Windows: Firefox 73
Firefox is available as a portable application for you to use on any computer even without administrator privileges. Version 73 accepts the ciphers used by the Math Placement Test. Or, if you like, you can install it if you have sufficient privileges on your machine.
If you've used a more recent version of Firefox, this version may not be able to read your Firefox profile and will then ask your permission to create a new profile. You should create a new profile if asked.
Portable version: Mozilla Firefox 73 Portable
Note: the portable version is compressed and ships as a self-extracting "installer" which will simply uncompress it in the folder of your choosing (which could even be your downloads folder).
Install version: Mozilla Firefox 73 Installer
Mac: Chromium 80
Chromium (the open-source version of the browser engine upon which many browsers are built) version 80 accepts the ciphers used by the Math Placement Test. It's available as a stand-alone .app that you don't have to install in order to run.
Extract the Chromium.app file from the zip archive to any folder you choose (your Desktop or Downloads folder will work fine) and then start that app. Depending on your security settings, you may have to right-click on the app and select "Open" in order to run it the first time.
Accessing the Test
Once you're running Firefox 73 or Chromium 80, just navigate back here to access the Math Placement Test. You can use the shortcut URL assess.math.sc.edu