This is quite correct, but the question is fraught with pitfalls for the unwary quiz contestant and question setter.
The following is my understanding. As I've said before, I am not a historian so I stand to be corrected.
First of all, in Russian history it's important to distinguish – as indeed this question does – between the titles 'Tsar' and 'Emperor'.
The title 'Tsar' was used from the 10th century onwards to designate East and South Slavic monarchs or supreme rulers of Eastern Europe – originally the Bulgarian monarchs. The first Russian ruler to style himself 'tsar' was Ivan III (1462–1505) – known as Ivan the Great. This followed the fall of the Byzantine Empire (see Question 2 in this round), as Russia developed ambitions to become the "third Rome".
Wikipedia explains how the powers of the Russian rulers grew in the 15th and 16th centuries. The Grand Duke Ivan IV, it relates, was crowned Tsar of All Rus' in 1547, when the state of Russia (apart from its constituent principalities) came into formal being. According to Wikipedia, he was thus recognised – at least by the Russian Orthodox Church – as Emperor. Ivan IV – known as 'the Terrible' – was the first Russian ruler to be officially designated by the title of Tsar.
(Incidentally: Wikipedia explains that Ivan IV was known in Russian as Ivan Grozny. The word grozny is customarily translated into English as 'the Terrible', but this results from the archaic usage of the English word – "inspiring fear or terror; dangerous, powerful, formidable" – rather than its more modern connotations of "evil" or "defective".)
Peter I ('the Great') came to the throne in 1682, shortly before his tenth birthday. He was proclaimed Emperor of All Russia – officially, "in the manner of the Roman Senate" – almost forty years later: in 1721, after his victory over Sweden in the Great Northern War. This title was used for all Russian rulers, up to the overthrow of Nicholas II in 1917.
To summarise: The first Russian ruler to style himself 'tsar' was Ivan III (1462–1505) – known as Ivan the Great. The first to be officially designated by the title of Tsar was Ivan IV – known as Ivan the Terrible. And the first Emperor of All Russia was Peter I – known as Peter the Great.
But: according to Wikipedia, as we've seen above, Ivan IV (the Terrible) was recognised – "at least by the Russian Orthodox Church" – as Emperor.
The Academicals' question avoids any ambiguity (for the well–informed contestant – by which I don't necessarily mean myself) in three ways: first of all by making it clear that the person in question was already a Tsar, secondly by including a date (1721), and thirdly by mentioning the adoption of the title 'Emperor of All Russia'. For the less well–informed contestant (by which I might well mean myself) some confusion may nevertheless have remained!
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