Yo, as we say in Texas, am I missing something here? When I took beginning theory, all they taught us was how to sing and play a scale, triad (major and minor) and then a seventh chord. AND! there was supposed to be some kind of Solfeggio training associated with this process, e.g. (Do, Re Mi, Fa, Sol, La, Ti, Do).
Per the OP, "I have an excellent teacher. . ." No offense, but for those who have posted here before me, I don't really think so.
So, what is most likely happening is some new pedagogical semantic weirdness on the part of the teacher and also the entity that hosts the exam. On point, Basic music theory is universal (I have seen and read it all), but I have never heard of "Pitch Recognition."
Therefore, per the OP, (and I am 65 years young with a Degree in Music) I recommend the following:
1) Get thou to a traditional music theory teacher, hopefully an Organist. These people know every permutation ever imagined, composed, or performed in music.
2) As far as your teacher is concerned, tell them thanks, but no thanks. At your age, you should have no time for this glorified falderal. Tangentially (time after time on this website), the problem discussed did not lay with the student. The problem (not "issue") was the teacher!
Additionally, I recommend for the OP, and most others:
1) The Berklee School of Music in Boston, MA, USA, has one of the finest Jazz matriculation programs in the world. What is not normally known is their OnLine school (well over 50,000 students enrolled worldwide).
As part of the multitude of many courses they offer are Music Theory, Harmony, and Ear Training (which I have successfully matriculated). It is somewhat pricey, but the teachers are phenomenal. Each lesson is taught on a weekly basis and is "self-paced," which is a very big deal!
https://online.berklee.edu/music-theory-harmony-and-ear-training2) Per the OP, if you need any further advice, please do not hesitate to contact me by PM. And most of all, do not forget that the study of basic music theory is SUPPOSED to be directly associated with a competent level of music performance.
3) Speaking as a pianist/philosopher, the epistemology associated with this type of study requires no more than a level of instruction associated with any pubescent pre-teen or teenager. That holds true if the individual who matriculates is GIVEN THE PROPER INSTRUCTION!
Good luck to you.