In the last few days, I’ve given you a first look at the new PSAT, the most radical change to the test in about a decade. Today’s post is the last of this series. If you missed anything, check it all out here: Part 1: New PSAT General Impressions Part 2: New PSAT Reading Part 3: New PSAT Writing & Language Part 4: New PSAT Math (this is the current post) Let’s dive right in. Okay, I’m not a math guy (though I got perfect 800s on the SAT Math and the SAT Math Level 2 Subject Tests in high school). I’ve always been a bit of a contrarian. Growing up in math/science-heavy Silicon Valley, I actually gravitated towards creative writing; my class even voted me “Most Likely to Become the Next New York Times Bestseller” hah! But I have actually grown quite fond of the current SAT’s math—it has weird tricks and devious traps, but I got really good at identifying those patterns and pitfalls. I found ways to get around the harder questions by not doing any real math, at least nothing like what students actually learn in math class. The way these questions were set up just lent themselves to crafty, roundabout approaches. In fact, doing things the “math way” often caused students to fall for the SAT’s carefully designed traps. Not so anymore. These questions are much more resistant to shortcut, cheap strategies. You’ve got to know your math. Though I was still able to handle all of them fine, I found these questions ostensibly harder. Or maybe I’m just not used to this style of questions yet. I winced when I realized I made a couple careless errors, so the patterns in the traps are different now too. The good news is that there are only 4 possible choices now, instead of 5. And there’s no longer a wrong answer penalty (currently, you lose ¼ of a point if you get a question wrong, as opposed to receiving a 0 for that question if you leave it blank), so never leave anything blank anymore. But another downer is that calculators are banned on the first math section! If you’re slow at mental math prone to simple calculation errors, you’re going to have a bad time here. Many questions seem to deal with understanding how to set up proper equations, something I’ve long steered my students away from as much as possible on the current SAT. Now we have no choice but to play their game. We have to understand what certain numbers mean, why we’re multiplying things together, or what role a plus or minus sign has. This is really going to give weaker math students a hard time because they tend to just plug numbers into random variables without truly understanding why they are performing a particular step. This haphazard approach might have worked on half of the current SAT questions just from sheer luck, but now, you really have to understand why the equation or formula is set up that way. The questions aren’t even asking you to calculate anything. They just want to know what the equation or a certain variable or number in it means. By the way, the ACT has always included this style of question, but I found these particular mock PSAT ones more challenging. Check it out: The new PSAT gives you an equation like n = 456 – 3T, where n is the number cups of hot chocolate sold per day and T is the average daily temperature, in degrees Fahrenheit. Then they ask you what the meaning of 3 in that equation is. I reasoned that it meant for every increase of 1 degree F, three fewer cups of chocolate would be sold. That’s actually the correct logic, but it isn’t an answer choice. I read too quickly and picked the one that said, “For every increase of 1 degree F, three more cups of hot chocolate will be sold” because I was just focusing on the increase of 1 degree. It was the only choice that mentioned an increase of 1 degree! But classic mistake…I should have read the second half more carefully. A temperature increase doesn’t actually increase the number of cups sold. The correct answer was the flip side of my initial thought. Saying, “For every decrease of 1 degree F, three more cups would be sold” is actually the same thing as saying, “For every increase of 1 degree, three fewer cups would be sold.” See how that can be tricky? They’re different sides of the same coin, but they are not opposites or contradictory. Stronger math students won’t have a problem with these types of questions, but I think they’re going to be one type of problem that weaker students will find especially challenging. I say this because one of my goals in math coaching is never to just tell my students the correct equation and have them solve it. Instead, I try to get them to explain why they need to set it up that way, but unfortunately, many times, the students have no idea. There are also four grid-in questions in the no calculators section. Following this section, you finally get to use your calculator again. I’m not a fan of putting so much math together either. I think the arrangement of sections on this new PSAT stinks. Not only are people going to lose focus on that hour-long reading section, but now they have to do 70 minutes of math in a row (25 minutes for the no calculator section, 45 minutes for the calculator permitted section)! There are an additional four grid-in questions in the calculators permitted section, making a total of eight student-produced responses. That’s the same as it is on the current SAT. Concept-wise, now the PSAT includes basic trigonometry, which was never tested on the PSAT or SAT before. Even though the Collegeboard pegs the trig question as a hard level question, it’s honestly the most basic trig possible. If you know SOHCAHTOA, you’re good. Nothing crazy here. The ACT math tests harder trig than this, though this is just one mock PSAT, so who knows…maybe the new SAT/PSAT will also include harder trig questions. I also saw some harder parabola questions that required knowing the y – k = (x-h)^2 format. There were also new statistics questions involving histograms, scatterplots, and line of best fit, all of which were nonexistent or heavily de-emphasized on the current SAT. Furthermore, there were some grouped math questions that dealt with shared data. Like, “Questions 14-16 refer to the following information” type questions. All in all, prepare for a harder, but more straightforward math test. It’s a lot closer to school math. Maybe in time, as I get more accustomed to these new style math questions, I’ll change my tune. Again, I didn’t find any of the questions unreasonably hard for a high schooler, but they are highly different. While I don’t think any of these new math questions would be out of place on the current PSAT/SAT, there was something “off” about them that I can’t quite put my finger on. It was the same feeling I got when the math changed from the pre-2005 SAT (the one I took in high school) to the current SAT (the one I’ve been coaching for nearly a decade). In time, I’m sure this new one will feel just as natural for me as I get familiarized. I also noticed a different geometry formula box at the beginning of the new math section. There were several 3D geometry formulas that aren’t on the current SAT. Although there were no 3D geometry questions on this mock PSAT, the inclusion of these new formulas probably means we can expect some 3D geometry questions, which aren’t currently tested. They are, however, currently tested on the SAT Math Level 1 and 2 Subject Tests. Also on the reference page, there is mention of radians (a unit usually associated with trigonometry), which were found only on the Subject Tests before. So let’s assume Collegeboard is bringing degree to radian conversions into the fray. If you’re feeling nerdy, feel free to try out the new PSAT yourself. You can download the test from the links HERE. Otherwise, I recommend letting test prep coaches like myself figure out all the details first, readjust our strategies, and come back to you with a new battle plan. I doubt the strategies will be much different than what I already teach, but there are some appreciable changes here that deserve a closer study. Now let me know what you think. Are you looking forward to these new changes? Leave a comment below. I read every comment.