(1) As for all questions, carefully read the chapters applying to each question (chapter 19 and 20 for question 12, chapters 21 through 23 for question 13).

(2) As for all questions, carefully read all web pages applying to each question. As shown in the online text table of contents, these can be found under Stellar Evolution (Summary of Stellar Formation and all pages listed below that, for question 12, Stellar Death and all pages listed with that, for question 13).

(3) Refer to the list of essay questions and read the detailed breakdown of each question, then reread the text and website material, noting where they apply to each question.

FOR QUESTION 12: There is plenty of material in the book and on the website to give a thorough answer. But be aware of the following:
(1) The question ends with "how long do Main Sequence stars last?". It is a common mistake to keep going, and discuss how they die. That is part of question 13, not question 12, and any discussion of how they die will have no value if you receive question 12.
(2) Note that stars do not just collapse from clouds of gas and dust to fully finished stars. Although that can happen in rare circumstances, most stars spend over 90% of their formation in a state of quasi-equilibrium contraction, as discussed in detail in the web pages about stellar formation.
(3) Massive stars do not form quickly because their larger gravity causes them to collapse faster. They form more quickly because their larger gravity compresses their gases more forcefully, which makes their gases hotter and therefore brighter. The quasi-equilibrium contraction mentioned above requires the stars to slowly contract, to make up for their loss of heat. If they are brighter they have to contract faster. Since massive stars' greater gravity makes them brighter they lose heat faster, and contract faster. But the gravity does not just cause them to simply collapse. THIS IS PARTICULARLY TRUE AFTER THEY BECOME PROTOSTARS, AND MORE OR LESS STABLE SAVE FOR THEIR LOSS OF HEAT.
(4) As stars "approach the Main Sequence", nuclear reactions begin in their cores, partially replacing the heat they lose. As a result, as discussed in the page on "The Main Sequence", their contraction slows down. They continue to contract, getting hotter and denser, and producing more nuclear energy. But because that replaces more of their heat loss, they contract slower and slower, and stop contracting completely when the nuclear reactions are equal to their heat loss. AS A RESULT, STARS DO NOT SUDDENLY STOP CONTRACTING AS THEY APPROACH THE MAIN SEQUENCE, BUT ONLY VERY SLOWLY.
(5) The stars are not hot and bright because of their nuclear reactions. They are hot and bright because of the compression of their gases, BEFORE THEY EVER STARTED nuclear reactions. Once the nuclear reactions begin they allow the stars to REMAIN hot and bright for longer than they would if there were no nuclear reactions. But they are actually FAINTER after the nuclear reactions begin than before.
Hopefully, careful attention to the material in the text and the website, and remembering the points above, will help you provide a very good answer. ESTIMATED VALUE OF STUDY MATERIALS: Textbook -- important background material, and filling-in of topics which might not be covered adequately on the website. Website -- critical information for anyone who wants to get a good grade on question 12. Notes on this page -- important reminders of points made on the website.

