Here are two sites with practice tests. Then second one also has answer keys to many of them.
http://latin.sasaustin.org/actestarchives.php
There are several different ways to practice for mythology. You can do none of these, one, or many -- whatever you feel up to and/or interested in.
1. Take practice tests and google any names you don't know, to read and learn about them.
2. http://www.theoi.com/ is a good website for learning about the characters and stories, b/c it summarizes, but also offers primary sources in English.
3. Systematically study the following in order :
Greek & Roman pantheon; myths of major gods/goddesses; creations myths. Know the Olympian gods and stories featuring them. Know the succession myth: how Ouranos and Gaia were followed by Cronos and Rhea, then Zeus and Hera.
Two good sources are the following:
The first 4 chapters of this Mythology Workbook.
Morford and Lenardon's Classical Mythology text (a more advanced college-level text).
Major Heroes: Perseus, Hercules, Theseus, Jason, Bellerophon, Meleager. Look them up on wikipedia or http://www.theoi.com/, learning the plots and characters of their stories.
The Trojan War – from the causes through the returns.
Homer's Iliad.
Homer's Odyssey.
Hesiod's Theogony.
Ovid's Metamorphoses.
Vergil's Aeneid.
Greek Tragedies by Aeschylus, Sophocles, and Euripides.
Apollonius Rhodius, Argonautica (a.k.a. "The Voyage of the Argo").
Beginners will use wikipedia or http://www.theoi.com/ or a general mythology book to look up these stories to become familiar with them.
More advanced students will read the primary sources themselves, the ancient writings in English translation.
Unless you are an exceptional reader with an amazing memory, you obviously will not have time to read all of the primary works in translation for the area competition in February. But if you like mythology and literature (or learning in general), and would enjoy reading the ancient classics for fun over the next year or two (esp. during next summer), then you could think about being very competitive long-term through a systematic study of these texts. They actually make for very interesting reading just for fun, not to mention the fact that they've been read, studied, pondered, and discussed by the best educated people for 2,000-2,500 years.
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Here is the NJCL official list of recommended texts:
MYTHOLOGY:
Classical Mythology, Mark Morford & Robert Lenardon, Third (or later) Edition, Longman, Inc., White Plains, NY, 1985. A good source for students beginning their study of myth.
Gods and Mortals in Classical Mythology: A Dictionary, Michael Grant & John Hazel, G. & C. Merriam Company, Springfield, MA, 1973. Often available from other publishers in paperback.
The Meridian Handbook of Classical Mythology, Edward Tripp, The American Library, Inc, New Jersey, 1970. Also available in paperback.
Dictionary of Classical Mythology, J. E. Zimmerman, Bantam Books, New York, 1964.
Myths and their Meaning, Max J. Herzberg, Prentice Hall School Division, Columbus, Ohiop, 1984. Available in paperback. A good source for the student studying myth for the first time.
The Penguin Dictionary of Mythology, Pierre Gremal, Penguin Books, 1996.
Advanced myth students should be familiar with the primary sources (in translation) of Homer, Hesiod, the Greek tragedians, Vergil, Ovid, & Apollonius Rhodius.
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Here are some resources with which to begin your exploration of ancient mythology. If you are a beginner, start with the Classical Mythology Workbook, and then move on to the primary sources. The theoi.com website (link below) is a nice web site to use, offering ancient texts and images from ancient art.
I have made .pdf files of a workbook which you may view online or download to your own computer. This way, you may read summaries of Greek myths and do some practice exercises with them. You may print them off and turn them in for extra credit in Latin; you may use them as a basis for JCL myth competition; or you may simply use them for fun. As you become a more advanced student, you will want to read primary sources, i.e. the ancient stories themselves (in English translation for now!).
Apollodorus' Library (of Greek Mythology).
This is a good ancient source for getting the basics of any particular myth. Use the Table of Contents to find the myth you wish to read.
Apollodorus (or pseudo-Apollodorus) was supposed to have been the author of a Greek work known as The Library (or Bibliotheca, in Greek), an anthology/summary of myths based upon old Greek epic and the plays of the Greek tragedians (esp. Aeschylus, Sophocles, and Euripides). The work was traditionally ascribed to Apollodorus of Alexandria, a Greek scholar who flourished in the 2nd century BCE, but scholars now dismiss his authorship and believe the Library was created in the 100s CE.
The most famous Greek account of the origins of the universe is the Theogony by Hesiod. The word "theogony" means "birth/generation of the gods" (theos – god + gon – generation/birth). Hesiod was a Greek epic poet who flourished in Boeotia, northwest of Athens, in the 700's BCE. Next to Homer, Hesiod was the most famous and honored old Greek poet.
Homer's Iliad.
Homer's Odyssey.
Ovid's Metamorphoses.
Vergil's Aeneid.
Greek Tragedies.
Theoi.com is a good website for learning ancient mythology, because it uses ancient sources themselves and cites the section numbers, and it offers images from ancient art.