diff --git a/filter/mathjaxloader/readme_moodle.txt b/filter/mathjaxloader/readme_moodle.txt
index a46c89569c7..7ace4042d7d 100644
--- a/filter/mathjaxloader/readme_moodle.txt
+++ b/filter/mathjaxloader/readme_moodle.txt
@@ -1,15 +1,19 @@
 Description of MathJAX library integration in Moodle
-=========================================================================================
+====================================================
 
-License: Apache 2.0
-Source: http://www.mathjax.org
+* Default MathJax version: 2.7.2
+* License: Apache 2.0
+* Source: https://www.mathjax.org/
 
-Moodle maintainer: Damyon Wiese
-
-=========================================================================================
 This library is not shipped with Moodle, but this filter is provided, which can be used to
 correctly load MathJax into a page from the CDN. Alternatively you can download the entire
 library and install it locally, then use this filter to load that local version.
 
-The only changes required to this filter to handle different MathJax versions is to update
-the default CDN urls in settings.php - and update the list of language mappings - in filter.php.
+Upgrading the default MathJax version
+-------------------------------------
+
+1. Update the default CDN URL in settings.php
+2. Perform an upgrade step to change the configured URL if it matches the
+   previous default.
+3. Check and eventually update the list of language mappings in filter.php.
+   Also see the unit test for the language mappings.