1.   Determine if the following conjecture is true or false? Explain.

Given: x2 = 4
Conjecture: x = 4 or x = -4
    A. False; the square root of a positive number is always a positive number.
    B. False; the square root of 4 is 2 or -2.
    C. True; two answers are always more accurate than one answer.
    D. True; squaring a positive number results in a positive number and squaring a negative number results in a positive number.
    Hint
  2.   Identify the hypothesis of the following if-then statement.
If Ralph does his math homework, then he will get a good grade on the quiz.
    A. Ralph may do his math homework.
    B. He will get a good grade on the quiz.
    C. Ralph does his math homework.
    D. He will not get a good grade on the quiz.
    Hint
  3.   The Law of Detachment and other laws of logic can be used to provide a system for reaching logical conclusions, called _____________.
    A. detachment reasoning B. deductive reasoning
    C. reasonable doubt D. inductive reasoning
    Hint
  4.   ''If two numbers are even, then their sum is even'' is a true conditional, and 8 and 24 are even numbers. Use the Law of Detachment to reach a logical conclusion.
    A. If the numbers 8 and 24 are even, then their sum is 32.
    B. If the numbers 8 and 24 are odd, then their sum is 32.
    C. The sum of 8 and 24 must be even.
    D. The sum of 8 and 24 must be odd.
    Hint
  5.   For the proof shown, provide statement 2.
   
   
    A. AB = BC, DE = EF B. AC = DF, BC = EF
    C. AC = DE, AB = DF D. AB = DE
    Hint
  6.   If and are vertical angles and and find
   
    A. 43 B. 23
    C. 68 D. 72
    Hint
  7.   What three things are accepted as true without verification or proof?
    A. conclusions, hypotheses, and postulates B. definitions, theorems, and postulates
    C. theorems, postulates, and undefined terms D. definitions, postulates, and undefined terms.
    Hint
  8.   Make a conjecture based on the following information. M is obtuse.
    A. M is straight B. M is acute
    C. mM is not 180 D. mM = 30
    Hint
  9.   Name the property that justifies the statement:

''2(x - 4) = 2x - 8''.
    A. Reflexive Property (=) B. Transitive Property (=)
    C. Distributive Property D. Symmetric Property
    Hint
  10.   Which cannot be used as a reason in a proof?
    A. Algebra properties B. postulates
    C. Definitions D. conjectures
    Hint
  11.   For the proof shown, provide the reason for part b.
   
   
    A. Definition of a line B. Symmetric Property (=)
    C. Definition of congruent segments D. Definition of Addition
    Hint
  12.   If 1 and 2 form a linear pair and m1 = 2x + 16 and
m2 = 50x + 60, find m2.
    A. 180 B. 160
    C. 20 D. 80
    Hint
  13.   A __________ is a compound statement formed by joining two or more statements with the word and.
    A. negation B. conjunction
    C. disjunction D. truth value
    Hint
  14.   Write a truth table for pq.
    A. B.
    C. D.
    Hint
  15.   Write the contrapositive of the statement a right angle measures 90 degrees.
    A. If an angle is not a right angle, then its measure is not 90 degrees.
    B. If an angle measures 90 degrees, then it is a right angle.
    C. If an angle does not measure 90 degrees, then it is not a right angle.
    D. If an angle is a right angle, then it measures 90 degrees.
    Hint
  16.   A group of 7 people get together for a meeting. Before the meeting starts, they each shake hands with every person at the meeting. If a person only shakes hands with another person once, how many handshakes were there before the meeting began?
    A. 15 B. 42
    C. 21 D. 7
    Hint

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