QUESTION 13: There is plenty of material in the book and on the website to give a thorough answer. But be aware of the following:
(1) Be sure to discuss all types of stellar death. Some students read "start with low-mass stars which... and finish with high-mass stars which...", and only talk about those stars. There are several types of stellar death listed immediately below, and a proper answer will discuss ALL of them in at least some detail.
(a) The lowest-mass stars become electron-degenerate without ever getting hot enough to burn nuclear fuel, and quickly cool off to become "brown dwarfs".
(b) Other relatively low-mass stars become hot enough to burn nuclear fuel, but are completely convective, burn ALL their fuel (only burning it in the core, but using up all their fuel), and not only last practically forever, but when they die can only shrink to become "helium brown dwarfs". Since the lifetimes of such stars are a thousand times longer than the current age of the Universe, no such stars currently exist. But eventually, there will be a lot of them. REFER TO THE PAGE ON HOW STARS MOVE TO THE MAIN SEQUENCE (part of Question 12) TO UNDERSTAND WHY STELLAR DEATH TYPES (a) and (b) OCCUR.
(c) Stars like the Sun, which move to the left in the HR Diagram before reaching the Main Sequence (again, refer to the page on stars moving to the Main Sequence), are NOT thoroughly mixed, and when they run out of fuel in the core, still have plenty of fuel left on the outside. As discussed in the page on the Sun's late-Main-Sequence life, the inevitable result of this is a gradual increase in brightness while on the Main Sequence (with interesting consequences for the future of the Earth, to be discussed on a page to be posted at a future date), and a very rapid increase in brightness when they completely run out of fuel in the core. This leads to a red giant stage in which the star is "dying", and because it is far brighter than it once was, cannot last long before ending its (easily) visible life. AS DISCUSSED ON THE PLANETARY NEBULA AND WHITE DWARF PAGE, such stars tend to become more and more unstable over time, and (usually) eject large amounts of mass before collapsing to form white dwarfs (which see, in the chapter on those "dead" stars).
(c1) ALL STARS WHICH HAVE EVER DIED EITHER BECAME (a) brown dwarfs, or (c) red giants, as (b) thoroughly mixed Main Sequence stars last longer than the current age of the Universe. But not all stars that become red giants die the same way. As outlined in the webpage on stellar death, there are several ways in which red giants can die:
(d) Low-mass red giants (less than 1/2 the mass of the Sun) never get hot enough to fuse helium, and eventually collapse to helium white dwarfs
(e) Middling-mass red giants (like the Sun) become hot enough to fuse helium, and eventually collapse to carbon white dwarfs
(e1) The lowest mass red giants that eventually burn helium will have catastrophic helium "flashes" and blow themselves to smithereens, but their lifetimes are longer than the age of the Universe, so no stars have died that way, yet.
(e2) Stars like the Sun have "milder" helium flashes which temporarily mix the core, and cause the stars to move back toward the Main Sequence, forming the "horizontal branch". However, they quickly run out of hydrogen in the remixed core, and resume their red giant "life", before finally collapsing to become carbon white dwarfs
(f) More massive stars are able to burn more exotic fuels due to the higher temperatures they can reach before their cores become electron-degenerate. Such stars can die in a variety of ways, but in general, unless their original mass exceeds 5 solar masses, most of them become some type of white dwarf (although some may suffer catastrophic events, such as a carbon "detonation", which completely destroy them).
(g) The most massive stars have no limit to the way they burn nuclear fuel, and toward the end of their lives turn carbon to oxygen, neon, silicon, and other materials, up to iron. However, iron cannot be burnt, as it uses more energy than burning it creates. So if a star starts to create iron, it develops an increasingly massive iron core, which for sufficiently massive stars will eventually exceed the Chandrasekhar mass limit, and try to collapse to zero size. When that happens, the rest of the star will try to follow the collapsing core inwards. When the core becomes as dense as an atomic nucleus, the electrons are forced into the protons, creating a pure neutron core, and producing a flood of neutrinos, which cannot escape the core because of its high density (several trillion tons per cubic inch). This creates a "neutrino shock" which temporarily (for a hundredth of a second or so) stops the collapse of the core. In that instant the rest of the star slams into the core, and its inward energy of motion is transformed into heat, raising its temperature to trillions of degrees, causing a firestorm of unimaginable intensity. In the next instant large amounts of trans-iron elements are created, including elements more massive and exotic than ever observed in any nuclear accelerator on Earth. The energy released in that instant is equal to millions of billions of Solar luminosities. That stops and reverses the collapse of the surrounding materials and blows the outer portion of the star to smithereens, resulting in what is referred to as an iron-core collapse supernova. NONE OF THE ENERGY OF THE FIRESTORM IN THE MIDDLE IS RELEASED BY THIS EXPLOSION. IT IS ALL USED UP REVERSING THE COLLAPSE. However, as the star is blown to bits, the light that was formerly trapped inside it, struggling to escape over hundreds or thousands of years, suddenly finds nothing in its way and escapes, temporarily making the star hundreds of billions of times brighter than the Sun. THERE ARE OTHER WAYS IN WHICH SUPERNOVAE CAN OCCUR, BUT THEY ARE ALL IN ONE WAY OR ANOTHER SIMILAR TO THIS, AND IRON-CORE COLLAPSE IS THOUGHT TO BE ONE OF THE MOST COMMON CAUSES OF SUPERNOVAE, BECAUSE SUCH EXPLOSIONS CREATE A MIXTURE OF HEAVY ELEMENTS EXACTLY THE SAME AS THAT OBSERVED IN NATURE. In other words, all the heavy elements of which we and our planet are made (that is, everything save for hydrogen and helium) are the result of such iron-core collapse supernovae -- meaning that in a very real sense, we are made of the ashes of such dead stars.
DENOUEMENT: After the star blows itself to bits, there may be part of it left (and in fact, probably is, save in the case of HYPERNOVAE, which may literally destroy the star completely). If the part left has a low enough mass, it may become a neutron star. If not, or if the collapse is not sufficiently slowed by the supernova explosion, the part that is left becomes a black hole.
ALL DEAD STARS -- white dwarfs, neutron stars, and black holes -- are very faint, and either difficult or impossible to observe. White dwarfs can be observed, but are so faint that recognizing them is not as easy as might be assumed. Neutron stars are so faint that they cannot be observed unless they have an unusual interaction with gases left around them after their formation (pulsars, X-ray bursters and the like; see the text, and the webpage on Mass Exchange in Binary Stars). Black holes literally cannot be observed at all, save for such interactions -- typically, involving some kind of accretion-disk emitter. However, since there is a whole chapter on dead stars in the text, there is little to say about them here save that BLACK HOLES DO NOT SWALLOW UP OTHER STARS, UNLESS THEY WOULD HAVE RUN INTO THEM EVEN BEFORE THEY BECAME BLACK HOLES. Outside the original surface of the star which became a black hole, the gravity of a black hole is the same as or (usually) less than the original star's gravity. It is only if something were doomed to run into the original star that it could run into the black hole it becomes. So although black holes may exist in large numbers, it is almost impossible to detect them, save under extremely rare circumstances.

Hopefully, the above notes, although painfully brief in some ways, will help those students who have the sense to read them to produce exceptionally good answers for questions 12 and 13, and do very well on whichever of those two questions ends up on the Final. Those students who do not bother to read this page have no one but themselves to blame if they do not do well on the exam. Still, I hope that all of you will take advantage of these notes, do well on the exams, and pass the class, as I get no pleasure from failing students. I would much rather "give" A's than F's -- but I do not give grades. I just evaluate the answers students provide, and decide what grade they have demonstrated they deserve. Remember that if you know something and do not put it down on your answer, I have no way to know that you know it. You MUST "demonstrate" what you know by putting it down, in as clear, correct and complete a way as you can manage. So again, good luck and good studying, and I hope that when you receive your grade it will be not only what your answer deserves, but one that you will be happy and proud to have achieved.