions and commands might be hidden, and you don't have to do extra steps (like setting up boundaries for intersections). Below are some test-taking strategies and calculator-tips and how-to's to support your ACT® prep.

**1.** **Don't use your calculator for every problem.**

The problems increase in difficulty as you work through them, so you should spend less time on those at the beginning compared to those at the end. Read the problems carefully - all the problems are solvable without a calculator, so if you can solve or evaluate in your head or quickly by hand, do so, as this will save time for those problems that require a bit more time/calculation and possibly a calculator. Most likely, those problems are near the end of the test, say #40-60, are going to be the ones where a calculator will be the most useful. Additionally, as part of the reading process, eliminate answers from your choices that are obviously wrong to narrow down your thinking.

**2. If you are stuck on a problem, make your best guess and come back to it later.**

Don't waste time on a problem that initially seems confusing or difficult. On the ACT, you do NOT get points deducted for wrong answers, so make your best guess and move on, BUT, mark it (circle it, star it, etc.) or jot down the number, to come back to it after completing your test. Continue to work and answer those problems that you can do. Do all the problems you know you can do first, and come back to those you made guesses on (and marked/recorded to review) to give yourself more time for those more challenging problems. Efficiency is key.

**3. Write on the problems and mark on the pictures to help visualize the quantities/situations/relationships.**

There are geometry problems, where they provide images. There are also word descriptions of situations with no images. If an image would help, draw it. If quantities or relationships (lengths, angles, congruency, parallel, etc.) are provided describing an image, mark those on the image. This helps focus you on what is being asked and helps you see the situation and relationships you might otherwise miss. Even if you are taking the digital version of the test, you are allowed scratch paper to do your work, so use that. See the example below:

In this example, the markings help identify the angle, and the opposite side and hypotenuse in order to set up the correct trig ratio. This is an example of a problem where you would NOT need a calculator.

**4. Examples of Problems Where a Calculator Would Be a Strategic Choice/Time Saver**

There are certain types of problems on the ACT where a calculator would be an efficient way to quickly solve. I have created some categories below that identify types of problems and also show you how to use the graphing calculator to quickly get to the solution. The important graph menus on the fx-991CW (or any other allowed Casio graphing calculator) are: **Run-Matrix** *(for calculations and function commands)*; **Graph*** (for graphing and solving equations)*; and **Equation** (*for solving simultaneous linear equations, polynomials, and specific equations for a given variable*).

__Graphing to Solve Equations, Systems, Compositions, Inequalities, Find Roots, Intersections, Key Points - GRAPH Menu__

*What is the value of x when 2x + 3 = 3x – 4 ? (Source:*__ACT® Released Items Set One__*)**What is the x-intercept of the graph of y = x2 – 4x + 4**(Source:*__ACT® Released Items Set Four__*)**Which of the following is a factor of the polynomial 2x2 – 3x – 5 ?*

*x*– 12

*x*– 32

*x*– 52

*x*+ 53

*x*+ 5*(Source:*__ACT® Released Items Set Two__*)*

These 3 problems would be more efficiently solved with the use of the calculator. Graphing and visually looking is often a great way to find solutions instead of the longer method of solving by hand or substituting in values. The **GRAPH** menu of Casio's graphing calculators can be used for so much more than just graphing, and is often the most efficient way to get to a solution. Without ever having to leave the **GRAPH** menu (meaning you don't need additional apps or programs), you can graph y=, x=, y- and x- inequalities, graph composition of functions and find specific values using **TYPE** & **VAR**S functionality. With **G-solv**e, you can quickly find key points, such as intersections, roots, max, min. With **TRACE** you can quickly narrow in on important points/sections of a graph. The video below shows all these abilities with the fx-9750GIII using the three example ACT® items above.

__Function Commands and Multi-Step Numeric Calculations - RUN-MATRIX Menu__

*What is the greatest common factor of 42, 126 and 210?**Solve: 3(8+5i) + .5(4+2i)**Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?*__(____Source - ACT® Practice Test Set One____)__(*Hint: for large numbers, use simpler numbers in calculations - i.e. don't enter 38,000,000 - enter 38)*

The above 3 problems are examples where, because of the size of the numbers and/or number of calculations, the need to use a function command, or do multi-step calculations, a calculator would be a good choice to get the solution quickly. Using the **RUN-MATRIX** menu, you can calculate quickly with the larger numbers, and you can use functions commands (**OPTN Button**) to do quick calculations (LCM/GCD/SUM/ABS/Complex as examples). You can easily change the mode of the menu by clicking **SHIFT - MENU** to do complex calculations. The video below shows the process, using the fx-9750GIII for these possible situations.

__Solving Simultaneous Linear Equations, Polynomials, and Equations - EQUATION Menu__

*A neighborhood recreation program serves a total of 280 children who are either 11 years old or 12 years old. The sum of the children’s ages is 3,238 years. How many 11-year-old children does the recreation program serve?**(Source:*__ACT® Released Items Set Four__*)**Which of the following is a factor of the polynomial 2x2 – 3x – 5 ? (Source:*__ACT® Released Items Set Two__*)**x + 2y = 5 and 2x + y =16. What does x + y equal?*

There are often several problems on the ACT* *where you are asked to find specific values for variables, solve simultaneous equations/inequalities, and factor polynomials. There are obviously multiple methods that could be employed to do this - substitution, multiplication/addition/subtraction, graphing (see above in the **GRAPH Men**u). Sometimes using the **EQUATION Menu** is a quicker way to find a solution, particularly if methods like substitution will take multiple steps and longer.

The video below uses the three examples above to show you the process of using the **EQUATION Menu** as a time-saving strategy and strategic use of the calculator. Once in the menu, you have three choices - **Simultaneous**, **Polynomial**, **Solver**. Choose the one that matches and then enter the **degree** and/or **unknowns**, and then it is a matter of simply entering the coefficients and constants and choosing **Solve**, making finding a solution much faster.

In my next post, I will follow up with tips on studying for the ACT and ways to use the calculator to deepen your understanding of mathematics. In the meantime, be sure to __register__ for the ACT before the deadlines! And start using the __ACT website__ to help prepare.

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