Math Tactics

The highly standardized format and content of the SAT, ACT, and math tests like them offer the opportunity and in some cases dictate the need for well-honed and disciplined tactics. Here are some of the most important math test tactics: (Please click the triangular bullets (‣) to expand the collapsible outline for detail/explanation.)

Pace yourself attentively from start to finish of each section.
◦ Every question on the ACT and SAT is worth just one point, which is important to remember when allocating time to each question.
◦ Questions generally increase in difficulty over the course of each math section; earlier questions tend to be easier and less time-consuming, while later questions are sometimes trickier and take longer to solve.
◦ Try to solve easier problems thoroughly in 30 seconds of less, thereby earning time to allocate to more difficult later problems.
◦ No question is worth much more than 1.5 minutes of your time for as long as there are other questions remaining unanswered.

•  Read the question thoroughly to assimilate everything you need to correctly answer and avoid errors.

Read and reread the question extra-carefully.
◦ One of the most common errors is rushing through the question stem and critically missing or misunderstanding a key detail.
◦ Read the question deliberately and attentively, focusing intently on each detail to ensure you properly understand it.
◦ Carefully reread if necessary any part of the question that you don't fully understand.

Annotate key details.
◦ Circle or underline essential details, especially if you're in danger of solving the problem without considering them.
◦ Circle or underline the solution you are asked to produce - especially when it is only one among many possible solutions you could have been asked for.
◦ Carefully review your annotations as you solve the problem and before you grid the answer, ensuring you are correctly using all of the key information.

Tag skills tested and question type.
◦ As you read and annotate the question, mentally assign tags that will help you focus on what's important to solve the problem and get the point. Specifically, tag:
• math skills the question tests
• the question type, if recognizable

Flag pitfalls, traps, and trouble spots.
◦ As you read and annotate the question, mentally assign flags to alert you to and help avoid predictable errors. Specifically, flag:
• common errors (pitfalls) to avoid that lurk in the tasks required by this particular question
• "gotchas" installed by the test authors as traps for the unwary
• challenging tasks called for by the question that generate potential trouble spots demanding extra rigor and special attention

•  Solve the problem powerfully and efficiently using all appropriate tools at your disposal and proactively rooting out errors.

Notate your solution clearly and completely.
◦ Use consistent and thorough notation as an ongoing check against careless errors.
◦ Lay out your notation in a clear, consistent, and logical approach that
• follows clear paths
• economizes on space
• plans realistically
• thoroughly includes all relevant notation (avoiding skipped steps or missing pieces of notation)
• is easy to follow and check
◦ Review your notation as you go, checking for any clear errors.
◦ As you notate your step-by-step solution, pay close attention to any pitfalls, traps, and trouble spots you flagged earlier.
◦ Check your notation carefully for errors if your solution does not check.
◦ Review your notation after the fact when and if you get a practice question wrong; use the notation to analyze your error and put improvements into practice.

Use your calculator carefully.
◦ Use your calculator when needed (and permitted), but only for single-step computations.
◦ Notate each single-step computation on the page before performing the next computation; do not enter multiple steps at once into the calculator.
◦ Perform a basic reality check on your calculator's results to ensure you didn't make an error using it - radians vs. degrees, for example? Order of operations?
◦ Practice mental arithmetic in your everyday life - it sharpens your math skills whether or not you're able to use a calculator in any particular situation.

Check your solution whenever possible.
◦ Always reread the question and given information as a check, carefully noting your annotations and ensuring you correctly integrated all of the details into your solution.
◦ To gain greater confidence that your answer is correct, carefully perform a check of your solution that is efficient yet thorough whenever possible.
◦ Notate your check when possible.