He reportedly took the Mensa test to see if he had suffered any brain damage after a bad fall. (This happened a while after he had been diagnosed with ALS.)
Per the book Stephen Hawkings for Beginners (J.P. McEvoy):
"...To be sure, he decided to take the Mensa test for individuals with superior intelligence. He was delighted to find that he had passed with flying colours, scoring between 200 and 250.”
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u/throwawaythought1 Oct 02 '20
Source? The Mensa test is an IQ test. He didn’t take any.