Name:___________________________Period:_____________________Date:________________
Directions: Show your statements, reasons, and work logically. Be sure to explain everything.
1. Consider the true statement: Every high school graduate in New Jersey must pass a U.S. government class.
a. Rewrite the statement in if-then form.
b. Rachel lives in New Jersey and has passed a U.S. government class. Can you conclude that she is a high school graduate? Why or why not? c. Sally just moved to New Jersey and passed a U.S. government class in Colorado. What can you conclude?
2. Consider the sequence of numbers 3, 12, 27, 48, 75, 108, 147, … a. The expression for calculating the nth term of this sequence is of the form kn 2 . Find the value of k that will give the above sequence. b. Find the differences of the successive numbers in the original sequence up to the 8 th term.
Term =
Seq. = n
S n
 kn
2
1
3
2
12
3
27
4
48
5
75
6
108
7
147
8
…
… n kn
2
Difference 9 … ??? c. Is the sequence of number that you obtained in Part b a linear, quadratic, or exponential sequence.
Explain your reasoning. d. What is the 20 th
term in the sequence? e. Use the pattern of differnces in Part a to write an expression in the form term n and term ( n

1 ) an
 b
in the original sequence. Find a closed expression for: for the differnce between
S n

1

S n
.

a.
If m FEG
 
, which lines must be parallel? Explain your reasoning. b.
If i .

CBE ii .

ICJ iii .

CBL

125
 and IH / / LG , find the measures of each angle, explain your reasoning.
4. In the diagram below, m 1 m 3 and line a is parallel to line b. Prove that m m 4

6. If lines and m are parallel, find the values of x and y in the diagram to the right. b. Are lines a and b parallel? Explain your reasoning.
7. Consider this statement: A triangle is isosceles if and only if two of its angles are equal. Write two ifthen statements that are implied.
8. Use the given information to name the segments that must be //. If there are no such segments, say so. a.
m 1 m 8
P A b.
2 7
5
6
7
8 c.
5 3 1
2 3
4
L d.
m 5 m 4 e.
m 5 m 6 m 3 m 4 f.

180
R

9. Give a deductive proof: Given: // Prove:
  
7 l k
4
3 7
8
1
2
5 t
6
10. Consider this statement: If Tommy has at least two 5 dollar bills, then he has at least 10 dollars. a. Is this a true statement? Justify your reasoning. b. Write the converse of this statement. c. Is the converse of this statement true? Justify your reasoning.
13. Prove inductive and deductive, or give a counter example: If there is an even integer, then
4(𝑛 2 + 𝑛 + 1) − 3𝑛 2
is even and divisible by four.

15. Prove inductive and deductive, or give a counter example: An integer ( n ) is odd if it’s square
16. Prove inductive and deductive, or give a counter example: If x is even then x + 1 is odd is odd.

17. Prove inductive and deductive, or give a counter example: The sum of four consective odd numbers is divisible by eight.
18. Prove inductive and deductive, or give a counter example: If you have two odd integers, then the difference of those integers is even.