For students heading into 11th or 12th grade, this year is all about SAT math preparation. This is unnerving for many students, especially those for whom mathematics comes far less naturally than the reading and writing portions of the exam. It takes a lot of time and effort to practice problem-solving and memorize formulae, so the sooner you start the better.
One way to set yourself up for success is to implement score-boosting strategies and enroll in an SAT math tutoring program at least 3 months before your test date. In doing so, you will consolidate your knowledge and sharpen your math skills for the test. However, to be truly prepared for SAT math, you also need to be able to recognize trick questions and navigate the more complex problems that you can usually identify at the end of multiple-choice or grid-in segments.
Let’s explore 3 of the most notoriously difficult SAT math problems below to help you get a head start on your test preparation. Keep in mind that while these are specific problems they also illustrate various types or categories of questions, and understanding this more structural dimension to the SAT will be extremely helpful as you prepare. Give yourself enough time to practice solving these types of problems before the big exam and make sure you address any difficulties you may have with your math teacher or tutor.
1. The “meanest” math question
According to a Quora thread, the meanest test problem ever reads as follows:
In a class of p students, the average (arithmetic mean) of the test scores is 70.
In another class of n students, the average of the scores for the same test is 92.
When the scores of the two classes are combined, the average of the test scores is 86.
What is the value of p/n?
Solving this notoriously difficult problem in a time-efficient manner requires a systematic approach. One especially helpful method is to translate each sentence into a mathematical equation. In fact, the SAT is populated with numerous problems that are made to seem far more complicated than they are by reducing the clarity of their mathematical contents. If a word problem seems like an indecipherable wall of text, odds are that your best first step is to identify mathematical components like quantities and variables, as well as operations, that may be presented in wordy language to slow you down.
To really dig into this, take a look at what Presh Talwalkar, math whiz and author of The Joy of Game Theory: An Introduction to Strategic Thinking, provides in his comprehensive post addressing this problem.
If you don’t want to spoil the fun, you can always reach out to your math teacher or tutor to tackle the challenge of solving this thought-provoking problem together.
2. The easily misread question
One of the SAT math problems people commonly misunderstand is a multiple-choice question that reads as follows:
Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p?
At first glance, students tend to assume that the question is asking you to calculate the discounted cost of the laptop plus tax. However, as the math wizards at Love the SAT point out, this question is instead asking you to identify which option represents the original price of the computer in terms of p. In essence, this question and others of its type try to trick you into over-complicating the situation through forcing you through dense, multi-clause sentences before asking for a simple identification. In the end, the question is clear as day, and you simply need to work backward from that simple end point.
While all questions on the SAT demand careful reading, questions of this type are especially slippery if sped through. You’ll likely need to read questions like this more than once or twice to really mentally organize things comfortably to begin your calculation. Although you can easily find step-by-step instructions on how to produce the right answer, we think it would be much more effective—and even fun—to solve it on your own or with the help of your math tutor.
3. The formula-focused question
In every SAT math test, there is at least one question that it’s not as tricky as it seems at first glance and can be easily solved if you memorize the right formula. These are make-or-break for testing the topics you’ve studied leading up to your test day: either you know the formula or you don’t, and in case you haven’t covered that particular node of math you’ll likely be forced to make an educated guess and hope for the best. One such example question reads as follows:
In a right triangle, one angle measures x°, where sin x° = 4/5.
What is cos(90° – x°)?
You could draw a diagram of the triangle to try to solve this problem through brute measurement, but that’s neither exact nor time-efficient. As with any standardized test, there’s only so much time you have to complete the test. So, given the time limit, speed is key. And the fastest way to solve this problem is to use the formulae for the sine and cosine of an angle. As PrepScholar explains:
“If you were a formula whiz and knew the complementary angle relationship for sine and cosine, which is sin(x°)=cos(90°−x°), you’d know immediately that the answer is cos(90°−x°)= 4/5 or 0.8.”
The big takeaway here is that you absolutely must make use of tried and true reference materials and test prep books and/or services in order to ensure you study the right material for the SAT. Covering the entirety of 10th grade geometry will only lead to burnout; instead, make sure you have a clear guide to important formulae and equation types that can help you organize your study period as efficiently as possible.
Practice, practice, practice!
There’s no shortage of tricky SAT math test questions that may create difficulties for you during the exam. The ones we’ve explored above are a mere sample of what you should expect, and one of the main reasons we’ve withheld a simple answer to each is to get you thinking about question structure as opposed to simple inputs and outputs. Understanding what a test is doing, in other words, is an extremely helpful way to build confidence in your studying and practice. So, start practicing these types of problems early on to ensure you consolidate your understanding and have enough time to memorize and comprehend any formulae you might be required to use.
To ensure you master the trickiest SAT math question on time for the big exam, enroll in an SAT math tutoring program. At OMC, we provide SAT preparation classes to students just like you who want to familiarize themselves with SAT test sections, question types, and challenges while also increasing their chances of scoring high through active, structured, and intensive practice under the supervision of a friendly and dedicated math expert.
If you want to know more about our program and tutors, please feel free to reach out to us and we’ll get back to you shortly with the information you requested.