PSAT Math practice set 3: Geometry and trigonometry
All problems are from Stroup and Stroup PrepPros The Complete Guide to Digital SAT® Math. If a problem does not have a diagram, it is often a good idea to draw one. Even if there is one provided, on the Bluebook exam you won’t be able to draw on the screen — consider sketching on your own paper rather than drawing in the book to practice that. The formulas provided in Bluebook can be found by scrolling to the bottom of this page.
1. p. 115 Ch. 14 #14
2. p. 116 Ch. 14 #21
3. p. 127 Ch. 15 #26
4. p. 128 Ch. 15 #36 (Note that the regular hexagon has not been drawn to scale. That doesn’t affect the solution.)
5. p. 129 Ch. 15 #44
6. p. 139 Ch. 16 #23
7. p. 140 Ch. 16 #28
8. p. 193 Ch. 20 #35
9. p. 194 Ch. 20 #40
10. p. 195 Ch. 20 #46
If you would like to request that we discuss any of these in the next class, fill out the form at https://forms.gle/PjvLgeZWQB1Hsfmg7.You can also ask more general questions there. Do this no later than Sunday evening, September 13. (Sept. 7 is the Labor Day holiday, and class will not meet; the next class is Sept. 14 if my jury duty does not conflict. I will let you know more as soon as I do.)
PSAT Math practice set 2: Nonlinear functions and equations
All problems are from Stroup and Stroup PrepPros The Complete Guide to Digital SAT® Math. A wide variety of types of questions fall into this category; some of them benefit from the use of Desmos, while others really don’t need it.
1. p. 4 Ch. 1 #15
2. p. 8 Ch. 2 #18
3. p. 13 Ch. 3 #12
4. p. 17 Ch. 4 #13
5. p. 29 Ch. 5 #40
6. p. 72 Ch. 10 #30
7. p. 73 Ch. 10 #46
8. p. 89 Ch. 11 #35
9. p. 276 Ch. 29 #14
10. p. 276 Ch. 29 #16
Videos with these worked out can be found in the YouTube playlist; the link was sent in an e-mail on Aug. 24.
PSAT Math practice set 1: Desmos basics
All problems are from Stroup and Stroup PrepPros The Complete Guide to Digital SAT® Math. (That book will be distributed during the first class session.) The questions have been chosen to exploit basic features of Desmos. Do not spend time doing algebra steps — no factoring, no algebraic manipulation, no completing the square, no complicated arithmetic by hand. If you need to work out a value, type the calculation into Desmos. If you’re not sure what to do, see if there’s something you can graph. Video solutions can be found in the YouTube playlist. A link for that was sent to your e-mail on Aug. 24.
1. p. 3 Ch. 1 #8
2. p. 13 Ch. 3 #14
3. p. 16 Ch. 4 #3
4. p. 26 Ch. 5 #10
5. p. 28 Ch. 5 #33
6. p. 49 Ch. 8 #10
7. p. 101 Ch. 12 #37
8. p. 106 Ch. 13 #30
9. p. 173 Ch. 19 #27
10. p. 262 Ch. 27 #24
PSAT vs. SAT
To prepare for the SAT is to prepare for the PSAT. You’ll find that most resources available say that they are for the SAT, not the PSAT. That’s not only fine, it’s desirable. The PSAT is just a slightly easier version of the SAT. The timing and format are identical. They are both tested using the same software with all the same features. My own experience with working the practice tests available in Bluebook for the PSAT and SAT is that the very hardest couple of problems in each SAT section seem somewhat more difficult than those on the PSAT — but the topics involved are the same.
The maximum score on each section of the SAT is 800; on the PSAT, scores max out at 760. And of course there’s a selection index for National Merit that is calculated for PSAT scores, but not for SAT.
When a link here refers to the SAT, you should not be deterred. I’ve only included things I thought might be useful in your PSAT preparation.
Adaptive testing on the PSAT and SAT
When you take the digital PSAT or SAT, there are two modules for each subject — two modules of Reading and Writing, two modules of Math. Everyone sitting the test with you should get the same module 1; which module 2 you get depends on how well you’ve done on module 1. If you get the easier module 2, you cannot get a really high score overall. The hardest questions won’t be available to you. It’s really important that you check module 1 over carefully to avoid careless errors. You can read more about this at https://www.edushaale.com/post/how-to-improve-your-psat-math-score, including an estimation of the number of questions you can miss before you get dropped down to the easier module 2 (in section 10 on that page).
TL;DR: If the second module seems harder than the first one, you’re doing fine.
Desmos
Videos
Learn SAT Math’s A Beginner’s Guide to Desmos on the SAT Math: https://www.youtube.com/watch?v=-pGNBb8M3LQ
This is about 17 minutes long, and he tries to be cool (calling himself a sigma male, for instance). He also mentions pasting equations from a problem into Desmos — something which is not possible in the Bluebook testing platform — but there is a lot of useful quick information if you don’t know much about how Desmos might be useful on the PSAT.
JW’s Math Tutoring’s Ultimate Desmos Guide to Digital SAT Math: https://tinyurl.com/ultimatedesmosguide
This is a playlist with close to 8 hours of Desmos-specific instruction. Some of it is quite advanced. I’ve gone through all of it and practiced with the examples. I don’t think you need or want to watch all of this, but if you are willing to invest a few hours, videos up through intermediate skills or the first advanced skills really could be useful. Speed up the replay until you get to something you’re not already fluent with. The videos include important techniques that aren’t addressed in the Learn SAT Math video above. If those turn out to be helpful, you might decide to invest time in the later videos. In all, he’s up to more than 70 example problems worked. You can find the problems and other things in downloadable format at https://morgantownmathtutor.wordpress.com/sat-resources/.
Using the percent key in Desmos: https://www.youtube.com/watch?v=lP6DryJX108
Introduction to many uses of regression in Desmos: https://www.youtube.com/watch?v=g4vgbNrWArk
Practice questions
The College Board has a freely accessible question bank. Someone has coded a better interface for that: https://satquestionbank.org. I like this better than the official one because Desmos is built right in, and the platform will let you enter and check answers on screen.
If you prefer to use the official version, you can check it out at https://mypractice.collegeboard.org/questionbank/search, which requires logging in to your CB account. There are more than 1200 math questions available (which should be the same as those on the other site), but you can’t enter your answers here; you can have it show you the answer and explanation and/or export those to a PDF.
Really, the kid who coded the alternate way to access these questions (Jacob Jackson, https://satquestionbank.org/about) did an amazing job.
Math reference sheet
I have not been able to find this on the College Board site to link to, so this is a screen shot from Bluebook. Please don’t sue me.
