Math and calculator tips for the SAT/ACT

By Jatin Rao

TI-83 Calculator. Image Credit: Rao Advisors LLC

The highest math level that is expected to be tested on the SAT is Algebra II, meaning that the questions are generally easier and less complex than the math questions on the ACT, which includes precalculus content as well.

There are 4 math subjects that are tested on the SAT Math section: 
  1. Heart of Algebra: This section mostly covers topics that are taught in Algebra I, and the questions are heavily focused on solving basic linear equations and linear inequalities. Mastering this section in Khan Academy is vital before moving on to practice the other two sections. There is also heavy emphasis on analyzing and interpreting graphs.
  2. Problem Solving and Data Analytics: This section includes some Algebra I topics, but also includes basic statistics and proportions problems. It is key to remember concepts such as mean and median, ratio laws, and exponent rules.
  3. Passport to Advanced Math: This section is almost all Algebra II topics and relatively advanced geometry. Most of the questions will require manipulating equations and solving for a single variable, thus requiring the most practice overall.
  4. Additional Topics: This section mostly covers Geometry topics and complex numbers. It is important to remember concepts such as the unit circle and other widely-used geometric theorems.

There are two subsections on the SAT Math test, a Calculator and a Non-Calculator section. The calculator section questions will generally be harder than those on the non-calculator section, because the College Board knows that the test-taker has a tool to help with calculations.
Non-Calculator: The section without a calculator comes first. There are 20 questions and a time limit of 25 minutes. Most of the questions are multiple-choice questions, with a few grid-in questions at the very end. Because this section is generally easier, expect questions from the Heart of Algebra, Data Analytics, and Geometry sections, but be prepared for some tricky algebra or manipulation questions. There will be some graph questions but not as many as the Calculator section. A lot of them will be simple "one-line" questions that only take a few seconds to read and roughly 30 seconds to solve, so it is important to prioritize picking up easy points on questions like these before moving on to the harder problems. 

Calculator: This section appears after the Non-Calculator section. There are 38 questions with a time limit of 55 minutes. There is a generally better spread of questions across the 4 sections, but the questions are more difficult because of the student's ability to use a calculator. Not all questions will require usage of the calculator, so try and save some time by not using it if possible.

While Precalculus topics will not be tested on the SAT, it is preferred that a student has taken Precalculus before taking the test. We recommend accelerating through one of the three preliminary math courses (Algebra I, Geometry, Algebra II) in order to make space for the student to take Precalculus during his/her sophomore year, and then take the SAT during the summer between the sophomore and junior years, preferably in August. Precalculus does an excellent job of acting as a comprehensive review course for the topics learned in all of the three preliminary math courses, so the student will have the ability to review concepts learned years prior, as well as learning useful new concepts such as the unit circle and trigonometric manipulation and proofs. They will also have the benefit of practicing problems at a higher skill level to prepare for more difficult questions on the SAT and ACT.

Of the two mainstream choices for calculators for standardized testing, the TI-83 Plus and the TI-84 Plus, which do we recommend using?

There are actually only a few differences between the TI-83 Plus and the TI-84 Plus, with the latter offering a few additional features and an improved screen interface for the user. Students should also consider the TI-84 Plus CE (color edition), which is the same as the TI-84 Plus, but with a smaller feel and a colored screen that can make graphs easier to interpret. There are also a few more built-in applications on the color edition TI-84.
SAT - The TI-83 Plus works just fine. Most of the calculations will be simple PEMDAS or graphing, and therefore will not require any of the advanced tools that are present in the TI-84. Be familiar with the functions in the MATH tab on the calculator, and how to store values and recall them later for more complicated solutions. Become an expert at quickly graphing functions using the "y=" tab, and analyzing the graphs using the TRACE and CALC tabs at the top right. Some of these may help solve some problems faster than doing the math on paper.

ACT - The TI-84 Plus is preferred over the TI-83 Plus. Because precalculus topics are tested on the ACT, it is useful if you can calculate summation formulas and type in complex fractions without the use of many parentheses that could confuse you. Pressing ALPHA + "y=" will open up a menu that can simplify entering fractions into the console. Functions like entering complex roots that are more than the square root, finding the logarithms of functions at a different base than 10, and using the many statistical tools in the STAT tab are all available in the TI-84 Plus, and will likely be used many times during the ACT Math section, where time is of the essence.

AP Exams - The TI-84 Plus or TI-84 Plus CE is the preferred choice. Heavily math-based AP exams like AP Physics, AP Chemistry, and AP Calculus BC will have several complicated problems that require the extra functionality that the TI-84 Plus calculator provides. Make good use of the built-in applications within the APPS tab, which has features that range from converting units to creating vectors to graphing vertical x functions. Especially for the AP Calculus test, being able to graph polar equations, differentiate multiple graphs by colors, type out long summation formulas, and entering integral equations in the TI-84 Plus CE is a big plus.

Overall, the TI-84 Plus color edition is the best calculator that offers many more useful features than the other models and it can be used for all three tests. Plus it can easily travel with the student to college.

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