2012 Ultimate Geometry Review Sheet
Present…
THE (ULTIMATE)
GEOMETRY REVIEW SHEET
(2012 Edition)
Some General Information
The Regents Exam Basics:
Time: 3 hours
Problems: 38
● Part I: 28 multiple choice problems (2 pts each) = 56 pts ● Part II: 6 short answer problems (2 pts each) = 12 pts ● Part III: 3 short answer problems (4 pts each) = 12 pts ● Part IV: 1 long answer problem (6 pts each) = 6 pts ● Total: 86 pts
The following playlist is useful, since it has most of the topics from geometry in one compact place: http://www.youtube.com/playlist?list=PL26812DF9846578C3&feature=plcp
Many thanks to the users of Khan Academy for their works here!
Below is the link to the Regents Prep site (feel free to poke around for other subjects as well!) This deals with the majority of Geometry:
http://www.regentsprep.org/Regents/math/geometry/mathGEOMETRY.htm
http://www.nysedregents.org/Geometry/ This is a link to all existing Geometry Regents exams—replete with answer keys, rubrics, and scaling paraphernalia for your perusal. A wealth of practice here!
http://www.nysedregents.org/SequentialMathematicsII/ This is a link to Regents exams back to 1998—back when Geometry was folded into something known as “Course II.” (Note: there will be some topics on these exams that are not in Geometry right now, and one notable topic—circles—is absent completely. Nevertheless, these are excellent resources for most of the other topics.)
TOPIC: LOGIC
1. Introduction to Logic
● Mathematical Sentences
● Nonmathematical Sentences
● Open Sentences (identify variable)
● Closed Sentences
2. Negation
● Symbol: ~
3. Conjunctions (And)
● Symbol:
● Truth Table:
p
q
p
q
T
T
T
T
F
F
F
T
F
F
F
F
4. Disjunctions (Or)
● Symbol:
● Truth Table:
p
q
p
q
T
T
T
T
F
T
F
F
T
F
T
F
5. Conditionals (If…, then…)
● Symbol:
● Truth Table:
p
q
p q
T
T
T
T
F
F
F
T
T
F
F
T
PRACTICE
6. Biconditionals (…if and only if…)
● Symbol:
● Truth Table:
p
q
p
q
T
T
T
T
F
F
F
T
F
F
F
T
7. Tautology
● Compound sentence that is always true (T)
8. Logically Equivalent Statements
● Two statements that always have the same truth values
9. De Morgan’s Law
● Premise:
~(p q)
Conclusion:
~p ~q
● Premise:
~(p q)
Conclusion:
~p ~q
10. Conditional, Converse, Inverse, Contrapositive
● Conditional:
p q
● Converse:
q p
● Inverse:
~p ~q
● Contrapositive:
~q ~p
● Conditionals and Contrapositives are logically equivalent: (p
11. Law of Contrapositives
● Premise:
p q
Conclusion:
~q ~p
12. Law of Modus Ponens (Law of Detachment)
● Premise:
p q
Premise:
p
Conclusion:
q
13. Law of Modus Tollens
● Premise:
p q
Premise:
~q
Conclusion:
~p
q)
(~q
~p)
14. Law of Disjunctive Inference
● Premise:
p q
Premise:
~p
Conclusion:
q
● Premise:
p q
Premise:
~q
Conclusion:
p
15. Law of Conjunction
● Premise:
p
Premise:
q
Conclusion:
p q
16. Law of Simplification
● Premise:
p q
Conclusion:
p
● Premise:
p q
Conclusion:
q
17. Law of Disjunctive Addition
● Premise:
p
Conclusion:
p q
18. Chain Rule (Law of Syllogism)
● Premise:
p q
Premise:
q r
Conclusion:
p r
19. Law of Double Negation
● Premise:
~(~p)
Conclusion
p
20. Logic Proofs
21. Indirect Proofs
PARALLEL LINES
Make sure you know how to identify the different types of angles formed when two lines are cut by a transversal: ...
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